[petalas]

Summary

Certify the exact coordinate-permutation stabilizer of the literal 104 P104 ports. It has order two, generated in zero-based coordinates by (0 3)(2 8)(4 7)(5 6). Consequently coordinate-only symmetry can identify at most two frame candidates. The exact plane quotient has 21,915 orbits, including 395 fixed planes.

literal P104 port set
  enumerate all 9! coordinate permutations
    exact stabilizer {identity, sigma}
      enumerate binary frames and count sigma-fixed frames
        exact Grassmannian quotient in every dimension

Claim type: finite certificate with a scoped counting proof. The written section-counting argument treats square-zero maps, then applies classical Gaussian subspace counting and orbit counting to this source. Proper invariant frames exist; this does not prove a full-dimension shared-frame obstruction. The new contribution is the exact source-specific group, its invariant-frame profile and the resulting limit on coordinate-only search compression.

Only six files in research/p104-coordinate-symmetry/ are added. The coverage-law card is explicitly changed to this geometry side result. This contribution was produced by Nick Petalas. Credit Matarener/PR6166 for the retained port list and E8 interpretation, Ali Romman/PR5827 and DreamingOfClouds/PR5907/PR6030 for the credited local-word lineage, and the retained decoder/native/compiler/outer contributors. No predecessor theorem or scientific replay was audited.

Evidence

Before quotienting, the plane domain has 43,435 elements. The exact coordinate action gives 21,915 classes. This is a finite equivalence-class count, not a measured runtime improvement. The fixed-frame counts in dimensions zero through nine are 1,31,395,1955,4371,4371,1955,395,31,1.

Local checks at 98bc47f847488c7909c6a80308998c792fd6a903, CPython 3.12.15, standard library:

• All 362,880 permutations, including all 960 survivors of the first weight filter; both final survivors preserve every original port.
• All 8,283,458 binary subspaces across all ten dimensions, with direct basis-invariance tests independent of the written counting formula. Sixteen small Jordan-type domains add 12,668 frames.
• Seven rejection controls and seven semantic controls pass in normal and optimized modes. Generated source/package-hash receipts are identical. The registered commands take 14.52 s and 15.01 s locally, each below its 180 s limit. These are check durations, not benchmark claims.
• Metadata/source pins, exact committed bytes, owner-execute modes and full source-history ancestry pass. Official seven-payload-file export integrity passes. Both direct modes pass in a read-only Git-free export with an empty executable PATH; all eight exported files, including the transport receipt, retain their bytes and modes.
• The current source-binding orientation prints PASS_RESEARCH_BASELINE_BINDINGS_ONLY; this is metadata orientation rather than a selected scientific replay.

From the repository root:

/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -W error -X dev -B research/p104-coordinate-symmetry/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -O -W error -X dev -B research/p104-coordinate-symmetry/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/research_package.py --package research/p104-coordinate-symmetry
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/check_research_commit.py --package research/p104-coordinate-symmetry --check-source-history --check-modes

A different CPython 3.12 executable may replace the interpreter prefix. The verifier emits PASS_P104_COORDINATE_SYMMETRY with errors: 0 and writes nothing. The package runner emits PASS_REGISTERED_RESEARCH_PACKAGE; the publication check emits PASS_RESEARCH_COMMIT_BYTES.

Limitations

The group is restricted to permutations of the nine literal binary coordinates. General binary linear stabilizers, signed root symmetries in other coordinates, changed port sets, and groups permuting several distinct frames are outside scope. A frozen caller may retain only the identity. No productive helper capacity, paid word, chronological delivery/restoration, native realization, precision/tape, stock, compiler, supplier admission or complete multiplication theorem is established. Selected cold replay, Lean, Docker, independent human review and formal proof-kernel review are unrun. The selected frontier and all five framework assumptions remain unchanged.

Open next questions

• Recover the full binary linear port stabilizer from incidence and intersect it with one actual caller contract. This may offer a larger quotient; port symmetry alone does not establish a legal word relabeling.
• Choose one proper invariant frame and one causal cut, then derive independent delivery, restoration and a complete signed invoice. The frame census provides candidate geometry rather than physical credit.

