core/docs/analysis/gsm8k-post-gate-a1-frontier-microscope-2026-06-17.md

GSM8K post-Gate-A1 frontier microscope lookback

Date: 2026-06-17 Branch: docs/gsm8k-post-gate-a1-frontier-microscope Main merge anchor: bb083004 (PR #805 Gate A1 implementation) Tool: scripts/gsm8k_post_gate_a1_frontier_microscope.py Scope: docs/tooling only — no runtime, no report.json rebaseline, no implementation ratification

Purpose

After Inc3 (#799/#801) and Gate A1 (#803/#805), the injector frontiers for rate_with_currency and comparative_with_unit are closed. Aggregate train_sample proxy remains 6/44/0 with wrong=0. This lookback runs a deterministic live microscope over ephemeral build_report(cases) to name the exact remaining refusal taxonomy and nominate the next ratification candidate (not an implementation decision).

Gate naming (fixed)

Name	Meaning
Gate A2 (roadmap)	Partition / chunking family
Gate A2a	Narrow ratification candidate within Gate A2: unit partition / chunking primitive
Gate A1b / Comparative-A2	Additive comparative (compare_additive) — not roadmap Gate A2

Measurement method

PYTHONPATH=. .venv/bin/python scripts/gsm8k_post_gate_a1_frontier_microscope.py

• Reads evals/gsm8k_math/train_sample/v1/cases.jsonl (50 cases)
• Builds ephemeral report via evals.gsm8k_math.train_sample.v1.runner.build_report
• Does not write evals/gsm8k_math/train_sample/v1/report.json
• Emits aggregate buckets plus a 44-row refusal_table with per-case blocking layer, candidate primitive, expected movement, and evidence snippet

Pinned artifact unchanged: report.json stays Inc1-era 6/44/0.

Live counts (ephemeral main @ bb083004)

Metric	Value
correct	6
refused	44
wrong	0
rate_with_currency no-injection	0
comparative_with_unit no-injection	0
total recognized_no_injection	31

Aggregate buckets (summary)

Top bucket	Count
recognized_no_injection	31
no_admissible_statement	7
no_admissible_question	5
no_solvable_branch	1

recognized_no_injection by category: discrete_count_statement 19, descriptive_setup_no_quantity 4, currency_amount 3, multiplicative_aggregation 3, temporal_aggregation 2

DCS subfamilies (19): dcs_composition_wall 14, dcs_misroute_fraction_change 2, dcs_misroute_unit_partition 1 (0002), dcs_misroute_comparative_multiplicative 1 (0033), dcs_misroute_comparative_additive 1 (0016)

Expected movement histogram: diagnostic_only 25, downstream_reclassification 19, correct_lift 0 (none nominated — composition/multi-step dominates)

Case-level refusal table (all 44 refused cases)

Full per-case reason strings are in the JSON refusal_table emitted by the microscope. Truncated reasons shown here for doc readability.

