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| # SPDX-License-Identifier: Apache-2.0 | |
| # © 2026 SZL Holdings · Stephen P. Lutar · ORCID 0009-0001-0110-4173 | |
| """Pure-PyTorch Lambda-Spine aggregator (Λ) for the szl-lambda-gate kernel. | |
| Λ(x) = ∏ xᵢ^{wᵢ}, Σwᵢ = 1, wᵢ > 0, xᵢ ∈ [0,1] (weighted geometric mean) | |
| This is a TORCH port of the canonical pure-Python reference | |
| (packages/puriq-os/puriq_os/lambda_aggregator.py — saved alongside this kernel | |
| as lambda_aggregator_source.py). It is a correctness reference, computed via | |
| logs in float32 for stability, differentiable (autograd works), and | |
| torch.compile-friendly. Depends ONLY on torch + the Python standard library | |
| (a Kernel Hub requirement for universal kernels). | |
| WHAT Λ IS / IS NOT (HONESTY — SZL Holdings doctrine v11): | |
| Λ is the *weighted-geometric-mean aggregator*: a non-compensatory way to | |
| combine axis scores in [0,1] into one number. It is ADVISORY governance | |
| signal — a conservative roll-up where any single zeroed axis drives the | |
| aggregate to 0. It is NOT "proven trust" and NOT a closed theorem. Its | |
| *uniqueness* (that the weighted geometric mean is the only aggregator | |
| satisfying the carried axioms) remains Conjecture 1 — OPEN (an unresolved | |
| CAUCHY_ND step plus a missing symmetry axiom in the Lean development). Do | |
| not describe Λ as proven trust anywhere. | |
| PRIOR ART (honest attribution): the weighted geometric mean as a *less- | |
| compensatory* composite-indicator aggregator is established practice — the | |
| UN HDI (arithmetic→geometric switch, 2010), the OECD Handbook on | |
| Constructing Composite Indicators (2008), and the UNECE well-being | |
| guidelines all use it "to limit the compensation effect". The veto / cut-off | |
| idea (a single failing criterion blocks a pass regardless of the others) is | |
| the ELECTRE veto threshold / "satisficing" minimum-threshold screen. The | |
| 13-axis conjunctive form exposed by :func:`yuyay_weights` is SZL's own | |
| yuyay_v3 "Heart" gate. None of this makes Λ "proven trust"; the gate is | |
| ADVISORY (a11oy: "the advisory Λ trust score is a research conjecture, not a | |
| pass/fail oracle"). | |
| PROVENANCE: backed by the Lean 4 formalization szl-holdings/lutar-lean | |
| (749 declarations / 14 axioms / 163 tracked sorries), | |
| DOI 10.5281/zenodo.20434308 (lutar-lean). | |
| Λ uniqueness = Conjecture 1 (open). | |
| Axioms carried (Lutar/Axioms.lean), available below as runtime self-checks: | |
| A1 IsMonotone — Λ is non-decreasing in each axis | |
| A2 IsHomogeneous — Λ(t·x) = t·Λ(x) (degree 1) | |
| A3 IsEgyptianExact — Λ(c,…,c) = c (the uniform-diagonal fixpoint) | |
| A4 IsBounded(by max) — Λ(x) ≤ maxᵢ xᵢ | |
| """ | |
| import warnings | |
| from typing import Optional | |
| import torch | |
| # ---- the deprecated implicit threshold ------------------------------------- # | |
| # lambda_gate / lambda_gate_batch / layers.LambdaGate used to default to 0.5. | |
| # That default stays, so there is no behaviour change, but omitting the | |
| # threshold now raises a DeprecationWarning. The admit policy value is | |
| # policy_tau in frontier/model_admit_contract.v1.json, and the strict | |
| # szl.lambda/v1 gate (_v1.lambda_v1_gate) takes tau as a required argument. | |
| _LEGACY_DEFAULT_THRESHOLD = 0.5 | |
| _DEFAULT_THRESHOLD_WARNING = ( | |
| "default threshold 0.5 differs from policy_tau 0.8; pass tau. Omitting the " | |
| "threshold of lambda_gate / lambda_gate_batch / LambdaGate is deprecated: " | |
| "pass threshold= explicitly (policy_tau is in " | |
