943614c522
ADR-0252 §5 geometric SME is NO-GO; this is Track B Increment 1. Adds role-predicate conversion from MathProblemGraph, S1 canonical skeleton, blind symbolic mapper (match/refuse + binding), and solve via classical verify plus multi-register certificate. Research report and holdout measures included. Serving reader unchanged; no S2–S4 generalization.
274 lines
9.3 KiB
Python
274 lines
9.3 KiB
Python
"""Solve an S1 binding through the existing multi-register certificate corridor.
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Reuses ``evals.multi_register_program`` (ADR-0249/0250 Hamiltonian path):
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compile graph → execute with ``relax_to_ground`` → require ``certified``.
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Emit only when the certificate chain verifies; else refuse.
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Also cross-checks classical ``math_solver.solve`` + ``math_verifier.verify``
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so derivation is independently replayable (right-for-right-reason).
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Off-serving. Does not touch the live reader dispatch.
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"""
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from __future__ import annotations
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from dataclasses import dataclass
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from typing import Mapping
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from evals.multi_register_program import (
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MultiRegisterError,
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compile_multi_register_program,
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execute_multi_register_program,
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)
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from generate.math_problem_graph import (
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Comparison,
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InitialPossession,
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MathProblemGraph,
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Operation,
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Quantity,
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Unknown,
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)
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from generate.math_solver import SolveError, solve
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from generate.math_verifier import VerificationError, verify
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from generate.structure_mapping.convert import graph_to_role_graph
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from generate.structure_mapping.mapper import (
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StructureMapRefuse,
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StructureMapResult,
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map_to_s1,
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)
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from generate.structure_mapping.role_predicate import RoleGraph
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@dataclass(frozen=True, slots=True)
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class S1SolveOutcome:
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"""Emit or refuse for one S1-mapped problem."""
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emitted: bool
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answer: float | None
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refusal_reason: str | None
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binding: Mapping[str, object] | None
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derivation: str | None
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"""Human-readable derivation for right-reason audits."""
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multi_register_certified: bool
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classical_verified: bool
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source_graph_hash: str | None = None
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def graph_from_s1_binding(binding: Mapping[str, object]) -> MathProblemGraph:
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"""Rebuild a pure S1 :class:`MathProblemGraph` from a role binding.
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Shape: contain(a)=a_value; compare_multiplicative b = k×a; unknown total.
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"""
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a = str(binding["a"])
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b = str(binding["b"])
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k = float(binding["k"]) # type: ignore[arg-type]
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a_value = float(binding["a_value"]) # type: ignore[arg-type]
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unit = str(binding.get("unit") or "units")
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return MathProblemGraph(
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entities=(a, b),
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initial_state=(
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InitialPossession(entity=a, quantity=Quantity(value=a_value, unit=unit)),
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),
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operations=(
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Operation(
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actor=b,
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kind="compare_multiplicative",
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operand=Comparison(
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reference_actor=a,
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delta=None,
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factor=k,
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direction="times",
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),
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),
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),
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unknown=Unknown(entity=None, unit=unit),
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)
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def solve_s1_binding(binding: Mapping[str, object]) -> S1SolveOutcome:
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"""Solve via multi-register certificate corridor; refuse if uncertified."""
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required = ("a", "b", "k", "a_value")
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missing = [k for k in required if k not in binding]
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if missing:
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return S1SolveOutcome(
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emitted=False,
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answer=None,
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refusal_reason=f"binding_incomplete:{','.join(missing)}",
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binding=dict(binding),
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derivation=None,
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multi_register_certified=False,
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classical_verified=False,
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)
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graph = graph_from_s1_binding(binding)
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a = str(binding["a"])
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b = str(binding["b"])
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k = float(binding["k"]) # type: ignore[arg-type]
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a_value = float(binding["a_value"]) # type: ignore[arg-type]
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expected_formula = a_value * (1.0 + k)
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derivation = (
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f"S1: {b} = {k} × {a}; {a} = {a_value}; "
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f"total = {a} + {b} = {a_value} + {k}*{a_value} = {expected_formula}"
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)
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# Classical solve + independent verify (replay certificate).
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classical_verified = False
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classical_answer: float | None = None
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try:
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trace = solve(graph)
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verdict = verify(graph, trace)
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classical_verified = bool(verdict.passed)
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classical_answer = float(trace.answer_value)
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except (SolveError, VerificationError, ValueError) as exc:
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return S1SolveOutcome(
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emitted=False,
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answer=None,
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refusal_reason=f"classical_solve_or_verify_failed:{type(exc).__name__}:{exc}",
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binding=dict(binding),
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derivation=derivation,
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multi_register_certified=False,
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classical_verified=False,
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)
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if not classical_verified:
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return S1SolveOutcome(
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emitted=False,
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answer=None,
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refusal_reason="classical_verifier_rejected",
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binding=dict(binding),
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derivation=derivation,
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multi_register_certified=False,
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classical_verified=False,
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)
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# Hamiltonian multi-register corridor (ADR-0250).
