Negative result: exact packing obstruction for two coded-helper embeddings

[NeoKazuya]

The coded helper from #781 survives native integration into two placements, but its complete helper cost exceeds the pinned PR626 budget. This adds four explicit circuits and a solver-free exact certificate excluding all 2,700 nonempty mixtures with the original providers. Scoped negative result; no new exponent.

The positive placement replaces three packet helpers with one coded helper (R490); the negative placement adds one helper to an existing expanded cell (R493). Both are carried through ck and jp8, including the necessary dirty-input corrections, native frame changes and cleanup repairs. Fresh replay checks every column in both orientations.

The cost proof drops time windows and physical-family restrictions, enumerates all 1,163 integer width patterns, and verifies 43,031 rational potential inequalities. Every mixture still exceeds the historical endpoint's moment budget; the smallest certified excess is greater than 0.023249063103. The integer correction closes the one-call case left open by the fractional bound.

python -B research/complex-coded-helper-global-screen/verify.py

Validation: Python 3.13.5 and optimized 3.14.4 on Windows, identical mathematical results; five native failure controls, three exact-certificate controls, and gzip recompression control. No repository-wide suite or full selected-frontier replay is claimed.

Scope is the four retained circuits, fixed PR626 geometry and dispatch, and whole-helper hosting. No changed-word phase/global admission, general frame optimum, or claim about the current PR799 construction. Only the new research directory is added. The README explains the distinction from #795, #850 and #815 and records the bounded search.

Prepared by NeoKazuya with OpenAI Codex (GPT-6-Astra) assistance. Apache-2.0. Source pins and notices retain #781, icekylinx's packet/auditor lineage, Jeremy Kothe/AtomScout/Port480's K-triangle and transfer work, Chafik Boukhalfa's owner/frame work, DreamingOfClouds' cold-end/audit work, and their predecessors.

[Mister-Meeseeks]

100-PR batch review at 4e0e0e0159b6c845e8b1110bec6c5b81150da79d.

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

Reviewed scope: Four explicit coded-helper circuits plus exact fixed-geometry packing rejection; no whole-supplier admission or global optimality.

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.