import math
import sys
from pathlib import Path

import torch
import torch.nn.functional as F

TOOLKIT_ROOT = Path(__file__).resolve().parents[1]
WORKSPACE_ROOT = TOOLKIT_ROOT.parent
if str(WORKSPACE_ROOT) not in sys.path:
    sys.path.insert(0, str(WORKSPACE_ROOT))

from SkingToolkit.dense_uv_parser.uv_layout import minecraft_layer_rects  # noqa: E402
from SkingToolkit.dense_uv_parser.uv_topology import (  # noqa: E402
    build_outer_uv_graph,
)

IGNORE_INDEX = 255
PART_CLASSES = 6
FACE_CLASSES = 6
LAYER_CLASSES = 2
LAYER_FACE_CLASSES = LAYER_CLASSES * FACE_CLASSES
ROUTE_ROLE_CLASSES = 3
ROUTE_INNER_PRIMARY = 0
ROUTE_OUTER_PRIMARY = 1
ROUTE_SECONDARY = 2
UV_SIZE = 64
SPLAT_COLOR_AGGREGATIONS = ("grid_mode", "texel_center", "exact_mode", "best")
SOLID_BACKGROUND_COLOR_TOLERANCE = 16.0 / 255.0
SOLID_BACKGROUND_MIN_CORNER_SUPPORT = 0.5
SECONDARY_TEXEL_MIN_PROBABILITY = 0.5


def parse_views(views):
    if isinstance(views, str):
        return [view.strip() for view in views.split(",") if view.strip()]
    return list(views)


def build_part_face_lookups(device=None):
    inner_part = torch.full((UV_SIZE, UV_SIZE), IGNORE_INDEX, dtype=torch.long, device=device)
    inner_face = torch.full((UV_SIZE, UV_SIZE), IGNORE_INDEX, dtype=torch.long, device=device)
    outer_part = torch.full((UV_SIZE, UV_SIZE), IGNORE_INDEX, dtype=torch.long, device=device)
    outer_face = torch.full((UV_SIZE, UV_SIZE), IGNORE_INDEX, dtype=torch.long, device=device)

    rects = minecraft_layer_rects(is_slim=False)
    for rect_index, (inner_x, inner_y, width, height, decor_dx, decor_dy) in enumerate(rects):
        part = rect_index // FACE_CLASSES
        face = rect_index % FACE_CLASSES
        inner_part[inner_y : inner_y + height, inner_x : inner_x + width] = part
        inner_face[inner_y : inner_y + height, inner_x : inner_x + width] = face

        outer_x = inner_x + decor_dx
        outer_y = inner_y + decor_dy
        outer_part[outer_y : outer_y + height, outer_x : outer_x + width] = part
        outer_face[outer_y : outer_y + height, outer_x : outer_x + width] = face

    return {
        "inner_part": inner_part,
        "inner_face": inner_face,
        "outer_part": outer_part,
        "outer_face": outer_face,
    }


def _grid_to_uv01(grid):
    return ((grid + 1.0) * 0.5).clamp(0.0, 1.0)


def _grid_to_xy(grid):
    coords = (_grid_to_uv01(grid) * (UV_SIZE - 1)).round().long()
    x = coords[..., 0].clamp(0, UV_SIZE - 1)
    y = coords[..., 1].clamp(0, UV_SIZE - 1)
    return x, y


def _renderer_surface_cache(renderer):
    cache = getattr(renderer, "_dense_uv_surface_cache", None)
    if cache is None:
        cache = {}
        setattr(renderer, "_dense_uv_surface_cache", cache)
    return cache


def _surface_metadata(grids, is_outer, lookups):
    uv_px = _grid_to_uv01(grids) * (UV_SIZE - 1)
    rounded_uv_px = uv_px.round()
    x = rounded_uv_px[..., 0].long().clamp(0, UV_SIZE - 1)
    y = rounded_uv_px[..., 1].long().clamp(0, UV_SIZE - 1)
    center_distance_sq = (uv_px - rounded_uv_px).square().sum(dim=-1)
    # A bilinear renderer is exact at integer UV centers and increasingly
    # mixes neighboring texels toward a cell boundary.  Keep a normalized
    # quality score for inverse color sampling; geometry/UV ownership still
    # uses the same rounded integer coordinates as before.
    texel_center_score = (1.0 - 2.0 * center_distance_sq).clamp(0.0, 1.0)
    inner_part = lookups["inner_part"][y, x]
    inner_face = lookups["inner_face"][y, x]
    outer_part = lookups["outer_part"][y, x]
    outer_face = lookups["outer_face"][y, x]
    return {
        "flat_uv": y * UV_SIZE + x,
        "layer": is_outer.long(),
        "part": torch.where(is_outer, outer_part, inner_part),
        "face": torch.where(is_outer, outer_face, inner_face),
        "outer_part": outer_part,
        "texel_center_score": texel_center_score,
    }


def build_static_surface_routing(renderer, view, device):
    """Build fixed UV candidates matching the renderer's direct/composite geometry paths."""
    device = torch.device(device)
    cache = _renderer_surface_cache(renderer)
    cache_key = (view, device.type, device.index)
    if cache_key in cache:
        return cache[cache_key]

    inner_grid = getattr(renderer, f"{view}_inner_grid").to(device=device)
    outer_grid = getattr(renderer, f"{view}_outer_grid").to(device=device)
    inner_mask = getattr(renderer, f"{view}_inner_mask").to(device=device).bool()
    outer_mask = getattr(renderer, f"{view}_outer_mask").to(device=device).bool()
    H, W = inner_mask.shape
    lookups = build_part_face_lookups(device=device)

    grids = [inner_grid, outer_grid]
    masks = [inner_mask, outer_mask]
    is_outer = [torch.zeros((H, W), dtype=torch.bool, device=device), torch.ones((H, W), dtype=torch.bool, device=device)]
    composite_count = 0
    geometry_count = 0

    composite_grid_name = f"{view}_composite_grid_layers"
    composite_decor_name = f"{view}_composite_is_decor_layers"
    if hasattr(renderer, composite_grid_name) and hasattr(renderer, composite_decor_name):
        composite_grids = getattr(renderer, composite_grid_name).to(device=device)
        composite_masks = getattr(renderer, f"{view}_composite_mask_layers").to(device=device).bool()
        composite_decor = getattr(renderer, composite_decor_name).to(device=device).bool()
        composite_count = composite_grids.shape[0]
        grids.extend(composite_grids.unbind(0))
        masks.extend(composite_masks.unbind(0))
        is_outer.extend(composite_decor.unbind(0))

    geometry_grid_name = f"{view}_geometry_grid_layers"
    if hasattr(renderer, geometry_grid_name):
        geometry_grids = getattr(renderer, geometry_grid_name).to(device=device)
        geometry_masks = getattr(renderer, f"{view}_geometry_mask_layers").to(device=device).bool()
        geometry_order = getattr(renderer, f"{view}_geometry_sort_indices").to(device=device).long()
        geometry_count = geometry_grids.shape[0]
        if geometry_count > 0:
            geometry_order = geometry_order.clamp(0, geometry_count - 1)
            sorted_grids = torch.gather(
                geometry_grids,
                0,
                geometry_order.unsqueeze(-1).expand(-1, -1, -1, 2),
            )
            sorted_masks = torch.gather(geometry_masks, 0, geometry_order)
            geometry_metadata = _surface_metadata(
                sorted_grids,
                torch.zeros_like(sorted_masks),
                lookups,
            )
            geometry_is_outer = geometry_metadata["outer_part"] != IGNORE_INDEX
            grids.extend(sorted_grids.unbind(0))
            masks.extend(sorted_masks.unbind(0))
            is_outer.extend(geometry_is_outer.unbind(0))

    surface_grids = torch.stack(grids, dim=0)
    surface_masks = torch.stack(masks, dim=0)
    surface_is_outer = torch.stack(is_outer, dim=0)
    metadata = _surface_metadata(surface_grids, surface_is_outer, lookups)
    metadata["layer_face"] = combine_layer_face(metadata["layer"], metadata["face"])
    static = {
        "grids": surface_grids,
        "masks": surface_masks,
        "flat_uv": metadata["flat_uv"],
        "layer": metadata["layer"],
        "part": metadata["part"],
        "face": metadata["face"],
        "layer_face": metadata["layer_face"],
        "texel_center_score": metadata["texel_center_score"],
        "direct_count": 2,
        "composite_count": composite_count,
        "geometry_count": geometry_count,
    }
    cache[cache_key] = static
    return static


def surface_class_count(renderer, views):
    device = renderer.bg_color.device
    return max(build_static_surface_routing(renderer, view, device)["grids"].shape[0] for view in parse_views(views))


def _select_static_surface(static, surface):
    B, H, W = surface.shape
    surface_count = static["grids"].shape[0]
    in_range = (surface >= 0) & (surface < surface_count)
    safe_surface = surface.clamp(0, max(surface_count - 1, 0))

    selected = {}
    for name in (
        "masks",
        "flat_uv",
        "layer",
        "part",
        "face",
        "texel_center_score",
    ):
        values = static[name].unsqueeze(0).expand(B, -1, -1, -1)
        selected[name] = values.gather(1, safe_surface.unsqueeze(1)).squeeze(1)
    selected["valid"] = in_range & selected["masks"]
    return selected


def _sample_surface_alpha(skins, static):
    B = skins.shape[0]
    surface_count, H, W, _ = static["grids"].shape
    grids = static["grids"].unsqueeze(0).expand(B, -1, -1, -1, -1).reshape(B * surface_count, H, W, 2)
    alpha = skins[:, 3:4].unsqueeze(1).expand(-1, surface_count, -1, -1, -1)
    alpha = alpha.reshape(B * surface_count, 1, skins.shape[-2], skins.shape[-1])
    sampled = F.grid_sample(alpha, grids, mode="bilinear", padding_mode="zeros", align_corners=True)
    return sampled.reshape(B, surface_count, H, W) * static["masks"].unsqueeze(0)


def classify_route_role(static, selected_layer, selected_flat_uv, valid):
    """Classify visible pixels as direct inner/outer surfaces or deeper backfaces."""
    B, H, W = selected_layer.shape
    safe_layer = selected_layer.clamp(0, LAYER_CLASSES - 1)
    direct_masks = static["masks"][:LAYER_CLASSES].unsqueeze(0).expand(B, -1, H, W)
    direct_uv = static["flat_uv"][:LAYER_CLASSES].unsqueeze(0).expand(B, -1, H, W)
    direct_valid = direct_masks.gather(1, safe_layer.unsqueeze(1)).squeeze(1)
    expected_uv = direct_uv.gather(1, safe_layer.unsqueeze(1)).squeeze(1)
    primary = valid & direct_valid & (selected_flat_uv == expected_uv)
    route_role = torch.full_like(selected_layer, IGNORE_INDEX)
    route_role[primary] = selected_layer[primary]
    route_role[valid & ~primary] = ROUTE_SECONDARY
    return route_role


def build_dense_parser_batch(skins, renderer, view, alpha_threshold=0.5):
    """Render skins and label the exact fixed surface that produced every pixel."""
    device = skins.device
    dtype = skins.dtype
    B = skins.shape[0]

    rendered = renderer.forward_view(skins, view)
    static = build_static_surface_routing(renderer, view, device)
    _, _, H, W = rendered.shape
    sampled_alpha = _sample_surface_alpha(skins, static)

    surface = torch.full((B, H, W), IGNORE_INDEX, dtype=torch.long, device=device)
    direct_visible = sampled_alpha[:, :2] > alpha_threshold
    inner_visible = direct_visible[:, 0] & ~direct_visible[:, 1]
    outer_visible = direct_visible[:, 1]
    surface[inner_visible] = 0
    surface[outer_visible] = 1

    composite_start = static["direct_count"]
    composite_count = static["composite_count"]
    composite_visible = None
    if composite_count > 0:
        composite_visible = sampled_alpha[:, composite_start : composite_start + composite_count] > alpha_threshold
        composite_indices = torch.arange(composite_count, device=device).view(1, composite_count, 1, 1)
        first_composite = torch.where(
            composite_visible,
            composite_indices,
            torch.full_like(composite_indices, composite_count),
        ).amin(dim=1)
        has_composite = first_composite < composite_count
        composite_surface = composite_start + first_composite.clamp(max=composite_count - 1)
        composite_route = _select_static_surface(static, composite_surface)
        trust_composite = has_composite & (
            (composite_route["layer"] == 1) | (first_composite <= 1)
        )
        surface[trust_composite] = composite_surface[trust_composite]

        geometry_start = composite_start + composite_count
        geometry_count = static["geometry_count"]
        if geometry_count > 0:
            geometry_visible = sampled_alpha[:, geometry_start : geometry_start + geometry_count] > alpha_threshold
            geometry_indices = torch.arange(geometry_count, device=device).view(1, geometry_count, 1, 1)
            last_geometry = torch.where(
                geometry_visible,
                geometry_indices,
                torch.full_like(geometry_indices, -1),
            ).amax(dim=1)
            has_geometry = last_geometry >= 0
            geometry_surface = geometry_start + last_geometry.clamp_min(0)
            front_decor = static["masks"][composite_start] & (static["layer"][composite_start] == 1)
            geometry_fallback = (
                front_decor.unsqueeze(0)
                & ~composite_visible[:, 0]
                & has_geometry
            )
            surface[geometry_fallback] = geometry_surface[geometry_fallback]

    selected = _select_static_surface(static, surface)
    valid = selected["valid"]
    layer = torch.where(valid, selected["layer"], torch.full_like(surface, IGNORE_INDEX))
    route_role = classify_route_role(static, selected["layer"], selected["flat_uv"], valid)
    part = torch.where(valid, selected["part"], torch.full_like(surface, IGNORE_INDEX))
    face = torch.where(valid, selected["face"], torch.full_like(surface, IGNORE_INDEX))
    uv = flat_uv_to_uv01(selected["flat_uv"], dtype).masked_fill(~valid.unsqueeze(1), 0.0)

    targets = {
        "foreground": valid.unsqueeze(1).to(dtype=dtype),
        "layer": layer,
        "route_role": route_role,
        "part": part,
        "face": face,
        "surface": torch.where(valid, surface, torch.full_like(surface, IGNORE_INDEX)),
        "uv": uv,
    }
    return rendered, targets


def randomize_render_background(rendered, probability=0.9, bg_color=(128, 128, 128)):
    """Replace rendered backgrounds while preserving the skin pixels and parser targets.

    The renderer produces RGBA images composited over a fixed gray background. The
    parser always receives RGB-style inputs (alpha fixed to one), with a random
    solid-color background for the requested fraction of samples.
    """
    if rendered.dim() != 4 or rendered.shape[1] != 4:
        raise ValueError(f"Expected RGBA render tensor as NCHW, got {tuple(rendered.shape)}.")

    B, _, H, W = rendered.shape
    device = rendered.device
    dtype = rendered.dtype
    alpha = rendered[:, 3:4].clamp(0.0, 1.0)
    source_bg = rendered.new_tensor(bg_color).view(1, 3, 1, 1) / 255.0
    probability = max(0.0, min(float(probability), 1.0))
    if probability > 0:
        active = torch.rand(B, device=device) < probability
        random_background = torch.rand(B, 3, 1, 1, device=device, dtype=dtype).expand(-1, -1, H, W)
        background = torch.where(active.view(B, 1, 1, 1), random_background, source_bg.expand(B, -1, H, W))
    else:
        background = source_bg.expand(B, -1, H, W)
    foreground_rgb = (rendered[:, :3] - (1.0 - alpha) * source_bg) / alpha.clamp_min(1e-4)
    composited_rgb = (alpha * foreground_rgb + (1.0 - alpha) * background).clamp(0.0, 1.0)

    return torch.cat([composited_rgb, torch.ones_like(alpha)], dim=1)


def estimate_solid_background_color(
    rendered,
    color_tolerance=SOLID_BACKGROUND_COLOR_TOLERANCE,
    min_corner_support=SOLID_BACKGROUND_MIN_CORNER_SUPPORT,
):
    if rendered.dim() != 4 or rendered.shape[1] < 3:
        raise ValueError(f"Expected NCHW RGB(A), got {tuple(rendered.shape)}.")
    if not 0.0 <= color_tolerance <= 1.0:
        raise ValueError("color_tolerance must be in [0, 1].")
    if not 0.0 <= min_corner_support <= 1.0:
        raise ValueError("min_corner_support must be in [0, 1].")

    rgb = rendered[:, :3].float()
    batch, _, height, width = rgb.shape
    patch = max(2, min(32, min(height, width) // 16))
    corners = torch.cat(
        [
            rgb[:, :, :patch, :patch].flatten(2),
            rgb[:, :, :patch, -patch:].flatten(2),
            rgb[:, :, -patch:, :patch].flatten(2),
            rgb[:, :, -patch:, -patch:].flatten(2),
        ],
        dim=2,
    )
    background_rgb = corners.median(dim=2).values.view(batch, 3, 1, 1)
    corner_distance = (corners - background_rgb.flatten(2)).abs().amax(dim=1)
    solid_background = (corner_distance <= color_tolerance).float().mean(dim=1) >= min_corner_support
    return background_rgb, solid_background


def estimate_solid_background_foreground(
    rendered,
    color_tolerance=SOLID_BACKGROUND_COLOR_TOLERANCE,
    min_corner_support=SOLID_BACKGROUND_MIN_CORNER_SUPPORT,
):
    """Find non-background pixels without deleting matching colors enclosed by the subject."""
    if min(rendered.shape[-2:]) < 8:
        return torch.ones(
            rendered.shape[0],
            *rendered.shape[-2:],
            dtype=torch.bool,
            device=rendered.device,
        )

    rgb = rendered[:, :3].float()
    batch, _, height, width = rgb.shape
    background_rgb, solid_background = estimate_solid_background_color(
        rendered,
        color_tolerance=color_tolerance,
        min_corner_support=min_corner_support,
    )

    background_candidate = (rgb - background_rgb).abs().amax(dim=1) <= color_tolerance
    candidate_u8 = background_candidate.to(torch.uint8)
    connected_to_border = (
        candidate_u8.cumprod(dim=2).bool()
        | candidate_u8.flip(2).cumprod(dim=2).flip(2).bool()
        | candidate_u8.cumprod(dim=1).bool()
        | candidate_u8.flip(1).cumprod(dim=1).flip(1).bool()
    )
    connected_to_border &= solid_background.view(batch, 1, 1)
    max_steps = max(height, width)
    for _ in range(max_steps):
        expanded = F.max_pool2d(
            connected_to_border.unsqueeze(1).float(), 3, stride=1, padding=1
        )[:, 0] > 0.0
        updated = connected_to_border | (background_candidate & expanded)
        if torch.equal(updated, connected_to_border):
            break
        connected_to_border = updated
    return ~connected_to_border


def estimate_top_left_flood_foreground(rendered, color_tolerance=8.0 / 255.0):
    """Remove only seed-colored pixels connected to the top-left image pixel.

    Each image in the batch owns its own RGB seed. Pixels with the same color
    elsewhere inside the character remain foreground unless a path of
    seed-colored pixels connects them to the top-left corner.
    """
    if rendered.dim() != 4 or rendered.shape[1] < 3:
        raise ValueError(f"Expected NCHW RGB(A), got {tuple(rendered.shape)}.")
    if not 0.0 <= color_tolerance <= 1.0:
        raise ValueError("color_tolerance must be in [0, 1].")

    rgb = rendered[:, :3].float()
    seed_rgb = rgb[:, :, :1, :1]
    background_candidate = (
        (rgb - seed_rgb).abs().amax(dim=1) <= color_tolerance
    )
    connected = torch.zeros_like(background_candidate)
    connected[:, 0, 0] = background_candidate[:, 0, 0]
    height, width = rendered.shape[-2:]
    for _ in range(height + width):
        # Four-connected expansion cannot leak diagonally through a one-pixel
        # corner where two foreground blocks merely touch.
        expanded = connected.clone()
        expanded[:, 1:, :] |= connected[:, :-1, :]
        expanded[:, :-1, :] |= connected[:, 1:, :]
        expanded[:, :, 1:] |= connected[:, :, :-1]
        expanded[:, :, :-1] |= connected[:, :, 1:]
        updated = connected | (background_candidate & expanded)
        if torch.equal(updated, connected):
            break
        connected = updated
    return ~connected


def build_color_sampling_support(
    rendered,
    observed_foreground,
    background_rgb,
    background_tolerance=None,
    foreground_inset=1,
):
    """Separate route occupancy from source pixels that are safe for RGB pickup.

    Flood fill intentionally keeps colors that merely resemble the background
    when they are not connected to the image border.  That is correct for
    occupancy, but an isolated background pocket or antialiased silhouette
    fringe must not beat a real character sample during inverse UV splatting.
    Only background-like *boundary* candidates are rejected.  Interior pixels
    remain valid even when a skin intentionally uses the background color.
    """
    if rendered.dim() != 4 or rendered.shape[1] < 3:
        raise ValueError(f"Expected NCHW RGB(A), got {tuple(rendered.shape)}.")
    expected = rendered.shape[:1] + rendered.shape[-2:]
    if observed_foreground.shape != expected:
        raise ValueError(
            f"Expected observed_foreground shape {expected}, got "
            f"{tuple(observed_foreground.shape)}."
        )
    if background_rgb.shape not in ((rendered.shape[0], 3), (rendered.shape[0], 3, 1, 1)):
        raise ValueError(
            "background_rgb must have shape (N, 3) or (N, 3, 1, 1)."
        )
    if background_tolerance is not None and not 0.0 <= background_tolerance <= 1.0:
        raise ValueError("background_tolerance must be in [0, 1].")
    if foreground_inset < 0:
        raise ValueError("foreground_inset must be non-negative.")

    observed = observed_foreground.to(device=rendered.device, dtype=torch.bool)
    interior = observed
    for _ in range(int(foreground_inset)):
        adjacent_background = F.max_pool2d(
            (~interior).unsqueeze(1).float(),
            kernel_size=3,
            stride=1,
            padding=1,
        )[:, 0] > 0.0
        interior = interior & ~adjacent_background

    background = background_rgb.to(
        device=rendered.device, dtype=rendered.dtype
    ).reshape(rendered.shape[0], 3, 1, 1)
    background_like = (
        (rendered[:, :3] - background).abs().amax(dim=1)
        <= float(background_tolerance)
        if background_tolerance is not None
        else torch.zeros_like(observed)
    )
    boundary = observed & ~interior
    rejected = boundary & background_like
    return {
        "valid": observed & ~rejected,
        "interior": interior,
        "background_like": background_like,
        "rejected": rejected,
    }


def affine_to_canonical_grid(affine, output_shape):
    """Build a grid that samples an augmented render at canonical coordinates."""
    if affine.dim() != 2 or affine.shape[1] != 3:
        raise ValueError(f"Expected affine shape (N, 3), got {tuple(affine.shape)}.")
    if affine.shape[0] != output_shape[0]:
        raise ValueError(
            f"Affine batch size {affine.shape[0]} does not match output batch size {output_shape[0]}."
        )

    scale = affine[:, 2].exp()
    theta = affine.new_zeros(affine.shape[0], 2, 3)
    theta[:, 0, 0] = scale
    theta[:, 1, 1] = scale
    theta[:, 0, 2] = affine[:, 0]
    theta[:, 1, 2] = affine[:, 1]
    return F.affine_grid(theta, output_shape, align_corners=False)


def canonicalize_tensor(tensor, affine, mode="bilinear"):
    """Undo the parser's predicted global translation/scale for an NCHW tensor."""
    affine = affine.to(device=tensor.device, dtype=tensor.dtype)
    grid = affine_to_canonical_grid(affine, tensor.shape)
    return F.grid_sample(
        tensor,
        grid,
        mode=mode,
        padding_mode="zeros",
        align_corners=False,
    )


def canonicalize_foreground_mask(mask, affine, min_coverage=1e-3):
    """Warp a foreground mask without dropping thin silhouette coverage.