| "frontier/model_admit_contract.v1.json), or use the strict " | |
| "lambda_v1_gate(axes, weights, tau). The legacy default 0.5 still applies." | |
| ) | |
| def _resolve_threshold(threshold: Optional[float], stacklevel: int) -> float: | |
| """``None`` (the threshold was omitted) -> the legacy 0.5, with a DeprecationWarning. | |
| ``stacklevel`` is what the calling entry point would pass to | |
| ``warnings.warn`` itself (2 = its caller), so the warning names the line | |
| that omitted the threshold. Dynamo cannot trace ``warnings.warn`` (a | |
| fullgraph compile would fail), so the warning is skipped while | |
| ``torch.compile`` traces; the default is applied either way. | |
| """ | |
| if threshold is not None: | |
| return threshold | |
| if not bool(getattr(torch.compiler, "is_compiling", lambda: False)()): | |
| warnings.warn(_DEFAULT_THRESHOLD_WARNING, DeprecationWarning, stacklevel=stacklevel + 1) | |
| return _LEGACY_DEFAULT_THRESHOLD | |
| # Compute reductions/log-sum in float32 for stability when inputs are low | |
| # precision; keep float64 inputs in float64 (downcasting would break gradcheck | |
| # and silently lose precision). | |
| _SUPPORTED_DTYPES = (torch.float16, torch.bfloat16, torch.float32, torch.float64) | |
| def _compute_dtype(in_dtype: torch.dtype) -> torch.dtype: | |
| return torch.float32 if in_dtype in (torch.float16, torch.bfloat16) else in_dtype | |
| def _check_axes(axes: torch.Tensor) -> None: | |
| """Cheap, allocation-free metadata guards on the axis-score tensor. | |
| Inspects only type / dtype / rank / last-dim, so it constant-folds under | |
| torch.compile and adds no tensor work on the happy path. | |
| """ | |
| if not isinstance(axes, torch.Tensor): | |
| raise TypeError(f"axes must be a torch.Tensor, got {type(axes).__name__}") | |
| if axes.dtype not in _SUPPORTED_DTYPES: | |
| raise TypeError( | |
| f"axes has unsupported dtype {axes.dtype}; " | |
| f"expected one of {tuple(str(d) for d in _SUPPORTED_DTYPES)}" | |
| ) | |
| if axes.dim() < 1: | |
| raise ValueError( | |
| "axes must have at least 1 dimension (the k axis scores live on " | |
| f"the last dim); got a {axes.dim()}-d tensor" | |
| ) | |
| if axes.shape[-1] < 1: | |
| raise ValueError("axes last dimension (k = number of axes) must be >= 1") | |
| def _resolve_weights( | |
| axes: torch.Tensor, | |
| weights: Optional[torch.Tensor], | |
| cdt: torch.dtype, | |
| ) -> torch.Tensor: | |
| """Return a normalized (Σw = 1) weight vector of shape (k,) in compute dtype. | |
| ``weights=None`` -> uniform 1/k (the Egyptian-exact diagonal). Otherwise the | |
| weights must be 1-D of length k, strictly positive, with a positive sum; | |
| they are normalized so Σwᵢ = 1. | |
| """ | |
| k = axes.shape[-1] | |
| if weights is None: | |
| return torch.full((k,), 1.0 / k, dtype=cdt, device=axes.device) | |
| if not isinstance(weights, torch.Tensor): | |
| raise TypeError(f"weights must be a torch.Tensor or None, got {type(weights).__name__}") | |
| if weights.device != axes.device: | |
| raise ValueError( | |
| f"weights is on device {weights.device} but axes is on {axes.device}; " | |
| "move them to the same device" | |
| ) | |
| if weights.dim() != 1 or weights.shape[0] != k: | |
| raise ValueError( | |
| f"weights must be 1-D with shape ({k},) to match the last dim of axes; " | |
| f"got shape {tuple(weights.shape)}" | |
| ) | |
| wf = weights.to(cdt) | |
| compiling = bool(getattr(torch.compiler, "is_compiling", lambda: False)()) | |
| if not compiling: | |
| if not bool(torch.all(torch.isfinite(wf))): | |
| raise ValueError("weights must all be finite (no NaN/Inf)") | |
