P3 — generate/math_candidate_graph.py:
Branch enumeration over per-sentence candidate choices (Cartesian
product, cap=64). Per-sentence ambiguity tiebreaker via most-grounded-
slots-wins (transfer beats subtract when 'to Tom' grounds). Decision
rule: 0 admissible -> refuse; 1 -> emit; >=2 same answer -> emit;
>=2 different answers -> refuse (preserves wrong==0 on genuine
ambiguity). End-to-end parse_and_solve(text) -> CandidateGraphResult.
Question extractor added to math_candidate_parser.py (CandidateUnknown,
total + entity question shapes mirroring math_parser).
22 new tests. Permissive verbs ('bought', 'ate', 'bakes') now produce
correct answers via the candidate-graph path; ambiguous 'gives to Tom'
resolves to transfer reading (Tom gets the apples) deterministically.
P4 — evals/gsm8k_math/runner.py:
New sibling function _score_one_candidate_graph(case) -> CaseOutcome.
Identical shape to _score_one; swaps parse_problem for parse_and_solve;
preserves verifier/realizer/expected-answer stages. Callers (e.g.
PR #160's train_sample/v1/runner.py) substitute the new function in
one line to evaluate the candidate-graph topology.
9 new wiring tests. Three groups:
- No regression: cases legacy solves, new also solves.
- Lift: cases legacy refuses, new solves (the architectural payoff).
- Wrong==0: out-of-grammar refuses, never wrong.
Regression: 714/714 existing math + runner tests still green.
ADR-0126 total: 74/74 tests green across P1+P2+P3+P4.
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