Records the increment-1 outcome straight (band-solve=0, ~30-band bet
falsified; foundations = banked byproduct not success) + the minimal-band
measurement: no small band converts; taxonomy not at bedrock (GSM8K statements
are per-sentence multi-capability); multi-compound highest-leverage (70/106
tractable needed-sets) but insufficient alone; q:complex biggest intractable
wall (~35 cases). Increment-2 recommendation = CASE-FIRST (target specific
closest cases, build their exact end-to-end needs) not capability-first, since
the taxonomy fragments. Foundations verified full-500 wrong=0, smoke 176.
The two reusable foundations of increment 1, both verified wrong=0:
- NEUTRAL_COUNT_VERBS (math_roundtrip): the shared positive-polarity ALLOWLIST
(production/acquisition/possession-count verbs), fail-closed. Extends ADD_VERBS
with curated neutral production verbs (score/write/teach/plant/harvest/produce/
draw/sing). Depletion/transfer (SUBTRACT/TRANSFER_VERBS) excluded by positive
determination — 'Alice lost twice as many' refuses, not via a blocklist.
- Seed reader: discrete_count matcher acquisition path aligned to the allowlist
(made/baked/grew/scored/wrote/taught now inject; depletion refuses).
- Comparison reader: _comparison_anchor_verb() allowlist extended to the same
NEUTRAL_COUNT_VERBS (keeps fail-closed; captures scored/caught/wrote frames).
Verified: production injects, depletion refuses; 71 pinned comparative tests
pass (polarity guards now via allowlist); tune wrong=0; smoke 176 green.
FINDING (measured 4 ways: yield harness, band map, band oracle, capability
histogram): band-1 as scoped {seed + forward-comparison + q:simple/summation}
converts 0 tune cases. Its otherwise-in-band cases STRAND on multi-compound (25)
and compare-additive (17) — capabilities outside the ~30 band. The conjunction
recurs at sub-capability granularity; the band-map taxonomy was too coarse.
Foundations validated + reuse-ready (done-when part 2); band-solve>0 (part 1)
needs the band to grow to +compare-additive(+multi-compound) — a scope/done-when
ruling for Josh. No merge until ruled.
Design-first plan, ruling before any build (same gate as #76). Band =
foundational spine core: seed-simple + comparison + question-arithmetic
(simple/summation/difference), on the shared #78 polarity substrate.
Bakes in Josh's four refinements: (1) deliberate ~30 smaller-band rationale
(first end-to-end reader conversion ever + two reusable foundations, zero new
hard capabilities beyond #78); (2) done-when reset to band-solve>0 wrong=0 +
foundations validated, ~40 bar cumulative across increments 1-3; (3) haircut
factor (real/upper-bound) as a named output; (4) TWO wrong=0 direction drivers
— #78 statement polarity AND q:difference question direction, both positively
determined + fail-closed. Grounds design on what EXISTS (question layer partly
built: summation works, q:difference partial). Schedules q:complex decomposition
next (may be corridor-tractable, could move the ~48% ceiling).
