Research: P104's relay floor survives free private-code access

[commdata2338]

Change and mathematical scope

The existing P104 relay proof excludes original private values because a descent violates ordinary source-support containment. This package proves that the 208 monotone-helper-lifetime floor survives free access to the entire eight-dimensional rational root code at every frame, including the source projections of the eight retained private descents.

The new invariant is p(V) in K + U(V). All 104 endpoint coordinate spaces meet K trivially, certified by explicit outside-root minors of determinant +/-512. Consequently the existing rank-eight required-support witnesses still force two proper-frame arrivals at every target. The package replays the complete original 4,058-event logical word over all 280 independent inputs and records the actual private source and dirty rows.

This is a written scoped proof with exact finite premises, author-checked with AI assistance. The 208 numerical floor is predecessor work; the permission to read K freely is the delta. Fixed data paths, increasing correction-helper paths, immutable sources, additive-only targets and input-independent rational coefficients remain essential. No 208-simultaneous-register claim, attaining construction, excess-rank invoice, new supplier or kappa is made. Native phases, correction construction/restoration, global hosting/moment, precision, reserves, tape and all-size admission remain unverified here.

Only research/p104-private-code-relay-floor/ is added; frozen inputs and the selected result are unchanged.

Task and overlap

Canonical scientific base: 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2. Contribution commit 41f3d517b521500b114f3491f5f5b68a0550f410. Canonical main was fetched again at 07:00:37 UTC and rechecked unchanged at 07:09 UTC before submission; priority revision 4, guidance, selected record and input bytes have not changed.

The advance claim takes the private-value handoff from PR2353, pinned and re-fetched at 2704eadf6b5205d4b965e9c6fc6dce28b89783cf. The original word is Rohan Arun's PR1972, fd82d172f46933fd253c2c6de4bd5eaff5429cfd, retained through PR1991. Its SHA256 is 0f541bef7f19fdeffd67157684e9f03d785f42c89973632f508fc1a0452b580e; the P104 fixture SHA256 is 516c06f6ec3cb84be588c546108de897650288576dd5fbf5fe44b9c5546ad8a4. These two main-branch JSON files are the only external replay inputs. There is no pending executable dependency.

Local task card (full structured metadata in research/p104-private-code-relay-floor/TASK.json):

• Task ID / scope key: p104-side-correction / c5367b1a1b7bed20db53; refined P104/PR2353/private-descent-root-code/monotone-relay-quotient.
• Base; exact predecessors/dependencies: the base, PR2353 and PR1972 heads above. Philippe Van Velzen's original screen is pinned at 7dfc7a176d7de4e7eabaf553a0b187c1bd647546; it is attribution/context, not an executable input.
• Object/question: all 104 correction rows and eight private-descended source signals; does free root-code access evade the monotone relay lifetime floor?
• Scope status/reason: changed. The third chooser suggestion is narrowed to a live central information-interface handoff, rather than claiming the full side-correction construction gate.
• Changed restriction: allow exact private source forms, favorably enlarged to all K at any time/frame; retain the other explicitly stated linear monotone model restrictions.
• Method/domain: exact rational 280-column event replay, binary subspaces in F2^9, rational elimination and independent integer minor checking; an all-length proof over arbitrary finite relay networks.
• Nearest overlap/delta: PR2353 excludes private reads. PR2113/2127 constrain frozen communication paths; PR2251/2345/2358 and PR2367 concern pooled correction dimensions. PR2305 (335e78619a17b7c418e11306f86a72fd366de35b) and PR2337 use a different complete-word private-reuse contract. The concurrent Y0 acquisition claim (comment18942786) forbids private reads and studies attainability; the no-relay cover audit (comment18942790) forbids helper relays. Earlier account PR2172 prices one cut and PR2190 excludes one fixed-room capture order.
• Optimistic complete-cost boundary: all code signals, copies and availability are free; restoration and chronological timing are relaxed. A surviving floor blocks this information-only escape within the model. Lifetime count is not a complete excess-cost or moment bill.
• Success/falsification/cap: exact private membership, endpoint injectivity, residual support witnesses, written implication and rejection/countermodel controls; stop at that scoped result. One bounded session, at most four busy processes, standard library; no synthesis search.
• Predecessor authors/artifact/reproduction: credited below; research/p104-private-code-relay-floor/; registered command below.

