docs(analysis): ratify Gate A2a unit partition primitive (#808)

docs/analysis/gsm8k-workstream-a-gate-a2a-unit-partition-ratification-2026-06-17.md

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+# GSM8K Workstream A Gate A2a — unit partition / chunking primitive ratification
+
+**Date:** 2026-06-17
+**Workstream:** A (GSM8K typed-operation ladder)
+**Gate:** A2a — first partition/chunking injection slice (roadmap Gate A2 family)
+**Status:** Ratified for implementation (BEFORE any code changes)
+**Scope lock:** Fixed-size unit chunking with source-grounded total + chunk size, exact integer quotient, statement-only v1. One narrow recognizer-injector bridge mirroring Inc3 rate and Gate A1 comparative discipline.
+
+**Prerequisites (met on main @ e134e53c):**
+- PR #801: Inc3 evidence closure (`rate_with_currency` `recognized_no_injection` = 0 on live runner).
+- PR #803/#805: Gate A1 multiplicative comparative ratification + implementation (`comparative_with_unit` no-injection = 0).
+- PR #806: Post-Gate-A1 frontier microscope (`docs/analysis/gsm8k-post-gate-a1-frontier-microscope-2026-06-17.md`).
+- PR #807: Lane-SHA hygiene (no GSM8K serving change).
+
+**Implementation branch (future):** `feat/gsm8k-workstream-a-gate-a2a-unit-partition-injection`
+
+**Gate naming (fixed — do not conflate):**
+
+| Name | Meaning |
+|---|---|
+| **Gate A2 (roadmap)** | Partition / chunking family |
+| **Gate A2a (this doc)** | Narrow v1: total measure → fixed-size chunks → chunk count |
+| **Gate A1b / Comparative-A2** | Additive comparative — **not** roadmap Gate A2 |
+| **PR-6d aggregate partition** | Combine facts → split equally into **N containers** — **distinct primitive**, already landed off-serving |
+
+---
+
+## 1. What exact Gate A2a slice is selected?
+
+**Unit partition / chunking:** a **total continuous (or count-measure) quantity** is split into **fixed-size chunks** with an explicit unit on the chunk size, producing an **exact integer chunk count**.
+
+The deliverable is a **recognizer-anchor injector** for a ratified serving category `ShapeCategory.UNIT_PARTITION` (taxonomy label exists today; **not** a live `_MATCHERS` / `_INJECTORS` entry) that emits a typed partition operation when a closed v1 template matches and all slots are source-grounded. The slice closes the **recognizer matched but produced no injection** frontier for the one confirmed DCS misroute (`dcs_misroute_unit_partition` on case **0002**), without widening discrete-count injection.
+
+**Confirmed code facts:**
+- `ShapeCategory.UNIT_PARTITION` and `_is_unit_partition` exist in `evals/refusal_taxonomy/shape_categories.py` (taxonomy only).
+- EX-6 hyphen-bonded unit extraction (`25-foot`) is landed in `generate/derivation/extract.py`.
+- `VALID_OPERATION_KINDS` in `generate/math_problem_graph.py` has **no** `unit_partition` today; bare `divide` apply stores quotient under **divisor unit**, which is **unsafe** for feet÷feet→sections without a `result_unit` contract.
+- PR-6d `_Partition` in `generate/quantitative_comprehension.py` is **aggregate-then-divide into N equal containers** — different semantics from fixed chunk size (see §5).
+
+This is **first partition subfamily only** — not full Gate A2 (inverse residual, yield questions, fractional partition, composition wall).
+
+---
+
+## 2. Lead exemplar
+
+**Case `gsm8k-train-sample-v1-0002`** (canonical seed pin in `tests/test_gsm8k_post_gate_a1_frontier_microscope.py`).
+
+**Full problem:**
+> Jan buys 1000 feet of cable. She splits it up into 25-foot sections. She gives 1/4 of that to a friend. She then puts half of the rest in storage. How much does she keep on hand? → **15**
+
+**Gate A2a v1 owns only the partition statement:**
+> *She splits it up into 25-foot sections.*
+
+**Prior total (separate statement, must be in graph state before partition inject):**
+> *Jan buys 1000 feet of cable.*
+
+**Gold partition step:** `1000 ÷ 25 = 40` sections.