    Nearest-neighbour sampling can erase a one-pixel hat brim or outer-layer
    protrusion after even a small predicted affine scale. Bilinear coverage
    with a low positive threshold keeps every output pixel touched by the
    transformed source mask. Later color/background and minimum-source filters
    remain responsible for rejecting unsupported edge colors.
    """
    if mask.dim() == 3:
        mask = mask.unsqueeze(1)
    if mask.dim() != 4 or mask.shape[1] != 1:
        raise ValueError(
            "Foreground mask must have shape NHW or N1HW, got "
            f"{tuple(mask.shape)}."
        )
    if not 0.0 < float(min_coverage) <= 1.0:
        raise ValueError("min_coverage must be in (0, 1].")
    coverage = canonicalize_tensor(
        mask.to(device=affine.device, dtype=torch.float32),
        affine,
        mode="bilinear",
    )
    return coverage[:, 0] >= float(min_coverage)


def canonicalize_index_tensor(index, affine):
    """Undo a global transform while preserving IGNORE_INDEX outside valid labels."""
    valid = (index != IGNORE_INDEX).unsqueeze(1).float()
    values = index.masked_fill(index == IGNORE_INDEX, 0).float().unsqueeze(1)
    affine = affine.to(device=values.device, dtype=values.dtype)
    grid = affine_to_canonical_grid(affine, values.shape)
    sampled_valid = F.grid_sample(
        valid,
        grid,
        mode="nearest",
        padding_mode="zeros",
        align_corners=False,
    ).squeeze(1) > 0.5
    sampled_values = F.grid_sample(
        values,
        grid,
        mode="nearest",
        padding_mode="zeros",
        align_corners=False,
    ).squeeze(1).round().long()
    sampled_values[~sampled_valid] = IGNORE_INDEX
    return sampled_values


def canonicalize_dense_targets(targets):
    """Return parser targets in the fixed renderer coordinate system."""
    if "affine" not in targets:
        raise ValueError("Global-affine targets require an 'affine' tensor.")
    affine = targets["affine"]
    canonical = {
        "foreground": canonicalize_tensor(targets["foreground"], affine, mode="nearest"),
        "layer": canonicalize_index_tensor(targets["layer"], affine),
        "route_role": canonicalize_index_tensor(targets["route_role"], affine),
        "part": canonicalize_index_tensor(targets["part"], affine),
        "face": canonicalize_index_tensor(targets["face"], affine),
        "surface": canonicalize_index_tensor(targets["surface"], affine),
        "uv": canonicalize_tensor(targets["uv"], affine, mode="nearest"),
        "affine": affine,
    }
    valid = (canonical["layer"] != IGNORE_INDEX).unsqueeze(1)
    canonical["foreground"] = canonical["foreground"] * valid.to(canonical["foreground"].dtype)
    canonical["uv"] = torch.where(valid, canonical["uv"], torch.zeros_like(canonical["uv"]))
    return canonical


def canonicalize_parser_outputs(outputs):
    """Warp dense parser logits into the fixed renderer coordinate system."""
    if "affine" not in outputs:
        return outputs
    affine = outputs["affine"]
    canonical = {}
    for name, value in outputs.items():
        if (
            name in (
                "affine",
                "route_role_prior_raw",
                "outer_uv_occupancy_logits",
                "outer_uv_occupancy_support",
            )
            or name == "outer_uv_global_context"
            or not torch.is_tensor(value)
            or value.dim() != 4
        ):
            canonical[name] = value
        else:
            canonical[name] = canonicalize_tensor(value, affine, mode="bilinear")
    return canonical


def canonicalize_parser_render(rendered, outputs, mode="nearest", fill_color=None):
    """Undo the global transform for colors without blending Minecraft texels."""
    if "affine" not in outputs:
        return rendered
    if fill_color is None:
        return canonicalize_tensor(rendered, outputs["affine"], mode=mode)
    if fill_color.dim() == 2:
        fill_color = fill_color.unsqueeze(-1).unsqueeze(-1)
    if fill_color.shape != (rendered.shape[0], rendered.shape[1], 1, 1):
        raise ValueError(
            "fill_color must have shape "
            f"{(rendered.shape[0], rendered.shape[1], 1, 1)}, got {tuple(fill_color.shape)}."
        )
    fill_color = fill_color.to(device=rendered.device, dtype=rendered.dtype)
    return canonicalize_tensor(
        rendered - fill_color, outputs["affine"], mode=mode
    ) + fill_color


def _mask_moments(weights):
    weights = weights.float()
    N, H, W = weights.shape
    y = torch.arange(H, device=weights.device, dtype=weights.dtype).view(1, H, 1)
    x = torch.arange(W, device=weights.device, dtype=weights.dtype).view(1, 1, W)
    total = weights.sum(dim=(1, 2)).clamp_min(1e-6)
    mean_x = (weights * x).sum(dim=(1, 2)) / total
    mean_y = (weights * y).sum(dim=(1, 2)) / total
    var_x = (weights * (x - mean_x.view(N, 1, 1)).square()).sum(dim=(1, 2)) / total
    var_y = (weights * (y - mean_y.view(N, 1, 1)).square()).sum(dim=(1, 2)) / total
    return total, mean_x, mean_y, var_x.clamp_min(1e-6).sqrt(), var_y.clamp_min(1e-6).sqrt()


def _soft_mask_dice(probability, target, support):
    probability = probability.float() * support.float()
    target = target.float()
    intersection = (probability * target).sum(dim=(1, 2, 3))
    denominator = probability.sum(dim=(1, 2, 3)) + target.sum(dim=(1, 2, 3))
    return (2.0 * intersection + 1e-6) / (denominator + 1e-6)


def refine_parser_affine(
    outputs,
    renderer,
    views,
    translation_radius_px=8.0,
    scale_radius=0.0,
    translation_step_px=0.5,
    observed_foreground=None,
):
    """Refine parser affine predictions against the fixed inner-layer silhouette."""
    if "affine" not in outputs or "foreground" not in outputs:
        return outputs.get("affine"), None
    if translation_radius_px < 0 or scale_radius < 0:
        raise ValueError("Affine refinement radii must be non-negative.")
    if translation_step_px <= 0:
        raise ValueError("translation_step_px must be positive.")

    views = parse_views(views)
    affine = outputs["affine"]
    if observed_foreground is None:
        foreground_prob = torch.sigmoid(outputs["foreground"])
    else:
        if observed_foreground.shape != outputs["foreground"].shape[:1] + outputs["foreground"].shape[-2:]:
            raise ValueError(
                "observed_foreground must match parser spatial output shape, got "
                f"{tuple(observed_foreground.shape)}."
            )
        foreground_prob = observed_foreground.to(
            device=outputs["foreground"].device,
            dtype=outputs["foreground"].dtype,
        ).unsqueeze(1)
    N, _, H, W = foreground_prob.shape
    if not views or N % len(views) != 0:
        raise ValueError(f"N={N} must be divisible by the number of views ({len(views)}).")

    target = foreground_prob.new_zeros(N, 1, H, W)
    for view_index, view in enumerate(views):
        static = build_static_surface_routing(renderer, view, foreground_prob.device)
        inner_mask = static["masks"][0]
        if inner_mask.shape != (H, W):
            raise ValueError(
                f"View {view!r} mapping shape {tuple(inner_mask.shape)} does not match parser shape {(H, W)}."
            )
        target[view_index::len(views), 0] = inner_mask.to(dtype=target.dtype)

    support_radius = max(math.ceil(translation_radius_px) + 2, 2)
    support = F.max_pool2d(
        target,
        kernel_size=support_radius * 2 + 1,
        stride=1,
        padding=support_radius,
    ).clamp(0.0, 1.0)

    base_canonical = canonicalize_tensor(foreground_prob, affine, mode="bilinear")
    base_score = _soft_mask_dice(base_canonical, target, support)
    target_stats = _mask_moments(target[:, 0])
    base_stats = _mask_moments(base_canonical[:, 0] * support[:, 0])
    target_total, _, _, target_std_x, target_std_y = target_stats
    base_total, _, _, base_std_x, base_std_y = base_stats
    enough_foreground = base_total > target_total * 0.25

    if scale_radius > 0:
        scale_delta = 0.5 * (
            (base_std_x / target_std_x).clamp_min(1e-6).log()
            + (base_std_y / target_std_y).clamp_min(1e-6).log()
        )
        scale_delta = scale_delta.clamp(-scale_radius, scale_radius)
        scale_affine = affine.clone()
        scale_affine[:, 2] = scale_affine[:, 2] + scale_delta.to(dtype=scale_affine.dtype)
        scale_canonical = canonicalize_tensor(foreground_prob, scale_affine, mode="bilinear")
    else:
        scale_delta = torch.zeros_like(base_score)
        scale_affine = affine
        scale_canonical = base_canonical
    _, pred_mean_x, pred_mean_y, _, _ = _mask_moments(scale_canonical[:, 0] * support[:, 0])
    _, target_mean_x, target_mean_y, _, _ = target_stats
    delta_x_px = (pred_mean_x - target_mean_x).clamp(-translation_radius_px, translation_radius_px)
    delta_y_px = (pred_mean_y - target_mean_y).clamp(-translation_radius_px, translation_radius_px)
    delta_x_px = (delta_x_px / translation_step_px).round() * translation_step_px
    delta_y_px = (delta_y_px / translation_step_px).round() * translation_step_px

    candidate_affine = scale_affine.clone()
    candidate_affine[:, 0] = candidate_affine[:, 0] + (2.0 * delta_x_px / W).to(candidate_affine.dtype)
    candidate_affine[:, 1] = candidate_affine[:, 1] + (2.0 * delta_y_px / H).to(candidate_affine.dtype)
    candidate_canonical = canonicalize_tensor(foreground_prob, candidate_affine, mode="bilinear")
    candidate_score = _soft_mask_dice(candidate_canonical, target, support)
    accepted = enough_foreground & (candidate_score > base_score + 1e-5)
    refined_affine = torch.where(accepted.unsqueeze(1), candidate_affine, affine)

    accepted_float = accepted.to(dtype=delta_x_px.dtype)
    details = {
        "accepted": accepted,
        "translation_px": torch.stack(
            [delta_x_px * accepted_float, delta_y_px * accepted_float],
            dim=1,
        ),
        "scale_percent": (scale_delta.exp() - 1.0) * 100.0 * accepted_float,
        "score_before": base_score,
        "score_after": torch.where(accepted, candidate_score, base_score),
    }
    return refined_affine, details


def _routing_from_affine_outputs(renderer, views, outputs, fg_threshold=0.5, semantic_gate=True):
    views = parse_views(views)
    if not views:
        raise ValueError("At least one renderer view is required for deterministic UV routing.")
    if "surface" not in outputs:
        raise ValueError("Affine parser outputs must include the static surface classifier.")
    foreground_prob = torch.sigmoid(outputs["foreground"])[:, 0]
    surface_prob = torch.softmax(outputs["surface"], dim=1)
    layer_prob = torch.softmax(outputs["layer"], dim=1)
    N, _, H, W = surface_prob.shape
    if N % len(views) != 0:
        raise ValueError(f"N={N} must be divisible by {len(views)} renderer views.")

    fg = torch.zeros_like(foreground_prob, dtype=torch.bool)
    layer = torch.zeros((N, H, W), dtype=torch.long, device=surface_prob.device)
    flat_uv = torch.zeros_like(layer)
    surface = torch.full_like(layer, IGNORE_INDEX)
    confidence = torch.zeros_like(foreground_prob)
    confidence_margin = torch.zeros_like(foreground_prob)
    confidence_margin_ratio = torch.zeros_like(foreground_prob)
    texel_center_score = torch.zeros_like(foreground_prob)
    semantic_fallback = torch.zeros_like(foreground_prob, dtype=torch.bool)
    expected_part = torch.full_like(layer, IGNORE_INDEX)
    expected_face = torch.full_like(layer, IGNORE_INDEX)

    for view_index, view in enumerate(views):
        selection = slice(view_index, N, len(views))
        static = build_static_surface_routing(renderer, view, surface_prob.device)
        if static["masks"].shape[-2:] != (H, W):
            raise ValueError(
                f"View {view!r} mapping shape {tuple(static['masks'].shape[-2:])} does not match parser shape {(H, W)}."
            )
        view_surface_prob = surface_prob[selection]
        view_batch = view_surface_prob.shape[0]
        surface_count = static["masks"].shape[0]
        if view_surface_prob.shape[1] < surface_count:
            raise ValueError(
                f"Parser has {view_surface_prob.shape[1]} surface classes, but view {view!r} requires {surface_count}."
            )

        candidate_score = view_surface_prob[:, :surface_count]
        physical_valid = static["masks"].unsqueeze(0).expand(view_batch, -1, -1, -1)
        candidate_valid = physical_valid.clone()
        semantic_score = torch.ones_like(candidate_score)

        # Re-rank only surfaces that physically exist at this screen pixel. This
        # converts the semantic heads from a rejection gate into useful routing
        # evidence and avoids holes caused by a globally invalid surface argmax.
        semantic_names = (
            ("part", "layer_face")
            if "layer_face" in outputs
            else ("layer", "part", "face")
        )
        for name in semantic_names:
            if name not in outputs:
                continue
            probabilities = torch.softmax(outputs[name][selection], dim=1)
            expected = static[name]
            known_semantic = expected != IGNORE_INDEX
            expected_safe = expected.clamp(0, probabilities.shape[1] - 1)
            expected_probability = probabilities.gather(
                1,
                expected_safe.unsqueeze(0).expand(view_batch, -1, -1, -1),
            )
            semantic_score = semantic_score * torch.where(
                known_semantic.unsqueeze(0),
                expected_probability,
                torch.ones_like(expected_probability),
            )
            if semantic_gate:
                candidate_valid = candidate_valid & (
                    ~known_semantic.unsqueeze(0)
                    | (probabilities.argmax(dim=1).unsqueeze(1) == expected_safe.unsqueeze(0))
                )

        candidate_score = candidate_score * semantic_score.clamp_min(1e-12).sqrt()
        if "uv_x" in outputs and "uv_y" in outputs:
            uv_x_prob = torch.softmax(outputs["uv_x"][selection], dim=1)
            uv_y_prob = torch.softmax(outputs["uv_y"][selection], dim=1)
            candidate_x = static["flat_uv"].remainder(UV_SIZE)
            candidate_y = static["flat_uv"].div(UV_SIZE, rounding_mode="floor")
            candidate_x_prob = uv_x_prob.gather(
                1,
                candidate_x.unsqueeze(0).expand(view_batch, -1, -1, -1),
            )
            candidate_y_prob = uv_y_prob.gather(
                1,
                candidate_y.unsqueeze(0).expand(view_batch, -1, -1, -1),
            )
            candidate_score = candidate_score * (
                candidate_x_prob * candidate_y_prob
            ).clamp_min(1e-12).sqrt()
        gated_score = candidate_score.masked_fill(~candidate_valid, -1.0)
        has_gated_candidate = candidate_valid.any(dim=1, keepdim=True)
        if semantic_gate:
            fallback_score = candidate_score.masked_fill(~physical_valid, -1.0)
            candidate_score = torch.where(has_gated_candidate, gated_score, fallback_score)
            semantic_fallback[selection] = (
                ~has_gated_candidate.squeeze(1) & physical_valid.any(dim=1)
            )
        else:
            candidate_score = gated_score
        best_score, selected_surface = candidate_score.max(dim=1)
        if surface_count > 1:
            top_scores = candidate_score.topk(k=2, dim=1).values
            route_margin = (top_scores[:, 0] - top_scores[:, 1]).clamp_min(0.0)
            route_margin_ratio = (
                route_margin / top_scores[:, 0].abs().clamp_min(1e-8)
            ).clamp(0.0, 1.0)
        else:
            route_margin = best_score.clamp_min(0.0)
            route_margin_ratio = (best_score > 0.0).to(best_score.dtype)

        routed = _select_static_surface(static, selected_surface)
        selected_layer = routed["layer"]
        selected_part = routed["part"]
        selected_face = routed["face"]
        has_candidate = best_score >= 0.0
        base_silhouette = static["masks"][0].unsqueeze(0).expand(view_batch, -1, -1)
        routed_fg = (
            ((foreground_prob[selection] > fg_threshold) | base_silhouette)
            & has_candidate
            & routed["valid"]
        )
        fg[selection] = routed_fg
        layer[selection] = selected_layer
        flat_uv[selection] = routed["flat_uv"]
        surface[selection] = torch.where(
            has_candidate,
            selected_surface,
            torch.full_like(selected_surface, IGNORE_INDEX),
        )
        confidence[selection] = foreground_prob[selection] * best_score.clamp_min(0.0)
        confidence_margin[selection] = route_margin
        confidence_margin_ratio[selection] = route_margin_ratio
        expected_part[selection] = selected_part
        expected_face[selection] = selected_face
        texel_center_score[selection] = routed["texel_center_score"]

    return {
        "foreground": fg,
        "layer": layer,
        "flat_uv": flat_uv,
        "surface": surface,
        "confidence": confidence,
        "confidence_margin": confidence_margin,
        "confidence_margin_ratio": confidence_margin_ratio,
        "semantic_fallback": semantic_fallback,
        "part": expected_part,
        "face": expected_face,
        "texel_center_score": texel_center_score,
    }


def _aggregate_role_probabilities_by_direct_texel(
    role_prob,
    static,
    foreground_prob=None,
    center_power=2.0,
):
    """Center-weight route probabilities within each projected Minecraft texel."""
    role_prob = role_prob.float()
    batch, role_count, height, width = role_prob.shape
    if foreground_prob is not None and foreground_prob.shape != (
        batch,
        height,
        width,
    ):
        raise ValueError(
            "foreground_prob must match the route map, got "
            f"{tuple(foreground_prob.shape)} and {(batch, height, width)}."
        )
    if center_power < 0:
        raise ValueError("center_power must be non-negative.")
    aggregated = []
    for layer_index in range(LAYER_CLASSES):
        valid = static["masks"][layer_index].reshape(1, 1, -1)
        flat_uv = static["flat_uv"][layer_index].reshape(1, 1, -1)
        center_weight = static["texel_center_score"][layer_index].float()
        center_weight = center_weight.clamp(0.0, 1.0).pow(center_power)
        pixel_weight = center_weight.reshape(1, 1, -1) * valid
        if foreground_prob is not None:
            pixel_weight = (
                pixel_weight
                * foreground_prob.float().clamp(0.0, 1.0).reshape(batch, 1, -1)
            )
        pixel_weight = pixel_weight.expand(batch, 1, -1)
        sums = role_prob.new_zeros(batch, role_count, UV_SIZE * UV_SIZE)
        sums.scatter_add_(
            2,
            flat_uv.expand(batch, role_count, -1),
            role_prob.flatten(2) * pixel_weight,
        )
        counts = role_prob.new_zeros(batch, 1, UV_SIZE * UV_SIZE)
        counts.scatter_add_(
            2,
            flat_uv.expand(batch, 1, -1),
            pixel_weight,
        )
        means = sums / counts.clamp_min(1e-6)
        aggregated.append(
            means.gather(2, flat_uv.expand(batch, role_count, -1)).reshape(
                batch, role_count, height, width
            )
        )
    return torch.stack(aggregated, dim=1)


def _project_outer_uv_occupancy_to_view(
    occupancy_probability,
    static,
    view_batch,
):
    """Gather a grouped 64x64 outer-alpha prior into one projected view."""
    if occupancy_probability is None:
        return None
    if occupancy_probability.shape != (view_batch, 1, UV_SIZE, UV_SIZE):
        raise ValueError(
            "outer_uv_occupancy probability must be grouped as "
            f"{(view_batch, 1, UV_SIZE, UV_SIZE)}, got "
            f"{tuple(occupancy_probability.shape)}."
        )
    probability = occupancy_probability.float().flatten(2)
    flat_uv = static["flat_uv"][ROUTE_OUTER_PRIMARY].reshape(
        1, 1, -1
    ).expand(view_batch, 1, -1)
    projected = probability.gather(2, flat_uv).reshape(
        view_batch, *static["flat_uv"].shape[-2:]
    )
    outer_valid = static["masks"][ROUTE_OUTER_PRIMARY].unsqueeze(0)
    return torch.where(outer_valid, projected, torch.zeros_like(projected))


def _outer_graph_component_labels(candidate, edge_index, max_steps=64):
    """Label candidate outer nodes by bounded min-label propagation."""
    batch, node_count = candidate.shape
    labels = torch.arange(
        node_count,
        device=candidate.device,
        dtype=torch.long,
    ).view(1, -1).expand(batch, -1).clone()
    labels[~candidate] = node_count
    source, target = edge_index
    expanded_target = target.view(1, -1).expand(batch, -1)
    connected_edge = candidate[:, source] & candidate[:, target]
    for _ in range(int(max_steps)):
        neighbour = torch.where(
            connected_edge,
            labels[:, source],
            torch.full_like(labels[:, source], node_count),
        )
        updated = labels.clone()
        updated.scatter_reduce_(
            1,
            expanded_target,
            neighbour,
            reduce="amin",
            include_self=True,
        )
        labels = updated
    return labels


