Research: source-bound screen of diagonal rank-16 child batches

[1337isnot1337]

The selected #1094 gauge44 provider has 2,412 rank-one children per orientation. This package tests a cross-column construction: sixteen adjacent rank-one child climbs on distinct destinations can be represented by one rank-16 child using diagonal block matrices. The hash-pinned chronology permits eight such groups (128 rank-one children). Even after waiving every new interface expense, the best local ceiling rises only 1.7191%, below the task's 5% gate. The result is a scoped construction screen; it claims no physical supplier or new κ.

Construction and bounded result

For block inputs X_i,Y_i, the exact identity

M16(diag(X_1,...,X_16), diag(Y_1,...,Y_16))
  = diag(X_1 Y_1,...,X_16 Y_16)

preserves the sixteen requested products; all off-diagonal outputs vanish. The provider trace has one contiguous run of 16 and one of 112 rank-one climbs, partitioned into seven more groups of 16. Both forward and backward orientations have the same windows. No child crosses a scalar, adapter, centre, or other-rank event.

The mass-preserving profile changes from {1:2412, 2:418, 3:432, 4:142, 5:82, 8:8} to {1:2284, 2:418, 3:432, 4:142, 5:82, 8:8, 16:8}; both have rank mass 5,586. The exact ceiling upper endpoint moves from 1690054109089/10^15 to 1719107428154/10^15 (gain 1.7191%). The 5% target is 0.00177455681454345, so the bounded family fails before adding the actual gathering, copies, frames, hosting, output storage, precision, or arbitrary-dirty restoration charges.

Pins and overlap

• Seed 95da2249593d8218c4c1e30f471d675f, track complex-mechanisms, card complex-rank-shape-decoder refined to contiguous cross-column diagonal batches, priority revision 3.
• Exact base 0b1cccf86e2f5132ed286a26ef0a681a495740ea; selected-record SHA-256 10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32.
• Selected replay archive SHA-256 f1da80610bf33c58527f18ad63b4350d0b864e1d4486141ee17ac9bed4d529d6; gauge44 provider member SHA-256 241fde27d4e43f5a9cb6b128f9f76c5131a53d09f0371676163f914d0b0fef3a.
• This complements Arham Tahir's open PR #1605 (head 488f2ecf1835c6d813e96543656dddf0062fdc9a) and Discussion #1596: their integer reblocking price leaves chronological batches open; this package bounds a source-exact, cross-column diagonal subfamily. It is distinct from the same-column frame assignment screens in Discussion #1659/PR #1686 and the one-touch same-column retiming of Discussion #1693/PR #1703.

Reproduction

python3 scripts/research_package.py --package research/complex-diagonal-child-batches-seed95da --check-only
python3.12 scripts/research_package.py --package research/complex-diagonal-child-batches-seed95da

Local registered replay passes: PASS_COMPLEX_DIAGONAL_CHILD_BATCH_SCREEN groups=8 rank1_repacked=128 profile_mass=5586 ... gain_percent=1.719076 target_percent=5 controls=3.

The physical M16 interface remains unimplemented: it would need its input/output storage, source and copy schedule, frames, hosting, precision and restoration charged. The selected result is unchanged. Next, any larger gain needs a pinned operand-ready/use-window model for nonconsecutive buffered batches and an end-to-end invoice.

Credit Sagar Thakrar/PR1012, Douglas Colkitt/PR1240, Arham Tahir/PR1605, Josie Elliston/Discussion #1596, Navinor/Discussion #1659 and the selected construction lineage. Prepared by Jose Manuel (@jmbarrancoml) with substantial OpenAI Codex assistance in source analysis, mathematical formulation, verifier, and writing; no subagents.

[JosieElliston]

Pointer from an audit of this PR's batch count: #1817 (no κ claim).

The 8-batch maximum here comes from the contiguous-run rule. A rank-1 climb on L r touches only L r, so it can move inside its phase past events that do not touch L r. With that move the same pinned gauge44 programs give 134 disjoint 16-batches on distinct destinations per orientation (per-phase cap 149). The retained hpe_audit_local.py accepts the reordered programs with an unchanged receipt. Your own contiguous rule counts 134 on them. Under this PR's zero-charge convention, 23 batches already pass the 5% gate, and 134 give +39.5%.

So the README's "bounded family fails" depends on the run restriction. The waived gathering, frame and restoration charges are what decide the route. Details: #1596 (reply in thread)

[Mister-Meeseeks]

Batch review at 5577f27d54355bc916efe0a23128dd0e0c169434.

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

Reviewed scope: Both pinned orientations contain only eight uninterrupted16-child batches on distinct destinations. Optimistic rank16 replacement preserves rank mass and raises the relaxed ceiling only1.7191%, below the5% screen. Diagonal identity and exact moment price checked; actual gathering/child/storage/restoration implementation absent.

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.