core/docs/analysis/gsm8k-capability-paradigm-sprint12-lookback-2026-06-17.md

GSM8K Capability Paradigm Sprint 12 — Lookback (2026-06-17)

1. Starting baseline

Metric	Value
correct	24
refused	26
wrong	0

After #824 (Sprint 11 calendar ClusterContract). Prerequisite satisfied.

2. Experience Flywheel output summary

scripts/gsm8k_experience_flywheel.py --limit 50 --out /tmp/gsm8k-experience-sprint12.json

Field	Value
retained_record_count	50
lift_refused_to_correct	0
scout serving	24 / 26 / 0

Top singleton signals:

• 0004 — joint_refusal, fraction_surface, not_promotable; no sealed-wrong on surface.
• 0007 — joint_refusal, unbound_target, not_promotable; no sealed-wrong on surface.
• Blocked families unchanged: sealed_elimination (0011, 0026), relation_hypothesis (0032, 0047), currency.
• No second calendar sibling under Sprint 11 contract.

3. Scout/frontier/microscope output summary

Regime	correct	refused	wrong
Serving	24	26	0
Sealed (resolve_pooled)	3	39	8

• lift_refused_to_correct: 0
• Dominant bottleneck: joint refusal (20/50)
• Sealed-wrong unchanged: 0011, 0018, 0019, 0025, 0026, 0028, 0032, 0047

Microscope: 0004 tagged fraction_operand; 0007 tagged conditional_question. Adjacent sealed-wrong neighbors 0026 and 0047 on distinct surfaces.

4. Candidate families ranked

Rank	Candidate	Lift	Wrong-risk neighbor	Verdict
1	nested_fraction_remainder_total (0004)	+1	0026 sealed_elimination	Selected (A2r)
2	loose_crayon_box_capacity (0007)	+1	0047 DCS/divisive	Selected (A2s)
3	calendar contract extension	+0	—	Rejected (no second sibling)
—	DCS / currency / sealed_elimination wholesale	—	blocked	Deferred

0004 and 0007 rank equally on flywheel; both admitted with hard neighbor confuser matrices.

5. ClusterContracts

nested_fraction_remainder_contract (Gate A2r)

ClusterContract:
  family_id: nested_fraction_remainder_total
  proposed_organs:
    - nested_fraction_remainder_total
  included_cases:
    - gsm8k-train-sample-v1-0004
  explicitly_excluded_cases:
    - gsm8k-train-sample-v1-0026  # sealed_elimination / currency / scoops
    - gsm8k-train-sample-v1-0011  # sealed_elimination
    - asks subgroup only (not root altogether)
    - multiple fraction relations
    - 3/4 bill-of-money surfaces
  positive_anchors:
    - "Half of the {population}"
    - "1/4 of the {population} going to {camp} camp"
    - "{camp} camp in the morning" + afternoon complement count
    - question asks root {population} altogether
  negative_anchors:
    - $ currency / each saved / scoops / bill / ice cream
    - 3/4 of total money
    - asks soccer-camp subgroup only
    - multiple fractions
  actor_binding_rule: shared population token across half/quarter/afternoon clauses
  target_binding_rule: question must ask root population altogether
  unit_binding_rule: afternoon count unit matches bound population
  quantity_obligations:
    - text-grounded afternoon complement count
    - exactly one 1/4 inner partition
  allowed_external_grounding: none
  blocked_sibling_families:
    - sealed_elimination
    - currency_amount
    - percent_partition
  sealed_wrong_neighbors:
    - 0026 (blocked by currency/each/scoops/3/4 bill hazards)
  serving_admission_rule: resolve_promotable_nested_fraction_remainder_total()
  implementation_allowed: true
  reason: Typed morning/afternoon complement chain + 0026 confuser matrix clears wrong-risk.

loose_crayon_box_capacity_contract (Gate A2s)

ClusterContract:
  family_id: loose_crayon_box_capacity
  proposed_organs:
    - loose_crayon_box_capacity
  included_cases:
    - gsm8k-train-sample-v1-0007
  explicitly_excluded_cases:
    - gsm8k-train-sample-v1-0047  # equal-distribution weight / eaten bag
    - asks per-box capacity (not more boxes)
    - equal number in bags
    - weight/ounce surfaces
  positive_anchors:
    - "{actor} has N full boxes of {item}"
    - "M loose {item}" before friend clause
    - "friend has K loose"
    - conditional "total of T" in question
    - "how many more boxes"
  negative_anchors:
    - ounces / macaroons / equal number / eats / Steve
    - asks per-box not more-boxes
    - DCS divisive packing
  actor_binding_rule: primary actor owns full boxes + loose; friend contributes loose only
  target_binding_rule: question asks additional boxes for all loose items
  unit_binding_rule: answer unit is boxes
  quantity_obligations:
    - total, loose_primary, loose_friend, num_full_boxes all text-grounded
  allowed_external_grounding: none
  blocked_sibling_families:
    - multiplicative_aggregate / DCS
    - currency_amount
  sealed_wrong_neighbors:
    - 0047 (blocked by weight/equal-number/eaten-bag hazards)
  serving_admission_rule: resolve_promotable_loose_crayon_box_capacity()
  implementation_allowed: true
  reason: Capacity derivation from boxed portion + loose aggregation; 0047 confuser matrix holds.