def outer_uv_topology_hysteresis(
    probability,
    seed_threshold=0.80,
    grow_threshold=0.50,
    min_component_size=2,
    max_steps=64,
):
    """Grow high-confidence outer seeds through topology-supported candidates."""
    if probability.dim() == 3:
        probability = probability.unsqueeze(1)
    if probability.dim() != 4 or probability.shape[1:] != (
        1,
        UV_SIZE,
        UV_SIZE,
    ):
        raise ValueError("Outer occupancy probability must be Bx1x64x64.")
    if not 0.0 <= float(grow_threshold) <= float(seed_threshold) <= 1.0:
        raise ValueError(
            "Require 0 <= grow_threshold <= seed_threshold <= 1."
        )
    if min_component_size < 1:
        raise ValueError("min_component_size must be positive.")
    flat_indices, edge_index = build_outer_uv_graph()
    flat_indices = flat_indices.to(probability.device)
    edge_index = edge_index.to(probability.device)
    nodes = probability.float().flatten(2)[:, 0].index_select(
        1, flat_indices
    )
    candidate = nodes >= float(grow_threshold)
    seeds = nodes >= float(seed_threshold)
    source, target = edge_index
    expanded_target = target.view(1, -1).expand(nodes.shape[0], -1)
    active = seeds.clone()
    connected_edge = candidate[:, source] & candidate[:, target]
    for _ in range(int(max_steps)):
        neighbour_active = torch.where(
            connected_edge,
            active[:, source],
            torch.zeros_like(active[:, source]),
        )
        propagated_active = torch.zeros_like(active, dtype=torch.uint8)
        propagated_active.scatter_reduce_(
            1,
            expanded_target,
            neighbour_active.to(torch.uint8),
            reduce="amax",
            include_self=False,
        )
        active = active | (candidate & propagated_active.bool())

    labels = _outer_graph_component_labels(
        candidate,
        edge_index,
        max_steps=max_steps,
    )
    node_count = nodes.shape[1]
    batch_offsets = (
        torch.arange(nodes.shape[0], device=nodes.device).view(-1, 1)
        * (node_count + 1)
    )
    component_index = labels + batch_offsets
    component_sizes = nodes.new_zeros(nodes.shape[0] * (node_count + 1))
    component_sizes.scatter_add_(
        0,
        component_index[candidate],
        torch.ones_like(nodes[candidate]),
    )
    node_component_size = component_sizes[component_index]
    active = active & (node_component_size >= int(min_component_size))
    grown = active & ~seeds
    # Connectivity determines eligibility, not confidence. Propagating a
    # single seed's score across the whole component made a 0.50 neighbour
    # behave like a 0.90 texel and amplified one false seed into a large outer
    # patch. Accepted nodes therefore retain their own calibrated score.
    structured_nodes = torch.where(active, nodes, torch.zeros_like(nodes))

    def scatter_nodes(node_values, dtype=None):
        atlas = node_values.new_zeros(
            node_values.shape[0],
            UV_SIZE * UV_SIZE,
            dtype=dtype,
        )
        atlas[:, flat_indices] = node_values.to(dtype=atlas.dtype)
        return atlas.reshape(-1, 1, UV_SIZE, UV_SIZE)

    return {
        "probability": scatter_nodes(structured_nodes),
        "accepted": scatter_nodes(active, dtype=torch.bool),
        "seed": scatter_nodes(seeds & active, dtype=torch.bool),
        "grown": scatter_nodes(grown, dtype=torch.bool),
        "rejected_candidate": scatter_nodes(
            candidate & ~active,
            dtype=torch.bool,
        ),
    }


def aggregate_direct_outer_values_by_view(
    renderer,
    views,
    values,
    center_power=2.0,
):
    """Pool image-space values into direct outer UV texels, keeping views separate."""
    views = parse_views(views)
    if not views:
        raise ValueError("At least one renderer view is required.")
    if values.dim() != 4:
        raise ValueError("values must be shaped NCHW.")
    if values.shape[0] % len(views) != 0:
        raise ValueError("The value batch must be divisible by the view count.")
    if center_power < 0.0:
        raise ValueError("center_power must be non-negative.")

    group_count = values.shape[0] // len(views)
    channel_count = values.shape[1]
    uv_count = UV_SIZE * UV_SIZE
    pooled_views = []
    supported_views = []
    for view_index, view in enumerate(views):
        selection = slice(view_index, values.shape[0], len(views))
        selected = values[selection].float()
        static = build_static_surface_routing(renderer, view, values.device)
        if static["masks"].shape[-2:] != values.shape[-2:]:
            raise ValueError(
                f"View {view!r} mapping shape "
                f"{tuple(static['masks'].shape[-2:])} does not match "
                f"value shape {tuple(values.shape[-2:])}."
            )

        valid = static["masks"][ROUTE_OUTER_PRIMARY].reshape(1, 1, -1)
        flat_uv = static["flat_uv"][ROUTE_OUTER_PRIMARY].reshape(1, 1, -1)
        center_weight = static["texel_center_score"][
            ROUTE_OUTER_PRIMARY
        ].float().clamp(0.0, 1.0).pow(float(center_power))
        weight = center_weight.reshape(1, 1, -1) * valid
        weight = weight.expand(group_count, 1, -1)
        indices = flat_uv.expand(group_count, channel_count, -1)

        sums = selected.new_zeros(group_count, channel_count, uv_count)
        sums.scatter_add_(
            2,
            indices,
            selected.flatten(2) * weight,
        )
        counts = selected.new_zeros(group_count, 1, uv_count)
        counts.scatter_add_(
            2,
            flat_uv.expand(group_count, 1, -1),
            weight,
        )
        pooled_views.append(sums / counts.clamp_min(1e-6))
        supported_views.append(counts[:, 0] > 1e-6)

    return (
        torch.stack(pooled_views, dim=1),
        torch.stack(supported_views, dim=1),
    )


def attach_projected_outer_uv_occupancy(
    model,
    outputs,
    renderer,
    views,
    observed_foreground=None,
    center_power=2.0,
):
    """Project dense parser features into UV space and run the topology head."""
    if not getattr(model, "predict_outer_uv_occupancy", False):
        return outputs
    if "outer_uv_features" not in outputs:
        raise ValueError(
            "Projected occupancy parser did not return outer_uv_features."
        )
    views = parse_views(views)
    feature_map = outputs["outer_uv_features"]
    layer_logits = outputs["layer"]
    foreground = torch.sigmoid(outputs["foreground"].float())
    if "affine" in outputs:
        affine = outputs["affine"]
        feature_map = canonicalize_tensor(feature_map, affine, mode="bilinear")
        layer_logits = canonicalize_tensor(
            layer_logits, affine, mode="bilinear"
        )
        foreground = canonicalize_tensor(
            foreground, affine, mode="bilinear"
        )
        if observed_foreground is not None:
            if observed_foreground.dim() == 3:
                observed_foreground = observed_foreground.unsqueeze(1)
            observed_foreground = canonicalize_tensor(
                observed_foreground.float(),
                affine,
                mode="bilinear",
            )
    elif observed_foreground is not None and observed_foreground.dim() == 3:
        observed_foreground = observed_foreground.unsqueeze(1)
    if observed_foreground is not None:
        foreground = observed_foreground.to(
            device=foreground.device,
            dtype=foreground.dtype,
        ).clamp(0.0, 1.0)

    outer_probability = torch.softmax(
        layer_logits.float(), dim=1
    )[:, ROUTE_OUTER_PRIMARY : ROUTE_OUTER_PRIMARY + 1].detach()
    values = torch.cat(
        [
            feature_map.float(),
            outer_probability,
            foreground.float().detach(),
        ],
        dim=1,
    )
    pooled, support = aggregate_direct_outer_values_by_view(
        renderer,
        views,
        values,
        center_power=center_power,
    )
    support_weight = support.unsqueeze(2).to(dtype=pooled.dtype)
    support_count = support_weight.sum(dim=1).clamp_min(1.0)
    feature_channels = feature_map.shape[1]
    pooled_mean = (
        (pooled * support_weight).sum(dim=1) / support_count
    )
    mean_features = pooled_mean[:, :feature_channels]
    mean_outer = pooled_mean[:, feature_channels : feature_channels + 1]
    mean_foreground = pooled_mean[:, feature_channels + 1 : feature_channels + 2]
    per_view_outer = pooled[:, :, feature_channels : feature_channels + 1]
    max_outer = torch.where(
        support_weight.bool(),
        per_view_outer,
        torch.zeros_like(per_view_outer),
    ).amax(dim=1)
    route_evidence = torch.cat([mean_outer, max_outer], dim=1)
    route_evidence_dropout = float(
        getattr(model, "outer_uv_route_evidence_dropout", 0.0)
    )
    if route_evidence_dropout >= 1.0:
        # The projected ownership classifier must remain independent from the
        # already-unreliable per-pixel route prediction. Keep the two channels
        # for checkpoint compatibility, but disable the shortcut in both
        # training and inference.
        route_evidence = torch.zeros_like(route_evidence)
    elif model.training and route_evidence_dropout > 0.0:
        # Drop the entire route-evidence pair per grouped skin. This prevents
        # the occupancy head from learning the shortcut "copy p_outer" while
        # leaving half of the batches available for useful route context.
        keep_route_evidence = (
            torch.rand(
                (route_evidence.shape[0],)
                + (1,) * (route_evidence.ndim - 1),
                device=route_evidence.device,
            )
            >= route_evidence_dropout
        )
        route_evidence = route_evidence * keep_route_evidence.to(
            dtype=route_evidence.dtype
        )
    support_fraction = (
        support_count / max(float(len(views)), 1.0)
    )
    atlas_features = torch.cat(
        [
            mean_features,
            route_evidence,
            mean_foreground,
            support_fraction,
        ],
        dim=1,
    ).reshape(
        mean_features.shape[0],
        feature_channels + 4,
        UV_SIZE,
        UV_SIZE,
    )
    logits = model.predict_projected_outer_uv_occupancy(
        atlas_features,
        outputs["outer_uv_global_context"],
    )
    outputs["outer_uv_occupancy_logits"] = logits
    outputs["outer_uv_occupancy_support"] = (
        support.any(dim=1).reshape(-1, 1, UV_SIZE, UV_SIZE)
    )
    return outputs


def _project_grouped_outer_texels_to_views(
    renderer,
    views,
    texel_values,
):
    """Project grouped outer-UV values back into every fixed input view."""
    views = parse_views(views)
    if texel_values.dim() != 2 or texel_values.shape[1] != UV_SIZE * UV_SIZE:
        raise ValueError(
            "texel_values must be shaped "
            f"(B, {UV_SIZE * UV_SIZE})."
        )
    projected = []
    for view in views:
        static = build_static_surface_routing(
            renderer, view, texel_values.device
        )
        flat_uv = static["flat_uv"][ROUTE_OUTER_PRIMARY].reshape(1, -1)
        gathered = texel_values.gather(
            1, flat_uv.expand(texel_values.shape[0], -1)
        ).reshape(texel_values.shape[0], *static["masks"].shape[-2:])
        valid = static["masks"][ROUTE_OUTER_PRIMARY].unsqueeze(0)
        projected.append(torch.where(valid, gathered, torch.zeros_like(gathered)))
    return torch.stack(projected, dim=1).reshape(
        texel_values.shape[0] * len(views),
        *projected[0].shape[-2:],
    )


def cross_view_outer_visibility_evidence(
    renderer,
    views,
    role_prob,
    observed_foreground,
    center_power=2.0,
    positive_confidence=0.70,
    positive_margin=0.20,
    negative_confidence=0.70,
    negative_margin=0.20,
    background_max_coverage=0.25,
    min_views=2,
):
    """Find shared outer texels with high-confidence cross-view contradictions.

    A contradiction requires at least one view that strongly supports outer and
    another view that either sees background at the projected outer texel or
    strongly supports inner. Weak predictions, missing mappings, and texels
    visible from only one view never form a veto.
    """
    for name, value in (
        ("positive_confidence", positive_confidence),
        ("positive_margin", positive_margin),
        ("negative_confidence", negative_confidence),
        ("negative_margin", negative_margin),
        ("background_max_coverage", background_max_coverage),
    ):
        if not 0.0 <= float(value) <= 1.0:
            raise ValueError(f"{name} must be in [0, 1].")
    if min_views < 2:
        raise ValueError("min_views must be at least 2.")
    if observed_foreground.shape != (
        role_prob.shape[0],
        *role_prob.shape[-2:],
    ):
        raise ValueError("observed_foreground must match the role probability map.")

    values = torch.cat(
        [
            role_prob.float(),
            observed_foreground.unsqueeze(1).float(),
        ],
        dim=1,
    )
    pooled, support = aggregate_direct_outer_values_by_view(
        renderer,
        views,
        values,
        center_power=center_power,
    )
    role_count = role_prob.shape[1]
    pooled_role = pooled[:, :, :role_count]
    foreground_coverage = pooled[:, :, role_count].clamp(0.0, 1.0)
    outer_score = pooled_role[:, :, ROUTE_OUTER_PRIMARY]
    outer_competitor = torch.maximum(
        pooled_role[:, :, ROUTE_INNER_PRIMARY],
        pooled_role[:, :, ROUTE_SECONDARY],
    )
    outer_margin_ratio = (
        (outer_score - outer_competitor).clamp_min(0.0)
        / outer_score.clamp_min(1e-8)
    ).clamp(0.0, 1.0)
    inner_score = pooled_role[:, :, ROUTE_INNER_PRIMARY]
    inner_competitor = torch.maximum(
        pooled_role[:, :, ROUTE_OUTER_PRIMARY],
        pooled_role[:, :, ROUTE_SECONDARY],
    )
    inner_margin_ratio = (
        (inner_score - inner_competitor).clamp_min(0.0)
        / inner_score.clamp_min(1e-8)
    ).clamp(0.0, 1.0)

    positive = (
        support
        & (foreground_coverage > float(background_max_coverage))
        & (outer_score >= float(positive_confidence))
        & (outer_margin_ratio >= float(positive_margin))
    )
    background_negative = support & (
        foreground_coverage <= float(background_max_coverage)
    )
    inner_negative = (
        support
        & ~background_negative
        & (inner_score >= float(negative_confidence))
        & (inner_margin_ratio >= float(negative_margin))
    )
    negative = background_negative | inner_negative
    shared = support.sum(dim=1) >= int(min_views)
    conflict = shared & positive.any(dim=1) & negative.any(dim=1)

    evidence_weight = support.to(dtype=outer_score.dtype)
    prior = (
        (outer_score * foreground_coverage * evidence_weight).sum(dim=1)
        / evidence_weight.sum(dim=1).clamp_min(1.0)
    ).clamp(0.0, 1.0)
    return {
        "prior": _project_grouped_outer_texels_to_views(
            renderer, views, prior
        ),
        "shared": _project_grouped_outer_texels_to_views(
            renderer, views, shared.float()
        ) > 0.5,
        "conflict": _project_grouped_outer_texels_to_views(
            renderer, views, conflict.float()
        ) > 0.5,
        "positive": _project_grouped_outer_texels_to_views(
            renderer, views, positive.any(dim=1).float()
        ) > 0.5,
        "negative": _project_grouped_outer_texels_to_views(
            renderer, views, negative.any(dim=1).float()
        ) > 0.5,
        "shared_texels": shared,
        "conflict_texels": conflict,
    }


def _soft_route_role_consensus(
    role_prob,
    static,
    foreground_prob,
    consensus_weight=0.60,
    preserve_outer_confidence=0.80,
    preserve_outer_margin=0.35,
    outer_confidence=0.80,
    outer_margin=0.35,
    outer_uv_occupancy=None,
    occupancy_blend_weight=0.0,
    occupancy_gate_threshold=0.15,
    occupancy_rescue_threshold=0.70,
    occupancy_rescue_route_threshold=0.30,
    cross_view_outer_prior=None,
    cross_view_outer_valid=None,
    cross_view_outer_veto=None,
    cross_view_outer_weight=0.50,
):
    """Denoise route roles without erasing strong local outer-layer evidence."""
    for name, value in (
        ("consensus_weight", consensus_weight),
        ("preserve_outer_confidence", preserve_outer_confidence),
        ("preserve_outer_margin", preserve_outer_margin),
        ("outer_confidence", outer_confidence),
        ("outer_margin", outer_margin),
        ("occupancy_blend_weight", occupancy_blend_weight),
        ("occupancy_gate_threshold", occupancy_gate_threshold),
        ("occupancy_rescue_threshold", occupancy_rescue_threshold),
        (
            "occupancy_rescue_route_threshold",
            occupancy_rescue_route_threshold,
        ),
        ("cross_view_outer_weight", cross_view_outer_weight),
    ):
        if not 0.0 <= float(value) <= 1.0:
            raise ValueError(f"{name} must be in [0, 1].")

    role_prob = role_prob.float()
    raw_role = role_prob.argmax(dim=1)
    raw_top = role_prob.topk(2, dim=1).values
    raw_margin = raw_top[:, 0] - raw_top[:, 1]
    raw_selected_score = role_prob.gather(1, raw_role.unsqueeze(1)).squeeze(1)
    raw_margin_ratio = (
        raw_margin / raw_selected_score.clamp_min(1e-8)
    ).clamp(0.0, 1.0)

    direct_scores = _aggregate_role_probabilities_by_direct_texel(
        role_prob,
        static,
        foreground_prob=foreground_prob,
        center_power=2.0,
    )
    batch = role_prob.shape[0]
    inner_valid = static["masks"][0].unsqueeze(0).expand(batch, -1, -1)
    outer_valid = static["masks"][1].unsqueeze(0).expand_as(inner_valid)
    has_direct_candidate = inner_valid | outer_valid

    texel_inner = direct_scores[:, 0, ROUTE_INNER_PRIMARY]
    texel_outer = direct_scores[:, 1, ROUTE_OUTER_PRIMARY]
    unavailable = role_prob.new_full(texel_inner.shape, -1.0)
    texel_secondary = torch.maximum(
        torch.where(
            inner_valid,
            direct_scores[:, 0, ROUTE_SECONDARY],
            unavailable,
        ),
        torch.where(
            outer_valid,
            direct_scores[:, 1, ROUTE_SECONDARY],
            unavailable,
        ),
    )

    local_weight = 1.0 - float(consensus_weight)
    fused_inner = torch.where(
        inner_valid,
        local_weight * role_prob[:, ROUTE_INNER_PRIMARY]
        + float(consensus_weight) * texel_inner,
        unavailable,
    )
    fused_outer = torch.where(
        outer_valid,
        local_weight * role_prob[:, ROUTE_OUTER_PRIMARY]
        + float(consensus_weight) * texel_outer,
        unavailable,
    )
    if cross_view_outer_prior is not None:
        if (
            cross_view_outer_valid is None
            or cross_view_outer_prior.shape != texel_outer.shape
            or cross_view_outer_valid.shape != texel_outer.shape
        ):
            raise ValueError(
                "Cross-view outer prior and validity must match the route map."
            )
        cross_view_outer_prior = cross_view_outer_prior.float().clamp(0.0, 1.0)
        cross_view_outer_valid = cross_view_outer_valid.bool()
        fused_outer = torch.where(
            outer_valid & cross_view_outer_valid,
            (1.0 - float(cross_view_outer_weight)) * fused_outer
            + float(cross_view_outer_weight) * cross_view_outer_prior,
            fused_outer,
        )
    if cross_view_outer_veto is None:
        cross_view_outer_veto = torch.zeros_like(outer_valid)
    elif cross_view_outer_veto.shape != texel_outer.shape:
        raise ValueError("Cross-view outer veto must match the route map.")
    else:
        cross_view_outer_veto = cross_view_outer_veto.bool()
    occupancy_available = outer_uv_occupancy is not None
    if occupancy_available:
        if outer_uv_occupancy.shape != texel_outer.shape:
            raise ValueError(
                "Projected outer occupancy must match the route map, got "
                f"{tuple(outer_uv_occupancy.shape)} and "
                f"{tuple(texel_outer.shape)}."
            )
        occupancy_prior = outer_uv_occupancy.float().clamp(0.0, 1.0)
        fused_outer = torch.where(
            outer_valid,
            (1.0 - float(occupancy_blend_weight)) * fused_outer
            + float(occupancy_blend_weight) * occupancy_prior,
            unavailable,
        )
        occupancy_allows_outer = (
            occupancy_prior >= float(occupancy_gate_threshold)
        )
    else:
        occupancy_prior = torch.ones_like(texel_outer)
        occupancy_allows_outer = torch.ones_like(outer_valid)
    # Secondary/backface observations remain strict cell-level decisions. The
    # soft blend is needed for the ambiguous inner/outer pair; retaining an
    # isolated secondary pixel would reintroduce exactly the speckle that
    # projected-texel consensus is meant to remove.
    fused_secondary = torch.where(
        has_direct_candidate,
        texel_secondary.clamp_min(0.0),
        unavailable,
    )

    raw_outer_score = role_prob[:, ROUTE_OUTER_PRIMARY]
    raw_outer_competitor = torch.maximum(
        role_prob[:, ROUTE_INNER_PRIMARY],
        role_prob[:, ROUTE_SECONDARY],
    )
    raw_outer_margin = (raw_outer_score - raw_outer_competitor).clamp_min(0.0)
    raw_outer_margin_ratio = (
        raw_outer_margin / raw_outer_score.clamp_min(1e-8)
    ).clamp(0.0, 1.0)
    raw_preserve_outer = (
        outer_valid
        & ~cross_view_outer_veto
        & occupancy_allows_outer
        & (raw_role == ROUTE_OUTER_PRIMARY)
        & (raw_outer_score >= float(preserve_outer_confidence))
        & (raw_outer_margin_ratio >= float(preserve_outer_margin))
    )

    fused_outer_competitor = torch.maximum(fused_inner, fused_secondary)
    fused_outer_margin = (fused_outer - fused_outer_competitor).clamp_min(0.0)
    fused_outer_margin_ratio = (
        fused_outer_margin / fused_outer.clamp_min(1e-8)
    ).clamp(0.0, 1.0)
    fused_outer_admitted = (
        outer_valid
        & (fused_outer >= float(outer_confidence))
        & (fused_outer_margin_ratio >= float(outer_margin))
    )
    # Raw outer confidence is deliberately not an admission shortcut. A
    # coherent inner texture (eyes, mouth, shirt graphics) can make the local
    # route head extremely confident while still being semantically wrong.
    # Every ordinary outer decision must therefore pass the fused texel gate.
    # Occupancy evidence remains the only explicit bypass because it predicts
    # atlas-level outer existence rather than repeating the local route score.
    outer_admitted = fused_outer_admitted & (
        (raw_role != ROUTE_OUTER_PRIMARY) | raw_preserve_outer
    )
    preserve_outer = raw_preserve_outer & fused_outer_admitted
    outer_gate_rejected = (
        outer_valid
        & ~cross_view_outer_veto
        & occupancy_allows_outer
        & (raw_role == ROUTE_OUTER_PRIMARY)
        & ~outer_admitted
    )
    occupancy_rescue = (
        outer_valid
        & occupancy_allows_outer
        & (occupancy_prior >= float(occupancy_rescue_threshold))
        & (
            raw_outer_score
            >= float(occupancy_rescue_route_threshold)
        )
    ) if occupancy_available else torch.zeros_like(outer_valid)
    allow_outer = (
        outer_valid
        & ~cross_view_outer_veto
        & occupancy_allows_outer
        & (outer_admitted | occupancy_rescue)
    )

    outer_candidate_score = torch.where(
        occupancy_rescue,
        torch.maximum(
            fused_outer,
            occupancy_prior,
        ),
        fused_outer,
    )
    eligible_outer = torch.where(allow_outer, outer_candidate_score, unavailable)
    eligible_secondary = torch.where(
        (fused_secondary >= SECONDARY_TEXEL_MIN_PROBABILITY)
        & has_direct_candidate,
        fused_secondary,
        unavailable,
    )
    eligible_scores = torch.stack(
        [fused_inner, eligible_outer, eligible_secondary],
        dim=1,
    )
    selected_score, selected_role = eligible_scores.max(dim=1)
    selected_role = torch.where(has_direct_candidate, selected_role, raw_role)
    selected_score = torch.where(
        has_direct_candidate,
        selected_score,
        raw_selected_score,
    )
    top_scores = eligible_scores.topk(2, dim=1).values
    selected_margin = (top_scores[:, 0] - top_scores[:, 1]).clamp_min(0.0)
    selected_margin_ratio = (
        selected_margin / selected_score.clamp_min(1e-8)
    ).clamp(0.0, 1.0)

