PR-6c adds the divisive comparative frame: "half as many" read as EXACT INTEGER
DIVISION. It is the divisor twin of PR-5c's multiplicative frame, and moves the
independent R1 gold's r1-02-half from refused → correct.
No serving path touched. No rational/fractional answer support added. Non-exact
division refuses.
Design (ADR-0134 amended — divide made symmetric with multiply):
- `_check_divide` now admits a SINGLE-DEP divide-by-dimensionless-literal
(item / dimensionless = item), the exact twin of single-dep multiply. The
2-dep rate-divide path is untouched. This keeps the IR's "literal operands
are not deps" invariant (proven in PR-6a) uniform across Mul AND Div, so the
reader builds both without a per-op special case and WITHOUT synthesizing a
divisor symbol that would pollute the setup-oracle's unit signature.
- `Div(Symbol, Literal)` IR node: "ref / divisor", operation_kind "divide",
projects to `divide_by`. Divisor-only contract mirrors the scalar-only one.
- Reader: `_DIVISOR_WORDS={half:2}` slots into the same 8-token "<WORD> as many"
template as the factor words; graph carries only the two entities.
- Gold reconciliation: r1-02 placeholder `times_as_many factor 0.5` → exact
`divide_by divisor 2` (gold 4). Makes the INDEPENDENT gold integer-faithful.
The wrong=0 boundary — exact divisibility:
the oracle admits `divide_by` only when `base % divisor == 0`. An odd base
halved REFUSES (gold_error), never floors to a wrong integer. Divisor must be
a nonzero int (0, 0.5, 1.5, bool all refuse); divisor=1 is intentionally the
identity (pinned). admissibility proves DIMENSION; the oracle proves EXACT VALUE.
Meaningful-fail (CLAUDE.md Schema-Defined Proof Obligations), both verified red:
- drop the `% divisor` guard → test_oracle_refuses_non_exact_division fails (returns 3).
- disable the single-dep divide branch → the admissibility test AND the reader's
`half` test fail (admissibility refuses → reader refuses → half stays refused).
Gates:
R1 setup: 3 correct / 0 wrong / 7 refused
R1 answers: 3 correct / 0 wrong / 7 refused / setup_wrong 0 / gold_error 0
15-case setup: 15 / 0 / 0
91 PR-6c tests + 60 relational lanes + 56 architectural invariants + 502
binding-graph/proof-chain/adapter tests green. All 8 SHA-content lanes match
(serving unmoved; admissibility has no generate.derivation/reliability_gate consumer).
Wires deterministic, refusal-first dimensional analysis into the
binding-graph adapter. Every BoundEquation emitted by
bind_math_problem_graph now carries either admissibility_status='admitted'
+ populated unit_proof or admissibility_status='refused' + typed
refusal_reason. No silent coercion; no invented units; no solver.
Adds:
- generate/binding_graph/units.py — pure unit algebra over a 6-dim
integer exponent vector (length, time, mass, money, count,
temperature). Closed vocabulary loaded once from en_units_v1
(ADR-0127) and memoized; composite "<num>_per_<denom>" resolved
recursively; conservative depluralization; refusal-first.
- generate/binding_graph/admissibility.py — check_admissibility with
per-operation-kind dispatch over the closed 8-string vocab, typed
AdmissibilityError (closed reason set), frozen UnitProof.
- ADR-0134 documenting the contract, invariants, and Phase 4-5
deferrals.
Adapter changes are surgical: synthesizes operand-literal symbols where
the verifier needs them (op<NNN>__multiplicand / __divisor / __rate),
then stamps each equation via check_admissibility. Input/output types
unchanged; bind_math_problem_graph still byte-equal across runs.
Tests: 226 total in the binding-graph lane (110 Phase 1+2 still pass; 47
units + 40 admissibility + 29 adapter-units new). Pyright clean on all
new files. No runtime wiring outside generate/binding_graph/.
Phase 4 (question-target binding) and Phase 5 (B3 / bounded grammar)
remain deferred per the brief.
