Construction: one coded helper for all-K packet delivery

[NeoKazuya]

A six-source all-K packet cell can share partial sums through one coded helper while preserving arbitrary dirty inputs. This PR adds an explicit circuit, a strict paid-profile comparison, and a rebuild inside the native complex word. It also retains the analytic single-pair obstruction and resolves the broader positive no-helper search that previously timed out.

The selected cell is pair (6,7), sign +1, chosen from OS seed 23 and the recorded salt. Existing supplier files and the selected certificate are unchanged; the package is confined to research/complex-packet-borrowing23/.

Constructive result

• The one-helper cell has 28 core additions, five zero-frame preconditioning additions and two full-frame cleanup additions. Exact rational replay checks all 13 arbitrary input columns in forward and inverse-transpose orientations, with the dirty helper restored.
• Its paid profile is 32 H1 + 17 H2 + 11 H3. The specified direct circuit with the same helper left idle has 48 H1 + 12 H2 + 6 H3 + H9. Both have rank mass 99.
• The difference -16 H1 + 5 H2 + 5 H3 - H9 strictly improves every recursive moment sum H_r r^s, 0 < s < 1; the README gives an analytic inequality, not a numerical scan. The local scalar operation count is 35 versus 30, so this is a recursive frame-cost comparison.
• Both circuits rebuild inside the pinned raw K492 constructor with 490 helpers. The unchanged native auditor independently derives dirty-input compensation and verifies every one of the 714 columns in both orientations, all native frame chains and dyadic primitives. Both have rank mass 6,266, and their full native profiles have exactly the same difference as the cell.

Exclusions and solver follow-up

The analytic proposition excludes source-dependent interactions on a single target pair without helpers, allowing arbitrary signed coefficients, read order and repeated pair operations. It binds to all eight signed all-K cells through explicit XOR-span checks and finite ordering controls.

An event-clock reformulation resolves the six-source no-helper search with arbitrary target-sharing graphs in the narrower positive unit-addition, disjoint-support domain. Z3 5.1.0 and CVC5 1.4.2 both return UNSAT on the same exported formula, in approximately 12.4 and 130.7 seconds. Direct-only and omitted-frame controls return SAT. The optional model, formula hash and solver receipts are included; no independently checked UNSAT proof object is claimed. The explicit constructive witness is verified without solver dependencies.

Validation

python3 -B research/complex-packet-borrowing23/verify.py

Passed on Python 3.13.5 and 3.14.0, including -I -O and a relocated minimal checkout with PYTHONOPTIMIZE=2; inherited workers always run with assertions enabled. Changed source pins, corrupted expected evidence and altered assignment data are rejected. Circuit controls reject missing compensation, cleanup and helper delivery. The packaged optional model reproduces the exact formula hash checked by both solvers.

Scope and credit

No new κ, globally admitted supplier, optimal circuit or general coding barrier is claimed. The native words are changed raw constructions; the later supplier transformations, phase lowering, wrappers, global owners and assembly have not been rebuilt for them. The comparison is against the specified matched-stock direct control, not the admitted incumbent.

The constructor, native auditor, source data and routing word are pinned and retain their upstream attribution. The package credits the #425/#433/#484/#531/#552/#622/#626 lineage and distinguishes the related scopes of #651 and #683. Prepared by NeoKazuya with substantial OpenAI Codex assistance (GPT-6-Astra), under Apache-2.0.

[Mister-Meeseeks]

100-PR batch review at 85f9cfad7708cc3873bd6b32492a618feb336e59.

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

Reviewed scope: One-helper complex packet cell: complete dirty-state restoration, both operand frame propagation and strict moment comparison; native/global admission remains separate.

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.