| if bool(torch.any(wf <= 0.0)): | |
| raise ValueError("weights must be strictly positive (wᵢ > 0)") | |
| sw = wf.sum() | |
| if not bool(sw > 0.0): | |
| raise ValueError("weights must sum to a positive value") | |
| return wf / sw | |
| # Compiled path stays in tensor-land. Non-positive weights are a misuse; | |
| # clamp them away from zero so the graph does not break, then normalize. | |
| # This path is outside szl.lambda/v1; _v1.lambda_v1 validates before it | |
| # gets here and is not meant to run under torch.compile. | |
| wf = torch.where(torch.isfinite(wf), wf, torch.ones_like(wf)) | |
| wf = torch.clamp(wf, min=torch.finfo(wf.dtype).tiny) | |
| return wf / wf.sum() | |
| def lambda_aggregate( | |
| axes: torch.Tensor, | |
| weights: Optional[torch.Tensor] = None, | |
| ) -> torch.Tensor: | |
| """Weighted geometric mean Λ(x) = ∏ xᵢ^{wᵢ} over the last dim of ``axes``. | |
| Λ is the (ADVISORY) Lambda-Spine aggregator. Axis scores are expected in | |
| [0,1] and are clamped into [0,1]; uniform weights (1/k) are used when | |
| ``weights`` is None — the Egyptian-exact diagonal. Computed via logs in | |
| float32 (or float64 for float64 inputs) for numerical stability: | |
| Λ(x) = exp( Σᵢ wᵢ · log(clamp(xᵢ, 0, 1)) ) | |
| Non-compensatory zero-routing (A4-consistent): any axis that is zero, OR | |
| that is NON-FINITE (NaN / ±Inf), is treated as a FAILING axis and drives | |
| the whole aggregate to exactly 0. This is the conservative governance | |
| choice — a garbage/invalid axis must never silently pass as a "perfect" | |
| (clamped-to-1) axis, and the output (and its gradient) stay finite and in | |
| [0,1] for every input. Zeros/non-finite axes are routed explicitly so | |
| log(0) = -inf and log(NaN) = NaN never produce a NaN value or gradient. | |
| Args: | |
| axes: tensor of shape (..., k) of axis scores in [0,1]. Batched: | |
| the reduction is over the last dim, leading dims are batch. | |
| weights: optional 1-D tensor of shape (k,); None -> uniform. Normalized | |
| internally so Σwᵢ = 1. | |
| Returns: | |
| tensor of shape (...) — Λ(x) ∈ [0,1] per batch row. Differentiable | |
| w.r.t. ``axes`` (and ``weights``). | |
| NOT the szl.lambda/v1 contract: this function clamps, zero-routes NaN/±Inf | |
| and renormalises (pinned in tests/test_lambda_v1_torch_divergence.py). For | |
| validated, coded errors use :func:`szl_lambda_gate._v1.lambda_v1`. | |
| HONESTY: this is a non-compensatory governance roll-up, NOT proven trust. | |
| Λ-uniqueness is Conjecture 1 (open). | |
| """ | |
| _check_axes(axes) | |
| in_dtype = axes.dtype | |
| cdt = _compute_dtype(in_dtype) | |
| xf = axes.to(cdt) | |
| w = _resolve_weights(axes, weights, cdt) # (k,), Σw=1 | |
| # A "bad" axis is one that fails non-compensatorily: a non-positive score | |
| # OR a non-finite value (NaN / ±Inf). clamp(+inf)=1 would otherwise count a | |
| # garbage axis as perfect, and clamp(NaN)=NaN would poison the product — we | |
| # treat BOTH as failing (zeroing) axes. Detect non-finite on the RAW input. | |
| finite_mask = torch.isfinite(xf) | |
| xc = xf.clamp(0.0, 1.0) | |
| bad_mask = (~finite_mask) | (xc <= 0.0) | |
| any_bad = torch.any(bad_mask, dim=-1) # (...) | |
| # Replace bad axes with 1.0 before the log purely to keep log finite and the | |
| # gradient well-defined; the bad-axis contribution is reinstated via any_bad. | |
| safe = torch.where(bad_mask, torch.ones_like(xc), xc) | |
| logx = torch.log(safe) # (..., k) | |
| acc = (logx * w).sum(dim=-1) # (...) weighted log-sum | |
| val = torch.exp(acc) # (...) Λ before zero-routing | |
| out = torch.where(any_bad, torch.zeros_like(val), val) | |
