Research: the P104 no-relay access-cover minimum is 4,580

[commdata2338]

Change and mathematical scope

The frozen P104 correction screen previously supplied a 4,480 no-relay carrier lower bound. This package independently reconstructs its exact weighted bound and strengthens it to 4,580 carrier lifetimes. A 0/1 dual marks 4,580 required entries with at most one per admissible carrier; a matching cover of all 4,992 correction entries proves the access-cover relaxation has minimum exactly 4,580, integrally and fractionally.

The new result is a finite certificate plus a written program-to-cover proof. The proof makes the fixed source/target chronology explicit: useful reads precede useful writes because X finishes at cut 1533 and Y starts moving at cut 2526. A two-dimensional interleaving example shows why retiming cannot silently be allowed. The primal is a support cover, not an attaining physical correction circuit. No paid recursive profile, stock bound, supplier or new kappa is claimed. Native phases, scalar coefficients, actual contact timing, restoration, hosting, precision and all-size admission remain separate obligations.

Task and overlap

Base 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2; contribution commit 2134975a339ccb6d011e2794d0382e2895fdf8e8; main was rechecked unchanged at 07:20 UTC before submission.

Base: 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2, priority revision 4. Final canonical-main refresh at 2026-10-15T07:12:17Z found the same commit, with no changes to guidance, the selected record or P104 inputs. Package: research/p104-no-relay-cover-audit/; full metadata is in TASK.json and SOURCES.json.

Task card:

Task ID / proposed scope key: independent-moment / c6f2494b197df3bc3591;
  P104/frozen-frame/no-relay/weighted-cover-program-bound.
Base commit; exact predecessor and dependency heads: main 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2;
  correction screen 7dfc7a176d7de4e7eabaf553a0b187c1bd647546;
  PR2353 2704eadf6b5205d4b965e9c6fc6dce28b89783cf;
  PR1972 fd82d172f46933fd253c2c6de4bd5eaff5429cfd;
  PR1991 6e222517e182e98499239bc9a4009f540e1c5520.
Concrete object and question: all no-relay carrier support envelopes for the
  frozen 104-port I-G/2 correction; validate and sharpen the weighted-cover floor.
Scope status: refined; independent source-ledger method retained, focused on
  a central P104 accounting implication explicitly excluded by the relay audit.
Existing restriction being changed (or claim audited): audit the reported
  24831791/5544 fractional bound and its program-level hypotheses; retain
  monotone no-relay carriers and the original X/Y chronology.
Method; explicit domain: all 4058 events, 104x104 root-derived coefficients,
  9-bit subspaces, complete contact chains, exact rational and 0/1 cover duals.
Nearest overlap: correction-screen owns the model and old floor; PR2353 proves
  a different relay-enabled 208 floor. PR2251/2345/2358/2367 concern pooled
  correction dimensions, not no-relay cover counts.
Optimistic full cost budget; required improvement: no favorable construction
  budget is claimed; a necessary lifetime bound is not a paid child invoice.
Success evidence; falsification and cap: matching exact primal/dual, complete
  independent chain enumeration, rejecting semantic controls; one bounded session.
Predecessor authors; artifact and reproduction: Philippe Van Velzen, kumagi,
  Rohan Arun, Chafik Boukhalfa, Adam Gall, Josie Elliston, Ali Romman and retained
  lineage; python3 scripts/research_package.py --package research/p104-no-relay-cover-audit.

Single chooser nonce 85db2a599d6e675795633f64d02d7e4c, track independent-verification. The alternative formal-interface-lemma card was passed over for this specific unverified implication. The claim is in Discussion #2245/comment18942790.

The nearest predecessor is Philippe Van Velzen's correction screen. PR2353 expressly does not audit that screen's no-relay calculation. This account's PR2172/2190 concern a priced cut and fixed-room capture order. Concurrent Y0 source-acquisition and retained-private-code relay claims allow relays or different information sources; they are distinct.

