# ADR-0138 — Comparative-Reference Layer **Status:** Draft (design-only) **Date:** 2026-05-23 **Parent:** [ADR-0136](./ADR-0136-statement-layer-corridor.md) **Informed by:** [ADR-0136.S3-post-rescan](./ADR-0136.S3-post-rescan.md), [ADR-0136.S2-post-rescan](./ADR-0136.S2-post-rescan.md) (ADR-0137 deferral note) **Supersedes (in scope):** [ADR-0137](../decisions/) — closed without merging; reopened here in a lighter, shape-driven form --- ## Context The S.x corridor is bounded. Each phase ships one closed regex shape and yields 0–1 admissions + ~1 barrier shift. After S.0/S.1/S.2/S.3 the GSM8K probe sits at **3/50 admitted, wrong=0**, with the next-largest blockers fragmented across heterogeneous shapes: ``` compound_statement 5 (heterogeneous — see ADR-0136.S.3 deferred list) novel_initial_form 5 (S.4 candidate) fraction_operand 4 ← target of this ADR novel_initial_verb 4 compound_comparative 3 ← target of this ADR conditional_question 3 context_filler 3 (correctly refused) ``` The seven cases under `fraction_operand` + `compound_comparative` are not seven separate regex shapes. They share a common deep structure: **a value-bearing phrase whose value is relative to either a numeric anchor in the same sentence or a referenced quantity from a previous sentence.** Per-case decomposition: | Case | Shape | Anchor source | |---|---|---| | 0005 | `decrease to 3/4 of its temperature` + `current temperature is 84` | sentence-internal numeric | | 0029 | `keyboard cost three times greater than the cost of the mouse` + `mouse cost $16` | sentence-internal numeric | | 0041 | `75% of the 2nd pan` (after `2 pans…16 pieces per pan`) | sentence-internal referent | | 0043 | `father gave twice as much as her mother` (after `mother gave $4`) | prior-sentence quantity | | 0010 | `Marion has 1/4 more than what Yun currently has, plus 7` | **prior-sentence derived quantity** | | 0004 | `Half of the kids…` + `1/4 of the kids going to soccer camp…` + `750 kids…in the afternoon` | inverse: known sub-quantity, unknown total | | 0036 | `as much again as Wednesday, Thursday and Friday combined` | multi-term aggregate reference | 0005 and 0041 admit sentence-internal grounding. **0029 is the forcing case for cross-sentence binding** — its comparative ("three times greater than the cost of the mouse") in one sentence resolves against a literal anchor ("the mouse cost $16") in a later sentence, with no ambiguity. 0043 requires a similar chain (`twice as much as her mother` after `mother gave $4`). 0010 is genuinely *ambiguous English* — its expected dataset answer requires a non-standard parse of "1/4 more than X"; this ADR refuses on it (see §Scope). 0004 and 0036 require additional machinery (inverse arithmetic, multi-term aggregation) and are out of scope. **Why this ADR, not S.x.** S.x ships one regex shape per phase. The comparative-reference cluster is one *deep* structure with multiple *surface* shapes. Treating each surface as a separate S.x phase wastes effort and produces a forest of overlapping regexes. A small typed layer that represents the deep structure once and consumes multiple surfaces is the right unit of work. **Why not ADR-0137 as drafted.** The closed-and-deferred ADR-0137 proposed a generic `DeferredCandidate` / `BindingProof` apparatus for any kind with open slots. Its deferral reason stands: subsuming the S.1/S.2 short-circuits (which are joins of grounded candidates, not deferred bindings) wouldn't have used the machinery. Now that gsm8k-0010 has surfaced a *real* deferred-binding case, the right response is not to revive the generic apparatus. It is to ship a **typed reference layer** with one shape — `QuantityReference` — that specifically handles cross-sentence quantity lookup, and to keep the machinery as light as the actual problem. --- ## Decision ### 1. Three typed phrase structures, no generic deferred-candidate apparatus Introduce three frozen, slotted dataclasses representing the deep structure of comparative/fractional phrases: ```python @dataclass(frozen=True, slots=True) class FractionOperand: """A fraction-shaped operand: 1/4, half, 75%, 3/4, etc.""" numerator: int # e.g. 1 denominator: int # e.g. 4 of_target: ReferenceTarget | None # e.g. "the 2nd pan", "the kids" source_span: str @dataclass(frozen=True, slots=True) class ComparativeOperand: """A comparison: 'three times greater than X', '1/4 more than X', 'twice as much as X', 'half as long as X'.""" direction: Literal["more", "less", "times_greater", "times_as_much", "fraction_more", "fraction_less"] modifier: FractionOperand | int | float # the multiplier or addend anchor: ReferenceTarget # what's