docs(ADR-0138): comparative-reference layer — design only (#209)
A small typed linguistic layer (FractionOperand, ComparativeOperand,
QuantityReference, ReferenceTarget) replacing the closed-and-deferred
ADR-0137 with a shape-driven design. Justified by the rescan-v3 ledger
showing 7 cases under fraction_operand + compound_comparative that
share a common deep structure (value relative to literal or
prior-sentence anchor) with multiple surface shapes.
Key commitments:
- Three typed phrase structures handle the closed surface set
(frac/percent of X, N times as much/greater than X, frac more/less
than X), where X is either a sentence-internal literal or a
QuantityReference to a prior grounded quantity.
- Binding pass is minimal: sentence-order lookup of QuantityReference
against prior grounded candidates with unique-match gating. No
generic DeferredCandidate apparatus.
- Pinned English convention: "N times greater" = N+1 multiplier
(documented + tested). Other reading requires explicit revisit.
- Supersedes ADR-0137 in scope; the deferral note's reopen criterion
is met by this lighter, more specific design.
- S.1/S.2 short-circuits stay as joins of grounded candidates;
this ADR does not subsume them.
Forcing case for cross-sentence binding: gsm8k-0029 ("three times
greater than the cost of the mouse" + "the mouse cost $16"). Clean,
unambiguous, two-sentence binding.
Self-correction caught before push: gsm8k-0010 was initially framed
as the forcing case, but its expected dataset answer requires a
non-standard English parse of "1/4 more than X" (the natural reading
gives 17; the dataset says 9, requiring X/4 + 7). Per non-negotiable
#2 the binding pass MUST refuse on this; 0010 is reclassified from
"expected admission" to "negative probe." 0029 takes the forcing-case
slot.
Honest expected admission delta: +1 to +2 (0005, 0029 high
confidence; 0041, 0043 partial credit only).
In scope: in the same PR family, fix the issue gsm8k-0029 surfaces by
implementing the binding pass. Out of scope: inverse arithmetic
(0004), multi-term aggregate references (0036), pronoun anchoring,
self-referential cycles.
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docs/decisions/ADR-0138-comparative-reference-layer.md
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# ADR-0138 — Comparative-Reference Layer
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**Status:** Draft (design-only)
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**Date:** 2026-05-23
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**Parent:** [ADR-0136](./ADR-0136-statement-layer-corridor.md)
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**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)
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**Supersedes (in scope):** [ADR-0137](../decisions/) — closed without merging; reopened here in a lighter, shape-driven form
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---
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## Context
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The S.x corridor is bounded. Each phase ships one closed regex shape and
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yields 0–1 admissions + ~1 barrier shift. After S.0/S.1/S.2/S.3 the
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GSM8K probe sits at **3/50 admitted, wrong=0**, with the next-largest
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blockers fragmented across heterogeneous shapes:
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```
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compound_statement 5 (heterogeneous — see ADR-0136.S.3 deferred list)
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novel_initial_form 5 (S.4 candidate)
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fraction_operand 4 ← target of this ADR
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novel_initial_verb 4
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compound_comparative 3 ← target of this ADR
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conditional_question 3
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context_filler 3 (correctly refused)
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```
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The seven cases under `fraction_operand` + `compound_comparative` are
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not seven separate regex shapes. They share a common deep structure:
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**a value-bearing phrase whose value is relative to either a numeric
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anchor in the same sentence or a referenced quantity from a previous
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sentence.**
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Per-case decomposition:
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| Case | Shape | Anchor source |
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|---|---|---|
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| 0005 | `decrease to 3/4 of its temperature` + `current temperature is 84` | sentence-internal numeric |
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| 0029 | `keyboard cost three times greater than the cost of the mouse` + `mouse cost $16` | sentence-internal numeric |
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| 0041 | `75% of the 2nd pan` (after `2 pans…16 pieces per pan`) | sentence-internal referent |
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| 0043 | `father gave twice as much as her mother` (after `mother gave $4`) | prior-sentence quantity |
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| 0010 | `Marion has 1/4 more than what Yun currently has, plus 7` | **prior-sentence derived quantity** |
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| 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 |
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| 0036 | `as much again as Wednesday, Thursday and Friday combined` | multi-term aggregate reference |
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0005 and 0041 admit sentence-internal grounding. **0029 is the
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forcing case for cross-sentence binding** — its comparative
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("three times greater than the cost of the mouse") in one sentence
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resolves against a literal anchor ("the mouse cost $16") in a later
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sentence, with no ambiguity. 0043 requires a similar chain
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(`twice as much as her mother` after `mother gave $4`). 0010 is
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genuinely *ambiguous English* — its expected dataset answer
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requires a non-standard parse of "1/4 more than X"; this ADR
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refuses on it (see §Scope). 0004 and 0036 require additional
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machinery (inverse arithmetic, multi-term aggregation) and are out
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of scope.
