MS-2 of multi-step composition. Extends the derivation model so a chain mixes
text-quantity operands and COMPARATIVE-scalar operands (twice->x2, 'N times'->xN,
half->x0.5), self-verifying the whole chain with completeness over body+question
and question-target matching.
- model.py: Step gains comparative flag.
- comparatives.py: ComparativeScalar gains number_token (the '<N> times' number,
so completeness counts the consumed body quantity); comparative_step(cs) bridges
a scalar into a Step (operand grounded by cue, not a text value token).
- verify.py: self_verifies exempts comparative operands from value-grounding
(clause 1) — they are cue-grounded (clause 2); completeness (Counter) counts a
digit comparative's number_token as consuming the body quantity. Adds target_units
to select_self_verified: a chain whose answer_unit isn't the asked unit is dropped
(question-target match; empty target_units imposes no constraint).
Proves the multi-step shapes from the gold structures: 0024 (text sum then 'three
times' scale -> 438), 0033 father-chain (digit-comparative '7 times' + fixed 'half'
+ text add -> 47). Full 0033 DAG (quantity reuse + the question's 25) deferred.
25 MS-2 tests; full derivation surface 69/69 (3a/3b/comparatives/ms1/ms2); ruff
clean; smoke 67. Not wired into serving (model ready for MS-3 target-guided search).
ADR-0175 Phase 3 splits wrong=0-first: build the gate (3a) and PROVE invariant #2
before the bounded search (3b) that could exploit gaps.
generate/derivation/:
- model.py: Quantity / Step / GroundedDerivation. A derivation is a left-fold over
text-sourced quantities; each Step carries its licensing cue (the lexeme the
search claims licenses the op).
- verify.py: self_verifies() — grounded operands ∧ grounded operation cues ∧ unit
consistency ∧ no divide-by-zero. Grounding REUSES the canonical primitives from
math_roundtrip (_tokens/_token_in/_value_grounds) so the gate cannot drift from
the round-trip contract. select_self_verified() adds the uniqueness rule:
unique self-verifying answer resolves; zero or disagreeing refuse (wrong=0).
INVARIANT #2 proven (TestInvariant2_NoSpuriousSelfVerification): the gate refuses
to self-verify a derivation that is not grounded+unit-consistent+unique even when
its value coincides with gold — the 20/5==4 class:
- invented operand not in text -> refused
- operation cue not in text -> refused (division not licensed by any present cue)
- value coincidence (20/5=4) with ungrounded op -> still refused
- add across units (pounds + reps) -> refused
- divide-by-zero -> refused
Plus uniqueness: disagreeing grounded derivations -> refuse; agreeing -> resolve.
Phase 3a is inert (nothing wires generate.derivation into serving). 3b is the
bounded search that produces derivations for this gate + measures the flip-curve
in the practice lane under perturbation.
Verified: 16/16; ruff clean; smoke 67/67; no serving import.
