# ADR-0136.S.2 — Conditional-Op Question (Statement-Layer Corridor)

**Status:** Active — *regex patterns scheduled for removal under [ADR-0164](./ADR-0164-incremental-comprehension-reader.md) Phase 3; closed-set vocabulary preserved as lexicon seed*
**Date:** 2026-05-23
**Parent:** [ADR-0136](./ADR-0136-statement-layer-corridor.md) — see [ADR-0136 §Amendment 2026-05-26](./ADR-0136-statement-layer-corridor.md)

---

## Context

After S.0 (context-sentence classifier) and S.1 (rate/event statement parsing)
landed, the GSM8K train-sample probe sat at **2/50** admitted (`gsm8k-0014`,
`gsm8k-0018`), `wrong == 0`.

A taxonomy pass over the remaining 48 refused cases identified `gsm8k-0042`
as the next single-barrier unlock:

```
Ella has 4 bags with 20 apples in each bag and six bags with 25 apples in
each bag.  If Ella sells 200 apples, how many apples does Ella has left?
```

The initial-state sentence already parses via `_CONJ_EMBEDDED_RE` (ADR-0131.G.4
embedded quantifier) to `InitialPossession(entity="Ella", value=230,
unit="apples")`. The **only** barrier is the question form, which neither
`_Q_ENTITY_RE` nor `_Q_TOTAL_RE` cover: the `If <Entity> <verb> <N> <unit>,
how many <unit2> does <Entity2> <aux> [left|...]?` shape combines a
conditional-action operand with the entity-recall question.

---

## Decision

Add a **conditional-op question** extractor and a corresponding short-circuit
in `parse_and_solve` that:

1. Matches the closed shape `If <Entity> <verb> <N> <unit>, how many <unit2>
   does <Entity2> <aux> [<qualifier>]?`
2. Classifies `<verb>` against two closed sets:
   - `_COND_SUBTRACT_VERBS` (sell/sells/sold, give/gives/gave, eat/eats/ate,
     use, lose, spend, donate, remove, take, send, pay, drop, throw)
   - `_COND_ADD_VERBS` (buy/buys/bought, get/gets/got, receive, find, add,
     collect, pick, earn, gain)
3. Refuses on any of: unknown verb, unit mismatch (`<unit>` vs `<unit2>`
   after canonicalization), entity mismatch (`<Entity>` vs `<Entity2>`
   case-insensitively), `N <= 0`.
4. In `parse_and_solve`: if the question yields exactly one
   `CandidateConditionalOpQuestion`, collect all `extract_initial_candidates`
   from every statement sentence and look for **exactly one** matching IC
   by `(entity, unit)`. If found, compute `initial_value ± operand` by verb
   polarity; emit only when `answer >= 0`. Refuses otherwise.

The short-circuit is structurally identical to the S.1 capacity/earnings
paths: it bypasses graph construction, returns `selected_graph=None`, and
preserves `wrong == 0` by refusing rather than guessing on any ambiguity.

---

## Invariants

- **`admitted_wrong == 0`** preserved by:
  - Single-match (entity, unit) requirement before emission
  - Non-negative answer gate
  - Closed verb sets — no wildcards
- **Context-filler safety rail** unchanged (S.0)
- **No solver/graph/verifier changes** — extractor lives in
  `math_candidate_parser.py`; short-circuit lives in `math_candidate_graph.py`

---

## Honest GSM8K delta

| Stage | Admitted | Wrong |
|---|---|---|
| Pre-S.0 | 0/50 | 0 |
| Post-S.1 | 1/50 (`0014`) | 0 |
| Post-S.0 classifier | 2/50 (`+0018`) | 0 |
| **Post-S.2** | **3/50** (`+0042`) | **0** |

`gsm8k-0042` admits with `answer == 30.0` (expected: 30).

---

## Consequences

- The S.x corridor now spans `parser` (S.1 capacity/earnings, S.2 question
  shape) and `pre-pass classifier` (S.0). Future phases (S.3 compound
  statements, S.4 coreference) extend this pattern.
- The canonical GSM8K runner (`evals/gsm8k_math/runner.py`) still asserts
  `selected_graph is not None` on admission and therefore cannot score the
  short-circuit admissions. The `report.json` artifact remains stale
  (0/50/0); the honest count is asserted via direct `parse_and_solve` test
  (`test_gsm8k_post_s2_admission_honest`). Aligning the canonical runner
  with the short-circuit paths is deferred (out of S.2 scope).

---

## Deferred

- Conditional-op question forms with **more than one** operand (e.g.
  "If she gives away 3 and buys 5, …") — needs two-op composition.
- Question forms without `does <Entity>` aux (e.g. "how many apples
  remain?") — needs a sibling regex.
- Conditional questions where the conditional and the question reference
  **different** units that are unit-related (e.g. dollars↔cents) — needs
  unit-relation taxonomy.
