Grounded in a ground-truth measurement of the 47 train_sample refusals
against GSM8K's own <<a*b=c>> calculator annotations:
- 37/47 (79%) use multiplication; 43/47 use mul-or-div; 0/47 single-step
- multiplication is the foundational general capability (breadth = the
anti-overfitting signal), but necessary-not-sufficient: no case flips
from an operation matcher alone
Solver already supports {add,subtract,transfer,multiply,divide,apply_rate,
compare_additive,compare_multiplicative}; the gap is the reader->injector->
Operation front-end (matcher extracts 0 anchors on real sentences).
Sub-phase sequence (biggest-chunk-first, measure-the-flip-gated):
- 5b.1 single-sentence multiplicative aggregate (cleanest proof, ~2-4)
- 5b.2 shallow 2-3 step composition (25/47, the real chunk)
- 5b.3 deep multi-step 4-7 (22/47) under held-hypothesis elimination
Generality guard: flipped cases must hold under ADR-0114a perturbation/OOD.
Explicitly NOT widening discrete_count injector (overfitting + wrong=0 hazard).
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