    # If fused outer still wins but does not clear the asymmetric admission
    # gate, keep its outer UV identity while marking it untrusted. Downstream
    # filtering can then leave the observation unknown (and preserve it as
    # rejected context) instead of writing an uncertain outer color into the
    # inner atlas. When fused inner actually wins, the ordinary argmax above
    # performs the intended outer-to-inner correction.
    deferred_outer = outer_gate_rejected & (
        fused_outer >= fused_outer_competitor
    )
    selected_role = torch.where(
        deferred_outer,
        torch.full_like(selected_role, ROUTE_OUTER_PRIMARY),
        selected_role,
    )
    selected_score = torch.where(deferred_outer, fused_outer, selected_score)
    selected_margin = torch.where(
        deferred_outer,
        fused_outer_margin,
        selected_margin,
    )
    selected_margin_ratio = torch.where(
        deferred_outer,
        fused_outer_margin_ratio,
        selected_margin_ratio,
    )

    return {
        "role": selected_role,
        "score": selected_score,
        "margin": selected_margin,
        "margin_ratio": selected_margin_ratio,
        "scores": torch.stack(
            [fused_inner, fused_outer, fused_secondary],
            dim=1,
        ),
        "has_direct_candidate": has_direct_candidate,
        "preserved_outer": preserve_outer,
        "outer_gate_rejected": outer_gate_rejected,
        "occupancy_rescued_outer": (
            occupancy_rescue
            & (raw_role != ROUTE_OUTER_PRIMARY)
            & (selected_role == ROUTE_OUTER_PRIMARY)
        ),
        "occupancy_rejected_outer": (
            outer_valid
            & (raw_role == ROUTE_OUTER_PRIMARY)
            & ~occupancy_allows_outer
        ),
        "cross_view_outer_veto": cross_view_outer_veto,
        "outer_uv_occupancy": (
            occupancy_prior if occupancy_available else None
        ),
        "changed": has_direct_candidate & (selected_role != raw_role),
        "inner_to_outer": (
            has_direct_candidate
            & (raw_role == ROUTE_INNER_PRIMARY)
            & (selected_role == ROUTE_OUTER_PRIMARY)
        ),
        "outer_to_inner": (
            has_direct_candidate
            & (raw_role == ROUTE_OUTER_PRIMARY)
            & (selected_role == ROUTE_INNER_PRIMARY)
        ),
    }


def _routing_from_geometry_outputs(
    renderer,
    views,
    outputs,
    fg_threshold=0.5,
    outer_threshold=0.5,
    texel_consensus=True,
    texel_consensus_weight=0.60,
    preserve_outer_confidence=0.80,
    preserve_outer_margin=0.35,
    consensus_outer_confidence=0.70,
    consensus_outer_margin=0.20,
    outer_uv_occupancy=False,
    outer_uv_occupancy_blend_weight=0.0,
    outer_uv_occupancy_gate_threshold=0.15,
    outer_uv_occupancy_rescue_threshold=0.70,
    outer_uv_occupancy_rescue_route_threshold=0.30,
    outer_uv_component_routing=False,
    outer_uv_component_seed_threshold=0.80,
    outer_uv_component_grow_threshold=0.50,
    outer_uv_component_min_size=2,
    observed_foreground=None,
    cross_view_outer_consistency=True,
    cross_view_outer_weight=0.50,
    cross_view_outer_positive_confidence=0.70,
    cross_view_outer_positive_margin=0.20,
    cross_view_outer_negative_confidence=0.70,
    cross_view_outer_negative_margin=0.20,
    cross_view_outer_background_max_coverage=0.25,
    cross_view_outer_min_views=2,
):
    """Route a fitted Steve render through fixed inner/outer cuboid UV maps."""
    views = parse_views(views)
    if not views:
        raise ValueError("At least one renderer view is required for geometry routing.")
    foreground_prob = torch.sigmoid(outputs["foreground"])[:, 0]
    if outputs["layer"].shape[1] != ROUTE_ROLE_CLASSES:
        raise ValueError(
            "geometry_fit requires a three-class route-role head "
            "(inner_primary, outer_primary, secondary_backface). Retrain the parser."
        )
    role_prob = torch.softmax(outputs["layer"].float(), dim=1)
    raw_route_role = role_prob.argmax(dim=1)
    route_role = raw_route_role.clone()
    outer_prob = role_prob[:, ROUTE_OUTER_PRIMARY].clone()
    inner_prob = role_prob[:, ROUTE_INNER_PRIMARY].clone()
    top_prob = role_prob.topk(2, dim=1).values
    role_margin = top_prob[:, 0] - top_prob[:, 1]
    N, H, W = outer_prob.shape
    if N % len(views) != 0:
        raise ValueError(f"N={N} must be divisible by {len(views)} renderer views.")

    fg = torch.zeros_like(outer_prob, dtype=torch.bool)
    layer = torch.zeros((N, H, W), dtype=torch.long, device=outer_prob.device)
    flat_uv = torch.zeros_like(layer)
    surface = torch.full_like(layer, IGNORE_INDEX)
    confidence = torch.zeros_like(outer_prob)
    confidence_margin = torch.zeros_like(outer_prob)
    confidence_margin_ratio = torch.zeros_like(outer_prob)
    texel_center_score = torch.zeros_like(outer_prob)
    part = torch.full_like(layer, IGNORE_INDEX)
    face = torch.full_like(layer, IGNORE_INDEX)
    consensus_changed = torch.zeros_like(fg)
    consensus_inner_to_outer = torch.zeros_like(fg)
    consensus_outer_to_inner = torch.zeros_like(fg)
    consensus_preserved_outer = torch.zeros_like(fg)
    consensus_outer_gate_rejected = torch.zeros_like(fg)
    occupancy_rescued_outer = torch.zeros_like(fg)
    occupancy_rejected_outer = torch.zeros_like(fg)
    projected_outer_occupancy = torch.zeros_like(outer_prob)
    projected_outer_component_seed = torch.zeros_like(fg)
    projected_outer_component_grown = torch.zeros_like(fg)
    projected_outer_component_rejected = torch.zeros_like(fg)
    occupancy_logits = (
        outputs.get("outer_uv_occupancy_logits")
        if outer_uv_occupancy
        else None
    )
    occupancy_details = None
    occupancy_probability = None
    if occupancy_logits is not None:
        raw_occupancy_probability = torch.sigmoid(occupancy_logits.float())
        if outer_uv_component_routing:
            occupancy_details = outer_uv_topology_hysteresis(
                raw_occupancy_probability,
                seed_threshold=outer_uv_component_seed_threshold,
                grow_threshold=outer_uv_component_grow_threshold,
                min_component_size=outer_uv_component_min_size,
            )
            occupancy_probability = occupancy_details["probability"]
        else:
            occupancy_probability = raw_occupancy_probability
    cross_view = None
    if cross_view_outer_consistency and len(views) >= cross_view_outer_min_views:
        if observed_foreground is None:
            observed_foreground = foreground_prob > float(fg_threshold)
        cross_view = cross_view_outer_visibility_evidence(
            renderer,
            views,
            role_prob,
            observed_foreground,
            positive_confidence=cross_view_outer_positive_confidence,
            positive_margin=cross_view_outer_positive_margin,
            negative_confidence=cross_view_outer_negative_confidence,
            negative_margin=cross_view_outer_negative_margin,
            background_max_coverage=(
                cross_view_outer_background_max_coverage
            ),
            min_views=cross_view_outer_min_views,
        )
    for view_index, view in enumerate(views):
        selection = slice(view_index, N, len(views))
        static = build_static_surface_routing(renderer, view, outer_prob.device)
        if static["masks"].shape[-2:] != (H, W):
            raise ValueError(
                f"View {view!r} mapping shape {tuple(static['masks'].shape[-2:])} "
                f"does not match parser shape {(H, W)}."
            )

        inner_valid = static["masks"][0].unsqueeze(0).expand(outer_prob[selection].shape[0], -1, -1)
        outer_valid = static["masks"][1].unsqueeze(0).expand_as(inner_valid)
        if (
            texel_consensus
            or cross_view is not None
            or occupancy_probability is not None
        ):
            view_occupancy = _project_outer_uv_occupancy_to_view(
                occupancy_probability,
                static,
                outer_prob[selection].shape[0],
            )
            if occupancy_details is not None:
                projected_outer_component_seed[selection] = (
                    _project_outer_uv_occupancy_to_view(
                        occupancy_details["seed"].float(),
                        static,
                        outer_prob[selection].shape[0],
                    )
                    > 0.5
                )
                projected_outer_component_grown[selection] = (
                    _project_outer_uv_occupancy_to_view(
                        occupancy_details["grown"].float(),
                        static,
                        outer_prob[selection].shape[0],
                    )
                    > 0.5
                )
                projected_outer_component_rejected[selection] = (
                    _project_outer_uv_occupancy_to_view(
                        occupancy_details["rejected_candidate"].float(),
                        static,
                        outer_prob[selection].shape[0],
                    )
                    > 0.5
                )
            consensus = _soft_route_role_consensus(
                role_prob[selection],
                static,
                foreground_prob[selection],
                consensus_weight=(
                    texel_consensus_weight if texel_consensus else 0.0
                ),
                preserve_outer_confidence=preserve_outer_confidence,
                preserve_outer_margin=preserve_outer_margin,
                outer_confidence=consensus_outer_confidence,
                outer_margin=consensus_outer_margin,
                outer_uv_occupancy=view_occupancy,
                occupancy_blend_weight=(
                    outer_uv_occupancy_blend_weight
                ),
                occupancy_gate_threshold=(
                    outer_uv_occupancy_gate_threshold
                ),
                occupancy_rescue_threshold=(
                    outer_uv_occupancy_rescue_threshold
                ),
                occupancy_rescue_route_threshold=(
                    outer_uv_occupancy_rescue_route_threshold
                ),
                cross_view_outer_prior=(
                    cross_view["prior"][selection]
                    if cross_view is not None
                    else None
                ),
                cross_view_outer_valid=(
                    cross_view["shared"][selection]
                    if cross_view is not None
                    else None
                ),
                cross_view_outer_veto=(
                    cross_view["conflict"][selection]
                    if cross_view is not None
                    else None
                ),
                cross_view_outer_weight=cross_view_outer_weight,
            )
            has_direct_candidate = consensus["has_direct_candidate"]
            route_role[selection] = consensus["role"]
            inner_prob[selection] = torch.where(
                has_direct_candidate,
                torch.where(
                    consensus["role"] == ROUTE_INNER_PRIMARY,
                    consensus["score"],
                    consensus["scores"][:, ROUTE_INNER_PRIMARY],
                ).clamp_min(0.0),
                inner_prob[selection],
            )
            outer_prob[selection] = torch.where(
                has_direct_candidate,
                torch.where(
                    consensus["role"] == ROUTE_OUTER_PRIMARY,
                    consensus["score"],
                    consensus["scores"][:, ROUTE_OUTER_PRIMARY],
                ).clamp_min(0.0),
                outer_prob[selection],
            )
            role_margin[selection] = consensus["margin"]
            consensus_changed[selection] = consensus["changed"]
            consensus_inner_to_outer[selection] = consensus["inner_to_outer"]
            consensus_outer_to_inner[selection] = consensus["outer_to_inner"]
            consensus_preserved_outer[selection] = consensus["preserved_outer"]
            consensus_outer_gate_rejected[selection] = consensus[
                "outer_gate_rejected"
            ]
            occupancy_rescued_outer[selection] = consensus[
                "occupancy_rescued_outer"
            ]
            occupancy_rejected_outer[selection] = consensus[
                "occupancy_rejected_outer"
            ]
            if view_occupancy is not None:
                projected_outer_occupancy[selection] = view_occupancy

        visible_outer = (
            (route_role[selection] == ROUTE_OUTER_PRIMARY)
            & (outer_prob[selection] >= outer_threshold)
        )
        # The Steve base layer is opaque and therefore supplies a complete
        # silhouette. Outer-only protrusions still need image foreground evidence.
        choose_outer = outer_valid & visible_outer & (
            inner_valid | (foreground_prob[selection] > fg_threshold)
        )
        choose_inner = inner_valid & (route_role[selection] == ROUTE_INNER_PRIMARY)
        selected_fg = choose_inner | choose_outer

        inner_flat_uv = static["flat_uv"][0].unsqueeze(0).expand_as(layer[selection])
        outer_flat_uv = static["flat_uv"][1].unsqueeze(0).expand_as(layer[selection])
        inner_part = static["part"][0].unsqueeze(0).expand_as(layer[selection])
        outer_part = static["part"][1].unsqueeze(0).expand_as(layer[selection])
        inner_face = static["face"][0].unsqueeze(0).expand_as(layer[selection])
        outer_face = static["face"][1].unsqueeze(0).expand_as(layer[selection])
        inner_center_score = static["texel_center_score"][0].unsqueeze(0).expand_as(
            confidence[selection]
        )
        outer_center_score = static["texel_center_score"][1].unsqueeze(0).expand_as(
            confidence[selection]
        )

        fg[selection] = selected_fg
        layer[selection] = choose_outer.long()
        flat_uv[selection] = torch.where(choose_outer, outer_flat_uv, inner_flat_uv)
        surface[selection] = torch.where(
            selected_fg,
            choose_outer.long(),
            torch.full_like(layer[selection], IGNORE_INDEX),
        )
        part[selection] = torch.where(
            selected_fg,
            torch.where(choose_outer, outer_part, inner_part),
            torch.full_like(layer[selection], IGNORE_INDEX),
        )
        face[selection] = torch.where(
            selected_fg,
            torch.where(choose_outer, outer_face, inner_face),
            torch.full_like(layer[selection], IGNORE_INDEX),
        )
        selected_confidence = torch.where(choose_outer, outer_prob[selection], inner_prob[selection])
        margin = role_margin[selection]
        confidence[selection] = selected_confidence
        confidence_margin[selection] = margin
        confidence_margin_ratio[selection] = (
            margin / selected_confidence.clamp_min(1e-8)
        ).clamp(0.0, 1.0)
        texel_center_score[selection] = torch.where(
            choose_outer, outer_center_score, inner_center_score
        )

    secondary = (route_role == ROUTE_SECONDARY) & (foreground_prob > fg_threshold)
    return {
        "foreground": fg,
        "layer": layer,
        "flat_uv": flat_uv,
        "surface": surface,
        "confidence": confidence,
        "confidence_margin": confidence_margin,
        "confidence_margin_ratio": confidence_margin_ratio,
        "semantic_fallback": torch.zeros_like(fg),
        "part": part,
        "face": face,
        "raw_route_role": raw_route_role,
        "route_role": route_role,
        "secondary": secondary,
        "texel_center_score": texel_center_score,
        "consensus_changed": consensus_changed,
        "consensus_inner_to_outer": consensus_inner_to_outer,
        "consensus_outer_to_inner": consensus_outer_to_inner,
        "consensus_preserved_outer": consensus_preserved_outer,
        "consensus_outer_gate_rejected": consensus_outer_gate_rejected,
        "occupancy_rescued_outer": occupancy_rescued_outer,
        "occupancy_rejected_outer": occupancy_rejected_outer,
        "projected_outer_occupancy": projected_outer_occupancy,
        "projected_outer_component_seed": projected_outer_component_seed,
        "projected_outer_component_grown": projected_outer_component_grown,
        "projected_outer_component_rejected": (
            projected_outer_component_rejected
        ),
        "outer_uv_occupancy_available": torch.full_like(
            fg, occupancy_logits is not None
        ),
        "cross_view_outer_shared": (
            cross_view["shared"] if cross_view is not None else torch.zeros_like(fg)
        ),
        "cross_view_outer_conflict": (
            cross_view["conflict"] if cross_view is not None else torch.zeros_like(fg)
        ),
        "cross_view_outer_vetoed": (
            cross_view["conflict"]
            & (raw_route_role == ROUTE_OUTER_PRIMARY)
            & (route_role != ROUTE_OUTER_PRIMARY)
            if cross_view is not None
            else torch.zeros_like(fg)
        ),
        "cross_view_outer_positive": (
            cross_view["positive"] if cross_view is not None else torch.zeros_like(fg)
        ),
        "cross_view_outer_negative": (
            cross_view["negative"] if cross_view is not None else torch.zeros_like(fg)
        ),
    }


def _aggregate_surface_scores_by_candidate_texel(candidate_score, static):
    """Average each surface candidate inside its projected Minecraft UV texel."""
    candidate_score = candidate_score.float()
    batch, surface_count, height, width = candidate_score.shape
    flat_uv = static["flat_uv"][:surface_count].reshape(1, surface_count, -1)
    valid = static["masks"][:surface_count].reshape(1, surface_count, -1)
    indices = flat_uv.expand(batch, -1, -1)
    values = candidate_score.flatten(2) * valid.to(dtype=candidate_score.dtype)

    sums = candidate_score.new_zeros(batch, surface_count, UV_SIZE * UV_SIZE)
    sums.scatter_add_(2, indices, values)
    counts = candidate_score.new_zeros(1, surface_count, UV_SIZE * UV_SIZE)
    counts.scatter_add_(
        2,
        flat_uv,
        valid.to(dtype=candidate_score.dtype),
    )
    means = sums / counts.clamp_min(1.0)
    return means.gather(2, indices).reshape(batch, surface_count, height, width)


def _static_candidate_roles(static):
    """Return the Minecraft layer and route role implemented by every surface pixel."""
    candidate_layer = static["layer"].clamp(0, LAYER_CLASSES - 1)
    direct_masks = static["masks"][:LAYER_CLASSES].gather(0, candidate_layer)
    direct_uv = static["flat_uv"][:LAYER_CLASSES].gather(0, candidate_layer)
    primary = static["masks"] & direct_masks & (static["flat_uv"] == direct_uv)
    candidate_role = torch.where(
        primary,
        candidate_layer,
        torch.full_like(candidate_layer, ROUTE_SECONDARY),
    )
    return candidate_layer, candidate_role


def _routing_from_geometry_surface_outputs(
    renderer,
    views,
    outputs,
    fg_threshold=0.5,
    texel_consensus=True,
    texel_consensus_weight=0.60,
    preserve_outer_confidence=0.80,
    preserve_outer_margin=0.35,
    consensus_outer_confidence=0.70,
    consensus_outer_margin=0.20,
    outer_uv_occupancy=False,
    outer_uv_occupancy_blend_weight=0.0,
    outer_uv_occupancy_gate_threshold=0.15,
    outer_uv_occupancy_rescue_threshold=0.70,
    outer_uv_occupancy_rescue_route_threshold=0.30,
    outer_uv_component_routing=False,
    outer_uv_component_seed_threshold=0.80,
    outer_uv_component_grow_threshold=0.50,
    outer_uv_component_min_size=2,
    observed_foreground=None,
    cross_view_outer_consistency=True,
    cross_view_outer_weight=0.50,
    cross_view_outer_positive_confidence=0.70,
    cross_view_outer_positive_margin=0.20,
    cross_view_outer_negative_confidence=0.70,
    cross_view_outer_negative_margin=0.20,
    cross_view_outer_background_max_coverage=0.25,
    cross_view_outer_min_views=2,
):
    """Route primary layers first, then use the surface head for secondary UVs.