+
+**Live refusal (pinned proxy):**
+> `candidate_graph: recognizer matched but produced no injection for statement: 'She splits it up into 25-foot sections.' (category=discrete_count_statement)`
+
+**Microscope classification:** `dcs_misroute_unit_partition` → candidate primitive `unit_partition` → movement `downstream_reclassification`.
+
+**Exemplar seed (mis-route documentation):** `teaching/admissibility_exemplars/discrete_count_statement_v1.jsonl` (`dcs-v1-0021`, `train_case_id: gsm8k-train-sample-v1-0002`).
+
+**Confuser spine:** `evals/gsm8k_math/confusers/v1/cases.jsonl` `confuser-v1-0007` — canonical 0002 misfire (pseudo-accumulation → 996 if partition read as Initial(25) only).
+
+---
+
+## 3. What is v1 in scope?
+
+### Closed template (statement-only)
+
+| Requirement | Rule |
+|-------------|------|
+| **Partition verb** | `split`, `cut`, `divide`, `separate`, or ratified synonym ∈ `DIVIDE_VERBS` (mirror existing divide lexicon; no broadening in v1) |
+| **Chunk size** | Hyphenated or explicit measure: `<N>-<unit>` (EX-6) or equivalent ratified span, e.g. `25-foot sections`, `20-inch pieces` |
+| **Total quantity** | Prior statement in the same problem must ground `(actor, total_unit)` with value ≥ chunk size; partition stmt does **not** carry total |
+| **Unit compatibility** | Dividend unit == chunk-size unit (same canonical unit); no implicit conversion |
+| **Quotient** | `total % chunk_size == 0`; exact positive integer chunk count |
+| **Output** | Emit typed **`unit_partition`** operation (§5) writing **chunk count** under a dimensionless or explicit count-noun unit (`section`, `piece`, … from counted noun in chunk phrase) |
+| **Actor** | Same actor chain as prior total statement (v1: same-sentence subject or ratified narrow antecedent — **no** cross-sentence pronoun binding beyond existing session rules) |
+| **Injection target** | **Statements only** — not question surfaces (mirror Gate A1) |
+| **DCS yield** | Partition-bearing stmt must **not** match `discrete_count_statement` first / must not emit `Initial(chunk_size, material_unit)` misread |
+
+### Positive admission surfaces (v1)
+
+| ID | Pattern | Notes |
+|----|---------|-------|
+| A01 | `1000 feet` … `splits into 25-foot sections` | Canonical 0002 pair |
+| A02 | `800 inches` … `cuts into 20-inch pieces` | Paraphrase (confuser-v1-0005 first clause) |
+| A04 | `12 feet` rope `cut into 4-foot sections` → 3 | Clean single-pair toy |
+
+### Expected v1 deliverable (implementation PR)
+
+- `unit_partition` (or ratified equivalent) on serving recognizer/injector path
+- Live bucket: **`unit_partition` recognized_no_injection = 0** (mirror Inc3/Gate A1 closure)
+- Case **0002** partition stmt: reclassification off DCS misroute (not guaranteed end-to-end solve)
+
+---
+
+## 4. What is explicitly out of v1?