| out = out.clamp(0.0, 1.0) | |
| return out.to(in_dtype) | |
| def lambda_gate( | |
| axes: torch.Tensor, | |
| weights: Optional[torch.Tensor] = None, | |
| threshold: Optional[float] = None, | |
| ): | |
| """ADVISORY governance gate over Λ(x): score plus a pass/fail vs threshold. | |
| Computes Λ(x) (see :func:`lambda_aggregate`) and compares it to | |
| ``threshold``: pass := Λ(x) >= threshold. | |
| DEPRECATED DEFAULT: omitting ``threshold`` (or passing ``None``) still uses | |
| the legacy 0.5 but raises a ``DeprecationWarning``, because 0.5 differs | |
| from the admit contract's policy_tau (0.8). Pass the threshold explicitly, | |
| or use the strict szl.lambda/v1 gate | |
| :func:`szl_lambda_gate._v1.lambda_v1_gate`, where tau is required. | |
| ``threshold`` must be a finite float within Λ's range ``[0, 1]`` (Λ is the | |
| weighted geometric mean over [0,1]). This bound is enforced: a threshold | |
| below 0 or above 1 is meaningless for the advisory gate and is rejected — | |
| see the non-compensatory rationale below. The domain edges are valid: | |
| ``0.0`` admits every candidate (a permissive "no-gate" boundary) and | |
| ``1.0`` admits only a Λ == 1 candidate. | |
| Returns a :class:`LambdaGateResult` namedtuple with fields: | |
| score — Λ(x) tensor of shape (...), in [0,1] | |
| passed — boolean tensor of shape (...), Λ(x) >= threshold | |
| threshold — the float threshold used | |
| advisory — always True; a STANDING reminder that this is a | |
| non-compensatory governance signal, NOT proven trust. | |
| Non-compensatory threshold hardening: because a failing/garbage candidate | |
| (a zero, NaN, or ±Inf axis) is routed to Λ = 0, a NEGATIVE threshold would | |
| advisory-"pass" exactly those fully-failing candidates (0 >= t for t < 0) — | |
| the opposite of a conservative admission gate. A threshold above 1 can | |
| never pass. Both are misconfigurations, so the [0,1] domain is enforced up | |
| front rather than silently producing a wrong pass mask. | |
| HONESTY: a "pass" is an ADVISORY signal only. Λ is the weighted-geometric- | |
| mean aggregator; its uniqueness is Conjecture 1 (open). Do not treat a | |
| pass as proven trust or a closed theorem. | |
| """ | |
| threshold = _resolve_threshold(threshold, stacklevel=2) | |
| t = float(threshold) | |
| if t != t or t == float("inf") or t == float("-inf"): | |
| raise ValueError(f"threshold must be a finite float, got {threshold!r}") | |
| if t < 0.0 or t > 1.0: | |
| raise ValueError( | |
| "threshold must be within Λ's range [0, 1] (Λ is the weighted " | |
| f"geometric mean over [0,1]); got {t!r}. A threshold below 0 would " | |
| "advisory-pass a fully-failing (Λ=0) candidate and one above 1 can " | |
| "never pass — both signal a misconfigured gate." | |
| ) | |
| score = lambda_aggregate(axes, weights) | |
| passed = score >= t | |
| return LambdaGateResult(score=score, passed=passed, threshold=t, advisory=True) | |
| def lambda_gate_batch( | |
| candidates: torch.Tensor, | |
| weights: Optional[torch.Tensor] = None, | |
| threshold: Optional[float] = None, | |
| ): | |
| """ADVISORY batch gate: score MANY candidate action-vectors in one call. | |
| This is the realistic way a model/agent uses the gate — one call per | |
| inference step that scores every proposed action-vector at once and returns | |
| the advisory pass mask (which candidates clear the threshold). | |
| ``candidates`` is a tensor of shape (..., N, k): the last dim ``k`` holds | |
| the per-axis scores of a single candidate, and the second-to-last dim ``N`` | |
| enumerates the candidates (any leading dims are extra batch). Equivalent to | |