Final cached overlap covered 587 open PRs including drafts (2026-10-15T07:07:38.026722Z) and 1116 Discussion records (07:09:50.407275Z), with complete pagination. The package retains the earlier precommit snapshot; the final targeted check found only this claim and package. Path queries used the 572-PR file index from 06:33:04.255876Z and found no matching package paths. Expected offline warnings apply; this is not a novelty guarantee. No pending predecessor executable is imported: scientific inputs are the two immutable JSON files already on main.

Validation

On CPython 3.12.3, standard library only:

python3 -B scripts/research_baseline.py
python3 scripts/research_package.py --package research/p104-no-relay-cover-audit --check-only
python3 scripts/research_package.py --package research/p104-no-relay-cover-audit

The source-binding baseline, metadata/pins and registered replay pass. The final registered replay took 9.963 seconds and includes both checkers and all five public-CLI tests. All package bytes remain unchanged by verification.

• Primary antichain DP: 221 source frames, 220 target frames, 5724 nested frame pairs, 5804 candidate rectangles and 4638 maximal rectangles. The old fraction 24831791/5544 is exactly reproduced.
• Separate set/recursive-chain replay, importing neither the primary checker nor predecessor code: 6942 unpruned rectangles; primal and dual both 4580.
• Certificate: 4368 forced singleton entries plus 212 additional marked entries and 212 additional rectangles. Deterministic regeneration is byte-identical; SHA256 311a169a98386a011639c360f0f3296e3b32bb06eee165e7c47698c6173e7633.
• Twelve primary control groups and two separate certificate controls pass. Five CLI tests pass for optimized read-only Git-free export, source/certificate/receipt corruption, deterministic regeneration and occupied-output protection. The focused readonly test passed during iteration; the complete focused test file passed in the final registered run.

Not run: native Gaussian recipes, all 280 scalar endpoint columns, a chronological coefficient/restoration construction, relay-enabled networks, global owners/hosting, productive coverage pricing, precision/all-size/compiler admission or the selected cold replay. Frozen sources and the selected frontier are unchanged. No hosted CI or independent human review is claimed.

The registered replay (both checkers) was run again on the final package bytes before submission, under an 8 GiB memory cap: it passed in about ten seconds and left the worktree unchanged. The certificate arithmetic checks by hand: 4,368 forced singletons plus 212 further dual witnesses give 4,580, equal to the primal cover; the previous fraction 24831791/5544 is about 4,479.04 and rounds up to 4,480.

Credit

Philippe Van Velzen (philippeVV) supplied the no-relay chain model, per-entry capacities and 4,480 floor. kumagi/PR2353 supplied the independent relay-floor audit and its stated no-relay coverage gap. Rohan Arun/PR1972 supplied the frozen scalar/frame channel; Chafik Boukhalfa/PR1991 supplied its native realization and retained inputs. Credit also Adam Gall/PR1940, Josie Elliston/PR1071, Ali Romman/PR1125 and the retained geometry/compiler lineage. The separate pooled-space results remain credited to Gonzalo Mier/PR2173, Gareth Davidson/PR2251 and AAAmirinu/PR2345/2358. New work is Apache-2.0 and existing source notices are unchanged.

Prepared for commdata2338 (@commdata2338), with substantial OpenAI Codex assistance.

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. No independent human review is claimed.

Open next questions

The access-cover relaxation is solved: stronger weights within it cannot beat 4,580. A further no-relay refinement would need actual contact-time or coefficient constraints; start with one 23-entry component only if that sharper obstruction would affect a decision. The route was already unfavorable under the prior screen.

A constructive direction must change the no-relay premise, for example through priced helper-to-helper relays or retained descending values. Check current Discussion #2245 claims first, then establish one target's source acquisition, dirty restoration and complete local bill. The 4,580 floor is not asserted for such networks. Structured questions and blockers are in TASK.json.

Workflow feedback (optional)

The explicit excluded-coverage paragraph in PR2353 made a useful independent audit easy to identify. The shorter board statement “at most 12 pairs, so 4480 carriers” hides the weighted argument; attaching the exact fractional objective and a one-line model boundary to future summaries would reduce repeated orientation and hypothesis drift.

🤖 Generated with Claude Code

https://claude.ai/code/session_01X86sCSXdoDd61SDFfC1PKG