case_id	verdict	top bucket	subfamily	recognizer cat	blocking layer	next primitive	movement	evidence	reason (truncated)
0001	refused	recognized_no_injection	no_injection_temporal_aggregation	temporal_aggregation	recognizer_injector	temporal_tariff	diagnostic_only	If she works more than 8 hours per shift, she is eligible for overtime, which is paid by your...	candidate_graph: recognizer matched but produced no injection for sta...
0002	refused	recognized_no_injection	dcs_misroute_unit_partition	discrete_count_statement	recognizer_injector	unit_partition	downstream_reclassification	She splits it up into 25-foot sections.	candidate_graph: recognizer matched but produced no injection for sta...
0003	refused	recognized_no_injection	dcs_composition_wall	discrete_count_statement	recognizer_injector	derivation_composer	diagnostic_only	The local bookstore donated 48 boxes of erasers.	candidate_graph: recognizer matched but produced no injection for sta...
0004	refused	no_admissible_statement	nested_fraction_partition	—	statement_parser	fraction_partition	diagnostic_only	Half of the kids are going to soccer camp, and 1/4 of the kids going to soccer camp are going...	candidate_graph: no admissible candidate for statement: 'Half of the ...
0005	refused	no_admissible_statement	affine_equation_fraction_target	—	statement_parser	fractional_delta	diagnostic_only	In one hour, Addison mountain's temperature will decrease to 3/4 of its temperature.	candidate_graph: no admissible candidate for statement: "In one hour,...
0006	refused	recognized_no_injection	no_injection_multiplicative_aggregation	multiplicative_aggregation	recognizer_injector	multiplicative_aggregate	diagnostic_only	Mandy started reading books with only 8 pages when she was 6 years old.	candidate_graph: recognizer matched but produced no injection for sta...
0007	refused	no_admissible_question	inverse_residual_more	—	question_parser	inverse_residual_question	downstream_reclassification	How many more boxes do they need if Francine has a total of 85 crayons?	candidate_graph: no admissible candidate for question: 'How many more...
0008	refused	no_admissible_question	production_yield_question	—	question_parser	yield_question_frame	downstream_reclassification	If 50 beads are used to make one bracelet, how many bracelets will Marnie be able to make out...	candidate_graph: no admissible candidate for question: 'If 50 beads a...
0009	refused	no_admissible_question	conditional_aggregate_total	—	question_parser	conditional_aggregate_question	downstream_reclassification	If Jen has 150 ducks, how many total birds does she have?	candidate_graph: no admissible candidate for question: 'If Jen has 15...
0010	refused	no_admissible_statement	affine_equation_fraction_delta	—	statement_parser	affine_equation	diagnostic_only	Marion has 1/4 more than what Yun currently has, plus 7.	candidate_graph: no admissible candidate for statement: 'Marion has 1...
0011	refused	no_solvable_branch	rate_graph_unsolvable	—	graph_composition	rate_composition	downstream_reclassification	Alexa has a lemonade stand where she sells lemonade for $2 for one cup.	candidate_graph: no branch produced a solvable graph
0012	refused	recognized_no_injection	no_injection_descriptive_setup_no_quantity	descriptive_setup_no_quantity	recognizer_injector	relation_hypothesis	diagnostic_only	He put all of them in his aquarium but his fish ate half of them.	candidate_graph: recognizer matched but produced no injection for sta...
0013	refused	recognized_no_injection	no_injection_multiplicative_aggregation	multiplicative_aggregation	recognizer_injector	multiplicative_aggregate	diagnostic_only	Allison, a YouTuber, uploads 10 one-hour videos of food reviews each day to her channel.	candidate_graph: recognizer matched but produced no injection for sta...
0015	refused	recognized_no_injection	dcs_composition_wall	discrete_count_statement	recognizer_injector	derivation_composer	diagnostic_only	Traveling from Manhattan to the Bronx, Andrew rides the subway for 10 hours, takes the train...	candidate_graph: recognizer matched but produced no injection for sta...
0016	refused	recognized_no_injection	dcs_misroute_comparative_additive	discrete_count_statement	recognizer_injector	compare_additive	downstream_reclassification	On Rudolph's car trip across town, he traveled 2 more than 5 miles and encountered 3 less tha...	candidate_graph: recognizer matched but produced no injection for sta...
0017	refused	recognized_no_injection	no_injection_temporal_aggregation	temporal_aggregation	recognizer_injector	temporal_tariff	diagnostic_only	He's charging $50.00 per day or $500.00 for 14 days.	candidate_graph: recognizer matched but produced no injection for sta...
0019	refused	recognized_no_injection	no_injection_currency_amount	currency_amount	recognizer_injector	currency_mutation	diagnostic_only	After the first appointment, John paid $100 for pet insurance that covers 80% of the subseque...	candidate_graph: recognizer matched but produced no injection for sta...
0020	refused	recognized_no_injection	dcs_composition_wall	discrete_count_statement	recognizer_injector	derivation_composer	diagnostic_only	Two puppies, two kittens, and three parakeets were for sale at the pet shop.	candidate_graph: recognizer matched but produced no injection for sta...
0021	refused	recognized_no_injection	dcs_composition_wall	discrete_count_statement	recognizer_injector	derivation_composer	diagnostic_only	He bench presses 15 pounds for 10 reps and does 3 sets.	candidate_graph: recognizer matched but produced no injection for sta...
0022	refused	recognized_no_injection	dcs_composition_wall	discrete_count_statement	recognizer_injector	derivation_composer	diagnostic_only	She goes out fishing today and catches twice as many fish as she caught in total in the past...	candidate_graph: recognizer matched but produced no injection for sta...
0023	refused	recognized_no_injection	no_injection_descriptive_setup_no_quantity	descriptive_setup_no_quantity	recognizer_injector	relation_hypothesis	diagnostic_only	Cindy collected twice as many, and Rex collected half of Nicole and Cindy's combined total.	candidate_graph: recognizer matched but produced no injection for sta...
