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This module intentionally imports no ``tom_world03`` or ``tom_world04r`` code.
It independently parses rational records, linearizes expressions, selects exact
roots, merges simultaneous operations, and constructs the semantic chain.
"""
from __future__ import annotations
from collections import defaultdict
from fractions import Fraction
import hashlib
import json
from typing import Any, Mapping
def _canonical(value: Any) -> bytes:
return json.dumps(value, sort_keys=True, ensure_ascii=False, separators=(",", ":"), allow_nan=False).encode("utf-8")
def _attach(record: Mapping[str, Any]) -> dict[str, Any]:
out = dict(record)
out.pop("content_hash", None)
out["content_hash"] = "sha256:" + hashlib.sha256(_canonical(out)).hexdigest()
return out
def _f(value: Any) -> Fraction:
if isinstance(value, Fraction):
return value
if isinstance(value, bool):
return Fraction(int(value), 1)
if isinstance(value, int):
return Fraction(value, 1)
if isinstance(value, str):
return Fraction(value)
if isinstance(value, Mapping):
return Fraction(int(value["num"]), int(value["den"]))
raise TypeError(f"cannot parse Fraction from {type(value).__name__}")
def _q(value: Fraction) -> dict[str, int]:
return {"num": value.numerator, "den": value.denominator}
def _qmap(values: Mapping[str, Fraction]) -> dict[str, dict[str, int]]:
return {name: _q(values[name]) for name in sorted(values)}
def _interval(value: Mapping[str, Any]) -> tuple[Fraction, Fraction]:
lo, hi = _f(value["lower"]), _f(value["upper"])
if hi < lo:
raise ValueError("baseline interval upper below lower")
return lo, hi
def _linear(
expr: Mapping[str, Any],
start: Fraction,
state: Mapping[str, Fraction],
rates: Mapping[str, Fraction],
) -> tuple[Fraction, Fraction] | None:
op = expr.get("op")
if op == "const":
return Fraction(0), _f(expr["value"])
if op == "time":
return Fraction(1), Fraction(0)
if op == "field":
name = str(expr["name"])
rate = rates[name]
return rate, state[name] - rate * start
if op == "neg":
inner = _linear(expr["value"], start, state, rates)
return None if inner is None else (-inner[0], -inner[1])
args = expr.get("args")
if not isinstance(args, list) or len(args) != 2:
raise ValueError("baseline binary expression requires two args")
left = _linear(args[0], start, state, rates)
right = _linear(args[1], start, state, rates)
if left is None or right is None:
return None
if op == "add":
return left[0] + right[0], left[1] + right[1]
if op == "sub":
return left[0] - right[0], left[1] - right[1]
if op == "mul":
if left[0] == 0:
return right[0] * left[1], right[1] * left[1]
if right[0] == 0:
return left[0] * right[1], left[1] * right[1]
return None
raise ValueError(f"unsupported baseline expression op {op}")
def _state_at(
start: Fraction,
state: Mapping[str, Fraction],
rates: Mapping[str, Fraction],
time: Fraction,
) -> dict[str, Fraction]:
return {name: state[name] + rates[name] * (time - start) for name in state}
def _support_ok(record: Mapping[str, Any], state: Mapping[str, Fraction]) -> bool:
for name, bound in record.get("bounds", {}).items():
lo, hi = _interval(bound)
if name not in state or not (lo <= state[name] <= hi):
return False
return True
def _compatibility_ok(record: Mapping[str, Any], state: Mapping[str, Fraction]) -> bool:
return all(name in state and state[name] == _f(expected) for name, expected in record.get("equals", {}).items())
def _merge(
relations: list[Mapping[str, Any]],
attribute: str,
source: Mapping[str, Fraction],
) -> dict[str, Fraction]:
grouped: dict[str, list[tuple[str, Fraction]]] = defaultdict(list)
for relation in relations:
operations = relation.get(attribute, [])
if not isinstance(operations, list):
raise ValueError(f"baseline {attribute} must be an array")
for operation in operations:
grouped[str(operation["field"])].append((str(operation["mode"]), _f(operation["value"])))
result = dict(source)
for field in sorted(grouped):
if field not in result:
raise ValueError(f"baseline operation names unknown field {field}")
modes = {mode for mode, _ in grouped[field]}
if len(modes) != 1:
raise ValueError(f"baseline mixed modes on {field}")
mode = next(iter(modes))
values = [value for _, value in grouped[field]]
if mode == "set":
if any(value != values[0] for value in values[1:]):
raise ValueError(f"baseline unequal set values on {field}")
result[field] = values[0]
elif mode == "add":
result[field] = result[field] + sum(values, Fraction(0))
elif mode == "xor":
if result[field].denominator != 1 or any(value.denominator != 1 for value in values):
raise ValueError("baseline xor requires integers")
merged = 0
for value in values:
merged ^= value.numerator
result[field] = Fraction(result[field].numerator ^ merged, 1)
else:
raise ValueError(f"unsupported baseline transition mode {mode}")
return result
def trusted_piecewise_baseline(world: Mapping[str, Any]) -> dict[str, Any]:
"""Exhaustively execute the literal world with independent arithmetic."""
