Prove a ten-contact obstruction to the fixed P104 room carrier

[commdata2338]

Change and mathematical scope

This resolves the released capture-order handoff in discussion #2131. No ordering completes the fixed P104 room capture stage: with the original G captures and query caps retained and frame paths monotone, the added carrier B0 cannot gather X2 + X4 inside R = span(32,196). This covers every ordering of the 418 captures, including orderings that start before either failed greedy prefix.

• Core: eight original captures and the two carrier captures already force a contradiction. Five sources each need two contacts with a different pair of the four helpers G1, G7, G20 and B0, and each source's initial label lies in exactly its two helpers' caps:

  Source	Label	Helpers	Capture events
  X2	228	G20, B0	1160, carrier
  X4	196	G7, B0	745, carrier
  X58	333	G7, G20	631, 1154
  X76	289	G20, G1	807, 1267
  X88	458	G1, G7	799, 945

  (Caps: G1 is bit_2 = 0, G7 is bit_5 = 0, G20 is bit_2 ⊕ bit_5 ⊕ bit_8 = 0, and B0 is {0, 32, 196, 228}.)

• Proof: a source's earlier contact must be its helper's first required contact. Otherwise that helper's frame already holds another source's label, which monotonicity carries into a cap that excludes it. That assignment is injective, and five sources cannot use four first contacts. Any complete schedule contains these ten contacts, so none exists. The argument uses only frame containment, so scalar coefficients and logical dirt cannot repair it.

• Status: a scoped proof with an exact finite certificate (registered as a negative result). No correction circuit, supplier or κ change.

Remaining obligations. Changed caps, replacement captures, other carrier rectangles and paid nonmonotone moves are outside the obstruction. No correction circuit, scattering or restoration schedule, native phase replay, paid histogram or moment, global owners, precision or tape, all-size admission, cold replay, formalization or independent human review.

Task and overlap

• Task ID / scope key: p104-side-correction (c5367b1a1b7bed20db53), refined to P104/single-room-32-196/X2-X4/carrier-capture-order/all416-fixed-caps. Chooser nonce fc691d86141767f8847a504c7bd1b4fa, track complex-mechanisms, priority revision 4; the card was the chooser's second suggestion, taken through CLAIM: P104 side correction with single-room mixed carriers and changed frame paths #2131's released handoff (passing over complex-new-helper-inventory and complex-rank-shape-decoder). No reroll.
• Base and exact heads: base 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2, rechecked unchanged at 22:54 UTC; contribution 0d6bf0ba8a92e9f35a097c47242b1bbe8d66ea20. The scientific input is PR Draft construction: P104 dirty-restored gather and low-rank channel with COPY56 (no new kappa) #1972's 4,058-event witness (fd82d172f46933fd253c2c6de4bd5eaff5429cfd, SHA-256 0f541bef7f19fdeffd67157684e9f03d785f42c89973632f508fc1a0452b580e), retained by PR Native Clifford realization of the P104 low-rank channel (no new kappa) #1991's native channel. Coefficients, query frames and source lines are reconstructed from the witness, not copied from the discussion.
• Scope status: changed: a complete ordering decision for the fixed component instead of the whole side correction, allowing replacement monotone paths.
• Nearest work: discussion CLAIM: P104 side correction with single-room mixed carriers and changed frame paths #2131 left the other orderings open. PR Prove sharp P104 temporal rank bound and correction-budget obstruction #2082, Sharp eight-query temporal cut for the frozen P104 itinerary #2090, Prove P104 rank-eight cut under arbitrary frame-path interleaving #2113 and Prove P104 transport floor with arbitrary added storage #2127 keep the original transports or their obligations; PR Construct a delayed-query P104 side word with full dirty restoration #2139 changes the side producer. This account's PR Certify the P104 cut-2429 nested-contact price: 864 rank units #2172 prices a frozen-cut network and PR Formalize P104 transport transcript capacity in Lean #2178 formalizes a transcript bound; neither decides this ordering.
• Claim and final check: the claim is in discussion #2131. A final overlap check of open PRs and Discussions (complete pagination), plus a live check of newer PRs, found no competing work.

Validation

python3 -I -B scripts/research_package.py --package research/p104-carrier-capture-order --check-only
python3 -I -B scripts/research_package.py --package research/p104-carrier-capture-order

Linux x86_64, CPython 3.12.3, standard library; no solver is needed to accept the result. The registered replay (normal and optimized) was run again on the final package bytes before submission, under an 8 GiB memory cap: it passed in about a second and left the worktree unchanged.

PASS_P104_CARRIER_CAPTURE_ORDER contacts=10 sources=5 helpers=4 legal_orders=0 deletion_controls=10 original_captures=416 no_new_kappa
PASS_REGISTERED_RESEARCH_PACKAGE research/p104-carrier-capture-order outcome=negative-result

• For a fixed order, the minimal common frame at each contact is contained in the frames of every other monotone realization, so the minimal realization decides each order. Two separately implemented recursions (cap-failure bit signatures, and actual binary subspaces) count every permutation and agree on zero legal orders (2,921 and 3,948 states).
• Deleting any one of the ten contacts admits legal orders, each with a replayed nine-contact witness, which shows the core is deletion-minimal. All 416 original captures pass in their original order without the carrier. Enlarging G1's cap or B0's cap alone admits 135,360 orders, which confirms the cap hypothesis is needed.
• The checker rejects every contact omission, both relaxed caps, a wrong initial label, altered coefficients, counts and JSON types, and duplicate keys.
• I checked the incidence table by hand: each label lies in exactly its two listed caps, and the five helper pairs are distinct.

Credit

• Hanhong Zhao (@Hope7Happiness): discussion CLAIM: P104 side correction with single-room mixed carriers and changed frame paths #2131's fixed component, the failed prefixes and the released handoff.
• Rohan Arun (PR Draft construction: P104 dirty-restored gather and low-rank channel with COPY56 (no new kappa) #1972) and Chafik Boukhalfa (PR Native Clifford realization of the P104 low-rank channel (no new kappa) #1991): the witness and native channel. Adam Gall (PR Research: chronological P104 schedule attains known 32-chain bound #1940), Josie Elliston (PR Research: delivery lower bounds for #968's frame-pair centers (no new κ) #1071), Ali Romman (PR Research: exact asynchronous P104 carrier bound across 7,168 decoders #1125) and the retained E8, native and compiler lineage.

New work is Apache-2.0; retained notices are unchanged.

AI assistance: submitted by @commdata2338 with substantial AI assistance. OpenAI Codex (GPT-6 Astra) did the derivation, the implementation, the checking and the writing; it was packaged and submitted with Claude Code. The small core was first found with Z3, which is not a dependency; the written proof and the two standard-library enumerations are the evidence. No independent human review is claimed.

Open next questions

See the package README and TASK.json. A changed room, carrier rectangle or cap contract would be a new question; any such proposal should first be checked against this incidence pattern (five sources on four helpers) before scheduling.

Workflow feedback (optional)

• What helped: the current-status summary in CLAIM: P104 side correction with single-room mixed carriers and changed frame paths #2131 separated the two failed prefixes from a claimed impossibility.
• Friction: the large local-only scheduling attempts in the thread cannot be replayed; the witness on main was enough to rebuild the contacts.
• Suggestion: scheduling handoffs could publish a small machine-readable list of the required contact occurrence IDs and cap bindings, even without a full schedule.

🤖 Generated with Claude Code

https://claude.ai/code/session_01X86sCSXdoDd61SDFfC1PKG