being compared to source_span: str @dataclass(frozen=True, slots=True) class ReferenceTarget: """An anchor: either a literal numeric value visible in the same sentence, or a typed reference to a quantity introduced earlier.""" kind: Literal["literal", "quantity_reference"] literal_value: int | float | None # set when kind == 'literal' quantity_reference: QuantityReference | None # set when kind == 'quantity_reference' @dataclass(frozen=True, slots=True) class QuantityReference: """A typed cross-sentence reference: 'what Yun currently has', 'the cost of the mouse', 'the 2nd pan', 'her mother [gave]'.""" entity: str | None # named entity (Yun), or None for "the X" descriptors descriptor: str | None # 'the 2nd pan', 'the cost of the mouse' qualifier: str | None # 'currently', 'initially' source_span: str @property def needs_binding(self) -> bool: return True ``` These types are **descriptive only** at the first pass. They carry no admissibility check on their own; they are slots that the binding pass (§3) closes. ### 2. Extractor responsibilities (first pass) Three new extractor functions in `generate/math_candidate_parser.py`, each producing typed phrases rather than full candidates: - `extract_fraction_operands(sentence)` → `list[FractionOperand]` - `extract_comparative_operands(sentence)` → `list[ComparativeOperand]` - (`QuantityReference` is constructed inside the above two when their anchor is non-literal.) These extractors emit phrases. They do **not** produce `CandidateInitial` or `CandidateOperation` directly. Promotion happens in the binding pass. ### 3. The binding pass (lighter than ADR-0137's draft) A single new control-flow stage between first-pass extraction and the existing Cartesian product. Its only job: **resolve `QuantityReference` slots against prior-sentence grounded candidates**, then promote fully-grounded `ComparativeOperand` / `FractionOperand` phrases into `CandidateInitial` (when they describe an entity's quantity) or slot-fillers for question candidates (when they describe a value asked about). The binding pass: 1. Iterates over `ComparativeOperand` + `FractionOperand` phrases in sentence order. 2. For each phrase with a non-literal anchor, looks up the `QuantityReference` against the cumulative grounded-candidate set from earlier sentences. 3. Resolves only when the reference is **unique** — single matching (entity, descriptor) → single quantity. Ambiguous references refuse the resolution (drop, not best-effort). 4. Computes the resolved value via the comparative/fractional rule: - `times_greater(N, anchor)`: `anchor * (N + 1)` (interpretation pinned by ADR-0138; *N times greater* is ambiguous in English and we pick one closed reading — see §Non-negotiables). - `times_as_much(N, anchor)`: `anchor * N` - `fraction_more(F, anchor)`: `anchor * (1 + F)` - `fraction_less(F, anchor)`: `anchor * (1 - F)` - `more(N, anchor)`: `anchor + N` - `less(N, anchor)`: `anchor - N` (refuses on negative result) 5. Promotes the resolved value into the existing `CandidateInitial` path via the same round-trip filter. No `DeferredCandidate` type. No `BindingProof` type. The pass is a deterministic lookup-and-promote operation. Replay determinism comes from the same JSON-sort-keys serialization the cognition eval already uses. ### 4. Sentence-internal grounding (no binding pass needed) When `ComparativeOperand.anchor.kind == "literal"`, the value is extracted in the first pass without involving the binding pass. This handles the 0005 / 0029 cases (sentence-internal numeric anchor) and 0041 (sentence-internal referent + same-sentence quantity). ### 5. ADR-0137 supersession The closed ADR-0137 is **superseded in scope** by this ADR. The deferral note in `ADR-0136.S2-post-rescan.md` stands; the binding machinery this ADR proposes is the answer to its "reopen criterion." This ADR is lighter because it commits to **one** typed reference shape (`QuantityReference`) rather than a generic `DeferredCandidate` apparatus. The S.1/S.2 short-circuits in `parse_and_solve` **stay** as joins of grounded candidates. They are not retrospective binding and this ADR does not subsume them. (The canonical-runner staleness issue is fixed separately by teaching the runner to score short-circuit admissions.) --- ## Scope ### In scope (this ADR + its implementation phases) - `FractionOperand`, `ComparativeOperand`, `ReferenceTarget`, `QuantityReference` type machinery - First-pass extractors for the closed surface set: - ` times greater than ` - ` times as much/many/long as ` - ` more than ` (where `` ∈ {1/2, 1/4, 3/4, half, twice} or `%`) - ` less than ` - ` of ` - `% of ` - Binding