Audit reframes the math roadmap entirely.
State of main: every named math capability axis (G1..G5, S1) passes
at 100% with wrong=0 on its controlled lane. binding_graph,
math_versor_arithmetic, math_symbolic_equivalence, math_parser,
math_candidate_parser, math_solver, math_verifier, math_realizer,
math_problem_graph — all landed. The worktrees on disk are stale
forks.
State of GSM8K (50-case train sample): correct=0, refused=50, wrong=0.
Every refusal reason is identical: "candidate_graph: no admissible
candidate for statement: <STATEMENT>".
The reframe: the gap is NOT in operator algebra, NOT in binding graph
internals, NOT in symbolic equivalence. The gap is in
generate/math_candidate_graph.py — the admissibility surface that
turns a natural-language statement into a candidate the downstream
pipeline can consume. The capability axes pass at 100% because they
test statement shapes the candidate-graph already admits. GSM8K
refuses at 100% because its statements span shapes the candidate-graph
has never been taught.
Six-phase plan to lift GSM8K under the thesis "decodes, not generates":
A. Refusal taxonomy (measure before building)
B. Exemplar corpora per shape category (≤20 statements each, ≤3 per round)
C. Contemplation runner ingests exemplars; emits DerivedRecognizer
proposals
D. Operator ratifies through ADR-0161 HITL queue (no new surface)
E. Re-baseline GSM8K train sample. Round 1 exit: correct ≥ 10, wrong = 0.
Round 2: ≥ 25. Round 3: ≥ 35.
F. Scale to public/v1 (200 cases, target correct ≥ 100), then
holdout (measurement-only — never tune against).
Three non-negotiables:
- wrong = 0 at every phase. Auto-rejected by replay gate, not by
operator vigilance.
- No hand-rolled recognizers in generate/. Every recognizer lands
via contemplation → proposal → review corridor.
- Active corpus mutation only via accept_proposal.
Status: proposed. Implementation lands as three PRs starting with
Phase A scaffolding.
Scope discipline: docs-only. No code, no eval changes, no corpus
mutation.
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