horizon_start, horizon_end = _interval(world["horizon"])
initial = world["initial_segment"]
start = _f(initial["domain"]["lower"])
state = {name: _f(value) for name, value in initial["start_state"].items()}
rates = {name: _f(initial["rates"].get(name, {"num": 0, "den": 1})) for name in state}
fired: set[str] = set(initial.get("fired_relations", []))
supports = {record["id"]: record for record in world["supports"]}
compatibilities = {record["id"]: record for record in world["compatibilities"]}
relations = list(world["relations"])
max_events = int(world.get("solver", {}).get("max_event_sets", 64))
realized: list[dict[str, Any]] = []
event_sets: list[dict[str, Any]] = []
sequence = 0
while True:
candidates: list[tuple[Fraction, int, str, str, str, Mapping[str, Any]]] = []
for relation in relations:
ident = str(relation["id"])
if ident in fired:
continue
if relation.get("fire_policy") != "once":
raise ValueError("baseline supports only once fire policy")
coeff = _linear(relation["expression"], start, state, rates)
if coeff is None:
raise ValueError(f"baseline relation {ident} is non-affine")
slope, intercept = coeff
if slope == 0:
if intercept == 0:
raise ValueError(f"baseline relation {ident} is identically zero")
continue
root = -intercept / slope
active_lo, active_hi = _interval(relation["active_time"])
if not (start < root <= horizon_end and active_lo <= root <= active_hi):
continue
root_state = _state_at(start, state, rates, root)
if not _support_ok(supports[relation["support_id"]], root_state):
continue
if not _compatibility_ok(compatibilities[relation["compatibility_id"]], root_state):
continue
candidates.append((
root,
int(relation.get("priority", 0)),
ident,
str(relation["event_id"]),
str(relation["content_hash"]),
relation,
))
candidates.sort(key=lambda item: item[:5])
if not candidates:
end_state = _state_at(start, state, rates, horizon_end)
realized.append({
"sequence": sequence,
"domain": {"lower": _q(start), "upper": _q(horizon_end)},
"start_state": _qmap(state),
"rates": _qmap(rates),
"end_state": _qmap(end_state),
})
final_state = end_state
break
if len(event_sets) >= max_events:
raise ValueError("baseline event-set budget exhausted")
root = candidates[0][0]
simultaneous = [item for item in candidates if item[0] == root]
selected_relations = [item[5] for item in simultaneous]
pre_state = _state_at(start, state, rates, root)
post_state = _merge(selected_relations, "transition", pre_state)
post_rates = _merge(selected_relations, "rate_transition", rates)
realized.append({
"sequence": sequence,
"domain": {"lower": _q(start), "upper": _q(root)},
"start_state": _qmap(state),
"rates": _qmap(rates),
"end_state": _qmap(pre_state),
})
relation_order = [str(item[2]) for item in simultaneous]
fired.update(relation_order)
event_sets.append({
"event_time": _q(root),
"event_order": [str(item[3]) for item in simultaneous],
"relation_order": relation_order,
"pre_state": _qmap(pre_state),
"post_state": _qmap(post_state),
"pre_rates": _qmap(rates),
"post_rates": _qmap(post_rates),
"fired_relations_after": sorted(fired),
})
sequence += 1
start, state, rates = root, post_state, post_rates
baseline_pin = world["corrected_v03_baseline"]
semantic = {
"schema": "TOM-CONTINUATION-SEMANTIC-CHAIN-0.4.1",
"world_hash": world["content_hash"],
"corrected_v03_zip_sha256": baseline_pin["archive_sha256"],
"corrected_interval_sha256": baseline_pin["interval_py_sha256"],
"realized_segments": realized,
"event_sets": event_sets,
"final_time": _q(horizon_end),
"final_state": _qmap(final_state),
"fired_relations": sorted(fired),
"boundary_policy": "event times are solver outputs; final boundary is the declared world horizon",
}
semantic_hash = "sha256:" + hashlib.sha256(_canonical(semantic)).hexdigest()
return _attach({
"schema": "TOM-INDEPENDENT-PIECEWISE-BASELINE-0.4.1",
"implementation": "standalone fractions.Fraction exhaustive event continuation",
"world_hash": world["content_hash"],
"event_set_count": len(event_sets),
"realized_segment_count": len(realized),
"semantic_chain": semantic,
"semantic_chain_sha256": semantic_hash,
})
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