+
+| Case / surface | Deferral reason |
+|----------------|-----------------|
+| **0002 full problem** (¼ give, half of rest, "keep on hand") | Fraction + rest-state + question binding — composition follow-up; confuser-v1-0007 must stay **refuse** until separately ratified |
+| **0007** inverse residual ("how many more boxes") | Question-parser slot; box capacity derivation — not stmt-level chunk partition |
+| **0008** yield ("50 beads per bracelet, how many bracelets") | Production/yield question frame; needs inventory aggregate first |
+| **0004** nested fraction partition | `Half of the kids…` — fractional subset-of-set, not fixed chunk size |
+| **0025** peer-pick ("three friends pick the same amount") | Multiplicative peer partition question — not measure chunking |
+| **0047** equal pack into N bags | Equal distribution into **N containers** (divisor = bag count), not **M-unit chunks**; taxonomy `discrete_count_statement` |
+| **0030** `2-hour drive` | Duration descriptor; taxonomy false positive via hyphen — must **refuse** |
+| **Non-integer quotient** | e.g. `1000 feet` → `30-foot sections` — refuse (no floor/ceil) |
+| **Missing total** | Partition stmt alone: `She splits it into 25-foot sections` — refuse |
+| **Missing chunk size** | `equal sections`, `into 40 sections` (count without unit size) — refuse |
+| **"Split into N groups/boxes"** | PR-6d / enumeration — divisor is **group count**, not chunk measure |
+| **Rate / per-unit** | `per hour`, `per kg`, `$2 for one cup` — Inc3/Gate A1 closed buckets |
+| **Broad DCS composition wall** | 14× `dcs_composition_wall` — forbidden without `derivation_composer` ratification |
+| **Affine equation / graph_planner** | Out of Workstream A injector ladder |
+| **Cross-sentence pronoun reference** | ADR-0138 — not proven safe |
+| **Remainder / subtract-after-partition** | Needs gain/loss chaining beyond v1 injector |
+
+**Widening discrete-count injector** to emit partition ops is **explicitly forbidden** (metric-inert / wrong=0 hazard per question-layer survey).
+
+---
+
+## 5. What typed primitive is required?
+
+### Ratified choice: **`unit_partition`** (new `Operation.kind`)
+
+**Not safe to reuse bare `divide` without extension** because:
+1. `_apply_divide` stores quotient under **divisor unit** (`feet`), not chunk count (`sections`).
+2. Existing `divide` encodes **equal N-way split** (`groups` dimensionless + material unit tag) — different from **fixed chunk size**.
+3. Candidate-graph parser does not emit serving `divide` today; partition requires a **new injector**, not parser reuse alone.
+
+**Not the same as PR-6d `_Partition`:** aggregate-then-divide into **N equal containers** with `perquery` pairing (`generate/quantitative_comprehension.py`). Gate A2a is **total ÷ fixed chunk measure → count**.
+
+### Minimal operation shape (conceptual — implementation must match or re-ratify)
+
+```python
+Operation(
+    actor=<subject>,
+    kind="unit_partition",
+    operand=Quantity(value=<chunk_size>, unit=<chunk_unit>),  # e.g. 25, foot
+    # implementation must also carry result_unit=<count_noun> or dimensionless count
+)
+```
+
+**Apply rule (wrong=0):**
+- Read `(actor, dividend_unit)` from prior grounded state.
+- Require `dividend_unit == chunk_unit` (after canonicalization).
+- Require `total % chunk_size == 0`.
+- Write `(actor, result_unit) = total // chunk_size` where `result_unit` is explicit count noun or dimensionless count — **not** dividend unit.
+
+**Stop/re-ratify trigger:** If implementation discovers the substrate can only safely use `divide` + mandatory `result_unit` fields without a new kind, implementation PR must cite this doc and either (a) prove equivalence in tests or (b) open amendment PR before merge.
+
+**Rejected names:** `unitize` (versor algebra collision); `partition_count` alone (ambiguous with PR-6d and equal-N split).
