Pin the EXACT reverse-solve semantics in the independent answer oracle before the
reader learns the inverse frame (PR-7b). A single more_than/fewer_than whose entity
is grounded and whose ref is the (otherwise ungrounded) query target inverts to the
base: base = entity -/+ delta (always integer-exact for +/-).
Refuses everything wider (each a meaningful-fail oracle test): more than one inverse
constraint, an inverse base that is not the query target (a chain), an already-grounded
base, a negative count result, or an inverse over times/divide. The duplicate-definition
guard moved into the per-kind branches so a grounded entity on a more/fewer_than is read
as an inverse constraint, not a redefinition; forward more/fewer/times/divide/sum paths
are unchanged (regression-guarded).
Contract only — the reader is NOT touched: r1-07 still refuses (admissibility_refused),
so R1 stays 6 / 0 / 4 and 15-case 15 / 0 / 0. r1-07 gold drops the non-consumed ask_base
(aligning with the reader's future projection) and gains gold=6, dormant until PR-7b.
Off-serving (only evals/tests import the oracle). SHA gate 8/9 (public_demo env flake).
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).
The falsifiable experiment's measurements #2 (ablation) and #3 (diversity). Builds the
competent, code-disjoint SYMBOLIC reader (the control arm AND the C3 capability path)
and the ablation instrument that runs both readers through the real
verify_tier2_agreement gate.
VERDICT: C3 — the field is decoration on this domain (a sanctioned, honest negative):
- field_wrong_commits = [] (wrong=0 holds; the per-step drift guard refuses bad ints)
- field_caught_symbolic_errors = [] (the field caught ZERO symbolic errors)
- per-class diversity = 0 everywhere (both readers agree and are both correct)
- the only admitted-set change is the field LOSING coverage at the precision ceiling.
Insight: on forward-substitutable relations, geometric translation IS arithmetic
addition, so there is no metric over-determination for the field to exploit — field and
symbol are common-mode (Knight-Leveson), not a genuine second derivation. This is the
deductive finding's twin: logic was combinatorial (field can't earn it), additive is
arithmetically trivial (field adds nothing). The field needs metric-nontrivial AND
arithmetically-hard structure to earn a reasoning role — dedicated research, not
near-term. Field-as-reasoner is NOT earned; no field vote enters any serving path; the
field stays a servant. Capability path = symbolic (C3), not shipped here.
- generate/relational_symbolic_reader.py: competent independent reader (pure int).
- evals/relational_metric/ablation.py: the reusable decoration instrument.
- docs/analysis/field-wedge-ablation-result-2026-06-04.md: the recorded verdict.
All prior artifacts STAY (field reader = real wrong=0 read demo + 3rd panel domain).
Green: full wedge suite 104; 53 architectural invariants.
Measurement #1 of the field-reasoner falsifiable experiment: does the CL(4,1) field,
given an honest metric encoding, read forward-substitutable quantitative-relational
problems from TEXT with wrong==0? It does — 14/15 correct, 0 wrong, 1 refused
(precision ceiling), scored against an independent arithmetic oracle.
- generate/relational_field_reader.py: reads problem text into conformal points on
the e1 number line; additive/part-whole relations are conformal TRANSLATOR versors
(versor_apply(T_delta, embed[x]) == embed[x+delta], exact); the answer reads back
by projective dehomogenization. Refusal-first: fences multiplicative/ratio (the
sign/orientation-blind cases), the precision ceiling, non-forward-substitutable
references, negatives. A per-step exactness self-check turns any f64 translator
drift into a refusal (precision_drift) — it NEVER commits a wrong integer. Its
parser is an independent reimplementation importing no generate.derivation/math_*.
- evals/relational_metric/: independent arithmetic oracle (computes gold from the
STRUCTURE, shares no code with the reader), 15-case fixture, and a runner that
enforces gold integrity + wrong==0.
- INV-25: relational_metric registered in INDEPENDENT_GOLD_LANES (oracle proven
code-disjoint from the field reader and the algebra engine). The independently
golded panel is now three domains: deductive, dimensional, relational-metric.
Green: smoke 87, 53 architectural invariants, 16 new tests; deductive + dimensional
lanes unperturbed (wrong=0).