| calling :func:`lambda_gate` on the whole tensor — the reduction is over the | |
| last dim — but named to make the agent-loop intent explicit. ``threshold`` | |
| inherits the same [0,1] domain guard as :func:`lambda_gate` (a threshold | |
| outside Λ's range is a misconfiguration and is rejected). Omitting it uses | |
| the legacy 0.5 with a ``DeprecationWarning``, as in :func:`lambda_gate`. | |
| Returns a :class:`LambdaGateResult` with: | |
| score — Λ tensor of shape (..., N), one score per candidate | |
| passed — boolean mask of shape (..., N): score >= threshold | |
| threshold — the float threshold used | |
| advisory — always True (NOT proven trust) | |
| HONESTY: the pass mask is an ADVISORY, non-compensatory signal. A "pass" | |
| is not proven trust; Λ-uniqueness is Conjecture 1 (open). | |
| """ | |
| threshold = _resolve_threshold(threshold, stacklevel=2) | |
| _check_axes(candidates) | |
| if candidates.dim() < 2: | |
| raise ValueError( | |
| "candidates must be at least 2-D, shape (..., N, k): the last dim is " | |
| f"the k axis scores and the one before it enumerates the N candidates; " | |
| f"got a {candidates.dim()}-d tensor" | |
| ) | |
| # Reuse the single-call gate — its reduction over the last dim already gives | |
| # one score per candidate, so the (..., N) layout falls out for free. | |
| return lambda_gate(candidates, weights=weights, threshold=threshold) | |
| # ---- A1..A4 axiom RUNTIME self-checks (real, verifiable) ------------------- # | |
| # These are honest empirical checks callers can run on concrete inputs. They | |
| # verify the carried axioms hold for THIS implementation on the given data — | |
| # they are NOT a proof of Λ-uniqueness (that is Conjecture 1, open). | |
| def is_egyptian_exact( | |
| c: float, | |
| k: int = 3, | |
| weights: Optional[torch.Tensor] = None, | |
| tol: float = 1e-5, | |
| ) -> bool: | |
| """A3 IsEgyptianExact: Λ(c, …, c) = c for a constant axis vector of length k. | |
| Builds the uniform vector (c repeated k times) and checks Λ equals c within | |
| ``tol``. ``c`` is clamped into [0,1] to match the aggregator's domain. | |
| """ | |
| if k < 1: | |
| raise ValueError("k must be >= 1") | |
| cc = min(max(float(c), 0.0), 1.0) | |
| axes = torch.full((k,), cc, dtype=torch.float64) | |
| val = lambda_aggregate(axes, weights) | |
| return bool(torch.abs(val - cc) <= tol) | |
| def is_bounded_by_max( | |
| axes: torch.Tensor, | |
| weights: Optional[torch.Tensor] = None, | |
| tol: float = 1e-6, | |
| ) -> bool: | |
| """A4 IsBounded: Λ(x) ≤ maxᵢ xᵢ (over the last dim), within ``tol``. | |
| Returns True iff the bound holds for every batch row. Non-finite axis | |
| values are clamped/zero-routed the same way the aggregator treats them, so | |
| the bound is checked on the conservative (finite) domain. | |
| """ | |
| _check_axes(axes) | |
| val = lambda_aggregate(axes, weights) # (...) | |
| xf = axes.to(_compute_dtype(axes.dtype)) | |
| # Mirror the aggregator: non-finite axes are failing (treated as 0) for the | |
| # purposes of the max bound, so the check matches the routed semantics. | |
| xf = torch.where(torch.isfinite(xf), xf, torch.zeros_like(xf)) | |
| mx = xf.clamp(0.0, 1.0).amax(dim=-1) # (...) | |
| return bool(torch.all(val.to(mx.dtype) <= mx + tol)) | |
| def is_homogeneous( | |
| axes: torch.Tensor, | |
| t: float, | |
| weights: Optional[torch.Tensor] = None, | |
| tol: float = 1e-5, | |
| ) -> bool: | |
| """A2 IsHomogeneous (degree 1): Λ(t·x) = t·Λ(x) for scalar t in [0,1]. | |
| Verified on the clamped domain: both ``axes`` and ``t*axes`` must remain in | |
