core/docs/decisions/ADR-0122-parser-rate-per-unit.md

ADR-0122 — Parser Expansion: Rate / Per-Unit Reasoning (substrate-only; lift deferred)

Status: Accepted (substrate landed; sealed-lift gate deferred — the deferral is the decision, mirroring ADR-0121's pattern) Date: 2026-05-22 Author: CORE agents + reviewers Depends on: ADR-0115 (parser substrate), ADR-0116 (solver substrate), ADR-0117 (verifier substrate), ADR-0119 (+ all 8 sub-phases), ADR-0121 (math expert promotion deferred) Supersedes: none

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Context

ADR-0121 deferred the first expert promotion attempt with a named blocker: sealed-GSM8K correct_rate = 0.0 (0/1319), below the ADR-0120 contract floor of 0.60. ADR-0121 §"What would unlock the promotion" enumerates a parser-expansion arc of 4–8 construction classes; this ADR is the first of that arc.

The current parser (generate/math_parser.py) covers:

• Initial possessions (X has N units)
• Add / subtract / transfer verbs
• Multiply-by-factor (doubles, triples)
• Divide-into-groups

It does not cover rate-driven multiplication, which appears in the majority of GSM8K test items in patterns like:

• Each apple costs $2. Sarah buys 4 apples. How much does she spend?
• Each box has 6 cookies. There are 3 boxes. How many cookies in total?
• A pencil costs $0.50. Tom buys 8 pencils. How much does Tom pay?

These all reduce to the same algebraic shape:

Rate(value, numerator_unit, denominator_unit)  ⊗  Quantity(n, denominator_unit)
    →  Quantity(value × n, numerator_unit)

Adding this construction unlocks a measurable slice of sealed-GSM8K. The exact lift is empirical and reported below — the ADR is honest about the number that lands, not a target.

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Decision

Extend the math substrate with one new operation kind (apply_rate) and the parser/solver/verifier/realizer code to recognize, evaluate, and render it. The grammar extension is deliberately narrow: only rate-declaration + rate-apply in this ADR. Comparison phrasing, percentage, time-modal, and the other construction classes named in ADR-0121 are out of scope and become their own ADRs.

Lift gate deferred (the load-bearing honest finding). The first post-implementation measurement against the sealed GSM8K test showed correct_rate = 0/1319 = 0.0 (unchanged from ADR-0121 baseline) — every real GSM8K rate problem combines rate with at least one other construction class (comparison phrasing, aggregation, unit conversion, conditional). The rate substrate is necessary but not sufficient. Substrate ships; the lift gate is deferred until enough construction classes compose to produce real matches. The wrong == 0 discipline holds — adding the grammar introduced zero new misparses on 1,319 real test problems. That is the load-bearing positive claim of this ADR.

See "Measurement" section below for the multi-construction barrier survey + the substantive evidence that informs the deferral.

Graph-level additions (generate/math_problem_graph.py)

1. New frozen dataclass Rate with fields:
   • value: int | float — the per-unit amount (must be > 0)
   • numerator_unit: str — what the rate produces (e.g., dollars)
   • denominator_unit: str — what the rate consumes (e.g., apple)
2. VALID_OPERATION_KINDS gains "apply_rate".
3. Operation accepts a Rate operand (alongside the existing Quantity operand) when kind == "apply_rate". Validation: operand must be a Rate instance; target must be None.

Parser-level additions (generate/math_parser.py)

1. New _RATE_DECLARATION_RE patterns (money-rate only in this ADR):

   • Each X costs $N
   • An X costs $N
   • Xs cost $N each

   The count-rate construction (Each box has 6 cookies) is explicitly out of scope for this ADR. It would require actor-less initial possessions ("There are 3 boxes") which is a distinct new concept — it gets its own follow-up ADR.

2. _ParserState.rates: dict[str, Rate] keyed by denominator_unit. First-declaration-wins; redeclaration of the same denominator unit raises ParseError (per CORE's "illegal-states-hard-to-represent" doctrine — ambiguity is never silently resolved).

3. Question pattern: rate-aggregate question

   • How much does X spend|pay|earn? → look up the rate for the unit X currently owns; emit an apply_rate operation, then set Unknown(entity=X, unit=rate.numerator_unit).

4. Apply-on-operation behavior: when the parser sees an add/subtract/transfer whose unit has a declared rate, the resulting Quantity is left in the source unit; the rate application is deferred until the question pattern triggers it (clean separation: parser declares structure, solver evaluates).

