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

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).

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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)

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)

.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)

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.