Phase 2 of the ADR-0114 expert-capability roadmap. Consumes the
MathProblemGraph from Phase 1 and emits a SolutionTrace — ordered
operation applications ending at a numeric answer, byte-deterministic
across runs, with each step's operation bound to a pack-resolved
lemma identifier.
What landed
generate/math_solver.py
- solve(graph) -> SolutionTrace; pure function, no I/O, no globals
- SolutionStep dataclass with before/after values per step (for
verifier replay; ADR-0117 hardens)
- SolutionTrace with canonical_bytes() byte-deterministic JSON
- SolveError typed refusal: missing pack, division by zero,
unknown-references-nothing
language_packs/data/en_arithmetic_v1/
- 5 operator lemmas: add / subtract / multiply / divide / transfer
- role=operational_base (vocabulary-only; no domain claim)
- SHA-256-anchored lexicon + glosses; manifest carries
provenance=adr-0116:operator_seed:2026-05-22
tests/test_math_solver.py — 109 cases pinning five invariants:
1. Phase 2 exit criterion: ≥ 0.80 on parser-correct dev set
(current: 50/50 = 1.00)
2. Determinism: two solves produce byte-equal trace
3. Trace replay reproduces answer_value (verifier rehearsal)
4. Typed refusal on under-determined inputs
5. Every step.pack_lemma_id resolves to a real lexicon entry
in en_arithmetic_v1
ADR-0114a obligation discharge
Four of ten anti-overfitting obligations now have load-bearing
implementations in code:
#3 replay-equal trace — discharged (solver-layer)
#4 typed refusal — discharged (solver-layer)
#9 determinism — discharged (solver-layer)
#10 operation provenance via pack — DISCHARGED IN FULL
Removing the en_arithmetic_v1 pack now breaks every solve loudly.
The "operations bind to concepts, not hardcoded strings" claim is
architecturally true, not rhetorical.
Tests: 109/109 green on solver suite; 67/67 smoke suite green;
parser + schema suites still green from prior phases.
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
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