0025	refused	no_admissible_question	multiplicative_peer_pick	—	question_parser	peer_partition_question	downstream_reclassification	If three of Lilibeth's friends pick the same amount as her, how many strawberries do Lilibeth...	candidate_graph: no admissible candidate for question: "If three of L...
0026	refused	no_admissible_statement	each_binding_currency	—	statement_parser	each_entity_binding	downstream_reclassification	Aaron and his brother Carson each saved up $40 to go to dinner.	candidate_graph: no admissible candidate for statement: 'Aaron and hi...
0027	refused	recognized_no_injection	no_injection_descriptive_setup_no_quantity	descriptive_setup_no_quantity	recognizer_injector	relation_hypothesis	diagnostic_only	The number of followers he has on Twitter is half the number of followers he has on Instagram...	candidate_graph: recognizer matched but produced no injection for sta...
0028	refused	recognized_no_injection	no_injection_currency_amount	currency_amount	recognizer_injector	currency_mutation	diagnostic_only	It cost $100,000 to open initially.	candidate_graph: recognizer matched but produced no injection for sta...
0030	refused	no_admissible_statement	numeric_expression_duration	—	statement_parser	duration_multiplier	downstream_reclassification	It is a 2-hour drive each way.	candidate_graph: no admissible candidate for statement: 'It is a 2-ho...
0031	refused	recognized_no_injection	dcs_composition_wall	discrete_count_statement	recognizer_injector	derivation_composer	diagnostic_only	Jeremie wants to go to an amusement park with 3 friends at the end of summer.	candidate_graph: recognizer matched but produced no injection for sta...
0032	refused	recognized_no_injection	dcs_composition_wall	discrete_count_statement	recognizer_injector	derivation_composer	diagnostic_only	He draws and colors 10 pictures.	candidate_graph: recognizer matched but produced no injection for sta...
0033	refused	recognized_no_injection	dcs_misroute_comparative_multiplicative	discrete_count_statement	recognizer_injector	compare_multiplicative	downstream_reclassification	Rachel is 12 years old, and her grandfather is 7 times her age.	candidate_graph: recognizer matched but produced no injection for sta...
0034	refused	recognized_no_injection	dcs_composition_wall	discrete_count_statement	recognizer_injector	derivation_composer	diagnostic_only	He can run 40 yards within 5 seconds.	candidate_graph: recognizer matched but produced no injection for sta...
0035	refused	no_admissible_question	inverse_residual_more	—	question_parser	inverse_residual_question	downstream_reclassification	How many more apples would Martha need to give away to be left with only 4 of them?	candidate_graph: no admissible candidate for question: 'How many more...
0036	refused	recognized_no_injection	dcs_composition_wall	discrete_count_statement	recognizer_injector	derivation_composer	diagnostic_only	She studied for 2 hours on Wednesday and three times as long on Thursday.	candidate_graph: recognizer matched but produced no injection for sta...
0037	refused	recognized_no_injection	dcs_composition_wall	discrete_count_statement	recognizer_injector	derivation_composer	diagnostic_only	Michael wants to lose 10 pounds by June.	candidate_graph: recognizer matched but produced no injection for sta...
0039	refused	recognized_no_injection	dcs_composition_wall	discrete_count_statement	recognizer_injector	derivation_composer	diagnostic_only	Orlando gained 5 pounds.	candidate_graph: recognizer matched but produced no injection for sta...
0040	refused	recognized_no_injection	dcs_composition_wall	discrete_count_statement	recognizer_injector	derivation_composer	diagnostic_only	He now has 2 horses, 5 dogs, 7 cats, 3 turtles, and 1 goat.	candidate_graph: recognizer matched but produced no injection for sta...
0041	refused	recognized_no_injection	dcs_misroute_fraction_change	discrete_count_statement	recognizer_injector	fraction_of_prior	diagnostic_only	The guests eat all of 1 pan, and 75% of the 2nd pan.	candidate_graph: recognizer matched but produced no injection for sta...
0043	refused	recognized_no_injection	no_injection_currency_amount	currency_amount	recognizer_injector	currency_mutation	diagnostic_only	Her mother gave her an additional $4, and her father twice as much as her mother.	candidate_graph: recognizer matched but produced no injection for sta...
0044	refused	recognized_no_injection	dcs_misroute_fraction_change	discrete_count_statement	recognizer_injector	fraction_of_prior	diagnostic_only	John invests in a bank and gets 10% simple interest.	candidate_graph: recognizer matched but produced no injection for sta...
0045	refused	recognized_no_injection	no_injection_multiplicative_aggregation	multiplicative_aggregation	recognizer_injector	multiplicative_aggregate	diagnostic_only	Each survey has 10 questions.	candidate_graph: recognizer matched but produced no injection for sta...
0046	refused	recognized_no_injection	no_injection_descriptive_setup_no_quantity	descriptive_setup_no_quantity	recognizer_injector	relation_hypothesis	diagnostic_only	Half of the students are girls, the other half are boys.	candidate_graph: recognizer matched but produced no injection for sta...
0047	refused	recognized_no_injection	dcs_composition_wall	discrete_count_statement	recognizer_injector	derivation_composer	diagnostic_only	He then packs an equal number of the macaroons in 4 different brown bags, ready for delivery.	candidate_graph: recognizer matched but produced no injection for sta...
0048	refused	no_admissible_statement	numeric_expression_recurrence	—	statement_parser	recurrence_frame	downstream_reclassification	Every week, he gets 6 cards.	candidate_graph: no admissible candidate for statement: 'Every week, ...
0049	refused	recognized_no_injection	dcs_composition_wall	discrete_count_statement	recognizer_injector	derivation_composer	diagnostic_only	Malcolm is trying to find the fastest walk to school and is currently comparing two routes.	candidate_graph: recognizer matched but produced no injection for sta...
0050	refused	no_admissible_statement	numeric_expression_recurrence	—	statement_parser	recurrence_frame	downstream_reclassification	Mark does a gig every other day for 2 weeks.	candidate_graph: no admissible candidate for statement: 'Mark does a ...