+
+---
+
+## 6. Grounding rules
+
+| Slot | Rule |
+|------|------|
+| **total_quantity** | From **prior statement** quantity anchor; literal span grounded; actor key matches partition subject |
+| **chunk_size** | From partition statement hyphenated or explicit measure token; literal substring in `matched_*_token` fields |
+| **chunk_unit** | Canonical unit from EX-6 / `_canonicalize_unit`; must match total unit |
+| **partition_verb** | Literal verb ∈ ratified divide verb set |
+| **counted_noun** | Optional: `sections`, `pieces` — drives `result_unit` label |
+| **source_span** | Full partition statement byte-identical to input |
+| **No inferred totals** | Partition stmt without prior total state → injector returns `()` or downstream refuse |
+| **No implicit conversion** | `feet` vs `inches` → refuse unless conversion ratified elsewhere |
+| **No LLM / heuristic fill** | Every slot maps to a literal substring (Inc2/Gate A1 doctrine) |
+
+### Matcher category and `parsed_anchors` (implementation PR)
+
+| Anchor key | Semantics |
+|------------|-----------|
+| `actor_token` | Partition statement subject |
+| `chunk_size_token` | Numeric chunk magnitude (e.g. `25`) |
+| `chunk_unit_token` | Unit phrase (e.g. `foot`) |
+| `counted_noun_token` | Plural noun after chunk phrase if present (`sections`) |
+| `partition_verb_token` | Matched split/cut verb |
+| `source_span` | Full statement |
+
+---
+
+## 7. wrong=0 guard
+
+| Condition | Behavior |
+|-----------|----------|
+| Ambiguous partition (two chunk sizes, competing interpretations) | **Refuse** — no injection |
+| Incompatible units (feet vs inches) | **Refuse** |
+| Non-exact division (`total % chunk_size != 0`) | **Refuse** at solve/verify — never floor |
+| Missing total or missing chunk size | **Refuse** — injector `()` |
+| Partition stmt matches DCS only | **Refuse** mis-injection — must not emit `Initial(N, material_unit)` |
+| Multiple partition cues in one sentence | **Refuse** |
+| Downstream composition (fractions, rest, question) | **Refuse** on serving until composition ratified — partial graph must not verify as full gold |
+| Numeric answer without verifier | **Forbidden** — `math_verifier.verify` must pass before `correct` (`evals/gsm8k_math/runner.py`) |
+
+**Architectural boundaries (INV-30 / INV-31):**
+- No `determine()`, no `answer=False`, no `FrameVerdict`, no CLOSE interaction on this path.
+- No `core.reliability_gate` as substitute for verifier replay on serving.
+
+**Serving path:** `parse_and_solve` → `solve` → `math_verifier.verify` → gold compare; `wrong == 0` hard.
+
+---
+
+## 8. Confusers future implementation must prove
+
+### Hard refuses (30+ structural — minimum bar in implementation PR)
+
+| ID | Surface class | Example | Expected |
+|----|---------------|---------|----------|
+| C01–C02 | Non-integer chunk | `1000 feet` → `7-foot` / `2.5-meter` | refuse |
+| C03–C06 | Missing total or chunk | stmt-only `25-foot sections`; `equal sections` | refuse |
+| C07 | Unit mismatch | `1000 feet` → `25-inch sections` | refuse |
+| C08 | Discrete packing | `48 cookies` → `boxes of 6` | refuse |
+| C09–C11 | N groups vs M-unit chunks | `equally into 4 bags`; `Half of the kids` | refuse |
+| C12 | Inverse residual (0007) | `how many more boxes` | refuse |
+| C13 | Yield (0008) | `50 beads per bracelet, how many…` | refuse |
+| C14–C16 | Fraction/rest follow-up | full 0002; `gives 1/4`; subtract sections | refuse |
+| C17 | Non-exact total | `999 feet` → `25-foot` | refuse |
+| C18–C20 | Rate/per-unit | `$18/hour`, `$20 per kg`, `$2 per cup` | refuse |
+| C21–C22 | Duration false positive | `2-hour drive`; `10 oysters in 5 minutes` | refuse |
+| C23–C26 | DCS / composition wall | routes, multi-entity lists, comparatives, fraction-of-prior | refuse |
+| C27 | Pseudo-accumulation twin | ribbon 800 + cut + give ¼ | refuse |
+| C28 | Additive comparative (0016) | `2 more than 5 miles` | refuse |
+| C29–C30 | Peer-pick / product each | 0025 question; `24 erasers each` | refuse |
+
+**Critical discrimination pairs:**
+- `1000 feet split into 25-foot sections` (**admit** partition inject) vs stmt-only `25-foot sections` (**refuse**)
+- `1000 feet split into 25 sections` (count divisor, no unit size) — **refuse**
+- `1000 feet split into bags` (missing chunk measure) — **refuse**
+
+### Admission tests (5 minimum)
+
+| ID | Proves |
+|----|--------|
+| A01–A02 | Canonical inject on 0002 / ribbon paraphrase |
+| A03 | Pair consistency: paired total+chunk vs stmt-only |
+| A05 | Category `unit_partition`, **not** `discrete_count_statement` |
+
+**Graduation rule (ADR-0163-F2):** Confusers graduate to solve only when a **general** composition mechanism is ratified and proven — not by regex widening.
