[bbMisk]

Change and mathematical scope

An individual E8 decoder term can cost six after 25 punctures when its normals are parallel roots. This package proves that every exact eight-term completion containing it costs at least 67 copies, and supplies an attaining completion. The minimum at 25 punctures over all exact eight-term complex decoders is 56, also attained. Thus the copy-cost floor extends from p<=24 to p<=25; the first dimension-seven support does not improve the complete copy invoice.

For arbitrary nonparallel complex normals with nonzero ordinary bilinear product, cost six first occurs at 26 punctures. This extends #1020's root-pair lower bound and reuses its credited attaining witness. No new kappa, physical supplier or selected-frontier change is claimed.

The written proof inherits #968's real E8 root-hyperplane classification F6. The finite replays establish its listed premises and examples; they are not a proof-assistant theorem or independent human review. Physical source/helper/frame/restoration costs, all-size/compiler realization, hosting, precision/tape, bit interfaces and analytic transfer remain outside this result.

Task and overlap

Base: ef5f39403610d231a0c27e8a6b4f08c10209bcd6. Contribution commit: 900658976e42a1501b3d23d46b2ea3cab228bc4c. OS assignment seed 31, complex-supplier track. Only research/complex-general-normal-boundary/ is added.

The scope is explicitly changed from the catalogue's complex-masked-decoder card to a deeper-puncture all-pairs boundary result. TASK.json records three candidates, the complete domain, stopping rule and local claim; no pinned coordination issue existed. The optimistic copy/port target fails before physical synthesis: 67/95 > 56/95 > 7/13.

The immediate pre-submission refresh covered 765 open PRs and 198 discussion records with complete pagination and no retrieval warnings; no competing result in this scope was identified.

Nearest work: #968/#1077 stop at 24 punctures; #1020 (bf4ee95df4ee6e3101a88f5d015c8aa85b688b6d) excludes only distinct nonorthogonal root normals through 25; #1180 extends factor-linear term counts only through 24. #1187/#1455 concern a prescribed P104 decoder at a different boundary. Exact source Git objects and SHA256 pins are in SOURCES.json; pending overlaps are not theorem premises.

Validation

python3.12 -B scripts/research_package.py --package research/complex-general-normal-boundary

Expected: PASS_REGISTERED_RESEARCH_PACKAGE research/complex-general-normal-boundary outcome=negative-result.

• Complete census of 7,560 boundary punctures, 63 per root, with verified symmetry transport.
• All 32,193 rational matrices checked by the primary integer-elimination replay and a separately written integer Gram-minor checker that imports no producer or predecessor code.
• Two complete 95-port decoder examples checked on all 18,050 live ordered pairs; all representative 67-copy completions checked.
• Eight primary controls and eight scoped tests reject wrong scale, undercharged bills, omitted cuts/functionals, false kernels/ranks and source corruption.
• Registered Python 3.12.2 replay passed on macOS arm64. Both checkers passed in an isolated read-only relocation under optimized Python 3.14.6. Source pins, selected-record integrity, Ruff and staged diff checks passed. VALIDATION.json binds the checked core files.

No full selected cold replay or native/hosted supplier admission was run. Hosted CI is separate from these local results.

Credit

Credit DreamingOfClouds (#717), themilkman216 (#968), woklerx (#1077/#1020), and the retained Rohan Arun/Jeremy Kothe/Hao Yan/bit-supplier lineage. The frame-pair attaining mechanism and 26-puncture witness retain predecessor credit.

Prepared by Hanson Sun (@bbMisk) with substantial OpenAI Codex assistance in research, proof, both implementations, verification and writing. Apache-2.0; frozen predecessor sources and upstream/ are unchanged.

Open next questions

The package README and TASK.json describe the unresolved complete decoder minimum at 26 punctures and a possible self-contained replacement for the cited F6 classification. Their first steps and blockers are explicit; neither is claimed completed here.

[Mister-Meeseeks]

Batch review at 900658976e42a1501b3d23d46b2ea3cab228bc4c.

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

Reviewed scope: Exact rank and symmetry certificates extend the conditional eight-term E8 decoder floor to 25 punctures and price cost-six parallel terms at total at least 67. The root-flat classification F6 remains an explicitly inherited premise; masked or overcomplete decoders are outside scope.

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.

[ywz65]

DONE: #2600 at ab07d67bf9c88fe72fccdc386bb39e3ff8fa681f supplies a self-contained chamber proof and independently checked finite certificate for the inherited F6 premise (Open next question 2). All 240 simple expansions, 1,920 reflection images, eight fundamental flats, 64 rational chamber fixtures, seven semantic mutants and Git-free/export controls pass. Arbitrary-real completeness is proved in the README; no new decoder floor or selected-kappa claim. Standard chamber method and original PR968/PR1521 contributors are credited.