| [0,1] for the identity to be meaningful, so ``axes`` is clamped to [0,1] and | |
| ``t`` to [0,1] before the comparison. | |
| """ | |
| _check_axes(axes) | |
| tt = min(max(float(t), 0.0), 1.0) | |
| x = axes.to(torch.float64).clamp(0.0, 1.0) | |
| lhs = lambda_aggregate(x * tt, weights) | |
| rhs = tt * lambda_aggregate(x, weights) | |
| return bool(torch.all(torch.abs(lhs - rhs) <= tol)) | |
| def is_monotone( | |
| axes: torch.Tensor, | |
| weights: Optional[torch.Tensor] = None, | |
| delta: float = 0.05, | |
| tol: float = 1e-7, | |
| ) -> bool: | |
| """A1 IsMonotone: Λ is non-decreasing in each axis. | |
| For each axis j, nudges that axis UP by ``delta`` (clamped to stay ≤ 1) on | |
| every batch row and checks Λ does not decrease (within ``tol``). Rows that | |
| cannot move (already at 1) are skipped for that axis. A real check on the | |
| given data — not a symbolic proof. | |
| """ | |
| _check_axes(axes) | |
| x = axes.to(torch.float64).clamp(0.0, 1.0) | |
| base = lambda_aggregate(x, weights) | |
| k = x.shape[-1] | |
| ok = True | |
| for j in range(k): | |
| bumped = x.clone() | |
| bumped[..., j] = (bumped[..., j] + float(delta)).clamp(0.0, 1.0) | |
| bumped_val = lambda_aggregate(bumped, weights) | |
| # Λ must not go DOWN when an axis goes UP. | |
| ok = ok and bool(torch.all(bumped_val - base >= -tol)) | |
| return ok | |
| # ---- Adversarial axiom search (honest: a falsification attempt) ------------ # | |
| def find_axiom_violation( | |
| k: int = 5, | |
| trials: int = 200, | |
| weights: Optional[torch.Tensor] = None, | |
| seed: Optional[int] = 0, | |
| tol: float = 1e-6, | |
| ): | |
| """Random-search for ANY A1–A4 violation on random axis/weight draws. | |
| Returns the first ``(axiom, axes, weights)`` triple that violates a carried | |
| axiom within ``tol``, or ``None`` if none is found in ``trials`` draws. This | |
| is an honest FALSIFICATION attempt on this implementation — finding nothing | |
| is empirical evidence, NOT a proof (Λ-uniqueness is Conjecture 1, open). | |
| """ | |
| gen = torch.Generator() | |
| if seed is not None: | |
| gen.manual_seed(int(seed)) | |
| for _ in range(int(trials)): | |
| x = torch.rand(k, generator=gen, dtype=torch.float64) | |
| w = weights | |
| if w is None: | |
| w = torch.rand(k, generator=gen, dtype=torch.float64) + 1e-3 | |
| # A3 on a constant draw | |
| c = float(torch.rand(1, generator=gen).item()) | |
| if not is_egyptian_exact(c, k=k, weights=w, tol=max(tol, 1e-5)): | |
| return ("A3_IsEgyptianExact", torch.full((k,), c, dtype=torch.float64), w) | |
| # A4 bounded-by-max | |
| if not is_bounded_by_max(x, w, tol=max(tol, 1e-6)): | |
| return ("A4_IsBounded", x, w) | |
| # A2 homogeneous at a random t | |
| t = float(torch.rand(1, generator=gen).item()) | |
| if not is_homogeneous(x, t, weights=w, tol=max(tol, 1e-5)): | |
| return ("A2_IsHomogeneous", x, w) | |
| # A1 monotone (leave headroom so an up-bump stays in range) | |
| if not is_monotone(x * 0.9, w, tol=max(tol, 1e-7)): | |
| return ("A1_IsMonotone", x * 0.9, w) | |
| return None | |
| # ---- Canonical 13-axis Yuyay preset (ADVISORY ONLY) ------------------------ # | |
| # SZL's own yuyay_v3 "Heart" gate is a 13-axis CONJUNCTIVE-AND screen (each axis | |
| # independently clears its floor — no compensation). We expose its published | |
| # axis NAMES and per-axis FLOORS as advisory metadata, and a uniform Λ weight | |
| # vector over the 13 axes. This is ADVISORY: Λ here is still the weighted | |
| # geometric mean, and a "pass" is a research-conjecture signal, NOT proven | |
| # trust. Source: yuyay_v3 spec (Lutar, 2026). | |
| YUYAY_AXES = ( | |