+
+---
+
+## 9. Partition-adjacent cases (frontier evidence)
+
+| case_id | Relevance | v1 |
+|---------|-----------|-----|
+| **0002** | **Lead** — `dcs_misroute_unit_partition` | **IN** (partition stmt inject) |
+| **0007** | Inverse box residual — question layer | **OUT** |
+| **0008** | Beads-per-bracelet yield — question + aggregate | **OUT** |
+| **0004** | Nested fraction subset | **OUT** |
+| **0025** | Peer-pick multiplication question | **OUT** |
+| **0047** | Equal pack into 4 bags — container count divisor | **OUT** |
+
+Only **0002** has confirmed `unit_partition` DCS misroute on live serving (`recognized_no_injection` subfamily count = 1).
+
+---
+
+## 10. Expected metric movement
+
+**Live ephemeral runner (main @ e134e53c):** 6 correct / 44 refused / 0 wrong; `rate_with_currency` and `comparative_with_unit` no-injection = **0**.
+
+**Expected after Gate A2a implementation:**
+
+| Metric | Expected |
+|--------|----------|
+| `wrong` | **0** (hard) |
+| `correct` | **≥ 6** (monotonic); **not guaranteed lift** |
+| `refused` | **≤ 44** (monotonic) |
+| **0002** | **Reclassification** — partition stmt moves off DCS no-injection; full 15 solve still refused until composition ratified |
+| `discrete_count_statement` no-injection | Likely **−1** (19→18) |
+| `unit_partition` no-injection | Target **0** on live runner |
+| Pinned `report.json` | **Unchanged** unless separate rebaseline PR |
+
+**Do not claim** aggregate correct-count lift in implementation PR body without per-case ephemeral evidence.
+
+---
+
+## 11. Explicit non-goals
+
+- **No implementation** in this ratification PR (docs only).
+- No `report.json` rebaseline.
+- No additive comparative (Gate A1b / Comparative-A2).
+- No Inc4 rate denom-state.
+- No broad DCS widening / `derivation_composer` without separate ratification.
+- No affine equation frame / `graph_planner.py` changes.
+- No sealed-lane / `scripts/verify_lane_shas.py` pin movement (unless accidental — revert).
+- No corpus / pack / policy / identity mutation.
+- No `determine()` / `FrameVerdict` / CLOSE / idle consolidation (**INV-30 / INV-31**).
+- No `answer=False` on open-world paths.
+- No LLM / stochastic generation.
+- No promotion of taxonomy `_HYPHENATED_UNIT_RE` alone into matcher (0030 hazard).
+- No conflation with PR-6d aggregate-partition template.
+- No full Gate A2 family in one PR.
+
+---
+
+## 12. Implementation touch list (future PR — not this PR)
+
+| File | Change |
+|------|--------|
+| `generate/math_problem_graph.py` | Add `unit_partition` to `VALID_OPERATION_KINDS` (if new kind) |
+| `generate/math_solver.py` | `_apply_unit_partition` with `result_unit` contract |
+| `generate/recognizer_match.py` | `_match_unit_partition`, `_MATCHERS` registration |
+| `generate/recognizer_anchor_inject.py` | `inject_unit_partition`, `_INJECTORS`; DCS yield guard |
+| `generate/math_verifier.py` / `math_roundtrip.py` | Roundtrip + verify hooks for new kind |
+| `teaching/admissibility_exemplars/` | `unit_partition_v1.jsonl` (Phase C corridor) |
+| `tests/test_recognizer_unit_partition_inject.py` | **new** — ≥15 unit tests |
+| `tests/test_math_candidate_graph_unit_partition_injection.py` | **new** — ≥8 graph tests |
+| `tests/test_gsm8k_frontier_report.py` | live `unit_partition` bucket closure |
+| `tests/test_candidate_graph_recognizer_wiring.py` | wrong=0 replay |
+| `tests/test_candidate_graph_completeness_guard.py` | pseudo-accumulation regressions |
+| `tests/test_adr_0163_f2_confusers.py` | confuser-v1-0005/0007/0008 |
+
+**Read-only unless proven necessary:** `generate/derivation/*` (off-serving), `core/reliability_gate/*`, `graph_planner.py`.