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**Why this ADR, not S.x.** S.x ships one regex shape per phase. The
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comparative-reference cluster is one *deep* structure with multiple
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*surface* shapes. Treating each surface as a separate S.x phase wastes
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effort and produces a forest of overlapping regexes. A small typed
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layer that represents the deep structure once and consumes multiple
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surfaces is the right unit of work.
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**Why not ADR-0137 as drafted.** The closed-and-deferred ADR-0137
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proposed a generic `DeferredCandidate` / `BindingProof` apparatus for
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any kind with open slots. Its deferral reason stands: subsuming the
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S.1/S.2 short-circuits (which are joins of grounded candidates, not
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deferred bindings) wouldn't have used the machinery. Now that
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gsm8k-0010 has surfaced a *real* deferred-binding case, the right
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response is not to revive the generic apparatus. It is to ship a
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**typed reference layer** with one shape — `QuantityReference` — that
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specifically handles cross-sentence quantity lookup, and to keep the
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machinery as light as the actual problem.
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---
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## Decision
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### 1. Three typed phrase structures, no generic deferred-candidate apparatus
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Introduce three frozen, slotted dataclasses representing the deep
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structure of comparative/fractional phrases:
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```python
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@dataclass(frozen=True, slots=True)
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class FractionOperand:
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"""A fraction-shaped operand: 1/4, half, 75%, 3/4, etc."""
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numerator: int # e.g. 1
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denominator: int # e.g. 4
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of_target: ReferenceTarget | None # e.g. "the 2nd pan", "the kids"
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source_span: str
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@dataclass(frozen=True, slots=True)
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class ComparativeOperand:
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"""A comparison: 'three times greater than X', '1/4 more than X',
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'twice as much as X', 'half as long as X'."""
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direction: Literal["more", "less", "times_greater", "times_as_much",
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"fraction_more", "fraction_less"]
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modifier: FractionOperand | int | float # the multiplier or addend
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anchor: ReferenceTarget # what's being compared to
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source_span: str
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@dataclass(frozen=True, slots=True)
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class ReferenceTarget:
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"""An anchor: either a literal numeric value visible in the same
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sentence, or a typed reference to a quantity introduced earlier."""
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kind: Literal["literal", "quantity_reference"]
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literal_value: int | float | None # set when kind == 'literal'
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quantity_reference: QuantityReference | None # set when kind == 'quantity_reference'
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@dataclass(frozen=True, slots=True)
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class QuantityReference:
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"""A typed cross-sentence reference: 'what Yun currently has',
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'the cost of the mouse', 'the 2nd pan', 'her mother [gave]'."""
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entity: str | None # named entity (Yun), or None for "the X" descriptors
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descriptor: str | None # 'the 2nd pan', 'the cost of the mouse'
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qualifier: str | None # 'currently', 'initially'
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source_span: str
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@property
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def needs_binding(self) -> bool:
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return True
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```
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These types are **descriptive only** at the first pass. They carry no
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admissibility check on their own; they are slots that the binding pass
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(§3) closes.
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### 2. Extractor responsibilities (first pass)
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Three new extractor functions in `generate/math_candidate_parser.py`,
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each producing typed phrases rather than full candidates:
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- `extract_fraction_operands(sentence)` → `list[FractionOperand]`
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- `extract_comparative_operands(sentence)` → `list[ComparativeOperand]`
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- (`QuantityReference` is constructed inside the above two when their
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anchor is non-literal.)
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These extractors emit phrases. They do **not** produce
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`CandidateInitial` or `CandidateOperation` directly. Promotion happens
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in the binding pass.
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### 3. The binding pass (lighter than ADR-0137's draft)
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A single new control-flow stage between first-pass extraction and the
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existing Cartesian product. Its only job: **resolve `QuantityReference`
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slots against prior-sentence grounded candidates**, then promote
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fully-grounded `ComparativeOperand` / `FractionOperand` phrases into
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`CandidateInitial` (when they describe an entity's quantity) or
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slot-fillers for question candidates (when they describe a value asked
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about).
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The binding pass:
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1. Iterates over `ComparativeOperand` + `FractionOperand` phrases in
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sentence order.
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2. For each phrase with a non-literal anchor, looks up the
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`QuantityReference` against the cumulative grounded-candidate set
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from earlier sentences.
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3. Resolves only when the reference is **unique** — single matching
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(entity, descriptor) → single quantity. Ambiguous references refuse
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the resolution (drop, not best-effort).