pass: sentence-order lookup of `QuantityReference` against prior grounded candidates with unique-match gating - Probe lane `RC1_comparative_reference` with the three cleanly in-scope cases (0029, 0041, 0010) plus negative probes (0005 — see below — 0004, 0036, 0043) - ADR-supersession note added to ADR-0136.S2-post-rescan.md acknowledging that 0137's reopen criterion is met by 0138 ### Out of scope (deferred to follow-up ADRs) - **Inverse arithmetic** (case 0004): "750 kids are afternoon, 1/4 are morning → total = 1000" requires solving for the unknown total from a known sub-quantity. Different machinery (inverse fraction inference). - **Multi-term aggregate references** (case 0036): "as much again as Wednesday, Thursday and Friday combined" requires summing multiple prior quantities through a single reference. Probably ADR-0139. - **Self-reference** (case 0005): "decrease to 3/4 of *its* temperature" — note this case is *in* the in-scope set as a *negative probe*: the binding pass must **refuse** on self-references (`its` resolves to the same entity whose value is being computed, yielding a circular binding). Confirm in the lane that 0005 still refuses. Wait — re-examining 0005: "Addison mountain's temperature will decrease to 3/4 of its temperature. If the current temperature is 84 degrees, what will the temperature decrease by?" The anchor *is* sentence-internal — "the current temperature is 84." The "its" refers to "Addison mountain's temperature" which is given as 84. So 0005 is actually in scope under sentence-internal grounding once the question-form is parsed. **Reclassified to in-scope.** Negative probes remain 0004 and 0036. ### Cases this ADR is expected to admit | Case | Expected outcome | Mechanism | |---|---|---| | 0005 | **admit (answer=21)** | sentence-internal fraction-of-anchor + question-resolution rule | | 0029 | **admit (answer=64)** | cross-sentence `QuantityReference` resolution: comparative in sentence 2 ("three times greater than the cost of the mouse") resolved against sentence 3's literal ("the mouse cost $16") | | 0041 | partial — likely still refuses | needs sentence-internal referent resolution; depends on whether `_INITIAL_HAS_RE` or its sibling grounds "2 pans" with a per-pan quantity | | 0043 | partial — needs chain (mother + father + total + purchase) | the comparative `twice as much as her mother` resolves cleanly; total-aggregation across the rest is multi-term, out of scope | Honest expected admission delta: **+1 to +2** (0005, 0029 at high confidence; 0041 and 0043 partial credit only if the linguistic structure composes with existing extractors). **On gsm8k-0010 (the case that surfaced the forcing function).** The forcing case for cross-sentence binding turned out to be **0029, not 0010**. 0010's sentence 2 ("Marion has 1/4 more than what Yun currently has, plus 7") has a genuinely ambiguous English reading. The dataset's expected answer is 9, which requires parsing the phrase as `(1/4) * Yun + 7 = (1/4)*8 + 7 = 9` — treating "1/4 more" as "1/4 [of what Yun has]" rather than "1/4 *more than* [Yun's quantity]." The natural English reading (`Yun * (1 + 1/4) + 7 = 17`) disagrees with the dataset. Per non-negotiable #2 of this ADR, **0010 must refuse**. Multiple plausible parses of the same surface yield different numeric values; the binding pass refuses rather than picks one. 0010 is reclassified from "expected admission" to "negative probe" — it stays refused, and the reason (ambiguity) becomes a regression assertion in the lane. This is the right outcome under refusal-first discipline, and it proves that the cross-sentence binding case must be justified by an unambiguous example. **0029 is that example.** --- ## Non-negotiables 1. **`wrong == 0` remains a hard CI gate.** Across the binding eval lane and the GSM8K probe. 2. **Ambiguous reference → refuse the binding.** If `QuantityReference` has multiple matching prior candidates with different values, the resolution refuses; the problem refuses; no best-effort. 3. **Pinned English-reading convention for "N times greater."** English usage is ambiguous (some readers: `anchor + anchor * N`; others: `anchor * N`). This ADR pins the additive reading (`anchor * (N + 1)`) and **documents the choice in the ADR + the lane test**. If a downstream case appears that requires the other reading, refuses-then-revisit; do not silently pick the other. 4. **No new short-circuit path in `parse_and_solve`.** Promoted candidates flow through the existing graph machinery. 5. **No solver/graph/verifier changes.** Linguistic layer ends at candidate emission. 6. **Determinism.