core/docs/analysis/cmb-a-combined-rate-ruler-2026-06-08.md

CMB-a — combined-rate setup ruler (model + gold + oracle)

As of: CMB-a, on main + feat/cmb-a-combined-rate-oracle.

CMB-a is the first rung of the combined-rate ladder. It claims exactly one thing: the combined-rate setup ruler is defined and gold-valid. No reader (CMB-c), no solver (CMB-b), no router/contemplation wiring (CMB-d) — and therefore no capability claim yet.

Combined rate is a new semantic object, not single-rate with a bigger parser: two explicit rates over one shared unit, combined by an explicit mode, then single-rate algebra over the result —

effective_rate = rate_a + rate_b   (sum        — cooperation: "working together")
effective_rate = rate_a - rate_b   (difference — opposing flow: "fills ... drains")
quantity = effective_rate × time | time = quantity ÷ effective_rate | effective_rate

so it gets its own organ (generate/combined_rate_comprehension/) and its own ruler (evals/combined_rate_oracle/), deliberately not folded into rate_comprehension. If the rate organs converge later, a shared rate algebra can be extracted then (the local RateUnit copy is the seam).

Lane state

• combined-rate gold 17 / 17 valid — 6 solved (the full combine_mode × query grid), 4 solver_refuses, 7 reader_refuses.
• R1 7/0/3 · R2 10/0/0 · R3 gold 13/13 / reader 9/0/4 — all unchanged.
• router-organ-hygiene invariant green · off-serving (imports no generate.derivation / core.reliability_gate, AST-checked) · GSM8K serving unchanged.

.venv/bin/python -m evals.combined_rate_oracle          # 17/17 valid
.venv/bin/python -m pytest tests/test_combined_rate_oracle.py -q   # 25 passed

Model — CombinedRateProblem

Two rates are always known (that is what makes it combined-rate); rate_unit is the single unit slot for both (so two different units is a reader refusal, not representable). The query selects the unknown:

query	known	unknown
quantity	time	quantity
time	quantity	time
effective_rate	—	both time and quantity

effective_rate is a derived property and may be <= 0 for difference (rate_a <= rate_b); the model does not refuse that — a non-positive net rate is the solver's boundary (non_positive_net_rate, CMB-b), not a malformed setup.

The 2×2 domain-entry grid (load-bearing for CMB-c/d hygiene)

Domain entry is two-dimensional (rate-count × combination cue), not cue-gated:

	combination cue	no cue
two rates	solved (sum/difference)	combine_mode_ambiguous
one rate	missing_second_rate	not_combined_rate_shaped

Two rates alone make it CMB's domain even with no cue (→ combine_mode_ambiguous, a substantive refusal). A single rate needs a combination cue to be CMB's substantive domain (missing_second_rate); without one it is single-rate R3 territory and CMB must step aside with not_combined_rate_shaped (→ the input_shape family, the router-organ-hygiene invariant). This is the CMB analogue of R3.1's missing_rate-only-when-duration-present fix.

Closed taxonomies

• combine_mode ∈ {sum, difference}; query ∈ {quantity, time, effective_rate}.
• solver_reasons: non_positive_net_rate, non_integer_solution.
• reader_reasons: rate_unit_mismatch, combine_mode_ambiguous, missing_second_rate, three_or_more_rates, reciprocal_work_rate_deferred, clock_interval_deferred, not_combined_rate_shaped.

The validator is non-vacuous (adversarial-verification finding)

A 5-lens adversarial pass (independent recompute, hygiene-boundary refutation, model/signature holes, proof-obligation rigor, forward wrong=0 hazards) + an adjudicator returned fix_first. The real hazard: the first-draft validate_fixture accepted any fixture labelled solver_refuses regardless of the arithmetic — a positive net rate (5−2=3) labelled non_positive_net_rate, or a quantity query (always integral) labelled non_integer_solution, would have been certified as valid gold and fed a wrong target to CMB-b. That is precisely the "schema obligation that can't meaningfully fail = decoration, not proof" case CLAUDE.md forbids (and the solved branch had the identical latent hole: a wrong gold with a self-consistent answer key).

Fix: a single canonical-outcome reference (_canonical_outcome) inside the oracle now validates both the solved gold and the solver_refuses reason against the real arithmetic — a mislabelled or arithmetically-impossible fixture is rejected (solver_refuses_is_actually_solvable / solver_reason_mismatch:… / gold_does_not_match_computed_answer). Each new branch has a dedicated meaningful-fail test.

Scope note (surfaced deliberately): the slice was scoped "oracle = canonical structure, not solving." Computing the canonical answer purely to validate gold coherence is slightly more than structure-only — but the meaningful-fail doctrine is a hard CLAUDE.md invariant, and a ruler that cannot check its own gold is decoration. _canonical_outcome is not a runtime solver (that is CMB-b) and does not touch reader-independence (which lives in text→setup, CMB-c).

Two coverage fixtures were also added for the eff<0 (cmb-07b) and eff=0/time (cmb-07c, which would otherwise divide by zero) cells, the dead determinism self-comparison was removed, and three uncovered validator branches got dedicated tests.

Sibling follow-up (noted, not fixed here): R3's evals/rate_oracle has the same latent vacuity — its solver_refuses branch does not cross-check non_integer_solution against the arithmetic. A later PR should port _canonical_outcome-style validation to the R3 oracle.

CMB ladder

CMB-a (this slice)  model + gold + setup oracle           "the ruler is defined and gold-valid"
CMB-b               exact solver (effective_rate algebra, int-or-refuse)
CMB-c               reader (prose -> CombinedRateProblem | Refusal), graded by this oracle
CMB-d               router/contemplation wiring + failure-family update (hygiene proven)
CMB-e              capability ledger entry

Deferred (named)

reciprocal work-rate (1/(1/a + 1/b)), 3+ rates, mixed-unit combined rates (cross with R3.2 time conversion), clock intervals, relative speed with opposite directions — each has a reader_reason in the ruler so it refuses cleanly until built.