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4. Computes the resolved value via the comparative/fractional rule:
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- `times_greater(N, anchor)`: `anchor * (N + 1)` (interpretation
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pinned by ADR-0138; *N times greater* is ambiguous in English and
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we pick one closed reading — see §Non-negotiables).
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- `times_as_much(N, anchor)`: `anchor * N`
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- `fraction_more(F, anchor)`: `anchor * (1 + F)`
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- `fraction_less(F, anchor)`: `anchor * (1 - F)`
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- `more(N, anchor)`: `anchor + N`
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- `less(N, anchor)`: `anchor - N` (refuses on negative result)
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5. Promotes the resolved value into the existing `CandidateInitial`
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path via the same round-trip filter.
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No `DeferredCandidate` type. No `BindingProof` type. The pass is a
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deterministic lookup-and-promote operation. Replay determinism comes
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from the same JSON-sort-keys serialization the cognition eval already
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uses.
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### 4. Sentence-internal grounding (no binding pass needed)
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When `ComparativeOperand.anchor.kind == "literal"`, the value is
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extracted in the first pass without involving the binding pass. This
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handles the 0005 / 0029 cases (sentence-internal numeric anchor) and
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0041 (sentence-internal referent + same-sentence quantity).
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### 5. ADR-0137 supersession
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The closed ADR-0137 is **superseded in scope** by this ADR. The
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deferral note in `ADR-0136.S2-post-rescan.md` stands; the binding
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machinery this ADR proposes is the answer to its "reopen criterion."
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This ADR is lighter because it commits to **one** typed reference
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shape (`QuantityReference`) rather than a generic `DeferredCandidate`
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apparatus.
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The S.1/S.2 short-circuits in `parse_and_solve` **stay** as joins of
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grounded candidates. They are not retrospective binding and this ADR
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does not subsume them. (The canonical-runner staleness issue is fixed
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separately by teaching the runner to score short-circuit admissions.)
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---
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## Scope
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### In scope (this ADR + its implementation phases)
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- `FractionOperand`, `ComparativeOperand`, `ReferenceTarget`,
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`QuantityReference` type machinery
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- First-pass extractors for the closed surface set:
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- `<N> times greater than <anchor>`
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- `<N> times as much/many/long as <anchor>`
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- `<fraction> more than <anchor>` (where `<fraction>` ∈ {1/2, 1/4,
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3/4, half, twice} or `<N>%`)
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- `<fraction> less than <anchor>`
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- `<fraction> of <descriptor>`
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- `<N>% of <descriptor>`
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- Binding pass: sentence-order lookup of `QuantityReference` against
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prior grounded candidates with unique-match gating
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- Probe lane `RC1_comparative_reference` with the three cleanly
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in-scope cases (0029, 0041, 0010) plus negative probes (0005 — see
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below — 0004, 0036, 0043)
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- ADR-supersession note added to ADR-0136.S2-post-rescan.md
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acknowledging that 0137's reopen criterion is met by 0138
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### Out of scope (deferred to follow-up ADRs)
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- **Inverse arithmetic** (case 0004): "750 kids are afternoon, 1/4 are
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morning → total = 1000" requires solving for the unknown total from a
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known sub-quantity. Different machinery (inverse fraction inference).
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- **Multi-term aggregate references** (case 0036): "as much again as
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Wednesday, Thursday and Friday combined" requires summing multiple
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prior quantities through a single reference. Probably ADR-0139.
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- **Self-reference** (case 0005): "decrease to 3/4 of *its*
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temperature" — note this case is *in* the in-scope set as a
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*negative probe*: the binding pass must **refuse** on self-references
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(`its` resolves to the same entity whose value is being computed,
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yielding a circular binding). Confirm in the lane that 0005 still
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refuses.
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Wait — re-examining 0005: "Addison mountain's temperature will
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decrease to 3/4 of its temperature. If the current temperature is 84
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degrees, what will the temperature decrease by?" The anchor *is*
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sentence-internal — "the current temperature is 84." The "its" refers
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to "Addison mountain's temperature" which is given as 84. So 0005 is
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actually in scope under sentence-internal grounding once the
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question-form is parsed. **Reclassified to in-scope.** Negative probes
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remain 0004 and 0036.
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### Cases this ADR is expected to admit
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| Case | Expected outcome | Mechanism |
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|---|---|---|
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| 0005 | **admit (answer=21)** | sentence-internal fraction-of-anchor + question-resolution rule |
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| 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") |
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| 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 |
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| 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 |
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Honest expected admission delta: **+1 to +2** (0005, 0029 at high
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confidence; 0041 and 0043 partial credit only if the linguistic
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structure composes with existing extractors).