Recommended next ratification candidate

Gate A2a unit partition / chunking primitive (within roadmap Gate A2 partition/chunking).

This is a ratification candidate, not an implementation decision. Implementation follows only after a ratification doc proves a shared narrow primitive with wrong=0 admission tests.

Why Gate A2a (evidence)

1. One confirmed DCS unit-partition misroute: case 0002 — 1000 feet split into 25-foot sections, blocked at recognizer_injector with dcs_misroute_unit_partition → candidate primitive unit_partition, movement downstream_reclassification.
2. Broader partition/chunk overlap exists but is not unified: heuristic tag partition_chunking also touches 0003 (multiplicative product) and 0035 (inverse residual question); parser-layer partition-adjacent cases include 0004, 0025, 0047. These do not share one primitive yet — ratification must name what is in/out of Gate A2a v1.
3. Inc3/Gate A1 precedent: closed injector buckets first with a ratified v1 template; aggregate 6/44/0 unchanged; movement is reclassification visibility.

Why this is ratification, not implementation

• Only one DCS misroute is confirmed for unit_partition on current serving code.
• Partition/chunk candidates appear across statement parser, question parser, and downstream composition buckets — implementation without ratification would smuggle scope (affine fractions, peer-pick questions, DCS composition wall).
• Ratification must prove a shared narrow primitive (total → chunk count → per-chunk unit) with exemplars, confusers, and wrong=0 replay before any injector/parser code.

Not next (explicit deferrals)

Track	Defer because
Gate A1b / Comparative-A2 (additive comparative)	Only one simple same-sentence DCS misroute (0016); no cluster of additive entity-comparison refusals at injector. Defer unless a future microscope pass finds ≥3 same-sentence more than / less than entity-comparison refusals with shared template.
Inc4 rate denom-state	Live rate cases refuse on overtime (0001), tariff (0017), profit/composition (0011 graph), not merely missing hour/kg/cup Initial. Downstream rate refusals = 2. Denom-state alone does not explain the frontier.
Broad DCS widening	14/19 DCS refusals are dcs_composition_wall → derivation_composer. Forbidden without a composition-wall ratification; metric-inert injector widening risks incomplete readings under wrong=0.
report.json rebaseline	Separate ratified PR only; pinned artifact remains historical 6/44/0 in this PR.

Gate A2a ratification seed (docs only — not ratified)

Candidate primitive names: unit_partition / partition_count / unitize

Template examples (from train_sample surfaces):

Surface pattern	Case hint	Notes
N total-units split into M-unit sections	0002: 1000 feet → 25-foot sections	Canonical Gate A2a exemplar
N beads per bracelet (yield/partition question)	0008: 50 beads → bracelets	Question-layer binding — may be out of v1
N crayons per box / residual box count	0007: boxes vs loose crayons	Inverse residual — likely out of v1

Open design questions (must be resolved in ratification):

1. Output unit: chunk count vs retained measure unit vs dual unknowns?
2. Divisibility: exact division required (0002: 1000/25) vs refuse non-integer chunk counts?
3. Fractional results: 1/4 given away + half stored (0002 full problem) — in v1 scope or composition follow-up?
4. Source grounding: total quantity referent vs chunk-size referent — which entity keys are grounded from the statement?
5. Inverse direction: “how many more boxes” (0007) — partition primitive or question-frame primitive?
6. Downstream question binding: per-chunk query (how much does she keep on hand) requires partition+remainder composition — v1 injector only or paired composition ratification?

Tests / validation (this PR)

git diff --check origin/main...HEAD
PYTHONPATH=. .venv/bin/python -m pytest tests/test_gsm8k_post_gate_a1_frontier_microscope.py -q
PYTHONPATH=. .venv/bin/python -m pytest tests/test_gsm8k_frontier_report.py -q
.venv/bin/core test --suite smoke -q

Explicit non-changes

• No Gate A2a implementation
• No Gate A1b / Comparative-A2 implementation
• No Inc4 denom-state
• No runtime / generate / solver / recognizer edits
• No report.json rebaseline