    The route-role head owns the inner/outer/secondary decision.  The surface
    head only disambiguates renderer slots that implement the selected role.
    Keeping those decisions hierarchical is important: many composite and
    geometry slots overlap a direct cuboid face, so a strong wrong surface
    logit must not turn a primary pixel into a secondary/back-facing pixel.
    """
    views = parse_views(views)
    if not views:
        raise ValueError("At least one renderer view is required for geometry-surface routing.")
    if outputs["layer"].shape[1] != ROUTE_ROLE_CLASSES:
        raise ValueError("Geometry-surface routing requires the three-class route-role head.")
    if "surface" not in outputs:
        raise ValueError("Geometry-surface routing requires a static surface classifier.")

    foreground_prob = torch.sigmoid(outputs["foreground"])[:, 0]
    role_prob = torch.softmax(outputs["layer"].float(), dim=1)
    surface_prob = torch.softmax(outputs["surface"].float(), dim=1)
    raw_route_role = role_prob.argmax(dim=1)
    N, _, H, W = surface_prob.shape
    if N % len(views) != 0:
        raise ValueError(f"N={N} must be divisible by {len(views)} renderer views.")

    fg = torch.zeros((N, H, W), dtype=torch.bool, device=surface_prob.device)
    layer = torch.zeros((N, H, W), dtype=torch.long, device=surface_prob.device)
    flat_uv = torch.zeros_like(layer)
    surface = torch.full_like(layer, IGNORE_INDEX)
    route_role = torch.full_like(layer, IGNORE_INDEX)
    confidence = torch.zeros_like(foreground_prob)
    confidence_margin = torch.zeros_like(foreground_prob)
    confidence_margin_ratio = torch.zeros_like(foreground_prob)
    texel_center_score = torch.zeros_like(foreground_prob)
    part = torch.full_like(layer, IGNORE_INDEX)
    face = torch.full_like(layer, IGNORE_INDEX)
    consensus_changed = torch.zeros_like(fg)
    consensus_inner_to_outer = torch.zeros_like(fg)
    consensus_outer_to_inner = torch.zeros_like(fg)
    consensus_preserved_outer = torch.zeros_like(fg)
    consensus_outer_gate_rejected = torch.zeros_like(fg)
    occupancy_rescued_outer = torch.zeros_like(fg)
    occupancy_rejected_outer = torch.zeros_like(fg)
    projected_outer_occupancy = torch.zeros_like(foreground_prob)
    projected_outer_component_seed = torch.zeros_like(fg)
    projected_outer_component_grown = torch.zeros_like(fg)
    projected_outer_component_rejected = torch.zeros_like(fg)
    occupancy_logits = (
        outputs.get("outer_uv_occupancy_logits")
        if outer_uv_occupancy
        else None
    )
    occupancy_details = None
    occupancy_probability = None
    if occupancy_logits is not None:
        raw_occupancy_probability = torch.sigmoid(occupancy_logits.float())
        if outer_uv_component_routing:
            occupancy_details = outer_uv_topology_hysteresis(
                raw_occupancy_probability,
                seed_threshold=outer_uv_component_seed_threshold,
                grow_threshold=outer_uv_component_grow_threshold,
                min_component_size=outer_uv_component_min_size,
            )
            occupancy_probability = occupancy_details["probability"]
        else:
            occupancy_probability = raw_occupancy_probability
    cross_view = None
    if cross_view_outer_consistency and len(views) >= cross_view_outer_min_views:
        if observed_foreground is None:
            observed_foreground = foreground_prob > float(fg_threshold)
        cross_view = cross_view_outer_visibility_evidence(
            renderer,
            views,
            role_prob,
            observed_foreground,
            positive_confidence=cross_view_outer_positive_confidence,
            positive_margin=cross_view_outer_positive_margin,
            negative_confidence=cross_view_outer_negative_confidence,
            negative_margin=cross_view_outer_negative_margin,
            background_max_coverage=(
                cross_view_outer_background_max_coverage
            ),
            min_views=cross_view_outer_min_views,
        )

    for view_index, view in enumerate(views):
        selection = slice(view_index, N, len(views))
        static = build_static_surface_routing(renderer, view, surface_prob.device)
        if static["masks"].shape[-2:] != (H, W):
            raise ValueError(
                f"View {view!r} mapping shape {tuple(static['masks'].shape[-2:])} "
                f"does not match parser shape {(H, W)}."
            )
        surface_count = static["masks"].shape[0]
        if surface_prob.shape[1] < surface_count:
            raise ValueError(
                f"Parser has {surface_prob.shape[1]} surface classes, but view {view!r} "
                f"requires {surface_count}."
            )

        candidate_layer, candidate_role = _static_candidate_roles(static)

        view_batch = surface_prob[selection].shape[0]
        view_role_prob = role_prob[selection]
        selected_role = raw_route_role[selection]
        selected_role_score = view_role_prob.gather(
            1, selected_role.unsqueeze(1)
        ).squeeze(1)
        role_top = view_role_prob.topk(2, dim=1).values
        role_margin = role_top[:, 0] - role_top[:, 1]

        if (
            texel_consensus
            or cross_view is not None
            or occupancy_probability is not None
        ):
            view_occupancy = _project_outer_uv_occupancy_to_view(
                occupancy_probability,
                static,
                view_batch,
            )
            if occupancy_details is not None:
                projected_outer_component_seed[selection] = (
                    _project_outer_uv_occupancy_to_view(
                        occupancy_details["seed"].float(),
                        static,
                        view_batch,
                    )
                    > 0.5
                )
                projected_outer_component_grown[selection] = (
                    _project_outer_uv_occupancy_to_view(
                        occupancy_details["grown"].float(),
                        static,
                        view_batch,
                    )
                    > 0.5
                )
                projected_outer_component_rejected[selection] = (
                    _project_outer_uv_occupancy_to_view(
                        occupancy_details["rejected_candidate"].float(),
                        static,
                        view_batch,
                    )
                    > 0.5
                )
            consensus = _soft_route_role_consensus(
                view_role_prob,
                static,
                foreground_prob[selection],
                consensus_weight=(
                    texel_consensus_weight if texel_consensus else 0.0
                ),
                preserve_outer_confidence=preserve_outer_confidence,
                preserve_outer_margin=preserve_outer_margin,
                outer_confidence=consensus_outer_confidence,
                outer_margin=consensus_outer_margin,
                outer_uv_occupancy=view_occupancy,
                occupancy_blend_weight=(
                    outer_uv_occupancy_blend_weight
                ),
                occupancy_gate_threshold=(
                    outer_uv_occupancy_gate_threshold
                ),
                occupancy_rescue_threshold=(
                    outer_uv_occupancy_rescue_threshold
                ),
                occupancy_rescue_route_threshold=(
                    outer_uv_occupancy_rescue_route_threshold
                ),
                cross_view_outer_prior=(
                    cross_view["prior"][selection]
                    if cross_view is not None
                    else None
                ),
                cross_view_outer_valid=(
                    cross_view["shared"][selection]
                    if cross_view is not None
                    else None
                ),
                cross_view_outer_veto=(
                    cross_view["conflict"][selection]
                    if cross_view is not None
                    else None
                ),
                cross_view_outer_weight=cross_view_outer_weight,
            )
            selected_role = consensus["role"]
            selected_role_score = consensus["score"]
            role_margin = consensus["margin"]
            consensus_changed[selection] = consensus["changed"]
            consensus_inner_to_outer[selection] = consensus["inner_to_outer"]
            consensus_outer_to_inner[selection] = consensus["outer_to_inner"]
            consensus_preserved_outer[selection] = consensus["preserved_outer"]
            consensus_outer_gate_rejected[selection] = consensus[
                "outer_gate_rejected"
            ]
            occupancy_rescued_outer[selection] = consensus[
                "occupancy_rescued_outer"
            ]
            occupancy_rejected_outer[selection] = consensus[
                "occupancy_rejected_outer"
            ]
            if view_occupancy is not None:
                projected_outer_occupancy[selection] = view_occupancy

        candidate_score = surface_prob[selection, :surface_count]
        candidate_valid = static["masks"].unsqueeze(0).expand(
            view_batch, -1, -1, -1
        )
        candidate_valid = candidate_valid & (
            candidate_role.unsqueeze(0) == selected_role.unsqueeze(1)
        )
        if texel_consensus:
            consensus_score = _aggregate_surface_scores_by_candidate_texel(
                candidate_score,
                static,
            )
            local_scores = candidate_score.masked_fill(~candidate_valid, -1.0)
            local_top = local_scores.topk(k=min(2, surface_count), dim=1).values
            if surface_count > 1:
                local_margin_ratio = (
                    (local_top[:, 0] - local_top[:, 1]).clamp_min(0.0)
                    / local_top[:, 0].abs().clamp_min(1e-8)
                ).clamp(0.0, 1.0)
                consensus_weight = (1.0 - local_margin_ratio).unsqueeze(1)
                candidate_score = (
                    candidate_score * (1.0 - consensus_weight)
                    + consensus_score * consensus_weight
                )
        candidate_score = candidate_score.masked_fill(~candidate_valid, -1.0)
        best_surface_score, selected_surface = candidate_score.max(dim=1)
        selected_secondary = selected_role == ROUTE_SECONDARY
        # Primary routes already have an exact direct cuboid surface and UV.
        # Do not let an equivalent composite slot bypass direct-layer coverage
        # filtering; the learned surface head is needed only for secondary UVs.
        selected_surface = torch.where(
            selected_secondary,
            selected_surface,
            selected_role,
        )
        if surface_count > 1:
            top_scores = candidate_score.topk(k=2, dim=1).values
            surface_margin = (top_scores[:, 0] - top_scores[:, 1]).clamp_min(0.0)
            surface_margin_ratio = (
                surface_margin / top_scores[:, 0].abs().clamp_min(1e-8)
            ).clamp(0.0, 1.0)
        else:
            surface_margin = best_surface_score.clamp_min(0.0)
            surface_margin_ratio = (best_surface_score > 0.0).to(
                best_surface_score.dtype
            )

        routed = _select_static_surface(static, selected_surface)
        has_candidate = best_surface_score >= 0.0
        base_silhouette = static["masks"][0].unsqueeze(0).expand(view_batch, -1, -1)
        routed_fg = (
            ((foreground_prob[selection] > fg_threshold) | base_silhouette)
            & has_candidate
            & routed["valid"]
        )
        role_margin_ratio = (
            role_margin / selected_role_score.clamp_min(1e-8)
        ).clamp(0.0, 1.0)
        selected_surface_score = best_surface_score.clamp_min(0.0)
        selected_confidence = torch.where(
            selected_secondary,
            (selected_role_score * selected_surface_score).sqrt(),
            selected_role_score,
        )
        if "route_confidence" in outputs:
            # The learned trust target already says whether the argmax route is
            # correct (and includes surface correctness for secondary routes).
            # Multiplying it by the class probability counts the same
            # uncertainty twice and makes a 0.80 outer gate nearly
            # unreachable.  A geometric mean keeps both signals necessary
            # without systematically collapsing otherwise well-calibrated
            # confidence.
            learned_trust = torch.sigmoid(
                outputs["route_confidence"][selection, 0].float()
            )
            primary_confidence = (
                selected_role_score * learned_trust
            ).clamp_min(0.0).sqrt()
            secondary_confidence = (
                selected_role_score
                * selected_surface_score
                * learned_trust
            ).clamp_min(0.0).pow(1.0 / 3.0)
            selected_confidence = torch.where(
                selected_secondary,
                secondary_confidence,
                primary_confidence,
            )
        selected_margin = torch.where(
            selected_secondary,
            torch.minimum(role_margin, surface_margin),
            role_margin,
        )
        selected_margin_ratio = torch.where(
            selected_secondary,
            torch.minimum(role_margin_ratio, surface_margin_ratio),
            role_margin_ratio,
        )

        fg[selection] = routed_fg
        layer[selection] = routed["layer"]
        flat_uv[selection] = routed["flat_uv"]
        surface[selection] = torch.where(
            routed_fg,
            selected_surface,
            torch.full_like(selected_surface, IGNORE_INDEX),
        )
        route_role[selection] = torch.where(
            routed_fg,
            selected_role,
            torch.full_like(selected_role, IGNORE_INDEX),
        )
        confidence[selection] = selected_confidence
        confidence_margin[selection] = selected_margin
        confidence_margin_ratio[selection] = selected_margin_ratio
        part[selection] = routed["part"]
        face[selection] = routed["face"]
        texel_center_score[selection] = routed["texel_center_score"]

    secondary = fg & (route_role == ROUTE_SECONDARY)
    return {
        "foreground": fg,
        "layer": layer,
        "flat_uv": flat_uv,
        "surface": surface,
        "confidence": confidence,
        "confidence_margin": confidence_margin,
        "confidence_margin_ratio": confidence_margin_ratio,
        "semantic_fallback": torch.zeros_like(fg),
        "part": part,
        "face": face,
        "raw_route_role": raw_route_role,
        "route_role": route_role,
        "secondary": secondary,
        "secondary_routed": secondary,
        "texel_center_score": texel_center_score,
        "consensus_changed": consensus_changed,
        "consensus_inner_to_outer": consensus_inner_to_outer,
        "consensus_outer_to_inner": consensus_outer_to_inner,
        "consensus_preserved_outer": consensus_preserved_outer,
        "consensus_outer_gate_rejected": consensus_outer_gate_rejected,
        "occupancy_rescued_outer": occupancy_rescued_outer,
        "occupancy_rejected_outer": occupancy_rejected_outer,
        "projected_outer_occupancy": projected_outer_occupancy,
        "projected_outer_component_seed": projected_outer_component_seed,
        "projected_outer_component_grown": projected_outer_component_grown,
        "projected_outer_component_rejected": (
            projected_outer_component_rejected
        ),
        "outer_uv_occupancy_available": torch.full_like(
            fg, occupancy_logits is not None
        ),
        "cross_view_outer_shared": (
            cross_view["shared"] if cross_view is not None else torch.zeros_like(fg)
        ),
        "cross_view_outer_conflict": (
            cross_view["conflict"] if cross_view is not None else torch.zeros_like(fg)
        ),
        "cross_view_outer_vetoed": (
            cross_view["conflict"]
            & (raw_route_role == ROUTE_OUTER_PRIMARY)
            & (route_role != ROUTE_OUTER_PRIMARY)
            if cross_view is not None
            else torch.zeros_like(fg)
        ),
        "cross_view_outer_positive": (
            cross_view["positive"] if cross_view is not None else torch.zeros_like(fg)
        ),
        "cross_view_outer_negative": (
            cross_view["negative"] if cross_view is not None else torch.zeros_like(fg)
        ),
        "learned_trust": (
            torch.sigmoid(outputs["route_confidence"][:, 0].float())
            if "route_confidence" in outputs
            else torch.ones_like(foreground_prob)
        ),
    }


def _surface_aware_outer_coverage(routing, trusted, selected_outer, renderer, views):
    """Measure outer support within the selected view/surface/UV texel."""
    views = parse_views(views)
    views_per_group = len(views)
    group_count = trusted.shape[0] // views_per_group
    static_views = [
        build_static_surface_routing(renderer, view, trusted.device)
        for view in views
    ]
    surface_count = max(static["masks"].shape[0] for static in static_views)
    uv_count = UV_SIZE * UV_SIZE
    view_stride = surface_count * uv_count
    group_stride = views_per_group * view_stride
    expected = routing["confidence"].new_zeros(group_stride)

    for view_index, static in enumerate(static_views):
        static_surface_count = static["masks"].shape[0]
        surface_offsets = (
            torch.arange(static_surface_count, device=trusted.device).view(-1, 1, 1)
            * uv_count
        )
        expected_indices = (
            view_index * view_stride
            + surface_offsets
            + static["flat_uv"][:static_surface_count]
        )
        expected_mask = (
            static["masks"][:static_surface_count]
            & (static["layer"][:static_surface_count] == 1)
        )
        selected_indices = expected_indices[expected_mask]
        expected.scatter_add_(
            0,
            selected_indices,
            torch.ones(
                selected_indices.shape[0],
                device=trusted.device,
                dtype=expected.dtype,
            ),
        )

    item_indices = torch.arange(trusted.shape[0], device=trusted.device)
    item_groups = item_indices // views_per_group
    item_views = item_indices % views_per_group
    selected_surface = routing["surface"].clamp(0, surface_count - 1)
    route_index = (
        item_views.view(-1, 1, 1) * view_stride
        + selected_surface * uv_count
        + routing["flat_uv"]
    )
    grouped_route_index = route_index + item_groups.view(-1, 1, 1) * group_stride
    observed_mask = trusted & selected_outer
    observed = routing["confidence"].new_zeros(group_count * group_stride)
    observed_indices = grouped_route_index[observed_mask]
    observed.scatter_add_(
        0,
        observed_indices,
        torch.ones(
            observed_indices.shape[0],
            device=trusted.device,
            dtype=observed.dtype,
        ),
    )
    coverage = observed.reshape(group_count, group_stride) / expected.clamp_min(1.0)
    pixel_coverage = coverage[item_groups.view(-1, 1, 1), route_index]
    # Composite and geometry slots can be partially occluded by nearer surfaces,
    # so their static masks are not valid coverage denominators. Their exact slot
    # classifier and texel consensus already reject isolated fragments.
    return torch.where(
        selected_surface >= LAYER_CLASSES,
        torch.ones_like(pixel_coverage),
        pixel_coverage,
    )


def _outer_silhouette_coverage(
    observed_foreground,
    flat_uv,
    renderer,
    views,
    dilation=0,
    min_pixels=4,
):
    """Measure whether an outer texel's protruding pixels exist in the cutout.

    Only pixels covered by the outer cuboid but not by the inner cuboid carry
    useful silhouette evidence. Interior projections are deliberately left
    unassessed because an absent outer texel and the inner surface behind it
    have the same foreground mask there.

    Coverage is calculated independently for every view and the least
    supported assessed view wins. Averaging views would let a texel that is
    visible in one view but absent in another pass at exactly 50% coverage,
    which creates the characteristic head-top and clothing-edge spikes.
    """
    views = parse_views(views)
    if not views:
        raise ValueError("At least one renderer view is required.")
    if observed_foreground.shape != flat_uv.shape:
        raise ValueError(
            "observed_foreground and flat_uv must have identical shapes."
        )
    if observed_foreground.shape[0] % len(views) != 0:
        raise ValueError("The routed batch must contain complete view groups.")
    if dilation < 0:
        raise ValueError("dilation must be non-negative.")
    if min_pixels < 1:
        raise ValueError("min_pixels must be positive.")

    observed = observed_foreground.to(dtype=torch.bool)
    if dilation > 0:
        kernel_size = 2 * int(dilation) + 1
        observed = F.max_pool2d(
            observed.unsqueeze(1).float(),
            kernel_size=kernel_size,
            stride=1,
            padding=int(dilation),
        )[:, 0] > 0.5

    views_per_group = len(views)
    group_count = observed.shape[0] // views_per_group
    uv_count = UV_SIZE * UV_SIZE
    expected = observed.new_zeros(
        (views_per_group, uv_count), dtype=torch.float32
    )
    supported = observed.new_zeros(
        (group_count, views_per_group, uv_count), dtype=torch.float32
    )
    for view_index, view in enumerate(views):
        static = build_static_surface_routing(
            renderer, view, observed.device
        )
        inner_silhouette = static["masks"][ROUTE_INNER_PRIMARY]
        outer_silhouette = static["masks"][ROUTE_OUTER_PRIMARY]
        protruding = outer_silhouette & ~inner_silhouette
        if not protruding.any():
            continue
        protruding_uv = static["flat_uv"][ROUTE_OUTER_PRIMARY][
            protruding
        ]
        expected[view_index].scatter_add_(
            0,
            protruding_uv,
            torch.ones_like(protruding_uv, dtype=expected.dtype),
        )
        observed_view = observed[view_index::views_per_group, protruding]
        supported[:, view_index].scatter_add_(
            1,
            protruding_uv.view(1, -1).expand(group_count, -1),
            observed_view.to(dtype=supported.dtype),
        )

    assessed_by_view = expected >= float(min_pixels)
    coverage_by_view = supported / expected.clamp_min(1.0).unsqueeze(0)
    coverage_by_view = torch.where(
        assessed_by_view.unsqueeze(0),
        coverage_by_view,
        torch.ones_like(coverage_by_view),
    )
    coverage_uv = coverage_by_view.amin(dim=1)
    assessed_uv = assessed_by_view.any(dim=0)
    item_groups = (
        torch.arange(observed.shape[0], device=observed.device)
        // views_per_group
    )
    pixel_coverage = coverage_uv[
        item_groups.view(-1, 1, 1), flat_uv
    ]
    pixel_assessed = assessed_uv[flat_uv]
    return pixel_coverage, pixel_assessed


def _grouped_uv_support(mask, flat_uv, group_size):
    """Broadcast per-pixel evidence to matching UV texels across all input views."""
    if mask.shape != flat_uv.shape:
        raise ValueError("mask and flat_uv must have identical shapes.")
    if group_size <= 0 or mask.shape[0] % group_size != 0:
        raise ValueError("group_size must evenly divide the routed batch.")

    group_count = mask.shape[0] // group_size
    item_groups = torch.arange(mask.shape[0], device=mask.device) // group_size
    grouped_uv = flat_uv + item_groups.view(-1, 1, 1) * (UV_SIZE * UV_SIZE)
    support_count = torch.zeros(
        group_count * UV_SIZE * UV_SIZE,
        device=mask.device,
        dtype=torch.float32,
    )
    selected_uv = grouped_uv[mask]
    support_count.scatter_add_(
        0,
        selected_uv,
        torch.ones(selected_uv.shape[0], device=mask.device, dtype=support_count.dtype),
    )
    return support_count[grouped_uv] > 0


def _geometry_supported_outer_texels(routing, renderer, views):
    """Find outer texels proven by outer-only silhouette or an exact secondary slot.

    A direct outer pixel outside the base cuboid silhouette cannot be explained by
    the inner layer. Likewise a routed secondary surface is tied to an exact
    renderer slot. Either observation is safe evidence for relaxing confidence
    gates on the same outer UV texel in another pixel or view.
    """
    views = parse_views(views)
    if not views:
        raise ValueError("At least one renderer view is required for outer rescue.")
    selected_outer = routing["layer"] == 1
    if selected_outer.shape[0] % len(views) != 0:
        raise ValueError("Routed batch must be divisible by the number of views.")

    outer_only = torch.zeros_like(selected_outer)
    selected_surface = routing.get("surface")
    for view_index, view in enumerate(views):
        selection = slice(view_index, selected_outer.shape[0], len(views))
        static = build_static_surface_routing(renderer, view, selected_outer.device)
        direct_outer = static["masks"][1] & ~static["masks"][0]
        if selected_surface is not None:
            direct_outer = direct_outer.unsqueeze(0) & (
                selected_surface[selection] == ROUTE_OUTER_PRIMARY
            )
        else:
            direct_outer = direct_outer.unsqueeze(0).expand(
                selected_outer[selection].shape[0], -1, -1
            )
        outer_only[selection] = direct_outer

    secondary = routing.get("secondary", torch.zeros_like(selected_outer))
    geometry_seed = selected_outer & (outer_only | secondary)
    supported_texel = _grouped_uv_support(
        geometry_seed,
        routing["flat_uv"],
        len(views),
    )
    return selected_outer & supported_texel


def _semantic_supported_outer_pixels(
    outputs,
    routing,
    group_size,
    presence_threshold=0.80,
    coverage_threshold=0.20,
):
    """Use image-level part semantics to identify plausible outer-layer pixels."""
    selected_outer = routing["layer"] == 1
    presence_logits = outputs.get("outer_presence_logits")
    predicted_coverage = outputs.get("outer_coverage")
    routed_part = routing.get("part")
    if (
        presence_logits is None
        or predicted_coverage is None
        or routed_part is None
    ):
        return torch.zeros_like(selected_outer)
    group_count = selected_outer.shape[0] // group_size
    if presence_logits.shape[:2] != (group_count, PART_CLASSES):
        return torch.zeros_like(selected_outer)
    if predicted_coverage.shape[:2] != (group_count, PART_CLASSES):
        return torch.zeros_like(selected_outer)

    item_groups = torch.arange(
        selected_outer.shape[0], device=selected_outer.device
    ) // group_size
    safe_part = routed_part.clamp(0, PART_CLASSES - 1)
    valid_part = routed_part != IGNORE_INDEX
    expanded_groups = item_groups.view(-1, 1, 1).expand_as(safe_part)
    presence = torch.sigmoid(presence_logits.float())[
        expanded_groups, safe_part
    ]
    coverage = predicted_coverage.float()[expanded_groups, safe_part]
    return (
        selected_outer
        & valid_part
        & (presence >= float(presence_threshold))
        & (coverage >= float(coverage_threshold))
    )


def _scatter_soft_uv(rgb_sum, weight_sum, source_rgb, weight, flat_uv, valid):
    """Differentiably accumulate weighted render pixels into fixed UV indices."""
    if not valid.any():
        return rgb_sum, weight_sum
    batch = source_rgb.shape[0]
    indices = flat_uv[valid].reshape(1, -1).expand(batch, -1)
    selected_weight = weight[:, valid]
    selected_rgb = source_rgb[:, :, valid] * selected_weight.unsqueeze(1)
    weight_contribution = weight_sum.new_zeros(batch, UV_SIZE * UV_SIZE).scatter_add(
        1,
        indices,
        selected_weight,
    )
    rgb_contribution = rgb_sum.new_zeros(batch, 3, UV_SIZE * UV_SIZE).scatter_add(
        2,
        indices.unsqueeze(1).expand(-1, 3, -1),
        selected_rgb,
    )
    return rgb_sum + rgb_contribution, weight_sum + weight_contribution


def soft_splat_geometry_predictions_to_uv(
    rendered,
    outputs,
    renderer,
    views,
    group_size=None,
    temperature=1.0,
    canonicalize=True,
    eps=1e-6,
    return_details=False,
):
    """Build a differentiable provisional UV atlas from geometry-parser probabilities.