6. Blocked families and why

Family	Blocked because
calendar extension	No second train_sample sibling under #824 policy
DCS 0032/0047	sealed-wrong; relation_hypothesis blocked
currency 0019/0028	sealed-wrong
sealed_elimination 0011/0026	sealed-wrong
wholesale multiplicative_aggregate	0025/0047 sealed-wrong

7. Research gate decision

Proceed with two independent singleton ClusterContracts (A2r + A2s). Calendar extension rejected for lack of sibling evidence.

8. Selected paradigm

Dual singleton organs under explicit contracts:

1. generate/derivation/nested_fraction_remainder_total.py — Gate A2r
2. generate/derivation/loose_crayon_box_capacity.py — Gate A2s

Wired in generate/math_candidate_graph.py after Gate A2q.

9. Typed chains for target cases

0004 (gold 2000):

• afternoon = 750 kids (3/4 of soccer-camp subgroup)
• subgroup = 750 / 0.75 = 1000
• total = 1000 × 2 = 2000 (half go to soccer camp)

0007 (gold 2):

• boxed = 85 − 5 = 80
• per_box = 80 / 5 = 16
• loose_total = 5 + 27 = 32
• boxes_needed = 32 / 16 = 2

10. Implemented organ(s)

Module	Gate	Promotion entry
nested_fraction_remainder_total.py	A2r	resolve_promotable_nested_fraction_remainder_total()
loose_crayon_box_capacity.py	A2s	resolve_promotable_loose_crayon_box_capacity()

11. Before/after score

Metric	Before	After	Δ
correct	24	26	+2
refused	26	24	−2
wrong	0	0	0

State A achieved: 26/24/0.

12. Newly solved IDs

0004, 0007

13. Preserved solved IDs

0001, 0002, 0003, 0005, 0006, 0008, 0009, 0010, 0013, 0014, 0015, 0017, 0018, 0021, 0024, 0025, 0029, 0030, 0035, 0037, 0038, 0042, 0045, 0046

14. Wrong=0 proof

• Full train_sample replay: 26 / 24 / 0
• tests/test_math_candidate_graph_sprint12_singleton_contract_lift.py
• Holdout_dev: wrong=0
• Regression lane: sprint6–12 + flywheel + scout + microscope

15. Confuser matrix

Confuser	Organ	Result
0026 sealed_elimination	A2r	refuse
asks subgroup only	A2r	refuse
multiple fractions	A2r	refuse
0047 equal-distribution weight	A2s	refuse
asks per-box capacity	A2s	refuse
equal number in bags	A2s	refuse

16. Sibling generality proof

Sibling	Expected	Result
music camp / 600 afternoon	1600	pass
four marker boxes / 67 total	6 boxes	pass

17. Sealed-wrong negative evidence used

• 0026: currency + each + scoops + 3/4 bill → A2r hazard refusal
• 0047: ounces + equal number + eaten bag → A2s hazard refusal

18. Composition-validation pin changes

None.

19. report.json untouched

Confirmed — no changes to committed report.json.

20. sealed artifacts untouched

Confirmed — no sealed lane artifact movement.

21. no case-id logic

Confirmed — admission via structural anchors and bindings only.

22. no hardcoded answer

Confirmed — arithmetic recomputed from grounded quantities.

23. no direct-answer shortcut

Confirmed — self-verified derivation chains required.

24. ClusterContract method enabled bigger lift

Yes — bundling two narrow singleton contracts under explicit neighbor exclusions delivered +2 with wrong=0, exceeding single-organ sprint cadence.

25. Sprint 13 recommendation

1. Practice-lane mini-family clustering — flywheel joint_refusal clusters (20 cases) may yield a 2-case mini-family safer than next singleton.
2. Deferred blocked surfaces — DCS 0032/0047 and currency 0019/0028 remain blocked until dedicated confuser ADRs land.
3. Calendar contract — revisit only if practice lane surfaces a genuine second piecewise sibling without policy expansion.
4. Target: 27+/23-/0 via one mini-family or two verified singletons with lowest sealed-wrong adjacency (candidates from flywheel: 0004/0007 neighbors exhausted; next scout frontier TBD).