| "moralGrounding", | |
| "measurabilityHonesty", | |
| "empiricalGrounding", | |
| "logicalConsistency", | |
| "sourceTransparency", | |
| "reproducibility", | |
| "licenseHygiene", | |
| "scopeDiscipline", | |
| "claimCalibration", | |
| "evalAwareness", | |
| "deceptionKeywords", | |
| "conflictingDirectives", | |
| "reversalDirective", | |
| ) | |
| # Published per-axis advisory floors for the CONJUNCTIVE screen: two "sacred" | |
| # axes at 0.95, seven "structural" at 0.90, four "introspection" at 0.90. | |
| YUYAY_FLOORS = ( | |
| 0.95, 0.95, # sacred | |
| 0.90, 0.90, 0.90, 0.90, 0.90, 0.90, 0.90, # structural (7) | |
| 0.90, 0.90, 0.90, 0.90, # introspection (4) | |
| ) | |
| def yuyay_weights( | |
| dtype: torch.dtype = torch.float64, | |
| device: Optional[torch.device] = None, | |
| ) -> torch.Tensor: | |
| """Canonical 13-axis Yuyay Λ weight vector (uniform 1/13), ADVISORY only. | |
| Returns a length-13 weight tensor for use as the ``weights`` argument to | |
| :func:`lambda_aggregate` / :func:`lambda_gate` over the 13 :data:`YUYAY_AXES`. | |
| Uniform by default (the Egyptian-exact diagonal). The published yuyay_v3 | |
| gate is a conjunctive AND with per-axis floors (:data:`YUYAY_FLOORS`); the | |
| Λ roll-up here is the weighted geometric mean and is ADVISORY — NOT proven | |
| trust (Λ-uniqueness is Conjecture 1, open). | |
| """ | |
| k = len(YUYAY_AXES) | |
| return torch.full((k,), 1.0 / k, dtype=dtype, device=device) | |
| # ---- Kernel self-check surface --------------------------------------------- # | |
| def selfcheck( | |
| k: int = 5, | |
| trials: int = 64, | |
| seed: Optional[int] = 0, | |
| ) -> dict: | |
| """Run the A1–A4 empirical self-checks and report a verdict + version. | |
| Returns a dict: | |
| version — kernel version string | |
| axioms — {A1..A4: bool} empirical pass on sampled inputs | |
| all_axioms_hold — bool, every sampled axiom check passed | |
| adversarial — {trials, violation} from a random falsification search | |
| (violation is None when no violation was found) | |
| advisory — always True | |
| lambda_status — Conjecture 1 (open) honesty string | |
| HONESTY: these are EMPIRICAL checks on sampled inputs, NOT a proof of | |
| Λ-uniqueness (Conjecture 1, open). A clean run is evidence, not proof. | |
| """ | |
| x = torch.rand(k, dtype=torch.float64) * 0.9 # headroom for the A1 up-bump | |
| w = torch.rand(k, dtype=torch.float64) + 1e-3 | |
| axioms = { | |
| "A1_IsMonotone": is_monotone(x, w), | |
| "A2_IsHomogeneous": is_homogeneous(x, float(torch.rand(1).item()), weights=w), | |
| "A3_IsEgyptianExact": is_egyptian_exact(float(torch.rand(1).item()), k=k, weights=w), | |
| "A4_IsBounded": is_bounded_by_max(x, w), | |
| } | |
| violation = find_axiom_violation(k=k, trials=trials, seed=seed) | |
| return { | |
| "version": __version__, | |
| "axioms": axioms, | |
| "all_axioms_hold": all(axioms.values()) and violation is None, | |
| "adversarial": {"trials": int(trials), "violation": violation}, | |
| "advisory": True, | |
| "lambda_status": "Conjecture 1 (open) — uniqueness unproven; advisory only", | |
| } | |
| # Kept in sync with the package __version__ (single source of truth lives in | |
| # __init__; duplicated here so _lambda is importable/selfcheck-able standalone). | |
| __version__ = "0.2.0" | |
| # Namedtuple result type for the gate. Defined after functions so docstrings | |
| # above can reference it; imported by __init__ and layers. | |
| from collections import namedtuple # noqa: E402 | |
| LambdaGateResult = namedtuple( | |
| "LambdaGateResult", ["score", "passed", "threshold", "advisory"] | |
| ) | |