    Primary inner/outer probabilities are splatted through their direct cuboid
    maps. Secondary probability is distributed through the learned exact
    surface probabilities. UV scatter indices stay fixed while all weights and
    the predicted affine remain differentiable.
    """
    if rendered.dim() != 4:
        raise ValueError(f"Expected rendered NCHW tensor, got {tuple(rendered.shape)}.")
    views = parse_views(views)
    if not views:
        raise ValueError("At least one renderer view is required for soft geometry splatting.")
    if group_size is None:
        group_size = len(views)
    if group_size != len(views):
        raise ValueError(f"group_size={group_size} must equal the number of views ({len(views)}).")
    if rendered.shape[0] % group_size != 0:
        raise ValueError(f"N={rendered.shape[0]} must be divisible by group_size={group_size}.")
    if temperature <= 0:
        raise ValueError("temperature must be positive.")
    if outputs["layer"].shape[1] != ROUTE_ROLE_CLASSES or "surface" not in outputs:
        raise ValueError(
            "Soft geometry splatting requires three route-role logits and exact surface logits."
        )

    if canonicalize:
        canonical_outputs = canonicalize_parser_outputs(outputs)
        canonical_rendered = canonicalize_parser_render(
            rendered,
            outputs,
            mode="bilinear",
        ).float()
    else:
        canonical_outputs = outputs
        canonical_rendered = rendered.float()
    role_prob = torch.softmax(canonical_outputs["layer"].float() / temperature, dim=1)
    surface_logits = canonical_outputs["surface"]
    surface_log_normalizer = torch.logsumexp(surface_logits / temperature, dim=1)
    foreground_prob = torch.sigmoid(canonical_outputs["foreground"][:, 0].float())
    groups = rendered.shape[0] // group_size
    reference = canonical_rendered
    rgb_sums = [
        reference.new_zeros(groups, 3, UV_SIZE * UV_SIZE)
        for _ in range(LAYER_CLASSES)
    ]
    weight_sums = [
        reference.new_zeros(groups, UV_SIZE * UV_SIZE)
        for _ in range(LAYER_CLASSES)
    ]
    expected = reference.new_zeros(LAYER_CLASSES, UV_SIZE * UV_SIZE)

    for view_index, view in enumerate(views):
        selection = slice(view_index, rendered.shape[0], group_size)
        static = build_static_surface_routing(renderer, view, rendered.device)
        if static["masks"].shape[-2:] != canonical_rendered.shape[-2:]:
            raise ValueError(
                f"View {view!r} mapping shape {tuple(static['masks'].shape[-2:])} "
                f"does not match parser shape {tuple(canonical_rendered.shape[-2:])}."
            )
        surface_count = static["masks"].shape[0]
        if surface_logits.shape[1] < surface_count:
            raise ValueError(
                f"Parser has {surface_logits.shape[1]} surface classes, but view {view!r} "
                f"requires {surface_count}."
            )

        source_rgb = canonical_rendered[selection, :3]
        view_foreground = foreground_prob[selection]
        view_role_prob = role_prob[selection]
        view_surface_logits = surface_logits[selection]
        view_surface_log_normalizer = surface_log_normalizer[selection]

        for layer_index in range(LAYER_CLASSES):
            valid = static["masks"][layer_index]
            flat_uv = static["flat_uv"][layer_index]
            weight = view_foreground * view_role_prob[:, layer_index]
            rgb_sums[layer_index], weight_sums[layer_index] = _scatter_soft_uv(
                rgb_sums[layer_index],
                weight_sums[layer_index],
                source_rgb,
                weight,
                flat_uv,
                valid,
            )
            expected[layer_index].scatter_add_(
                0,
                flat_uv[valid],
                torch.ones_like(flat_uv[valid], dtype=expected.dtype),
            )

        candidate_layer, candidate_role = _static_candidate_roles(static)
        for surface_index in range(LAYER_CLASSES, surface_count):
            secondary = (
                static["masks"][surface_index]
                & (candidate_role[surface_index] == ROUTE_SECONDARY)
            )
            if not secondary.any():
                continue
            surface_weight = (
                view_foreground
                * view_role_prob[:, ROUTE_SECONDARY]
                * torch.exp(
                    view_surface_logits[:, surface_index].float() / temperature
                    - view_surface_log_normalizer.float()
                )
            )
            for layer_index in range(LAYER_CLASSES):
                valid = secondary & (candidate_layer[surface_index] == layer_index)
                if not valid.any():
                    continue
                rgb_sums[layer_index], weight_sums[layer_index] = _scatter_soft_uv(
                    rgb_sums[layer_index],
                    weight_sums[layer_index],
                    source_rgb,
                    surface_weight,
                    static["flat_uv"][surface_index],
                    valid,
                )

    stacked_rgb_sum = torch.stack(rgb_sums, dim=1)
    stacked_weight_sum = torch.stack(weight_sums, dim=1).unsqueeze(2)
    expected = expected.view(1, LAYER_CLASSES, 1, UV_SIZE * UV_SIZE).clamp_min(1.0)
    layer_alpha = (stacked_weight_sum / expected).clamp(0.0, 1.0)
    total_rgb_sum = stacked_rgb_sum.sum(dim=1)
    total_weight = stacked_weight_sum.sum(dim=1)
    rgb = total_rgb_sum / total_weight.clamp_min(eps)
    alpha = layer_alpha.amax(dim=1)
    pred_uv = torch.cat([rgb, alpha], dim=1).reshape(groups, 4, UV_SIZE, UV_SIZE)
    support = total_weight.reshape(groups, 1, UV_SIZE, UV_SIZE)
    if return_details:
        return pred_uv, {
            "support": support,
            "layer_weight": stacked_weight_sum.reshape(
                groups, LAYER_CLASSES, UV_SIZE, UV_SIZE
            ),
            "layer_alpha": layer_alpha.reshape(
                groups, LAYER_CLASSES, UV_SIZE, UV_SIZE
            ),
            "canonical_rendered": canonical_rendered,
            "canonical_outputs": canonical_outputs,
        }
    return pred_uv


def render_direct_uv(skins, renderer, view):
    """Differentiably render the direct inner/outer cuboids without deep composites."""
    if skins.dim() != 4 or skins.shape[1:] != (4, UV_SIZE, UV_SIZE):
        raise ValueError(f"Expected skins shaped (N, 4, 64, 64), got {tuple(skins.shape)}.")
    batch = skins.shape[0]
    dtype = skins.dtype
    inner_grid = getattr(renderer, f"{view}_inner_grid").to(dtype=dtype)
    outer_grid = getattr(renderer, f"{view}_outer_grid").to(dtype=dtype)
    inner_mask = getattr(renderer, f"{view}_inner_mask").to(dtype=dtype)
    outer_mask = getattr(renderer, f"{view}_outer_mask").to(dtype=dtype)
    inner = F.grid_sample(
        skins,
        inner_grid.unsqueeze(0).expand(batch, -1, -1, -1),
        mode="bilinear",
        padding_mode="zeros",
        align_corners=True,
    ) * inner_mask.view(1, 1, *inner_mask.shape)
    outer = F.grid_sample(
        skins,
        outer_grid.unsqueeze(0).expand(batch, -1, -1, -1),
        mode="bilinear",
        padding_mode="zeros",
        align_corners=True,
    ) * outer_mask.view(1, 1, *outer_mask.shape)
    bg = renderer.bg_color.to(device=skins.device, dtype=dtype).view(1, 3, 1, 1)
    inner_rgb = inner[:, 3:4] * inner[:, :3] + (1.0 - inner[:, 3:4]) * bg
    rgb = outer[:, 3:4] * outer[:, :3] + (1.0 - outer[:, 3:4]) * inner_rgb
    alpha = outer[:, 3:4] + (1.0 - outer[:, 3:4]) * inner[:, 3:4]
    return torch.cat([rgb, alpha], dim=1)


def render_outer_alpha_uv(skins, renderer, view):
    """Differentiably project only the outer-layer alpha into one view."""
    if skins.dim() != 4 or skins.shape[1:] != (4, UV_SIZE, UV_SIZE):
        raise ValueError(
            f"Expected skins shaped (N, 4, 64, 64), got {tuple(skins.shape)}."
        )
    batch = skins.shape[0]
    dtype = skins.dtype
    outer_grid = getattr(renderer, f"{view}_outer_grid").to(dtype=dtype)
    outer_mask = getattr(renderer, f"{view}_outer_mask").to(dtype=dtype)
    return F.grid_sample(
        skins[:, 3:4],
        outer_grid.unsqueeze(0).expand(batch, -1, -1, -1),
        mode="bilinear",
        padding_mode="zeros",
        align_corners=True,
    ) * outer_mask.view(1, 1, *outer_mask.shape)


def flat_uv_to_uv01(flat_uv, dtype):
    return torch.stack(
        [
            (flat_uv.remainder(UV_SIZE) / float(UV_SIZE - 1)).to(dtype),
            (flat_uv.div(UV_SIZE, rounding_mode="floor") / float(UV_SIZE - 1)).to(dtype),
        ],
        dim=1,
    )


def splat_parser_predictions_to_uv_conditioning(
    rendered,
    outputs,
    renderer=None,
    views=None,
    group_size=1,
    fg_threshold=0.5,
    bg_color=(128, 128, 128),
    semantic_gate=True,
    affine_refine=True,
    affine_refine_translation_px=8.0,
    affine_refine_scale=0.0,
    route_confidence_threshold=0.0,
    route_margin_threshold=0.0,
    outer_route_confidence_threshold=None,
    outer_route_margin_threshold=None,
    outer_uv_min_coverage=0.5,
    outer_uv_min_source_pixels=1,
    outer_silhouette_consistency=True,
    outer_silhouette_min_coverage=0.50,
    outer_silhouette_dilation=0,
    outer_silhouette_min_pixels=4,
    outer_geometry_rescue=False,
    outer_semantic_rescue=True,
    outer_semantic_presence_threshold=0.80,
    outer_semantic_coverage_threshold=0.20,
    outer_rescue_confidence_threshold=0.60,
    outer_rescue_margin_threshold=0.25,
    outer_rescue_min_coverage=0.10,
    color_aggregation="grid_mode",
    geometry_outer_threshold=0.5,
    geometry_route_texel_consensus=True,
    geometry_route_texel_consensus_weight=0.60,
    geometry_route_preserve_outer_confidence=0.80,
    geometry_route_preserve_outer_margin=0.35,
    geometry_route_consensus_outer_confidence=0.70,
    geometry_route_consensus_outer_margin=0.20,
    geometry_cross_view_outer_consistency=False,
    geometry_cross_view_outer_weight=0.50,
    geometry_cross_view_outer_positive_confidence=0.70,
    geometry_cross_view_outer_positive_margin=0.20,
    geometry_cross_view_outer_negative_confidence=0.70,
    geometry_cross_view_outer_negative_margin=0.20,
    geometry_cross_view_outer_background_max_coverage=0.25,
    geometry_cross_view_outer_min_views=2,
    outer_uv_occupancy=False,
    outer_uv_occupancy_blend_weight=0.0,
    outer_uv_occupancy_gate_threshold=0.15,
    outer_uv_occupancy_rescue_threshold=0.70,
    outer_uv_occupancy_rescue_route_threshold=0.30,
    outer_uv_component_routing=False,
    outer_uv_component_seed_threshold=0.80,
    outer_uv_component_grow_threshold=0.50,
    outer_uv_component_min_size=2,
    observed_foreground=None,
    background_color_tolerance=SOLID_BACKGROUND_COLOR_TOLERANCE,
    color_background_tolerance=None,
    color_foreground_inset=1,
    reject_semantic_fallback=False,
    reject_inner_semantic_fallback=False,
    include_rejected_context=True,
    rejected_context_confidence_threshold=0.35,
    rejected_context_margin_threshold=0.10,
    rejected_context_alpha_confidence_threshold=0.50,
    rejected_context_alpha_margin_threshold=0.10,
    include_confidence=False,
    return_details=False,
    observed_color_support=None,
    head_color_separation_inset=0,
):
    """Route parser outputs to UV, using static mappings for affine-parser checkpoints."""
    if not 0.0 <= route_confidence_threshold <= 1.0:
        raise ValueError("route_confidence_threshold must be in [0, 1].")
    if not 0.0 <= route_margin_threshold <= 1.0:
        raise ValueError("route_margin_threshold must be in [0, 1].")
    if outer_route_confidence_threshold is None:
        outer_route_confidence_threshold = route_confidence_threshold
    if outer_route_margin_threshold is None:
        outer_route_margin_threshold = route_margin_threshold
    if not 0.0 <= outer_route_confidence_threshold <= 1.0:
        raise ValueError("outer_route_confidence_threshold must be in [0, 1].")
    if not 0.0 <= outer_route_margin_threshold <= 1.0:
        raise ValueError("outer_route_margin_threshold must be in [0, 1].")
    if not 0.0 <= outer_uv_min_coverage <= 1.0:
        raise ValueError("outer_uv_min_coverage must be in [0, 1].")
    if outer_uv_min_source_pixels < 1:
        raise ValueError("outer_uv_min_source_pixels must be positive.")
    if not 0.0 <= outer_silhouette_min_coverage <= 1.0:
        raise ValueError("outer_silhouette_min_coverage must be in [0, 1].")
    if outer_silhouette_dilation < 0:
        raise ValueError("outer_silhouette_dilation must be non-negative.")
    if outer_silhouette_min_pixels < 1:
        raise ValueError("outer_silhouette_min_pixels must be positive.")
    if not (
        0.0
        <= outer_uv_component_grow_threshold
        <= outer_uv_component_seed_threshold
        <= 1.0
    ):
        raise ValueError(
            "Require outer component grow <= seed threshold in [0, 1]."
        )
    if outer_uv_component_min_size < 1:
        raise ValueError("outer_uv_component_min_size must be positive.")
    if not 0.0 <= outer_rescue_confidence_threshold <= 1.0:
        raise ValueError("outer_rescue_confidence_threshold must be in [0, 1].")
    if not 0.0 <= outer_rescue_margin_threshold <= 1.0:
        raise ValueError("outer_rescue_margin_threshold must be in [0, 1].")
    if not 0.0 <= outer_rescue_min_coverage <= 1.0:
        raise ValueError("outer_rescue_min_coverage must be in [0, 1].")
    if not 0.0 <= outer_semantic_presence_threshold <= 1.0:
        raise ValueError("outer_semantic_presence_threshold must be in [0, 1].")
    if not 0.0 <= outer_semantic_coverage_threshold <= 1.0:
        raise ValueError("outer_semantic_coverage_threshold must be in [0, 1].")
    for name, value in (
        (
            "geometry_route_texel_consensus_weight",
            geometry_route_texel_consensus_weight,
        ),
        (
            "geometry_route_preserve_outer_confidence",
            geometry_route_preserve_outer_confidence,
        ),
        (
            "geometry_route_preserve_outer_margin",
            geometry_route_preserve_outer_margin,
        ),
        (
            "geometry_route_consensus_outer_confidence",
            geometry_route_consensus_outer_confidence,
        ),
        (
            "geometry_route_consensus_outer_margin",
            geometry_route_consensus_outer_margin,
        ),
        (
            "geometry_cross_view_outer_weight",
            geometry_cross_view_outer_weight,
        ),
        (
            "geometry_cross_view_outer_positive_confidence",
            geometry_cross_view_outer_positive_confidence,
        ),
        (
            "geometry_cross_view_outer_positive_margin",
            geometry_cross_view_outer_positive_margin,
        ),
        (
            "geometry_cross_view_outer_negative_confidence",
            geometry_cross_view_outer_negative_confidence,
        ),
        (
            "geometry_cross_view_outer_negative_margin",
            geometry_cross_view_outer_negative_margin,
        ),
        (
            "geometry_cross_view_outer_background_max_coverage",
            geometry_cross_view_outer_background_max_coverage,
        ),
        (
            "outer_uv_occupancy_blend_weight",
            outer_uv_occupancy_blend_weight,
        ),
        (
            "outer_uv_occupancy_gate_threshold",
            outer_uv_occupancy_gate_threshold,
        ),
        (
            "outer_uv_occupancy_rescue_threshold",
            outer_uv_occupancy_rescue_threshold,
        ),
        (
            "outer_uv_occupancy_rescue_route_threshold",
            outer_uv_occupancy_rescue_route_threshold,
        ),
    ):
        if not 0.0 <= float(value) <= 1.0:
            raise ValueError(f"{name} must be in [0, 1].")
    if not 0.0 <= rejected_context_confidence_threshold <= 1.0:
        raise ValueError("rejected_context_confidence_threshold must be in [0, 1].")
    if not 0.0 <= rejected_context_margin_threshold <= 1.0:
        raise ValueError("rejected_context_margin_threshold must be in [0, 1].")
    if not 0.0 <= rejected_context_alpha_confidence_threshold <= 1.0:
        raise ValueError(
            "rejected_context_alpha_confidence_threshold must be in [0, 1]."
        )
    if not 0.0 <= rejected_context_alpha_margin_threshold <= 1.0:
        raise ValueError(
            "rejected_context_alpha_margin_threshold must be in [0, 1]."
        )
    if not 0.0 <= background_color_tolerance <= 1.0:
        raise ValueError("background_color_tolerance must be in [0, 1].")
    if (
        color_background_tolerance is not None
        and not 0.0 <= color_background_tolerance <= 1.0
    ):
        raise ValueError("color_background_tolerance must be in [0, 1].")
    if color_foreground_inset < 0:
        raise ValueError("color_foreground_inset must be non-negative.")
    if geometry_cross_view_outer_min_views < 2:
        raise ValueError("geometry_cross_view_outer_min_views must be at least 2.")
    if "affine" not in outputs:
        conditioning = splat_predictions_to_uv_conditioning(
            rendered,
            outputs,
            group_size=group_size,
            fg_threshold=fg_threshold,
            bg_color=bg_color,
        )
        if return_details:
            return conditioning, {"rendered": rendered, "outputs": outputs, "routing": None, "alignment": None}
        return conditioning

    if renderer is None or views is None:
        raise ValueError("Affine parser routing requires both renderer and views.")
    views = parse_views(views)
    if group_size != len(views):
        raise ValueError(f"group_size={group_size} must equal the number of views ({len(views)}).")

    if observed_foreground is None:
        observed_foreground = estimate_solid_background_foreground(
            rendered,
            color_tolerance=background_color_tolerance,
        )
    else:
        if observed_foreground.shape != rendered.shape[:1] + rendered.shape[-2:]:
            raise ValueError(
                "observed_foreground must have shape "
                f"{rendered.shape[:1] + rendered.shape[-2:]}, got {tuple(observed_foreground.shape)}."
            )
        observed_foreground = observed_foreground.to(
            device=rendered.device, dtype=torch.bool
        )
    source_background_rgb, _ = estimate_solid_background_color(rendered)
    source_fill = rendered.new_ones(rendered.shape[0], rendered.shape[1], 1, 1)
    source_fill[:, :3] = source_background_rgb.to(dtype=rendered.dtype)

    alignment = None
    routing_outputs = outputs
    if affine_refine:
        refined_affine, alignment = refine_parser_affine(
            outputs,
            renderer,
            views,
            translation_radius_px=affine_refine_translation_px,
            scale_radius=affine_refine_scale,
            observed_foreground=observed_foreground,
        )
        routing_outputs = dict(outputs)
        routing_outputs["affine"] = refined_affine

