[petalas]

Summary

336 alternating-plane ports
  84 orthogonal triples + 33 orthogonal pairs + 18 singletons
  -> exact fitting rank 135
  -> full-plane additive COPY mass 672

Finite exact construction with a scoped rank and tariff proof. The new fitting matrix has rank 135, 33 below the minimum of the spectral family cited in Ali Romman's merged #5624. Its indicator-block factorization still costs 672, so no COPY surplus, supplier admission or new kappa is claimed. The complete fitting minimum and optimality of 135 remain open.

This contribution was produced by Nick Petalas. Credit Ali Romman #5624 for the port geometry, fitting convention, spectral comparison and changed-matrix question. Credit Mark / Matarener, CubeJerry #4365, Ryanson Jonathan, Philippe Van Velzen, Cinna Davis, Adam Gall, Chris R / Clear1nsight, Chafik Boukhalfa, Rohan Arun, icekylinx and the retained full-plane/native lineage. Predecessor results are cited rather than audited or replayed.

The advance CLAIM sought a full 112-triple partition. The bounded backtracking and 45-second integer-program attempts produced no witness or exclusion. The first deterministic greedy construction gave rank 135, and further search stopped. The delivered scope is this explicit partial-clique partition.

Evidence

• Before: the cited fixed spectral family has minimum rank 168. After: the new block matrix has a literal 135-term factorization and an identity minor of order 135, over every scalar field.
• Complete checks cover all 112,896 fitting entries, 18,225 identity-minor entries, every source/reader support tariff and independent vector-pair/RREF plane enumerations. Eight rejection controls pass; three actual optimized CLI corruptions reject omitted coverage, a doubled coefficient and a lowered tariff.
• Local CPython 3.12.15, macOS 27.0.1 arm64: normal and optimized registered commands pass, timed separately at 0.435 and 0.431 seconds. Metadata/pins, exact committed bytes/source history, source compilation, official export integrity and both read-only Git-free exported replays pass. Generated stdout receipts bind all six package files. Ruff was unavailable.

Exact reproduction from the repository root:

/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -B -W error research/orthogonal-plane-triple-decoder/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -O -B -W error research/orthogonal-plane-triple-decoder/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/research_package.py --package research/orthogonal-plane-triple-decoder
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/check_research_commit.py --package research/orthogonal-plane-triple-decoder --check-source-history

Any CPython 3.12 interpreter can replace the absolute local path. The direct check prints PASS_ORTHOGONAL_PLANE_TRIPLE_DECODER rank=135 copy_mass=672; no solver or predecessor executable is required.

Limitations

The finite geometry, fitting matrix and declared additive support tariff are the entire result. Physical acquisition/delivery, native conversion, dirty restoration, ownership, compiler closure, routing, precision, stock, BIT compatibility and the complete outer caller remain unpriced. No Lean, Docker, selected cold replay, predecessor scientific replay, independent human review or formal proof-kernel review was run or claimed. The selected frontier is unchanged.

Open next questions

• Does a full 112-triple partition exist? The 1,120 admissible triples give an exact-cover starting point; the bounded searches here settle neither existence nor nonexistence.
• Can another exact fitting factorization have COPY mass below 672? Its complete support-pairing tariff and eventual physical caller must be supplied.

Related open work

The closeout refresh read the titles and bodies of all ten other open account PRs created since the advance CLAIM at 2026-10-27T15:15:06Z. None studies this 336-plane fitting matrix or computes a competing rank or COPY tariff for it. No extra computations were run to check those contributions.

• Prove hub excess 4h(h+1) for every hub count (no new κ) #5951 studies actual-reader charges in a P112 hub-star model, with a different port set and tariff contract; it does not compute this fitting rank or full-plane tariff.
• Speed complete Eisenstein replay by 35% with exact rational rank #5954 accelerates rational-rank calls in an Eisenstein verifier, a different matrix fixture; it does not change this 336-plane construction or its tariff.

#5624 is the merged source of the changed-matrix question and cited spectral comparison. Other P112 plane-port results use different port sets and masks. No numerical comparison with those objects is claimed. These publication searches do not cover unpublished work or arbitrary historical code diffs.

CI notes

Both hosted checks passed at f61985212dd751675aef38430eeaf36124eb6c8f in run 40530728452: plan in 4m41s and replay (research/orthogonal-plane-triple-decoder) in 1m50s. The completed checks were read once, and the run head matches the PR head.

The registered replay certifies the bounded package checks, not independent human or formal proof-kernel acceptance of the written proof. All local checks listed above passed. No CI failure remains.

Merge Danger

Door: two-way

Blast Radius: isolated

Six new files under research/orthogonal-plane-triple-decoder/. Shared code, frozen sources and the selected result are unchanged. Archive retention would not establish supplier admission.