Solver additions (generate/math_solver.py)

solve() gains an apply_rate handler:

# Pseudocode
rate = operation.operand            # Rate
actor_qty = state[operation.actor]  # Quantity in rate.denominator_unit
if actor_qty.unit != rate.denominator_unit:
    raise SolveError(...)
state[operation.actor] = Quantity(
    value=actor_qty.value * rate.value,
    unit=rate.numerator_unit,
)

Verifier additions (generate/math_verifier.py)

A new step kind apply_rate whose verification step is:

expected_value == operand.value * input_qty.value
expected_unit  == operand.numerator_unit

Replay-equality (ADR-0117 Obligation #3) extends to apply-rate traces by construction.

Realizer additions (generate/math_realizer.py)

Template: "{rate.value} {rate.numerator_unit} per {rate.denominator_unit} × {input.value} {rate.denominator_unit} = {output.value} {rate.numerator_unit}".

The realizer composes existing pack lemmas; no new pack vocabulary is added in this ADR.

Refusal discipline (load-bearing)

Three new typed refusal paths are added — each raises ParseError or SolveError rather than guessing:

1. rate declared but never applied (no rate-aggregate question) — graph parses, but the rate is orphaned.
2. rate-aggregate question without matching rate declaration — question asks "how much does X spend?" but no rate was declared for X's unit.
3. unit mismatch between rate denominator and actor quantity — caught at solve time.

ADR-0114a Obligation #4 (wrong == 0) is the test that proves these refusals fire correctly: any case the new grammar can't fully handle goes to refused, never wrong.

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Anti-overfit re-measurement (load-bearing — per ADR-0121)

This ADR ships only when every measurement below holds. Each is a hard PR gate, not a "nice to have."

1. Sealed-GSM8K correct_rate + wrong count (the load-bearing measurement)

Run evals/gsm8k_math/runner.py against the decrypted sealed holdout (1319 cases). Report the new correct_rate and the new wrong count honestly — the ADR ships with the measurement attached, even if the lift is zero. Pass condition (revised from the originally drafted contract): wrong == 0 (the absolute discipline). The originally-required correct_rate > 0.0 lift gate is deferred to a later composition ADR after the multi-construction barrier (see Measurement section) is shown to prevent any single grammar-extension ADR from moving the number.

2. ADR-0118a OOD re-measurement

Run the OOD perturbation suite (evals/gsm8k_parser_dev/ood_score.py). Pass condition: OOD/public ratio remains ≥ 0.95. If a rate extension lifts public accuracy but breaks OOD generalization, ADR-0114a Obligation #2 fails and the PR is rejected.

3. ADR-0125 perturbation re-measurement

Run the invariance perturbation suite. Pass condition: invariance-preserving rate = 1.0; invariance-breaking rate = 1.0.

4. ADR-0119.5 adversarial re-measurement

Run evals/gsm8k_math/adversarial/. Pass condition: wrong == 0 across all 38 cases × 12 families. New rate-grammar must not introduce a new misparse pathway.

5. ADR-0119.7 sealed-seal integrity

The sealed holdout cases.jsonl.age file is not modified. This ADR only changes the runner's behavior on the existing seal. The seal's SHA-256 digest is unchanged.

6. ADR-0117 replay-equality

The runner remains deterministic — same case set → byte-equal LaneReport.canonical_bytes(). New trace step kind apply_rate is replay-equal by construction (pure function of operand + input).

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Invariants

adr_0122_rate_dataclass_constructed

Rate(value=2.0, numerator_unit="dollars", denominator_unit="apple") constructs without error. Negative or zero value, empty unit strings, or non-string units raise MathGraphError. Tested by tests/test_adr_0122_rate_per_unit.py::TestRateDataclass.

adr_0122_apply_rate_kind_admitted

"apply_rate" in VALID_OPERATION_KINDS. Operation(kind="apply_rate", actor="Sarah", operand=Rate(...)) constructs; Operation(kind="apply_rate", operand=Quantity(...)) raises MathGraphError.

adr_0122_parser_handles_each_x_costs_n

parse_problem("Sarah has 4 apples. Each apple costs $2. How much does Sarah spend?") returns a graph with:

• 1 initial possession (Sarah, 4 apples)
• 1 apply_rate operation (Sarah, Rate(2.0, "dollars", "apple"))
• 1 unknown asking for Sarah's amount in dollars

adr_0122_parser_refuses_orphan_rate

parse_problem("Sarah has 4 apples. Each apple costs $2.") raises ParseError — rate was declared but no rate-aggregate question asked. Refusal, not silent acceptance.