    canonical_rendered = canonicalize_parser_render(
        rendered,
        routing_outputs,
        mode="nearest",
        fill_color=source_fill,
    )
    canonical_observed_foreground = canonicalize_foreground_mask(
        observed_foreground,
        routing_outputs["affine"],
    )
    canonical_observed_foreground_nearest = canonicalize_tensor(
        observed_foreground.unsqueeze(1).to(dtype=rendered.dtype),
        routing_outputs["affine"],
        mode="nearest",
    )[:, 0] > 0.5
    canonical_foreground_coverage_rescued = (
        canonical_observed_foreground
        & ~canonical_observed_foreground_nearest
    )
    color_support = build_color_sampling_support(
        canonical_rendered,
        canonical_observed_foreground,
        source_background_rgb,
        background_tolerance=color_background_tolerance,
        foreground_inset=color_foreground_inset,
    )
    if observed_color_support is not None:
        if observed_color_support.shape != observed_foreground.shape:
            raise ValueError('Observed color support must match observed foreground')
        safe_source=canonicalize_tensor(observed_color_support[:,None].to(rendered.device,rendered.dtype),routing_outputs['affine'],mode='nearest')[:,0]>.5
        color_support['rejected'] |= color_support['valid'] & ~safe_source
        color_support['valid'] &= safe_source
    canonical_outputs = canonicalize_parser_outputs(routing_outputs)
    if "surface" in canonical_outputs and "part" not in canonical_outputs:
        routing = _routing_from_geometry_surface_outputs(
            renderer,
            views,
            canonical_outputs,
            fg_threshold=fg_threshold,
            texel_consensus=geometry_route_texel_consensus,
            texel_consensus_weight=geometry_route_texel_consensus_weight,
            preserve_outer_confidence=geometry_route_preserve_outer_confidence,
            preserve_outer_margin=geometry_route_preserve_outer_margin,
            consensus_outer_confidence=geometry_route_consensus_outer_confidence,
            consensus_outer_margin=geometry_route_consensus_outer_margin,
            outer_uv_occupancy=outer_uv_occupancy,
            outer_uv_occupancy_blend_weight=(
                outer_uv_occupancy_blend_weight
            ),
            outer_uv_occupancy_gate_threshold=(
                outer_uv_occupancy_gate_threshold
            ),
            outer_uv_occupancy_rescue_threshold=(
                outer_uv_occupancy_rescue_threshold
            ),
            outer_uv_occupancy_rescue_route_threshold=(
                outer_uv_occupancy_rescue_route_threshold
            ),
            outer_uv_component_routing=outer_uv_component_routing,
            outer_uv_component_seed_threshold=(
                outer_uv_component_seed_threshold
            ),
            outer_uv_component_grow_threshold=(
                outer_uv_component_grow_threshold
            ),
            outer_uv_component_min_size=outer_uv_component_min_size,
            observed_foreground=canonical_observed_foreground,
            cross_view_outer_consistency=(
                geometry_cross_view_outer_consistency
            ),
            cross_view_outer_weight=geometry_cross_view_outer_weight,
            cross_view_outer_positive_confidence=(
                geometry_cross_view_outer_positive_confidence
            ),
            cross_view_outer_positive_margin=(
                geometry_cross_view_outer_positive_margin
            ),
            cross_view_outer_negative_confidence=(
                geometry_cross_view_outer_negative_confidence
            ),
            cross_view_outer_negative_margin=(
                geometry_cross_view_outer_negative_margin
            ),
            cross_view_outer_background_max_coverage=(
                geometry_cross_view_outer_background_max_coverage
            ),
            cross_view_outer_min_views=geometry_cross_view_outer_min_views,
        )
    elif "surface" not in canonical_outputs and "part" not in canonical_outputs:
        routing = _routing_from_geometry_outputs(
            renderer,
            views,
            canonical_outputs,
            fg_threshold=fg_threshold,
            outer_threshold=geometry_outer_threshold,
            texel_consensus=geometry_route_texel_consensus,
            texel_consensus_weight=geometry_route_texel_consensus_weight,
            preserve_outer_confidence=geometry_route_preserve_outer_confidence,
            preserve_outer_margin=geometry_route_preserve_outer_margin,
            consensus_outer_confidence=geometry_route_consensus_outer_confidence,
            consensus_outer_margin=geometry_route_consensus_outer_margin,
            outer_uv_occupancy=outer_uv_occupancy,
            outer_uv_occupancy_blend_weight=(
                outer_uv_occupancy_blend_weight
            ),
            outer_uv_occupancy_gate_threshold=(
                outer_uv_occupancy_gate_threshold
            ),
            outer_uv_occupancy_rescue_threshold=(
                outer_uv_occupancy_rescue_threshold
            ),
            outer_uv_occupancy_rescue_route_threshold=(
                outer_uv_occupancy_rescue_route_threshold
            ),
            outer_uv_component_routing=outer_uv_component_routing,
            outer_uv_component_seed_threshold=(
                outer_uv_component_seed_threshold
            ),
            outer_uv_component_grow_threshold=(
                outer_uv_component_grow_threshold
            ),
            outer_uv_component_min_size=outer_uv_component_min_size,
            observed_foreground=canonical_observed_foreground,
            cross_view_outer_consistency=(
                geometry_cross_view_outer_consistency
            ),
            cross_view_outer_weight=geometry_cross_view_outer_weight,
            cross_view_outer_positive_confidence=(
                geometry_cross_view_outer_positive_confidence
            ),
            cross_view_outer_positive_margin=(
                geometry_cross_view_outer_positive_margin
            ),
            cross_view_outer_negative_confidence=(
                geometry_cross_view_outer_negative_confidence
            ),
            cross_view_outer_negative_margin=(
                geometry_cross_view_outer_negative_margin
            ),
            cross_view_outer_background_max_coverage=(
                geometry_cross_view_outer_background_max_coverage
            ),
            cross_view_outer_min_views=geometry_cross_view_outer_min_views,
        )
    else:
        routing = _routing_from_affine_outputs(
            renderer,
            views,
            canonical_outputs,
            fg_threshold=fg_threshold,
            semantic_gate=semantic_gate,
        )
    from SkingToolkit.dense_uv_parser.accessories import apply_accessory_routing
    accessory_supported = apply_accessory_routing(
        routing, canonical_outputs, canonical_observed_foreground, renderer, views)
    raw_foreground = routing["foreground"]
    routing["secondary"] = routing.get(
        "secondary", torch.zeros_like(raw_foreground)
    ) & canonical_observed_foreground
    selected_outer = routing["layer"] == 1
    confidence_threshold = torch.where(
        selected_outer,
        routing["confidence"].new_tensor(outer_route_confidence_threshold),
        routing["confidence"].new_tensor(route_confidence_threshold),
    )
    margin_threshold = torch.where(
        selected_outer,
        routing["confidence_margin_ratio"].new_tensor(outer_route_margin_threshold),
        routing["confidence_margin_ratio"].new_tensor(route_margin_threshold),
    )
    strict_trusted = (
        raw_foreground
        & canonical_observed_foreground
        & (routing["confidence"] >= confidence_threshold)
        & (routing["confidence_margin_ratio"] >= margin_threshold)
    )
    outer_consensus_gate_rejected = routing.get(
        "consensus_outer_gate_rejected",
        torch.zeros_like(selected_outer),
    )
    # A deferred outer route is intentionally unknown. It may be restored by
    # exact geometry or atlas occupancy evidence below, but broad semantic part
    # presence must not turn the rejected local observation back into outer.
    deferred_outer_gate_rejected = (
        selected_outer & outer_consensus_gate_rejected
    )
    strict_trusted = strict_trusted & ~deferred_outer_gate_rejected
    if reject_semantic_fallback:
        rejected_fallback = routing["semantic_fallback"] & (
            selected_outer | reject_inner_semantic_fallback
        )
        strict_trusted = strict_trusted & ~rejected_fallback
    geometry_supported_outer = torch.zeros_like(selected_outer)
    semantic_supported_outer = torch.zeros_like(selected_outer)
    occupancy_supported_outer = torch.zeros_like(selected_outer)
    outer_geometry_rescued = torch.zeros_like(selected_outer)
    outer_semantic_rescued = torch.zeros_like(selected_outer)
    outer_occupancy_rescued = torch.zeros_like(selected_outer)
    if outer_geometry_rescue:
        geometry_supported_outer = _geometry_supported_outer_texels(
            routing,
            renderer,
            views,
        )
        rescue_trusted = (
            raw_foreground
            & canonical_observed_foreground
            & geometry_supported_outer
            & (routing["confidence"] >= outer_rescue_confidence_threshold)
            & (
                routing["confidence_margin_ratio"]
                >= outer_rescue_margin_threshold
            )
        )
        if reject_semantic_fallback:
            rescue_trusted = rescue_trusted & ~rejected_fallback
        outer_geometry_rescued = rescue_trusted & ~strict_trusted
        trusted = strict_trusted | rescue_trusted
    else:
        trusted = strict_trusted
    if outer_semantic_rescue:
        semantic_supported_outer = _semantic_supported_outer_pixels(
            canonical_outputs,
            routing,
            group_size,
            presence_threshold=outer_semantic_presence_threshold,
            coverage_threshold=outer_semantic_coverage_threshold,
        )
        semantic_rescue_trusted = (
            raw_foreground
            & canonical_observed_foreground
            & semantic_supported_outer
            & ~deferred_outer_gate_rejected
            & (routing["confidence"] >= outer_rescue_confidence_threshold)
            & (
                routing["confidence_margin_ratio"]
                >= outer_rescue_margin_threshold
            )
        )
        if reject_semantic_fallback:
            semantic_rescue_trusted = semantic_rescue_trusted & ~rejected_fallback
        outer_semantic_rescued = semantic_rescue_trusted & ~trusted
        trusted = trusted | semantic_rescue_trusted
    occupancy_available = routing.get(
        "outer_uv_occupancy_available",
        torch.zeros_like(selected_outer),
    )
    occupancy_supported_outer = (
        selected_outer
        & occupancy_available
        & (
            routing.get(
                "projected_outer_occupancy",
                torch.zeros_like(routing["confidence"]),
            )
            >= float(outer_uv_occupancy_rescue_threshold)
        )
    )
    if outer_uv_occupancy and occupancy_supported_outer.any():
        occupancy_rescue_trusted = (
            raw_foreground
            & canonical_observed_foreground
            & occupancy_supported_outer
            & (routing["confidence"] >= outer_rescue_confidence_threshold)
            & (
                routing["confidence_margin_ratio"]
                >= outer_rescue_margin_threshold
            )
        )
        if reject_semantic_fallback:
            occupancy_rescue_trusted = (
                occupancy_rescue_trusted & ~rejected_fallback
            )
        outer_occupancy_rescued = occupancy_rescue_trusted & ~trusted
        trusted = trusted | occupancy_rescue_trusted
    trusted = trusted | accessory_supported
    outer_silhouette_coverage = torch.ones_like(routing["confidence"])
    outer_silhouette_assessed = torch.zeros_like(selected_outer)
    outer_silhouette_rejected = torch.zeros_like(selected_outer)
    if outer_silhouette_consistency:
        (
            outer_silhouette_coverage,
            outer_silhouette_assessed,
        ) = _outer_silhouette_coverage(
            # A one-pixel antialias/background fringe often survives flood
            # fill. It is unsafe silhouette evidence even when it is already
            # excluded from RGB pickup. Use the inset foreground here so that
            # such a fringe cannot validate a false outer shell.
            color_support["interior"],
            routing["flat_uv"],
            renderer,
            views,
            dilation=outer_silhouette_dilation,
            min_pixels=outer_silhouette_min_pixels,
        )
        outer_silhouette_rejected = (
            trusted
            & selected_outer
            & outer_silhouette_assessed
            & (
                outer_silhouette_coverage
                < float(outer_silhouette_min_coverage)
            )
        )
        # Thin crown teeth need not fill most of a projected square. A learned
        # whole-object decision plus confident pixel semantics may preserve them;
        # foreground and valid outer geometry are still mandatory. All other
        # objects retain the established silhouette veto.
        crown_rescue = torch.zeros_like(trusted)
        if 'headwear_presence_logits' in canonical_outputs and 'headwear_supported' in routing:
            crown_rescue = (routing['headwear_supported'] & (routing['headwear_family']==4)
                            & (routing['headwear_probability']>=.8)
                            & canonical_observed_foreground & selected_outer)
        routing['headwear_silhouette_rescued'] = outer_silhouette_rejected & crown_rescue
        outer_silhouette_rejected &= ~crown_rescue
        trusted = trusted & ~outer_silhouette_rejected
    outer_uv_coverage = torch.ones_like(routing["confidence"])
    outer_required_coverage = torch.zeros_like(routing["confidence"])
    if outer_uv_min_coverage > 0.0:
        views_per_group = len(views)
        group_count = trusted.shape[0] // views_per_group
        if "surface" in canonical_outputs:
            pixel_coverage = _surface_aware_outer_coverage(
                routing,
                trusted,
                selected_outer,
                renderer,
                views,
            )
        else:
            expected = routing["confidence"].new_zeros(UV_SIZE * UV_SIZE)
            for view in views:
                static = build_static_surface_routing(renderer, view, trusted.device)
                expected_uv = static["flat_uv"][1][static["masks"][1]]
                expected.scatter_add_(
                    0,
                    expected_uv,
                    torch.ones(expected_uv.shape[0], device=trusted.device, dtype=expected.dtype),
                )

            item_groups = torch.arange(trusted.shape[0], device=trusted.device) // views_per_group
            grouped_uv = routing["flat_uv"] + item_groups.view(-1, 1, 1) * (UV_SIZE * UV_SIZE)
            observed_mask = trusted & selected_outer
            observed = routing["confidence"].new_zeros(group_count * UV_SIZE * UV_SIZE)
            observed_uv = grouped_uv[observed_mask]
            observed.scatter_add_(
                0,
                observed_uv,
                torch.ones(observed_uv.shape[0], device=trusted.device, dtype=observed.dtype),
            )
            coverage = observed.reshape(group_count, UV_SIZE * UV_SIZE) / expected.clamp_min(1.0)
            pixel_coverage = coverage[item_groups.view(-1, 1, 1), routing["flat_uv"]]
        outer_uv_coverage = torch.where(selected_outer, pixel_coverage, outer_uv_coverage)
        required_coverage = torch.full_like(pixel_coverage, outer_uv_min_coverage)
        if (
            outer_geometry_rescue
            or outer_semantic_rescue
            or outer_uv_occupancy
        ):
            required_coverage = torch.where(
                geometry_supported_outer
                | semantic_supported_outer
                | occupancy_supported_outer,
                required_coverage.new_tensor(
                    min(outer_uv_min_coverage, outer_rescue_min_coverage)
                ),
                required_coverage,
            )
        outer_required_coverage = torch.where(
            selected_outer,
            required_coverage,
            outer_required_coverage,
        )
        trusted = trusted & (~selected_outer | (pixel_coverage >= required_coverage) | accessory_supported)
    outer_source_support = torch.zeros_like(routing["flat_uv"])
    outer_source_rejected = torch.zeros_like(selected_outer)
    if outer_uv_min_source_pixels > 1:
        views_per_group = len(views)
        group_count = trusted.shape[0] // views_per_group
        item_groups = (
            torch.arange(trusted.shape[0], device=trusted.device)
            // views_per_group
        )
        grouped_uv = routing["flat_uv"] + item_groups.view(-1, 1, 1) * (
            UV_SIZE * UV_SIZE
        )
        outer_candidates = trusted & selected_outer
        source_counts = torch.zeros(
            group_count * UV_SIZE * UV_SIZE,
            dtype=torch.long,
            device=trusted.device,
        )
        source_counts.scatter_add_(
            0,
            grouped_uv[outer_candidates],
            torch.ones_like(grouped_uv[outer_candidates]),
        )
        outer_source_support = source_counts[grouped_uv]
        outer_source_rejected = (
            outer_candidates
            & (outer_source_support < int(outer_uv_min_source_pixels))
            & ~accessory_supported
        )
        trusted = trusted & ~outer_source_rejected
    routing["raw_foreground"] = raw_foreground
    routing["observed_foreground"] = canonical_observed_foreground
    routing["canonical_foreground_coverage_rescued"] = (
        canonical_foreground_coverage_rescued
    )
    routing["background_rejected"] = raw_foreground & ~canonical_observed_foreground
    routing["rejected"] = raw_foreground & ~trusted
    routing["outer_geometry_supported"] = geometry_supported_outer
    routing["outer_geometry_rescued"] = outer_geometry_rescued & trusted
    routing["outer_semantic_supported"] = semantic_supported_outer
    routing["outer_semantic_rescued"] = outer_semantic_rescued & trusted
    routing["outer_occupancy_supported"] = occupancy_supported_outer
    routing["outer_occupancy_rescued"] = outer_occupancy_rescued & trusted
    routing["outer_required_coverage"] = outer_required_coverage
    routing["outer_silhouette_coverage"] = outer_silhouette_coverage
    routing["outer_silhouette_assessed"] = outer_silhouette_assessed
    routing["outer_silhouette_rejected"] = outer_silhouette_rejected
    routing["outer_source_support"] = outer_source_support
    routing["outer_source_rejected"] = outer_source_rejected
    routing["foreground"] = trusted
    color_foreground = trusted & color_support["valid"]
    boundary_excluded = torch.zeros_like(trusted)
    if head_color_separation_inset > 0:
        # A layer boundary is also an RGB mixing boundary. Keep occupancy, but
        # do not let a thin contaminated inner fringe become an inpainting seed.
        radius=int(head_color_separation_inset)
        head_outer=trusted&(routing['layer']==1)&(routing['part']==0)
        near_outer=F.max_pool2d(head_outer[:,None].float(),2*radius+1,1,radius)[:,0]>.5
        boundary_excluded=near_outer&(routing['layer']==0)&(routing['part']==0)
        phone=routing.get('headphone_colour_conflict')
        if phone is not None:
            # Compare a semantic accessory observation with nearby accepted outer
            # geometry; exclude contradictory RGB without inventing outer texels.
            nearby=F.max_pool2d(head_outer[:,None].float(),17,1,8)[:,0]>.5
            conflict=phone&nearby&(routing['layer']==0)&(routing['part']==0)
            boundary_excluded|=conflict
            routing['headphone_colour_rejected']=conflict
        color_foreground &= ~boundary_excluded
    headwear_layer = routing.get('headwear_layer')
    if headwear_layer is not None:
        # A component outside the chosen layer's projected support is unknown;
        # sampling it into the other layer would duplicate its material.
        conflict = (headwear_layer >= 0) & (routing['layer'] != headwear_layer) & (routing['part'] == 0)
        color_foreground &= ~conflict
        family = routing['headwear_family']
        boundary = torch.zeros_like(trusted)
        for component in (1,2,3,4):
            region = (family == component) & routing['headwear_supported']
            interior = -F.max_pool2d(-region[:,None].float(),3,1,1)[:,0] > .5
            boundary |= region & ~interior
        color_foreground &= ~boundary
        routing['headwear_color_rejected'] = conflict | boundary
    routing['head_color_boundary_excluded']=boundary_excluded
    routing["color_foreground"] = color_foreground
    routing["color_interior"] = color_support["interior"]
    routing["color_background_like"] = color_support["background_like"]
    routing["color_rejected"] = trusted & color_support["rejected"]
    if "secondary_routed" in routing:
        routing["secondary_rejected"] = routing["secondary"] & ~trusted
        routing["secondary_routed"] = routing["secondary"] & trusted
    routing["outer_uv_coverage"] = outer_uv_coverage
    conditioning = splat_to_uv_conditioning(
        canonical_rendered,
        color_foreground,
        routing["layer"],
        routing["flat_uv"],
        group_size=group_size,
        bg_color=bg_color,
        confidence=routing["confidence"],
        sampling_quality=(
            routing.get("texel_center_score")
            + 0.05 * color_support["interior"].to(
                dtype=routing["confidence"].dtype
            )
        ),
        color_aggregation=color_aggregation,
        include_confidence=include_confidence,
    )
    rejected_context = (
        raw_foreground
        & canonical_observed_foreground
        & ~trusted
        & color_support["valid"]
        & (routing["confidence"] >= rejected_context_confidence_threshold)
        & (
            routing["confidence_margin_ratio"]
            >= rejected_context_margin_threshold
        )
    )
    if reject_semantic_fallback:
        rejected_context = rejected_context & ~rejected_fallback
    rejected_context_alpha_supported = (
        rejected_context
        & selected_outer
        & (geometry_supported_outer | semantic_supported_outer)
        & (
            routing["confidence"]
            >= rejected_context_alpha_confidence_threshold
        )
        & (
            routing["confidence_margin_ratio"]
            >= rejected_context_alpha_margin_threshold
        )
    )
    context_alpha_rescue_uv = conditioning.new_zeros(
        conditioning.shape[0], 1, UV_SIZE, UV_SIZE
    )
    if include_rejected_context and include_confidence and rejected_context.any():
        context = splat_to_uv_conditioning(
            canonical_rendered,
            rejected_context,
            routing["layer"],
            routing["flat_uv"],
            group_size=group_size,
            bg_color=bg_color,
            confidence=routing["confidence"],
            sampling_quality=(
                routing.get("texel_center_score")
                + 0.05 * color_support["interior"].to(
                    dtype=routing["confidence"].dtype
                )
            ),
            color_aggregation=color_aggregation,
            include_confidence=True,
        )
        for offset in (0, 6):
            trusted_evidence = conditioning[:, offset + 4 : offset + 5] > 0.5
            context_evidence = context[:, offset + 4 : offset + 5] > 0.5
            fill = ~trusted_evidence & context_evidence
            conditioning[:, offset : offset + 4] = torch.where(
                fill.expand(-1, 4, -1, -1),
                context[:, offset : offset + 4],
                conditioning[:, offset : offset + 4],
            )
            conditioning[:, offset + 5 : offset + 6] = torch.where(
                fill,
                context[:, offset + 5 : offset + 6],
                conditioning[:, offset + 5 : offset + 6],
            )
        if rejected_context_alpha_supported.any():
            alpha_context = splat_to_uv_conditioning(
                canonical_rendered,
                rejected_context_alpha_supported,
                routing["layer"],
                routing["flat_uv"],
                group_size=group_size,
                bg_color=bg_color,
                confidence=routing["confidence"],
                sampling_quality=(
                    routing.get("texel_center_score")
                    + 0.05 * color_support["interior"].to(
                        dtype=routing["confidence"].dtype
                    )
                ),
                color_aggregation=color_aggregation,
                include_confidence=True,
            )
            context_alpha_rescue_uv = alpha_context[:, 10:11] > 0.5
    routing["rejected_context"] = rejected_context
    routing["rejected_context_alpha_supported"] = (
        rejected_context_alpha_supported
    )
    if return_details:
        return conditioning, {
            "rendered": canonical_rendered,
            "color_source_support": color_support["valid"],
            "outputs": canonical_outputs,
            "routing": routing,
            "alignment": alignment,
            "context_alpha_rescue_uv": context_alpha_rescue_uv,
        }
    return conditioning


def splat_deterministic_targets_to_uv_conditioning(
    rendered,
    targets,
    renderer,
    views,
    group_size=1,
    bg_color=(128, 128, 128),
    color_aggregation="grid_mode",
):
    """Splat ground-truth labels through the same fixed mapping used by affine mode."""
    views = parse_views(views)
    if group_size != len(views):
        raise ValueError(f"group_size={group_size} must equal the number of views ({len(views)}).")
    canonical_rendered = canonicalize_tensor(rendered, targets["affine"], mode="nearest")
    canonical_targets = canonicalize_dense_targets(targets)
    requested_surface = canonical_targets["surface"]
    N, H, W = requested_surface.shape
    fg = torch.zeros_like(requested_surface, dtype=torch.bool)
    routed_layer = torch.zeros_like(requested_surface)
    flat_uv = torch.zeros_like(requested_surface)
    texel_center_score = canonical_rendered.new_zeros(requested_surface.shape)

    for view_index, view in enumerate(views):
        selection = slice(view_index, N, len(views))
        static = build_static_surface_routing(renderer, view, requested_surface.device)
        if static["masks"].shape[-2:] != (H, W):
            raise ValueError(
                f"View {view!r} mapping shape {tuple(static['masks'].shape[-2:])} does not match target shape {(H, W)}."
            )
        routed = _select_static_surface(static, requested_surface[selection])
        fg[selection] = (
            (canonical_targets["foreground"][selection, 0] > 0.5)
            & (requested_surface[selection] != IGNORE_INDEX)
            & routed["valid"]
        )
        routed_layer[selection] = routed["layer"]
        flat_uv[selection] = routed["flat_uv"]
        texel_center_score[selection] = routed["texel_center_score"]

    return splat_to_uv_conditioning(
        canonical_rendered,
        fg,
        routed_layer,
        flat_uv,
        group_size=group_size,
        bg_color=bg_color,
        sampling_quality=texel_center_score,
        color_aggregation=color_aggregation,
    )