+
+---
+
+## 13. Validation obligations (implementation PR — not this PR)
+
+```bash
+.venv/bin/python -m pytest tests/test_recognizer_unit_partition_inject.py -q
+.venv/bin/python -m pytest tests/test_math_candidate_graph_unit_partition_injection.py -q
+.venv/bin/python -m pytest tests/test_gsm8k_frontier_report.py -q
+.venv/bin/python -m pytest tests/test_gsm8k_post_gate_a1_frontier_microscope.py -q
+.venv/bin/python -m pytest tests/test_candidate_graph_recognizer_wiring.py -q
+.venv/bin/python -m pytest tests/test_candidate_graph_completeness_guard.py -q
+.venv/bin/python -m pytest tests/test_adr_0163_f2_confusers.py -q
+.venv/bin/python -m pytest tests/test_adr_0175_phase2_practice_lane.py -q
+.venv/bin/python -m pytest tests/test_architectural_invariants.py -q -k "INV_30 or INV_31"
+.venv/bin/python scripts/verify_lane_shas.py
+.venv/bin/core test --suite smoke -q
+# Ephemeral only — do not commit unless ratified:
+# build_report(cases) → wrong==0
+```
+
+---
+
+## 14. Validation obligations (this ratification PR — docs only)
+
+```bash
+git diff --check origin/main...HEAD
+git diff --name-status origin/main...HEAD
+```
+
+Expected: single added file `docs/analysis/gsm8k-workstream-a-gate-a2a-unit-partition-ratification-2026-06-17.md`.
+
+---
+
+## 15. Open risks (honest)
+
+| Risk | Severity | Mitigation |
+|------|----------|------------|
+| Over-recognition on any `\d+-(foot\|hour\|…)` | **Critical** | Closed verb+chunk template; 0030/0014 confusers; refuse duration |
+| DCS wins match race on 0002 | **High** | Explicit DCS yield guard + matcher priority tests |
+| Bare `divide` quotient unit bug | **Critical** | Ratify `unit_partition` + `result_unit`; never store 40 under `feet` |
+| PR-6d conflation | **High** | Refuse `into N bags` / `perquery` shapes in v1 |
+| Pseudo-accumulation 996 misfire | **Critical** | confuser-v1-0007 green; completeness guard |
+| Claiming 0002 full solve | **High** | Doc + tests: injector closure only |
+| Composition pressure (fractions/rest) | **Medium** | Explicit out-of-v1; separate ratification |
+| No guaranteed correct lift | **Low** (expected) | PR body documents reclassification only |
+| `result_unit` noun ambiguity (`sections` vs dimensionless) | **Medium** | Resolve in implementation tests; amend if dual |
+
+---
+
+## 16. Arena reconciliation summary
+
+| Agent | Key finding |
+|-------|-------------|
+| **Partition substrate mapper** | Bare `divide` unsafe; PR-6d distinct; ratify new `unit_partition` kind with `result_unit`; EX-6 + taxonomy landed, injector missing |
+| **Frontier evidence auditor** | 0002 lead exemplar confirmed; 0007/0008/0004/0025/0047 OUT of v1; reclassification-only metric |
+| **Over-recognition adversary** | 30 hard refuses + 5 admission tests; duration/rate/DCS wall highest risk |
+| **Truth-boundary auditor** | INV-30/31; verifier before correct; no determine/FrameVerdict/CLOSE |
+| **Test-plan auditor** | Inc2/Gate A1 ladder mirror; 15+8 unit/graph tests; frontier bucket closure; this PR docs-only |
+
+This ratification closes the docs-first gate. Implementation may proceed only after this document merges to `main`.