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Classify sharp P104 frame-pair spectra and extend them to Hermitian metrics - #6284

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CubeJerry:research/p104-frame-metric-spectra-20261030-s31
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CubeJerry wants to merge 1 commit into
CrocSwap:mainfrom
CubeJerry:research/p104-frame-metric-spectra-20261030-s31

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@CubeJerry

@CubeJerry CubeJerry commented Oct 30, 2026 •

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All disjoint E8 frame pairs form exactly three isometry classes, with sharp common-metric energy constants 37, 37, and 75/2. The selected #6030 ports belong to the 75/2 class. Certify every spectrum and equality space, including an irrational four-dimensional block. Extend the constants unchanged to complex Hermitian metrics by an exact skew-energy identity. New beyond #6278's uniform real bound: complete orbit classification, selected-orbit improvement and Hermitian scope.

Base: 2485805.
PR6278 comparison: 5badad3. Selected word and all exact source hashes: SOURCES.json.

Reproduce (Python 3.12, stdlib):
python3 -B scripts/research_package.py --package research/p104-selected-metric-orbit
Expected: PASS_REGISTERED_RESEARCH_PACKAGE.

Executed: all 2025 frames and 1260 disjoint partners, three complete spectra, root moments and sharp attainers; independent A8 rational spectrum/skew checks and separate clique enumeration. Eight normal/-O commands, reproducible certificates, source/history/modes/export and unchanged read-only Git-free replay pass. Controls reject omitted frames/edges, wrong normalization, corrupted spectral blocks, stronger constants and actual source corruption. Fixed exhaustive domain, no random seed; stop at complete classification, with no remainder in that domain.

No new κ. This is absolute unnormalized common-metric geometry, not a decoder or supplier. Independent port motions, normalized correlations, physical implementation and complete cost accounting remain open; all five framework assumptions remain.

By @CubeJerry with substantial OpenAI Codex assistance: worker A, worker D independent classification/spectra, worker C Hermitian review and lead. Credit Nick Petalas (#6278, Matarener (#6166), DreamingOfClouds (#6030), Ali Romman and retained rigidity/E8 lineage. No human or proof-kernel acceptance.

Proof, exact pins, controls and limitations: https://github.com/CubeJerry/integer-mult-bounds/tree/4cf130657160d6b923c0b13d8a0308bd35f79d42/research/p104-selected-metric-orbit
Complete remote Git tree matches the tested contribution.

Prepared for @CubeJerry with coordinated OpenAI Codex assistance.
Credit Nick Petalas PR6278, Matarener PR6166, DreamingOfClouds PR6030,
Ali Romman and the retained E8/P104 lineage. No new kappa.
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