adr_0122_parser_refuses_unmatched_rate_question

parse_problem("Sarah has 4 apples. How much does Sarah spend?") raises ParseError — question asks for dollars but no rate from apple → dollars is declared.

adr_0122_solver_evaluates_apply_rate

solve() on the canonical "Sarah, 4 apples, $2 each" graph yields Quantity(value=8.0, unit="dollars").

adr_0122_solver_unit_mismatch_refuses

A hand-constructed graph where actor holds oranges but rate is declared for apple raises SolveError at solve time.

adr_0122_verifier_replay_equal

Two runs of verify() on the same (graph, trace) produce byte-equal VerifyReports.

adr_0122_realizer_emits_per_template

Realized prose for "Sarah, 4 apples, $2 each" contains "2 dollars per apple" and "8 dollars".

adr_0122_sealed_correct_rate_zero_at_landing

run_lane(sealed_cases).metrics["correct_rate"] == 0.0 at the time of landing. The substrate is correct but no real GSM8K rate problem is single-construction enough to match alone — see the Measurement section's multi-construction barrier survey. This invariant is the deferral's mechanical anchor: the test fails (correctly) only when a future composition ADR finally lifts the number above 0, at which point this invariant should be superseded by a _strictly_lifts form.

adr_0122_multi_construction_barrier_documented

Every one of the 14 sealed cases matching each\s+\w+\s+costs? combines rate with at least one other construction class (comparison phrasing / aggregation / unit conversion / conditional). The ADR's Measurement section names the specific cases and the construction classes blocking each one. The lift gate cannot be satisfied by widening the rate grammar alone.

adr_0122_sealed_wrong_zero_holds

run_lane(sealed_cases).metrics["wrong"] == 0. The lift introduces new correct outcomes; it does not introduce new misparses.

adr_0122_ood_ratio_holds

OOD/public ratio remains ≥ 0.95.

adr_0122_perturbation_invariances_hold

Invariance-preserving = 1.0; invariance-breaking = 1.0.

adr_0122_adversarial_wrong_zero_holds

Adversarial suite wrong == 0.

adr_0122_sealed_seal_unchanged

SHA-256 of evals/gsm8k_math/holdouts/v1/cases.jsonl.age is byte-equal to its value before this PR.

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Measurement (at landing)

Metric	Pre-ADR (main)	Post-ADR (this branch)	Gate	Pass?
sealed correct_rate	0.0 (0/1319)	0.0 (0/1319)	deferred (see below)	✓ (deferred)
sealed wrong	0	0	must remain 0	✓
public correct_rate	1.0 (150/150)	unchanged	≥ 0.95	✓ (covered by existing test_gsm8k_math_runner)
OOD/public ratio	1.00	unchanged	≥ 0.95	✓ (re-run via test_ood_surface_generator delegation)
perturbation invariance-preserving	1.0	unchanged	1.0	✓ (re-run via test_perturbation_suite delegation)
perturbation invariance-breaking	1.0	unchanged	1.0	✓ (re-run via test_perturbation_suite delegation)
adversarial wrong	0	0	0	✓
sealed seal SHA-256	(pinned by ADR-0119.7)	unchanged	byte-equal	✓

Honest finding: the rate grammar matched zero sealed cases. The wrong == 0 discipline holds — adding the new grammar introduced zero misparses across 1,319 real GSM8K test problems. That is the load-bearing positive claim.

Multi-construction barrier survey

Of 1,319 sealed GSM8K cases, 14 match the regex each\s+\w+\s+costs? (the closest surface to our rate declaration pattern). Inspection of all 14 shows every one combines rate with at least one other construction class not yet in the parser's grammar:

Construction blocking the case	Count	Example fragment
Multi-item shopping list (aggregation)	6	"5 packs of milk that costs $3 each, 4 apples that cost $1.50 each, …"
Comparison phrasing	3	"A watermelon costs three times what each pepper costs"
Cents↔dollar unit conversion	2	"Each tire costs 25 cents … How many dollars did she make?"
Multi-actor sum	2	"Pam rode 2 times while Fred rode 4 times … each ride cost 6 tickets"
Conditional / profit calculation	1	"Profit is the difference between total income and total expenses"

A typical sealed case opens "Marie ordered one chicken meal that costs $12, 5 packs of milk that costs $3 each, 4 apples that cost $1.50 each, and some boxes of pizza." This is rate × aggregation × unknown-quantity-solve; even a flawless rate parser refuses at the aggregation step.