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**On gsm8k-0010 (the case that surfaced the forcing function).** The
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forcing case for cross-sentence binding turned out to be **0029, not
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0010**. 0010's sentence 2 ("Marion has 1/4 more than what Yun
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currently has, plus 7") has a genuinely ambiguous English reading.
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The dataset's expected answer is 9, which requires parsing the phrase
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as `(1/4) * Yun + 7 = (1/4)*8 + 7 = 9` — treating "1/4 more" as
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"1/4 [of what Yun has]" rather than "1/4 *more than* [Yun's
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quantity]." The natural English reading
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(`Yun * (1 + 1/4) + 7 = 17`) disagrees with the dataset.
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Per non-negotiable #2 of this ADR, **0010 must refuse**. Multiple
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plausible parses of the same surface yield different numeric values;
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the binding pass refuses rather than picks one. 0010 is reclassified
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from "expected admission" to "negative probe" — it stays refused, and
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the reason (ambiguity) becomes a regression assertion in the lane.
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This is the right outcome under refusal-first discipline, and it
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proves that the cross-sentence binding case must be justified by an
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unambiguous example. **0029 is that example.**
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---
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## Non-negotiables
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1. **`wrong == 0` remains a hard CI gate.** Across the binding eval
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lane and the GSM8K probe.
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2. **Ambiguous reference → refuse the binding.** If `QuantityReference`
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has multiple matching prior candidates with different values, the
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resolution refuses; the problem refuses; no best-effort.
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3. **Pinned English-reading convention for "N times greater."**
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English usage is ambiguous (some readers: `anchor + anchor * N`;
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others: `anchor * N`). This ADR pins the additive reading
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(`anchor * (N + 1)`) and **documents the choice in the ADR + the
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lane test**. If a downstream case appears that requires the other
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reading, refuses-then-revisit; do not silently pick the other.
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4. **No new short-circuit path in `parse_and_solve`.** Promoted
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candidates flow through the existing graph machinery.
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5. **No solver/graph/verifier changes.** Linguistic layer ends at
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candidate emission.
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6. **Determinism.** Same input → byte-equal `BindingPassResult`s,
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byte-equal promoted-candidate set, byte-equal `report.json`.
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7. **Closed surface vocabulary.** All comparative + fractional surface
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markers are enumerated. No wildcards. New markers require
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extending the closed set (in the same PR as the test case that
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forces them).
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---
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## Probe set
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### Required admissions
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| Case | Source | Why this exercises the layer |
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|---|---|---|
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| 0005 | GSM8K | sentence-internal fraction-of-anchor + literal-value path |
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| 0029 | GSM8K | cross-sentence `QuantityReference` resolution; **the forcing case** for the binding pass |
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### Required refusals (negative probes)
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- **gsm8k-0010** — ambiguous English (`1/4 more than X` parses as
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either `X * (1 + 1/4)` or `(1/4) * X`); the binding pass must refuse
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per non-negotiable #2
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- **gsm8k-0004** — inverse arithmetic (must continue to refuse pending
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ADR-0139)
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- **gsm8k-0036** — multi-term aggregate reference (must continue to
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refuse pending ADR-0139)
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- A synthetic ambiguous-reference case where two prior sentences
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introduce the same `(entity, unit)` with different values — must
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refuse (uniqueness gate)
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### Axis cases (synthetic, ≥15)
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Closed combinations of the surface vocabulary × anchor kinds:
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- `<frac> of <literal>` ≥3
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- `<frac> of <reference>` ≥3
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- `<N> times as much as <literal>` ≥3
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- `<N> times greater than <reference>` ≥3
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- `<frac> more than <reference>` ≥3 (covers 0010's shape)
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---
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## Phased rollout
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One branch per phase. The 2026-05-23 worktree-race lesson stands.
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| Phase | Deliverable | Branch |
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|---|---|---|
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| 0138.D | This ADR | `docs/adr-0138-comparative-reference-layer` (this PR) |
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| 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` |
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| 0138.B | Binding pass + `QuantityReference` resolution + 0010 admission + 0005/0029 admissions | `feat/adr-0138-binding-pass` |
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| 0138.C | Eval lane `RC1_comparative_reference` + probe set | `feat/adr-0138-rc1-lane` |
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Each phase is its own PR. Each must hold `wrong == 0`, preserve all
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existing axis lanes (S.1, S.2, S.3, S.4 if landed), and not regress
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the rescan-v3 invariants.
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After 0138.B lands, run a rescan v4 to record barrier shifts and
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update the post-rescan ADR.
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---
|
||||
|
||||
## 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.
|
||||
Loading…
Reference in a new issue