** Same input → byte-equal `BindingPassResult`s, byte-equal promoted-candidate set, byte-equal `report.json`. 7. **Closed surface vocabulary.** All comparative + fractional surface markers are enumerated. No wildcards. New markers require extending the closed set (in the same PR as the test case that forces them). --- ## Probe set ### Required admissions | Case | Source | Why this exercises the layer | |---|---|---| | 0005 | GSM8K | sentence-internal fraction-of-anchor + literal-value path | | 0029 | GSM8K | cross-sentence `QuantityReference` resolution; **the forcing case** for the binding pass | ### Required refusals (negative probes) - **gsm8k-0010** — ambiguous English (`1/4 more than X` parses as either `X * (1 + 1/4)` or `(1/4) * X`); the binding pass must refuse per non-negotiable #2 - **gsm8k-0004** — inverse arithmetic (must continue to refuse pending ADR-0139) - **gsm8k-0036** — multi-term aggregate reference (must continue to refuse pending ADR-0139) - A synthetic ambiguous-reference case where two prior sentences introduce the same `(entity, unit)` with different values — must refuse (uniqueness gate) ### Axis cases (synthetic, ≥15) Closed combinations of the surface vocabulary × anchor kinds: - ` of ` ≥3 - ` of ` ≥3 - ` times as much as ` ≥3 - ` times greater than ` ≥3 - ` more than ` ≥3 (covers 0010's shape) --- ## Phased rollout One branch per phase. The 2026-05-23 worktree-race lesson stands. | Phase | Deliverable | Branch | |---|---|---| | 0138.D | This ADR | `docs/adr-0138-comparative-reference-layer` (this PR) | | 0138.A | `generate/comparative/{types,extractors}.py` + tests for the type machinery and the closed surface vocabulary (no binding pass yet) | `feat/adr-0138-types-and-extractors` | | 0138.B | Binding pass + `QuantityReference` resolution + 0010 admission + 0005/0029 admissions | `feat/adr-0138-binding-pass` | | 0138.C | Eval lane `RC1_comparative_reference` + probe set | `feat/adr-0138-rc1-lane` | Each phase is its own PR. Each must hold `wrong == 0`, preserve all existing axis lanes (S.1, S.2, S.3, S.4 if landed), and not regress the rescan-v3 invariants. After 0138.B lands, run a rescan v4 to record barrier shifts and update the post-rescan ADR. --- ## Open questions (deferred to implementation ADRs, not this one) - **Promotion of fractional-of-set phrases.** "Half of the kids" with no prior quantification of "the kids" produces a refusal in 0138.B (no resolvable reference). Case 0004's full solution requires inverse arithmetic on this same shape. Future ADR-0139 (inverse arithmetic) will compose with this layer. - **Pronoun resolution depth.** "Marion has 1/4 more than what *Yun* currently has" names Yun explicitly. Cases like "*he* has 1/4 more than what *she* has" need pronoun resolution against the prior-actor set. Out of scope; refuse on pronoun-anchored references until a future ADR. - **Telemetry.** Whether `QuantityReference` resolution events emit into the existing turn-event telemetry sink. Probably no for now; cognition runtime is not consuming math problems on the hot path. --- ## Consequences - The forcing function for retrospective binding (denied at #204 closure, surfaced at #208 rescan v3) is met by a typed reference layer rather than a generic deferred-candidate apparatus. Smaller, more specific, easier to audit. - The S.x corridor continues for shape-specific extensions (`novel_initial_form`, `novel_initial_verb`, the remaining `compound_statement` shapes). 0138 is *parallel* to S.x, not its replacement. - The corpus of `comparative + fraction-of-quantity` problems is large in GSM8K's full set (not just the 50-case train sample). This layer's value compounds as the probe widens beyond the train sample. - The pinned "N times greater = N+1 multiplier" reading is a CORE convention. If we later encounter a case that requires the other reading, the lane test will flag it and the closed-set decision becomes revisitable rather than buried. --- ## What this ADR is not - Not a code change. No `generate/comparative/` module exists at merge time. - Not a generic deferred-candidate framework. It commits to one typed reference shape (`QuantityReference`) and one binding rule (unique-match cross-sentence lookup). - Not a replacement for the S.x corridor. The two are parallel. - Not a license to add semantic guessing. Every comparative, fractional, and reference shape is a closed-set surface pattern with a deterministic resolution rule. - Not in conflict with CLAUDE.md. The binding pass is exactly the shape of "comprehend → recall → think" — hold a typed reference, bind it deterministically when the prior quantity is grounded, refuse when ambiguous.