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mr_certified = False
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mr_answer: float | None = None
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try:
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program = compile_multi_register_program(graph)
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outcome = execute_multi_register_program(program)
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mr_certified = bool(outcome.certified)
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mr_answer = float(outcome.answer)
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except MultiRegisterError as exc:
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return S1SolveOutcome(
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emitted=False,
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answer=None,
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refusal_reason=f"multi_register_error:{exc.reason}",
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binding=dict(binding),
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derivation=derivation,
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multi_register_certified=False,
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classical_verified=True,
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)
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except Exception as exc: # noqa: BLE001 — refuse, never crash-as-signal
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return S1SolveOutcome(
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emitted=False,
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answer=None,
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refusal_reason=f"multi_register_unexpected:{type(exc).__name__}:{exc}",
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binding=dict(binding),
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derivation=derivation,
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multi_register_certified=False,
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classical_verified=True,
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)
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if not mr_certified:
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return S1SolveOutcome(
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emitted=False,
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answer=None,
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refusal_reason="multi_register_chain_not_certified",
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binding=dict(binding),
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derivation=derivation,
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multi_register_certified=False,
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classical_verified=True,
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)
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# Agreement gate: classical and multi-register must agree (wrong=0).
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if classical_answer is None or mr_answer is None:
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return S1SolveOutcome(
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emitted=False,
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answer=None,
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refusal_reason="missing_answer_after_cert",
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binding=dict(binding),
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derivation=derivation,
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multi_register_certified=mr_certified,
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classical_verified=classical_verified,
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)
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if abs(classical_answer - mr_answer) > 1e-6 * max(1.0, abs(classical_answer)):
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return S1SolveOutcome(
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emitted=False,
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answer=None,
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refusal_reason=(
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f"corridor_disagreement:classical={classical_answer},mr={mr_answer}"
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),
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binding=dict(binding),
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derivation=derivation,
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multi_register_certified=mr_certified,
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classical_verified=classical_verified,
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)
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# Emit the classically verified scalar once the multi-register chain is
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# certified and both corridors agree within relative 1e-6. Geometric
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# relaxation leaves ~1e-8 relative float noise on the MR decode; the
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# classical solver answer is the exact integer arithmetic of the binding
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# and is independently replay-verified. Refusing to emit the noisier MR
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# float is not a shortcut around the certificate — ``mr_certified`` must
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# still be True.
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return S1SolveOutcome(
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emitted=True,
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answer=classical_answer,
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refusal_reason=None,
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binding=dict(binding),
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derivation=derivation,
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multi_register_certified=True,
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classical_verified=True,
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source_graph_hash=None,
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)
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def try_s1_structure_map_and_solve(
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graph: MathProblemGraph | None = None,
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*,
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role_graph: RoleGraph | None = None,
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) -> S1SolveOutcome:
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"""Convert (if needed) → map_to_s1 → solve corridor. Full S1 vertical slice.
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Accepts either a surface graph or a prebuilt role graph. Never takes a
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gold structure label.
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"""
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if role_graph is None:
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if graph is None:
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return S1SolveOutcome(
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emitted=False,
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answer=None,
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refusal_reason="no_graph_provided",
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binding=None,
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derivation=None,
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multi_register_certified=False,
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classical_verified=False,
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)
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role_graph = graph_to_role_graph(graph)
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mapped = map_to_s1(role_graph)
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if isinstance(mapped, StructureMapRefuse):
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return S1SolveOutcome(
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emitted=False,
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answer=None,
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refusal_reason=f"structure_map_refuse:{mapped.reason}",
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binding=None,
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derivation=None,
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multi_register_certified=False,
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classical_verified=False,
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source_graph_hash=role_graph.source_graph_hash,
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)
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assert isinstance(mapped, StructureMapResult)
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out = solve_s1_binding(mapped.binding)
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return S1SolveOutcome(
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emitted=out.emitted,
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answer=out.answer,
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refusal_reason=out.refusal_reason,
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binding=out.binding,
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derivation=out.derivation,
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multi_register_certified=out.multi_register_certified,
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classical_verified=out.classical_verified,
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source_graph_hash=role_graph.source_graph_hash,
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)
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