Record the P104 fiber-tag mismatch on one row/column pair.

[unpaidmoon]

Change and mathematical scope

On the 104 published P104 labels, the phase-uniform row tag z ⊗ q_j and the column tag r_i ⊗ z are never the same 81-bit translation. They disagree on the one-dimensional shared line exactly when the two labels have different weight classes modulo 4. The published witness (386, 405) is a mixed pair: shared-line flips 0 and 1, Hamming distance 20, separated by bit 11.

This is a finite tag obstruction. It is not a scalar saving, a paid-profile improvement, or a κ change. Selected conditional κ stays 836330098538459/500000000000000000 (0.001672660197076918). The inherited scaffold excess 44,096 is untouched. Minimum Hamming distance on the 10,816 ordered pairs is 6, so a shared-line agreement is never a full-address agreement.

Task and overlap

• Base: bb4bccbf42844d2801487450727c2f63e10d1d0f (canonical CrocSwap/integer-mult-bounds main, priority revision 6).
• Task: p104-side-correction, scope refined. The card allows one chronological cut or one hosting obstruction. The full correction program is not constructed.
• Handoff: Handoffs and requests for independent checks #1166 (reply in thread)
• Ordered eligible Handoffs and requests for independent checks #1166 handoffs after dropping work already delivered, matched by an open PR, or listed in this round through Price the cut58 ADDRESS swap against the separable response menu. #4149:
  1. (7, 18) / (7, 20) functional census (comment 19021170, question 1). Question 2 is the soundness proof in Prove codimension-one L/2 substitution soundness on double transversals. #4148.
  2. Invoice-level audit of the composed T488 ownership and outputs (comment 19022532, question 1). Question 2 is closed by Audit (no new kappa): the composed T488 profile is exactly PR3642's optimal packing vertex #3796.
  3. Physical rank-8/u2 source/consumer contract (comment 19029639).
  4. Downstream consumer that keeps the research: consume P104 residuals in actual cleanup and price source return #3943 encoded endpoint (comment 19032700, task 2). Task 1 is Audit matched P104 source-return adapters and their 192-ADD difference #3956.
  5. This fiber-tag reconciliation (comment 19034676).
• Dropped before that cut: the Reduce helpers 644/660 from width 8 to 7; conditional κ > 0.00173 #3605 wrapper (open Replay the complete PR3605 wrapper with a fresh retained bootstrap #3681); typed actual-width H (Add a typed one-round actual-width H and rounded return. #4123, Price one typed actual-width physical H and its toward-zero return #4127); single-hub and third-hub tariffs (Prove the exceptional single-hub literal charge is 48. #4124, Record the three-hub extremal actual-reader charge. #4145); the L22 census refinements (Record the coset-wide one-point pair ceiling #4117–Record that revisit 1 forbids joint length-4 and length-6 returns. #4120); the six-tape F0 ledger (Ledger intermediate F0 magnitudes on the L359 dirty ray. #4114); tensor-pairing review (Review the common-map tensor-pairing bound independently. #4113); shear words and transvections (Prove faithful integer-shear words fail the supplier moment test. #4126, research: stop the one-XOR shear carrier on a lossless integer payload #4135, Price integer transvections on the shear target B^k. #4146); the research: certify local-first two-ADD obstruction on staged544 #3942 review and two-neighbour invoices (Review the staged544 fixed-frame new-gap reduction. #4134, Price one moved-ADD crossed-frame pair at histogram delta zero. #4122, Show that commuting staged544 moves cannot retarget a rank-1 ADD line #4128, Record nonnegative raw-moment invoices for two-neighbour ADD moves. #4144); the Research: source-bind R437 ordinary coupling at c=1/576 (no κ claim) #3690 adapter refresh (open Refresh R437/OQ4 adapter and bind actual rank26/COPY515 physical returns #3967); adjacent uniform completion (Certify the literal-slot defect that blocks a uniform P104 adjacent c… #4133, Certify that uniform P104 completion misses a port-dependent chart. #4136, Prove uniform completion fails on the physical P104 encoding. #4140); the separated A2 audit (Audit the separated A2 composition and cleanup split #4112); the index bridge, encoder fiber, and (N-P)⊗M consumer (Audit the P104 index-to-tensor bridge without replaying events. #4125, Record that one P104 encoder fiber equals axis-0 U. #4131, Price one (N-P) tensor M consumer at 199680 unit additions. #4143); many-axis guard (Review the encoded many-axis production_axis guard. #4142); event 58 (Price the cut58 ADDRESS swap against the separable response menu. #4149); stock floors and the log_q parent (Record the exact floor-stable shifts of both bootstrap savings. #4130, Correct the log_q parent term of the finite m=73 stock. #4141).
• Predecessor labels, witness, and gauge z = 420: PR research: derive P104 two-axis endpoint intertwiners and cost gate #3954 head f1e2839819959cd0534d008be91ed5b79ec55a6a, retained by PR Prove P104 phase-uniform gauge and unavoidable completion tag #3966 head 3e2d70630fde46847c8938564576d78da48d101d. RESULT.json SHA-256 ce05a27ebc98677bec4febaa488fa03f5b6fc60216aa43b34298444d12f7ab6c. That head is not a Git object on this base. labels.json is the vendored array.
• Overlap refresh at 2026-10-20T03:11:19Z covered 842 open PR bodies and 2670 discussion records. No open PR compares these two fiber tags on the published witness.

Validation

CPython 3.12.3. Registered replay:

python3.12 -B scripts/research_package.py --package research/p104-fiber-tag-seam

Passed locally as PASS_REGISTERED_RESEARCH_PACKAGE research/p104-fiber-tag-seam outcome=negative-result.

Direct checks, including -O:

python3.12 -B research/p104-fiber-tag-seam/verify.py

print PASS_P104_FIBER_TAG_SEAM pairs=10816 full_equal=0 mixed_shared_disagree=5376 same_shared_agree=5440 min_hamming=6 witness=386/405 shared_flips=0/1 ham=20 helper_disagrees_on_witness=true no_new_kappa.

scripts/research_package.py --check-only passed. scripts/check_research_commit.py --check-source-history passed at 4ffcdaee5d6255a9cea1fe53a5424435068089d0, with source history bb4bccbf42844d2801487450727c2f63e10d1d0f. python3 -B scripts/research_baseline.py returned PASS_RESEARCH_BASELINE_BINDINGS_ONLY.

The checker tests O on all 512 vectors, the marginal-sum separation from the uniform tag, every ordered pair, the witness character at bit 11, and a control that the zero image can agree. Not run: the PR #3954 and PR #3966 executables, Lean, Docker, and the selected cold replay.

Credit

Chris R / Clear1nsight for PR #3954 and PR #3966, including the labels, the witness, the gauge, and the open fiber-tag question. Prepared by unpaidmoon with substantial Cursor Grok assistance. No independent human or formal-kernel review is claimed. New work is Apache-2.0.

Open next questions

Linked from research/p104-fiber-tag-seam/TASK.json:

1. Can a paid correction of the six disagreeing bits on a same-class pair, such as label 32 against itself, be hosted without repaying the inherited excess 44,096?
2. Does a non-orthogonal address change make the witness pair (386, 405) share one translation on the full address and on the helper tag a?

Workflow feedback (optional)

#1200

Sibling sessions published incompatible #1166 orderings. This list keeps one still-open next task per handoff comment, in comment-id order, and drops a task when an open PR or this round's listed PRs perform it.