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).
Declares SemanticSymbolicBindingGraph the universal problem-structure interlingua
(the corpus callosum where the geometric field and symbolic ROBDD decodings meet
and must agree). INV-26 enforces that neutrality structurally: 26a no binding-graph
module imports field/algebra/eval/vault/chat/core/sensorium; 26b the core imports
no domain reader (only allowlisted bridges adapter/question_target may); 26c proven
non-vacuous (flags pipeline.py's field import + the adapter's domain import).
Amends the plan doc with the structurally-diverse checkable panel (logic/grounding/
dimensional/execution/constraint, each with independent gold) and the 'a capability
change must move >=2 structurally-distinct domains or it is suspected overfitting'
rule, woven in from Phase 2 — the anti-overfit instrument the train_sample breach
proved we need.
Validated: architectural invariants 49 + binding_graph model = 118 passed.
proof_chain phase 2.1: the acyclicity guard at the shared binding-graph
construction boundary, before phase 2.2 wiring can build a cyclic-capable structure.
- generate/binding_graph/acyclicity.py: pure find_cycle(adjacency) detector
(deterministic three-colour DFS; isolated, no model import).
- model.py __post_init__: builds {lhs: deps} adjacency over equations and raises
BindingGraphError(circular_dependency ...) on a cycle. Runs on every binding
graph (math + future proof) — illegal states unrepresentable for all consumers.
- tests/test_binding_graph_acyclicity.py: 17 tests (pure checker + construction
enforcement); mutation-verified non-vacuous.
- ADR-0203: new ADDITIVE invariant referencing ADR-0132 (not an amendment —
preserves the why-added-later history).
Math-lane regression proof: the only producer (math adapter) is acyclic by
construction (fresh result symbol per op, deps point backward); full
binding-graph + admissibility surface 392 green; guard refuses no existing graph.
Honesty boundary (load-bearing): through phase 2.3, proof_chain is SOUND OVER
DECLARED ATOMS, not grounded in recognized input (grounding is phase 2.4).
full binding-graph/admissibility surface: 392 passed. smoke: 67 passed.
Refines BoundUnknown from "the symbol whose value the solver determines"
to "the symbol at a specific temporal/state index with a specific
question-form". Two new required fields on BoundUnknown — state_index
(initial/terminal/Operation(operation_index)) and question_form
(count/rate/total/difference/ratio/identity) — populated by the new
pure-function resolver in generate/binding_graph/question_target.py.
The adapter (ADR-0133) now delegates Unknown -> BoundUnknown construction
to bound_unknown_from_math_problem_graph. No runtime wiring, no solver
invocation. Phase 5 (bounded-grammar / B3 integration) remains deferred.
Refusal-first via the new QuestionTargetError (sibling of AdapterError /
AdmissibilityError). Closed reason vocab: not_a_math_problem_graph,
unknown_entity_not_in_entities, apply_rate_unit_mismatch,
unmappable_question_form. Closed precedence rule on question_form
documented in ADR-0135 (compare_multiplicative > compare_additive >
apply_rate{numerator|denominator unit-match} > count); ambiguity refuses.
SemanticSymbolicBindingGraph.__post_init__ gains a cross-collection
guard: Operation(operation_index) must satisfy operation_index <
len(equations). canonical_string emission widened to include
state=... form=... tokens (hash differs from Phase 3 main by design —
not a regression; byte-equal across runs preserved).
Parents: ADR-0132 / ADR-0133 / ADR-0134.
Tests: +70 new (45 unit in test_binding_graph_question_target.py +
25 integration in test_binding_graph_adapter_question_target.py); 5
Phase 1+3 BoundUnknown fixtures migrated. Total binding-graph lane
295/1 pass (1 pre-existing test_symbol_binding_uses_slots failure on
Python 3.14, unrelated to Phase 4 — exists on origin/main). Pyright
clean on new and modified files. No edits to algebra/, chat/, core/,
or runtime hot path. Field invariant untouched.
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.