Related open work

• research: P104 B-form floor follow-up: RootFact/SpanFact proved (hand + Lean), Cases II/III without the census (no κ claim) #6218 proves P104 B-form root/span facts and decoder cases; this contribution computes a coordinate action and its frame quotient.
• research: P104 wire routing obstructions (scoped negative, no κ) #6217 studies P104 wire routing and A2 covers; this contribution concerns coordinate permutations of its underlying port object.
• Prove the P104 disjoint A2 packing maximum is 33 (no κ) #6219 determines the disjoint A2 packing maximum; this contribution concerns frame orbits rather than triangle packing.
• Prove sharp 68-point E8 plane unions and isolate the P104 puncture step (no κ) #6221 bounds quadratic live-set unions and isolates the P104 puncture step; this contribution uses literal binary-coordinate permutations.
• Prove E8 span inputs over every odd-characteristic field (no new κ) #6198 proves E8 span inputs across odd characteristics; this contribution works over F2 and counts invariant binary frames.
• Prove sharp 1/4 error for every real rank-seven P104 approximation (no κ) #6191 studies real rank-seven approximation of the P104 Gram block; this contribution counts exact label symmetries.
• Exhibit complex rank-seven P104 approximations below the real 1/4 floor (no κ) #6211 studies complex rank-seven approximation of the same Gram block; this contribution supplies no approximation bound.
• Independent audit of #6144 and #6167: replay, deltas, invoice, full dense native, caller and funding all pass (κ 0.003128645 corroborated, no new κ) #6214 audits the PR6144/PR6167 words and funding; this contribution leaves those words and invoices unchanged.
• Exclude birth-lowered P104 markets without paid deletions (no κ) #6197 excludes a fixed class of birth-lowered P104 markets; this contribution bounds a different coordinate-symmetry relaxation.
• Exclude arbitrary-plane temporal rails on the fixed PR1094 word (no κ) #6223 closes arbitrary-plane temporal rails on the fixed PR1094 word; this contribution supplies no rail price or temporal-closure invoice.
• Construct optimal 39/8-bit P104 labels with length-preserving updates #6224 codes a P104 defect signature with length-preserving updates; this contribution concerns the nine-bit port-coordinate action.
• Conditional κ 0.00309871 from a prepared P104 split helper #5606 proposes a prepared P104 helper split; this contribution supplies no changed supplier invoice.
• Two successor hand-offs on the P104 word: conditional κ 0.0030428242 #5553 proposes two P104 word handoffs; this contribution supplies a coordinate-symmetry side result.
• Draft construction: P104 dirty-restored gather and low-rank channel with COPY56 (no new kappa) #1972 constructs a dirty-restored P104 low-rank channel; this contribution supplies finite symmetry information for the underlying port geometry.
• research: price full P104 end-cut correction #3894 prices a complete P104 end-cut correction; this contribution establishes no correction tariff.
• Research P104 singular-mixing lifetime floor #3907 reviews P104 singular-mixing lifetime floors; this contribution establishes a coordinate-search quotient.
• Add P104 flag 0 coefficient transport audit #3915 audits one P104 flag coefficient; this contribution imports no flag transport or coefficient claim.
• Non-dense fitting B: every E8 term with x·y ≠ 0 has rank ≥ 9; square root-code floors E8 ≥ 72, P112 ≥ 64, P104 ≥ 56, D4 ≥ 12 for any fitting B (no κ claim) #3045 studies fitting-pairing decoder floors including P104; this contribution computes a different finite invariant.
• Decoder floors: universality, projection transfer and batching reductions; C(P112) ≥ 64 reduced to named conjectures, C(P120) ≥ 72 restated on N₀ (no κ claim) #2832 studies decoder projection/batching reductions including P104; this contribution supplies no decoder-cost bound.
• Tooling: 3.09× faster production frame-pair enumeration via eight-bit neighborhoods with identical receipts #2375 accelerates production frame-pair enumeration; this contribution gives an exact coordinate-symmetry cap without a runtime claim.
• Isolate explicit historical receipt adapters from P104 research #4103 isolates historical P104 receipt adapters; this package imports none of those adapters.

CI notes

Hosted CI is pending for 98bc47f847488c7909c6a80308998c792fd6a903. No hosted check or scientific CI success is claimed. Local registered normal/optimized replay passes. Any hosted failure will be recorded with its exact cause after the checks finish.

Merge Danger

Door: two-way. The change adds one isolated research package and its opt-in replay declaration.

Blast Radius: package. It changes no shared implementation, frozen source, selected result or other contributor's credit.