def splat_predictions_to_uv_conditioning(
    rendered,
    outputs,
    group_size=1,
    fg_threshold=0.5,
    bg_color=(128, 128, 128),
):
    """Splat parser predictions into the parser's layered UV evidence layout."""
    foreground_prob = torch.sigmoid(outputs["foreground"])[:, 0]
    fg = foreground_prob > fg_threshold
    fg = fg & (rendered[:, 3] > 1e-4)
    layer_prob = torch.softmax(outputs["layer"], dim=1)
    layer_confidence, layer = layer_prob.max(dim=1)
    flat_uv = prediction_flat_uv(outputs)
    confidence = foreground_prob * layer_confidence
    if "uv_x" in outputs and "uv_y" in outputs:
        uv_x_confidence = torch.softmax(outputs["uv_x"], dim=1).amax(dim=1)
        uv_y_confidence = torch.softmax(outputs["uv_y"], dim=1).amax(dim=1)
        confidence = confidence * torch.sqrt((uv_x_confidence * uv_y_confidence).clamp_min(1e-8))

    return splat_to_uv_conditioning(
        rendered,
        fg,
        layer,
        flat_uv,
        group_size=group_size,
        bg_color=bg_color,
        confidence=confidence,
    )


def prediction_flat_uv(outputs):
    if "uv_x" in outputs and "uv_y" in outputs:
        x = outputs["uv_x"].argmax(dim=1).clamp(0, UV_SIZE - 1)
        y = outputs["uv_y"].argmax(dim=1).clamp(0, UV_SIZE - 1)
    else:
        uv = outputs["uv"].clamp(0.0, 1.0)
        x = (uv[:, 0] * (UV_SIZE - 1)).round().long().clamp(0, UV_SIZE - 1)
        y = (uv[:, 1] * (UV_SIZE - 1)).round().long().clamp(0, UV_SIZE - 1)
    return y * UV_SIZE + x


def prediction_uv01(outputs):
    if "uv_x" in outputs and "uv_y" in outputs:
        x = outputs["uv_x"].argmax(dim=1).to(dtype=outputs["uv"].dtype) / (UV_SIZE - 1)
        y = outputs["uv_y"].argmax(dim=1).to(dtype=outputs["uv"].dtype) / (UV_SIZE - 1)
        return torch.stack([x, y], dim=1)
    return outputs["uv"].clamp(0.0, 1.0)


def splat_targets_to_uv_conditioning(rendered, targets, group_size=1, bg_color=(128, 128, 128)):
    if rendered.dim() != 4:
        raise ValueError(f"Expected rendered tensor as NCHW, got {tuple(rendered.shape)}.")
    layer = targets["layer"]
    fg = (targets["foreground"][:, 0] > 0.5) & (layer != IGNORE_INDEX) & (rendered[:, 3] > 1e-4)
    uv = targets["uv"].clamp(0.0, 1.0)
    x = (uv[:, 0] * (UV_SIZE - 1)).round().long().clamp(0, UV_SIZE - 1)
    y = (uv[:, 1] * (UV_SIZE - 1)).round().long().clamp(0, UV_SIZE - 1)
    flat_uv = y * UV_SIZE + x
    safe_layer = torch.where(layer == IGNORE_INDEX, torch.zeros_like(layer), layer)
    return splat_to_uv_conditioning(rendered, fg, safe_layer, flat_uv, group_size=group_size, bg_color=bg_color)


def _select_exact_mode_candidates(
    values,
    target_uv,
    scores,
    color_tie_break=None,
):
    """Select one real source pixel from the most frequent 8-bit RGB value per UV texel."""
    if target_uv.numel() == 0:
        return values, target_uv, scores

    rgb8 = (values[:3].clamp(0.0, 1.0) * 255.0).round().long()
    color_code = rgb8[0] | (rgb8[1] << 8) | (rgb8[2] << 16)
    color_count = 1 << 24
    combined_key = target_uv.long() * color_count + color_code
    unique_keys, inverse = torch.unique(combined_key, sorted=False, return_inverse=True)
    votes = scores.new_zeros(unique_keys.shape[0])
    votes.index_add_(0, inverse, torch.ones_like(scores))
    tie_break_votes = None
    if color_tie_break is not None:
        tie_break_votes = scores.new_zeros(unique_keys.shape[0])
        tie_break_votes.index_add_(0, inverse, color_tie_break.float())

    positions = torch.arange(target_uv.shape[0], device=target_uv.device)
    first_position = torch.full(
        (unique_keys.shape[0],),
        target_uv.shape[0],
        dtype=torch.long,
        device=target_uv.device,
    )
    first_position.scatter_reduce_(0, inverse, positions, reduce="amin", include_self=True)

    unique_uv = unique_keys.div(color_count, rounding_mode="floor")
    best_votes = votes.new_full((UV_SIZE * UV_SIZE,), -torch.inf)
    best_votes.scatter_reduce_(0, unique_uv, votes, reduce="amax", include_self=True)
    tied_winner = votes >= (best_votes[unique_uv] - 1e-7)
    if tie_break_votes is not None:
        best_tie_break = tie_break_votes.new_full(
            (UV_SIZE * UV_SIZE,), -torch.inf
        )
        best_tie_break.scatter_reduce_(
            0,
            unique_uv[tied_winner],
            tie_break_votes[tied_winner],
            reduce="amax",
            include_self=True,
        )
        tied_winner = tied_winner & (
            tie_break_votes >= (best_tie_break[unique_uv] - 1e-7)
        )
    earliest_winner = torch.full(
        (UV_SIZE * UV_SIZE,),
        target_uv.shape[0],
        dtype=torch.long,
        device=target_uv.device,
    )
    earliest_winner.scatter_reduce_(
        0,
        unique_uv[tied_winner],
        first_position[tied_winner],
        reduce="amin",
        include_self=True,
    )
    winning_unique = tied_winner & (first_position == earliest_winner[unique_uv])
    winning_key = torch.full(
        (UV_SIZE * UV_SIZE,),
        -1,
        dtype=torch.long,
        device=target_uv.device,
    )
    winning_key[unique_uv[winning_unique]] = unique_keys[winning_unique]
    in_winning_color = combined_key == winning_key[target_uv]

    values = values[:, in_winning_color]
    target_uv = target_uv[in_winning_color]
    scores = scores[in_winning_color]
    best_scores = scores.new_full((UV_SIZE * UV_SIZE,), -torch.inf)
    best_scores.scatter_reduce_(0, target_uv, scores, reduce="amax", include_self=True)
    tied_representative = scores >= (best_scores[target_uv] - 1e-7)
    positions = torch.arange(target_uv.shape[0], device=target_uv.device)
    first_representative = torch.full(
        (UV_SIZE * UV_SIZE,),
        target_uv.shape[0],
        dtype=torch.long,
        device=target_uv.device,
    )
    first_representative.scatter_reduce_(
        0,
        target_uv[tied_representative],
        positions[tied_representative],
        reduce="amin",
        include_self=True,
    )
    selected = tied_representative & (positions == first_representative[target_uv])
    return values[:, selected], target_uv[selected], scores[selected]


def splat_to_uv_conditioning(
    rendered,
    fg,
    layer,
    flat_uv,
    group_size=1,
    bg_color=(128, 128, 128),
    confidence=None,
    sampling_quality=None,
    color_aggregation="grid_mode",
    include_confidence=False,
):
    if rendered.dim() != 4:
        raise ValueError(f"Expected rendered tensor as NCHW, got {tuple(rendered.shape)}.")
    N, _, _, _ = rendered.shape
    if N % group_size != 0:
        raise ValueError(f"N={N} must be divisible by group_size={group_size}.")
    if color_aggregation not in SPLAT_COLOR_AGGREGATIONS:
        raise ValueError(
            f"Unknown color_aggregation={color_aggregation!r}; "
            f"expected one of {SPLAT_COLOR_AGGREGATIONS}."
        )

    groups = N // group_size
    device = rendered.device
    dtype = rendered.dtype
    accum = rendered.new_zeros(groups, LAYER_CLASSES, 4, UV_SIZE * UV_SIZE)
    counts = rendered.new_zeros(groups, LAYER_CLASSES, 1, UV_SIZE * UV_SIZE)
    confidence_map = rendered.new_zeros(
        groups, LAYER_CLASSES, 1, UV_SIZE * UV_SIZE
    )

    if confidence is None:
        confidence = rendered.new_ones(fg.shape)
        select_highest_confidence = False
    else:
        select_highest_confidence = True
    if sampling_quality is None:
        sampling_quality = rendered.new_ones(fg.shape)
    elif sampling_quality.shape != fg.shape:
        raise ValueError("sampling_quality must have the same shape as fg.")

    for group in range(groups):
        group_start = group * group_size
        group_end = group_start + group_size
        for layer_index in range(LAYER_CLASSES):
            candidate_values = []
            candidate_uv = []
            candidate_confidence = []
            candidate_sampling_quality = []
            for item in range(group_start, group_end):
                item_mask = fg[item] & (layer[item] == layer_index)
                if not item_mask.any():
                    continue
                candidate_values.append(rendered[item, :, item_mask])
                candidate_uv.append(flat_uv[item, item_mask])
                candidate_confidence.append(confidence[item, item_mask])
                candidate_sampling_quality.append(
                    sampling_quality[item, item_mask]
                )
            if not candidate_uv:
                continue

            values = torch.cat(candidate_values, dim=1)
            target_uv = torch.cat(candidate_uv, dim=0)
            scores = torch.cat(candidate_confidence, dim=0).float()
            quality = torch.cat(candidate_sampling_quality, dim=0).float()
            if color_aggregation == "texel_center":
                # Lexicographic selection: prefer the source sample closest to
                # the integer UV center, then use parser confidence only to
                # break effectively equal geometric samples. This recovers an
                # original texel from bilinear renders instead of choosing a
                # top/left boundary blend by scan order.
                selection_score = quality + scores.clamp(0.0, 1.0) * 1e-6
                best_quality = selection_score.new_full(
                    (UV_SIZE * UV_SIZE,), -torch.inf
                )
                best_quality.scatter_reduce_(
                    0,
                    target_uv,
                    selection_score,
                    reduce="amax",
                    include_self=True,
                )
                is_best = selection_score >= (
                    best_quality[target_uv] - 1e-7
                )
                candidate_indices = torch.arange(
                    target_uv.shape[0], device=device
                )
                first_best = torch.full(
                    (UV_SIZE * UV_SIZE,),
                    target_uv.shape[0],
                    dtype=torch.long,
                    device=device,
                )
                first_best.scatter_reduce_(
                    0,
                    target_uv[is_best],
                    candidate_indices[is_best],
                    reduce="amin",
                    include_self=True,
                )
                selected_indices = first_best[
                    first_best < target_uv.shape[0]
                ]
                values = values[:, selected_indices]
                target_uv = target_uv[selected_indices]
                scores = scores[selected_indices]
            if color_aggregation == "grid_mode":
                # The fitted renderer grid owns UV membership. Select the
                # dominant real 8-bit RGB within each layer/UV cell; UV-center
                # quality is only a tie-break between equally frequent colors.
                values, target_uv, scores = _select_exact_mode_candidates(
                    values,
                    target_uv,
                    scores,
                    color_tie_break=quality,
                )
            if color_aggregation == "exact_mode":
                values, target_uv, scores = _select_exact_mode_candidates(
                    values, target_uv, scores
                )
            if color_aggregation == "best" and select_highest_confidence:
                best_scores = scores.new_full((UV_SIZE * UV_SIZE,), -torch.inf)
                best_scores.scatter_reduce_(0, target_uv, scores, reduce="amax", include_self=True)
                is_best = scores >= (best_scores[target_uv] - 1e-7)
                candidate_indices = torch.arange(target_uv.shape[0], device=device)
                first_best = torch.full(
                    (UV_SIZE * UV_SIZE,),
                    target_uv.shape[0],
                    dtype=torch.long,
                    device=device,
                )
                first_best.scatter_reduce_(
                    0,
                    target_uv[is_best],
                    candidate_indices[is_best],
                    reduce="amin",
                    include_self=True,
                )
                selected_indices = first_best[first_best < target_uv.shape[0]]
                values = values[:, selected_indices]
                target_uv = target_uv[selected_indices]
                scores = scores[selected_indices]

            accum[group, layer_index].index_add_(1, target_uv, values)
            counts[group, layer_index, 0].index_add_(
                0,
                target_uv,
                torch.ones(target_uv.shape[0], dtype=dtype, device=device),
            )
            confidence_map[group, layer_index, 0].scatter_reduce_(
                0,
                target_uv,
                scores.to(dtype=dtype),
                reduce="amax",
                include_self=True,
            )

    known = (counts > 0).to(dtype=dtype)
    aggregated = accum / counts.clamp_min(1.0)
    bg = rendered.new_tensor(bg_color, dtype=dtype).view(1, 1, 3, 1) / 255.0
    rgb = torch.where(
        known.expand(-1, -1, 3, -1) > 0,
        aggregated[:, :, :3],
        bg.expand(groups, LAYER_CLASSES, 3, UV_SIZE * UV_SIZE),
    )
    alpha = torch.where(known > 0, aggregated[:, :, 3:4], torch.zeros_like(aggregated[:, :, 3:4]))
    layer_channels = [rgb, alpha, known]
    if include_confidence:
        layer_channels.append(confidence_map * known)
    layers = torch.cat(layer_channels, dim=2).reshape(
        groups, -1, UV_SIZE, UV_SIZE
    )
    return layers.clamp(0.0, 1.0)


def conditioning_to_pred_uv(conditioning):
    """Merge two-layer parser conditioning into a preliminary RGBA skin atlas.

    Conditioning stores either ``RGBA + evidence`` (legacy 10-channel input)
    or ``RGBA + evidence + confidence`` (12-channel input) for each layer.
    Their Minecraft UV rectangles normally do not overlap, but outer data wins
    if both layers mark the same texel as observed.
    Unknown RGB retains the conditioning background as a useful placeholder;
    unknown alpha remains transparent until Minecraft base-alpha finalization.
    """
    squeeze_batch = conditioning.dim() == 3
    if squeeze_batch:
        conditioning = conditioning.unsqueeze(0)
    if conditioning.dim() != 4 or conditioning.shape[1] not in (10, 12):
        raise ValueError(
            "Expected 10- or 12-channel parser conditioning, "
            f"got {tuple(conditioning.shape)}."
        )

    inner_rgba = conditioning[:, 0:4]
    inner_known = conditioning[:, 4:5] > 0.5
    outer_offset = 6 if conditioning.shape[1] == 12 else 5
    outer_rgba = conditioning[:, outer_offset : outer_offset + 4]
    outer_known = conditioning[:, outer_offset + 4 : outer_offset + 5] > 0.5
    known = inner_known | outer_known

    rgba = torch.where(outer_known.expand_as(outer_rgba), outer_rgba, inner_rgba)
    rgba[:, 3:4] = torch.where(
        known,
        rgba[:, 3:4],
        torch.zeros_like(rgba[:, 3:4]),
    )
    rgba = rgba.clamp(0.0, 1.0)
    return rgba[0] if squeeze_batch else rgba


PART_PALETTE = (
    (239, 83, 80),
    (255, 202, 40),
    (102, 187, 106),
    (38, 166, 154),
    (66, 165, 245),
    (171, 71, 188),
)
LAYER_PALETTE = (
    (72, 169, 166),
    (255, 179, 71),
)
ROUTE_ROLE_PALETTE = (
    (72, 169, 166),
    (255, 179, 71),
    (218, 112, 232),
)
FACE_NAMES = ("front", "back", "left", "right", "top", "bottom")
FACE_PALETTE = (
    (239, 83, 80),
    (171, 71, 188),
    (66, 165, 245),
    (38, 166, 154),
    (255, 202, 40),
    (117, 117, 117),
)
LAYER_FACE_PALETTE = (
    (183, 28, 28),
    (106, 27, 154),
    (21, 101, 192),
    (0, 121, 107),
    (245, 166, 35),
    (84, 84, 84),
    (255, 128, 125),
    (218, 112, 232),
    (126, 208, 255),
    (102, 221, 203),
    (255, 224, 130),
    (210, 210, 210),
)


def combine_layer_face(layer, face):
    """Encode inner/outer x six cube faces as 12 visualization classes."""
    valid = (layer != IGNORE_INDEX) & (face != IGNORE_INDEX)
    combined = torch.full_like(layer, IGNORE_INDEX)
    combined[valid] = layer[valid] * FACE_CLASSES + face[valid]
    return combined


def bg_tensor(bg_color, reference):
    return reference.new_tensor(bg_color).view(1, 3, 1, 1) / 255.0


def colorize_labels(labels, palette, bg_color, reference):
    N, H, W = labels.shape
    bg = bg_tensor(bg_color, reference).expand(N, 3, H, W).clone()
    valid = labels != IGNORE_INDEX
    if not valid.any():
        return bg
    palette_tensor = reference.new_tensor(palette, dtype=reference.dtype) / 255.0
    safe_labels = labels.clamp(0, len(palette) - 1)
    out = bg.permute(0, 2, 3, 1)
    out[valid] = palette_tensor[safe_labels[valid]]
    return bg


def build_geometry_grid_debug(renderer, views, item_count, reference, bg_color=(128, 128, 128)):
    """Build fitted inner/outer cuboid face maps with projected UV texel boundaries."""
    views = parse_views(views)
    if not views:
        raise ValueError("At least one view is required for geometry-grid debug output.")
    colors = [[], []]
    masks = [[], []]
    edges = [[], []]
    for item_index in range(item_count):
        static = build_static_surface_routing(renderer, views[item_index % len(views)], reference.device)
        for layer_index in range(LAYER_CLASSES):
            mask = static["masks"][layer_index]
            face = static["face"][layer_index]
            flat_uv = static["flat_uv"][layer_index]
            labels = combine_layer_face(
                torch.full_like(face, layer_index),
                torch.where(mask, face, torch.full_like(face, IGNORE_INDEX)),
            ).unsqueeze(0)
            color = colorize_labels(labels, LAYER_FACE_PALETTE, bg_color, reference[:1])[0]

            edge = torch.zeros_like(mask)
            different_x = (flat_uv[:, 1:] != flat_uv[:, :-1]) | (face[:, 1:] != face[:, :-1])
            different_y = (flat_uv[1:, :] != flat_uv[:-1, :]) | (face[1:, :] != face[:-1, :])
            edge[:, 1:] |= mask[:, 1:] & mask[:, :-1] & different_x
            edge[1:, :] |= mask[1:, :] & mask[:-1, :] & different_y
            interior = -F.max_pool2d(-mask.float().unsqueeze(0).unsqueeze(0), 3, 1, 1)[0, 0]
            edge |= mask & (interior < 0.5)
            edge_color = reference.new_tensor((0.08, 0.08, 0.08)).view(3, 1, 1)
            color = torch.where(edge.unsqueeze(0), edge_color, color)

            colors[layer_index].append(color)
            masks[layer_index].append(mask)
            edges[layer_index].append(edge)

    return (
        torch.stack(colors[0]),
        torch.stack(colors[1]),
        torch.stack(masks[0]),
        torch.stack(masks[1]),
        torch.stack(edges[0]),
        torch.stack(edges[1]),
    )


def fill_geometry_grid_debug(rendered, foreground, layer, geometry_debug, bg_color=(128, 128, 128)):
    """Show only source RGB pixels actually routed to each predicted layer."""
    del geometry_debug
    rgb = rendered[:, :3]
    bg = rgb.new_tensor(bg_color).view(1, 3, 1, 1) / 255.0

    def fill(layer_index):
        classified = (foreground & (layer == layer_index)).unsqueeze(1)
        return torch.where(classified, rgb, bg.expand_as(rgb))

    return fill(0), fill(1)


def overlay_geometry_grid_debug(
    rendered,
    geometry_debug,
    tint_alpha=0.12,
    base_images=None,
):
    """Overlay fitted inner/outer UV texel grids on the canonical source image."""
    if not 0.0 <= tint_alpha <= 1.0:
        raise ValueError(f"tint_alpha must be in [0, 1], got {tint_alpha}.")

    rgb = rendered[:, :3]
    if base_images is None:
        base_images = (rgb, rgb)
    if len(base_images) != LAYER_CLASSES:
        raise ValueError(
            f"base_images must contain {LAYER_CLASSES} tensors, got {len(base_images)}."
        )
    masks = geometry_debug[2:4]
    edges = geometry_debug[4:6]
    fill_colors = (
        rgb.new_tensor((0.10, 0.85, 0.95)),
        rgb.new_tensor((1.00, 0.65, 0.10)),
    )
    edge_colors = (
        rgb.new_tensor((0.00, 1.00, 1.00)),
        rgb.new_tensor((1.00, 0.25, 0.85)),
    )

    overlays = []
    for base, mask, edge, fill_color, edge_color in zip(
        base_images, masks, edges, fill_colors, edge_colors
    ):
        if base.shape != rgb.shape:
            raise ValueError(
                f"Geometry overlay base shape {tuple(base.shape)} does not match RGB {tuple(rgb.shape)}."
            )
        fill_color = fill_color.view(1, 3, 1, 1)
        edge_color = edge_color.view(1, 3, 1, 1)
        tinted = base * (1.0 - tint_alpha) + fill_color * tint_alpha
        overlay = torch.where(mask.unsqueeze(1), tinted, base)
        overlay = torch.where(edge.unsqueeze(1), edge_color, overlay)
        overlays.append(overlay)
    return tuple(overlays)


def colorize_surface(labels, bg_color, reference):
    """Colorize fixed renderer surface slots without assuming a fixed slot count."""
    N, H, W = labels.shape
    bg = bg_tensor(bg_color, reference).expand(N, 3, H, W).clone()
    valid = labels != IGNORE_INDEX
    if not valid.any():
        return bg
    surface = labels.clamp_min(0).to(dtype=reference.dtype)
    colors = torch.stack(
        [
            (surface.mul(47.0).remainder(191.0) + 32.0) / 255.0,
            (surface.mul(83.0).remainder(191.0) + 32.0) / 255.0,
            (surface.mul(131.0).remainder(191.0) + 32.0) / 255.0,
        ],
        dim=1,
    )
    return torch.where(valid.unsqueeze(1), colors, bg)


def colorize_foreground(mask, bg_color, reference):
    N, H, W = mask.shape
    bg = bg_tensor(bg_color, reference).expand(N, 3, H, W)
    fg = reference.new_ones(N, 3, H, W)
    return torch.where(mask.unsqueeze(1), fg, bg)


def colorize_uv(uv, mask, bg_color):
    N, _, H, W = uv.shape
    bg = bg_tensor(bg_color, uv).expand(N, 3, H, W)
    zeros = uv.new_zeros(N, 1, H, W)
    uv_rgb = torch.cat([uv[:, 0:1], uv[:, 1:2], zeros], dim=1)
    return torch.where(mask.unsqueeze(1), uv_rgb, bg)