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.
Sibling to math_parser.py — pure candidate-extraction functions that
emit list[CandidateOperation] per sentence without mutating any state.
State threading defers to P3 (per-branch graph assembly).
Topology change vs legacy:
- No first-match-wins; every verb-kind regex runs independently.
- Ambiguous verbs ('gives', 'returns') emit multiple candidates;
P1's round-trip filter + P3's decision rule resolve.
- Out-of-grammar sentences return [], NOT ParseError. Empty list
is the deterministic 'no candidate' signal.
Permissive verb tables (imported from math_roundtrip.KIND_TO_VERBS)
mean past-tense and production verbs ('bought', 'ate', 'bakes')
that the legacy parser refused are now admissible — the round-trip
filter is the safety mechanism, not regex narrowness.
P2 scope (canonical Subject-verb-Value-Unit-[to-Target] shape only):
- extract_initial_candidates(sentence) for 'X has N units'
- extract_operation_candidates(sentence) for add/subtract/transfer
Out of scope (deferred to later sub-phases):
- Pronoun resolution / unit inheritance (needs per-branch state)
- Multiply / divide / rate / comparison (same machinery, more matchers)
Regression: existing math suite 701/701 green. Zero changes to
math_parser.py, math_solver.py, math_verifier.py, math_realizer.py.