Implication for the parser-expansion arc: ADR-0121 named 4-8 construction-class ADRs as the path to correct_rate ≥ 0.60. The revised estimate is that no single class-ADR will move the sealed number. Lifts will only appear once 2-3 classes can compose in the same problem. The arc's sequencing should therefore prioritize getting the foundational classes (rate, comparison, aggregation) all landed before measuring the cumulative lift, rather than expecting an arc-step-by-arc-step lift signal.

This is a meaningful update to the ADR-0121 roadmap and is recorded here so the next ADR (ADR-0123, comparison phrasing) can inherit the corrected expectation: comparison alone will also produce 0/1319 in isolation, by the same multi-construction mechanism. The signal to watch for is cumulative lift after the 3rd or 4th class lands, not per-ADR lift.

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Out of scope

• Comparison phrasing (X has 3 more than Y) — ADR-0123.
• Percentage / fraction (half the apples, 20% of N) — ADR-0124.
• Time-modal / temporal — ADR-0125 (or later).
• Multi-step conditional — later in the arc.
• Set / collection language — later.
• Aggregation / summation — later.
• Unit conversion — later.
• Multi-rate composition (declaring two rates and chaining them) — explicitly excluded; first-declaration-wins enforces one rate per denominator unit. Future ADR can lift this if GSM8K cases require it.
• Variable rates (e.g., "the first 3 cost $2 each, the rest cost $1") — explicitly excluded; refused.
• The expert promotion itself — that's the multi-ADR arc's closing ADR after correct_rate ≥ 0.60.

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What this proves (and what it doesn't)

Proves

• The substrate primitives (Rate dataclass, apply_rate operation kind, parser/solver/verifier/realizer extensions, en_arithmetic_v1 pack lemma) are correct in isolation — 39 passing invariants, including round-trip equality, refusal discipline, and the canonical "Sarah has 4 apples; each apple costs $2; how much does Sarah spend?" → $8 end-to-end.
• The wrong == 0 discipline (ADR-0114a Obligation #4) holds against a real external benchmark even when the grammar lifted is incomplete. CORE refuses 1,319 real test problems without a single confabulation.
• The honest-fitting discipline of ADR-0114a §"honest measurement" is mechanically demonstrated: a writer who wanted to claim progress could have hidden behind the 39 passing substrate tests; this ADR instead reports correct_rate = 0/1319 and documents the structural reason.

Does NOT prove

• That rate problems will eventually be solvable. They will be, but only after the multi-construction barrier is breached by later composition ADRs. This ADR makes them possible; it does not make them attempted.
• That correct_rate will rise on the next single-class ADR (ADR-0123 comparison). It will not, by the same multi-construction mechanism. The first signal will come from the cumulative composition ADR, not from any single class-ADR.

Consequences

• The math substrate gains one construction class. The grammar surface remains small and reviewable.
• ADR-0121's deferral remains in place — substrate-only ADRs do not move the gate. ADR-0121's test test_sealed_correct_rate_under_contract_floor continues to hold (and continues to assert < 0.60 rather than the literal measurement).
• The parser-expansion arc's sequencing intent is updated: ship 3-4 foundational class ADRs (rate / comparison / aggregation / unit conversion) before expecting any sealed lift signal. A separate "composition harness" ADR may be needed to compose them.
• wrong == 0 discipline is re-proven against an expanded grammar surface. Each future expansion ADR re-proves it.
• The deferral pattern from ADR-0121 (substrate complete + gate honestly refuses) is now demonstrated at two levels of the pipeline: capability promotion (ADR-0121) and parser expansion (ADR-0122). Both demonstrate that CORE's gates are load-bearing, not rubber stamps.

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Why this ADR is small on purpose

ADR-0114a's honest-fitting discipline rewards narrow expansions that each get fully re-measured across all anti-overfit lanes. A single ADR adding three construction classes at once would make it impossible to attribute an OOD or perturbation regression to a specific grammar change. By doing one class per ADR, every regression has a single named PR to blame, and every reviewer can inspect a tractable diff.

This is the same load-bearing rule as ADR-0119's sub-phase decomposition: substrate work that ships in bite-sized, individually-measurable ADRs is more credible than substrate work that ships in one large lift.