[petalas]

Summary

Scoped mathematical obstruction with an exact finite boundary certificate. No new kappa.

 helper 572 overwritten after event 13637 of selected PR6030
- PR6088: two added ADDs cannot repair the declared chart-595/603 seam
+ arbitrary finite rational linear bank recoding cannot repair that seam

Six protected output equations force the single transported form to recover the displaced original helper value. It therefore cannot also carry the new independent input. This permits temporary changes to original-input rows and removes the scalar-operation-count bound. The prefix, two correction regions, one transferred field, owned lifetimes and suffix remain fixed.

The new result was produced by Nick Petalas. JoyboyBrian retains PR6088's seam/question and bounded exclusion; apoursh PR6067, Jonathan Capalbo PR6069 and JosieElliston PR6108 retain the carrier/information/cross-time lineage. Credit PR6040/5994/5718, Ali Romman, DreamingOfClouds and all retained P104 predecessors. No predecessor census or exclusion theorem is rerun as this contribution.

Evidence

Before, arbitrary-length corrections that change original rows were outside PR6088's two-ADD result. After, PROOF.md proves failure for arbitrary 6-by-6 and 3-by-3 bank maps, including singular maps, through a single transported scalar.

The source-bound checker establishes eight independent input forms with minor determinant 1/32, a six-protected-output minor with determinant 8, all original-input boundary identities, both exceptional suffix columns at every public output, and the frozen chronology. It enumerates 722 small-field rank-one products, accepts a two-channel scope control, and rejects a singular minor, four changed seam/original-input fixtures and changed source bytes. These finite checks support the written unbounded-length theorem.

Local CPython 3.12.15/macOS arm64, standard library only:

/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -W error -B research/p104-unrestricted-572-seam/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -O -W error -B research/p104-unrestricted-572-seam/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/research_package.py --package research/p104-unrestricted-572-seam
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/check_research_commit.py --package research/p104-unrestricted-572-seam --check-source-history --check-modes

Both registered checks pass and each completes in under one second locally, against separate 60-second limits. Expected marker: PASS_P104_UNRESTRICTED_572_SEAM. Committed bytes, modes and source history pass for the six package files and sole live word input. The official seven-payload-file export passes integrity/input checks. Normal and optimized direct replays also pass in a read-only, Git-free export, produce identical generated hash-bound receipts, and preserve all eight exported files and their modes.

Scientific base: canonical main a5bff3bf133e482541c09eba4e773884bdb2b1b7, refreshed before commitment and unchanged. The source-binding baseline passes and resolves the selected conditional kappa to .003125804. Live open/account PRs, merged/main searches and local reservations found no same-scope target within the recorded coverage. Remote overlap pagination is complete; sparse local-note coverage is explicitly incomplete.

Limitations

Only homogeneous rational linear recoding within the declared two regions is covered. A second independent transfer, later correction window, pre-cut save, new storage, nonlinear encoding or another word may change the conclusion. No physical/native supplier, complete paid/target invoice, normalization or multiplication theorem is claimed. No selected scientific cold/native/compiler/caller/outer replay, Lean or Docker check was run. All five selected framework assumptions remain. Independent human and formal proof-kernel review are unclaimed.

Open next questions

1. Specify a second legal transferred form, solve its complete arbitrary-input endpoint equations, and price its frames, restoration and full signed invoice.
2. Pin one changed cut or pre-cut save with its owned lifetime and determine whether its new protected-output minor still creates a one-channel deficit.

Related open work

• Construct optimal 39/8-bit P104 labels with length-preserving updates #6224 gives variable-length P104 defect labels; it changes storage coding rather than the fixed scalar seam.
• Prove unbounded activation arity for parallel helper cuts (no κ) #6222 gives activation under parallel helper pooling; this theorem keeps one transported form and does not price pooled cuts.
• Prove sharp 68-point E8 plane unions and isolate the P104 puncture step (no κ) #6221 studies E8 plane unions and a P104 puncture reduction; it does not analyze chronological recoding.
• Prove the exact fixed-cubic coframe rank frontier (no new κ) #6220 determines a fixed-cubic coframe tariff; its symplectic rank frontier is outside this scalar endpoint condition.
• Exclude arbitrary-plane temporal rails on the fixed PR1094 word (no κ) #6223 studies arbitrary-plane frame rails on historical PR1094; our frame schedule is fixed on PR6030.
• Prove the P104 disjoint A2 packing maximum is 33 (no κ) #6219 settles disjoint A2 packing on the P104 ports; no packing count is computed in this package.
• research: P104 B-form floor follow-up: RootFact/SpanFact proved (hand + Lean), Cases II/III without the census (no κ claim) #6218 studies geometric compatible-plane decoder bounds; no two-chart recoding or shared seam number is computed there.
• research: P104 wire routing obstructions (scoped negative, no κ) #6217 studies A2 wire routing on P104; it changes the routing architecture rather than the fixed seam.
• 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 newer Conditional κ .003128386 (+2.582e-6 over #6030): owned registers 770, 771 and 772 descend through the frames of helpers 705, 706 and 731, which no longer relay them; helper 732 reads 771 at frame 117 #6144/Conditional κ = 0.003128645 (+2.59e-7 over #6144): retain an operand to remove a root stop #6167 words and their complete invoices; this result concerns one scalar boundary of selected Conditional κ .003125804 (+5.22e-7 over #5907): remove helper 470's frame-593 rung, the twin of #5907's removal #6030 and supplies no admission.
• Exhibit complex rank-seven P104 approximations below the real 1/4 floor (no κ) #6211 and Prove sharp 1/4 error for every real rank-seven P104 approximation (no κ) #6191 study complex and real approximate rank-seven P104 Gram realizations; this theorem is an exact scalar chronological obstruction.
• Prove E8 span inputs over every odd-characteristic field (no new κ) #6198 studies E8 span inputs over odd-characteristic fields; this result uses rational input forms and no root-span census.
• Exclude birth-lowered P104 markets without paid deletions (no κ) #6197 excludes birth-lowered P104 markets without paid deletions; the present obstruction concerns a unit overwrite and subsequent recoding.
• Reduce complete first P104 fold time by 29.94% (no new κ) #6187 accelerates a complete P104 fold replay; this package proves an additional source-bound exclusion and claims no timing improvement.
• Prove a sharp 1/4 error floor for contractive P104 mode deletion (no κ) #6183 studies contractive P104 mode deletion; its approximation contract differs from protected exact original-input outputs here.
• Conditional κ 0.00309871 from a prepared P104 split helper #5606 constructs a prepared P104 split-helper reuse; this theorem excludes only the named frozen two-region alternative.
• Two successor hand-offs on the P104 word: conditional κ 0.0030428242 #5553 proposes successor P104 interfaces; their changed words and conditional prices are outside this seam certificate.

No competing same-instance endpoint value is reported by these open PRs. No additional computations were run to compare their results. The immediate seam predecessors #6088/#6067/#6069/#6108 are merged; their archival status is not scientific acceptance.

CI notes

CI pending at publication head 5d9b3d792358bc423fd64cf3a15c2f46dbf91a97. Local registered normal/optimized replay, committed-byte/source-history/mode checks and portable export replay pass. Hosted CI has not yet certified this contribution.

Advance claim.

Merge Danger

Door: two-way. One isolated opt-in research package.

Blast Radius: package. No selected frontier, shared code or frozen predecessor changes.