Research: diagonal rank-16 batches under register commutation, 134 not 8 (audit of #1779; no κ claim)

[JosieElliston]

Audit of one implication in open PR #1779. No new κ; the selected record is unchanged.

PR #1779 (1337isnot1337, head 1e3128bf) counts 8 rank-16 diagonal batches of rank-1 climbs in the selected gauge44 provider. That gives +1.72% on the zero-charge ceiling, below the complex-rank-shape-decoder 5% gate. The count uses only contiguous runs: any computational event breaks a run, and chunks are 16-aligned.

That restriction, not the provider, makes the count small. A rank-1 climb on L r touches only L r, so inside its phase it can move past events that do not touch L r. Allowing only that move gives:

• 134 disjoint 16-batches on distinct destinations per orientation (earliest-deadline greedy; 2,144 of 2,412 rank-1 climbs). The per-phase cap is 149; by phase A 58/58, B 52/67, cleanup_tail 4/4, final 20/20.
• The retained independent local checker (research/complex-571-cold14-k492b/code/hpe_audit_local.py, unchanged; literal scalar/frame/wrapper replay with 25 mutation controls) accepts the reordered programs. Their receipt equals the original's, which equals the pinned selected INDEPENDENT-LOCAL-REPLAY.json. Two added mutations are rejected: a climb moved past a scalar on its own register, and a climb moved into the next phase.
• PR Research: source-bound screen of diagonal rank-16 child batches #1779's own contiguous rule, re-implemented, counts 8 on the original programs and 134 on the reordered ones.
• Exact ceilings (ceiling.py, grid 10⁻¹⁵, Research: source-bound screen of diagonal rank-16 child batches #1779's mass-preserving zero-charge convention): 22 batches miss the gate (+4.87%), 23 pass (+5.11%), and 134 give a < 0.002358018698467 (+39.5%).
• Sharp charge headroom at 134 batches under discussion 1596's idle-displacing convention: 1,258 extra rank-1 children per call pass the gate and 1,259 fail (about 9.4 per batch).

What this changes. The selected chronology does not close the diagonal-batch route below the gate. The route is decided by the charge #1779 waived: gathering 16 registers at different frames into one diagonal rank-16 child, plus copies, frames, hosting, storage, precision and dirty restoration. This package inherits #1779's diagonal-child premise and does not examine it. Batch counts are a greedy lower bound. The bit supplier binds well before +39% (#1605).

Task card. Chooser seed e37fae49558c99b32d319ec695f4f266, track complex-mechanisms, card complex-rank-shape-decoder, scope refined to an audit of #1779 (reason in TASK.json). Base 0b1cccf86e2f5132ed286a26ef0a681a495740ea. Same archive and member pins as #1779. Claim and finding: #1596 (comment)

Reproduce

python3 -I -B research/diagonal-batch-commutation/verify.py      # ~12 s, PASS_DIAGONAL_BATCH_COMMUTATION
python3.12 scripts/research_package.py --package research/diagonal-batch-commutation

Checked on Python 3.10 and 3.12. The package check and replay pass, and test_research_*.py passes (42 tests). This is a finite certificate on the pinned programs, not a construction. Not checked: the physical contract of a diagonal rank-16 child, any gathering/restoration charge, whether global hosting and the idle-remainder frame audit (which use helper busy windows) are insensitive to positions inside a phase (only local replay was re-run), the on-top charge convention, the exact phase-B maximum, full selected cold replay, and independent review.

Open next questions (in the README): what a diagonal rank-16 child of frame climbs at different frames costs, set against the 1,258-unit headroom; the on-top convention headroom; and the exact phase-B maximum (52–67).

Credit: 1337isnot1337 (#1779, diagonal batching premise and contiguous count); Arham Tahir (#1605 / discussion 1596, rank-shape budgets); Douglas Colkitt (#1240 packing ceiling); PR1012 (coverage law); the icekylinx / PR514 / PR433 local-checker lineage; the selected construction lineage.

AI assistance: prepared for Josie Elliston by Claude Code (Claude Opus 5.5) in one donated session, with no independent review.

🤖 Generated with Claude Code

[Mister-Meeseeks]

Batch review at ac3a759e874e8e526bc884fc2cb8eb114695b063.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: Dependency-respecting local commutation constructs134 disjoint16-way batches versus8 contiguous batches, with unchanged independent local semantics/profile replay. Greedy count is attained locally, not optimal; diagonal child realization and global hosting remain unproved. Relaxed39.5% complex ceiling is not a kappa result.

The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions.

Batch review, attribution and evidence. Thank you for the contribution.