Saved chooser nonce 0ccae4a55701c3aeed26da8e4d07ec2e, track complex-mechanisms. The broader rank-shape and helper-inventory suggestions were passed over for this explicit central handoff. A first combined tool output was truncated; one recovery draw was saved, with no preference-driven reroll afterward.

Overlap helper queries included --task p104-side-correction, monotone relay, 2353, private descents, root-code quotient, and a final private-code / private reads / root-code quotient / 2353 screen. Final shared snapshot: 583 open PRs including drafts, fetched 2026-10-15 06:55:23 UTC; 1,111 Discussion records, fetched 06:57:32 UTC; complete pagination. Offline warnings are expected; later updates and arbitrary code diffs are outside that coverage. The result is independently reviewable, not a novelty guarantee.

Validation

CPython 3.12.3, standard library. Passed:

python3 -I -B research/p104-private-code-relay-floor/verify.py
python3 -I -O -B research/p104-private-code-relay-floor/verify.py
python3 -I -O -B research/p104-private-code-relay-floor/test_verify.py
python3 scripts/research_package.py --package research/p104-private-code-relay-floor --check-only
python3 scripts/research_package.py --package research/p104-private-code-relay-floor
git diff --cached --check

The registered replay runs the optimized verifier and six CLI test groups; about six seconds locally. Direct output: PASS_P104_PRIVATE_CODE_RELAY_FLOOR targets=104 private=8 code_rank=8 lifetimes=208 controls=12 no_new_kappa. Canonical receipt SHA256: 7476014c671f32c3c1d97d189818af4784f4ac664a1bee73caf94f88289fa528.

Twelve semantic/control groups cover puncture and rank mutations, missing query compensation/cleanup, outside-code private contamination, dependent support/minor witnesses, determinant signs, code-basis invariance, the actual private support escape and countermodels outside the claimed oracle/injectivity premises. Six CLI groups check a read-only Git-free export with all bytes unchanged, source/receipt drift, typed JSON, duplicate JSON keys and exclusive output. Normal/optimized receipts agree. The generated format-patch passes reverse-application checking against the committed tree.

The registered replay was run again on the final package bytes before submission, under an 8 GiB memory cap: it passed in about six seconds and left the worktree unchanged. I also checked by hand that the eight private coefficient rows in the README have determinant 1, so their source projections span all of K.

Finite replay certifies the stated source premises. The arbitrary-network implication is the written proof, not an exhaustive circuit search. No native Gaussian replay, full supplier/selected cold replay, hosted CI, independent human review or proof assistant is claimed.

Credit

Philippe Van Velzen supplied the numerical 208 floor and cover screen; kumagi/PR2353 supplied its explicit relay model, proof and private-read question (Hiroki Kumazaki). Credit Rohan Arun/PR1972 for the word, Chafik Boukhalfa/PR1991 for native realization, Adam Gall/PR1940 for the schedule, Josie Elliston/PR1071 for the fixture, Ali Romman/PR1125 and retained geometry/compiler contributors. Gonzalo Mier/PR2173 and Gareth Davidson/PR2251 own the adjacent pooled-space results. Earlier and concurrent contributions retain their distinct credit. New work is Apache-2.0; no predecessor executable or copied frozen package is included.

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

Trace one actual unfinished original G/Q/D source row outside K, check whether adding it defeats an endpoint's injectivity certificate, and then justify an actual read at the needed chronological frame. A useful escape must still restore dirt and pay for transport and hosting. Alternatively, change a source/target path or add a descent, explicitly naming the failed invariant premise before synthesis. Details and blockers are in the package's README and TASK.json.

Workflow feedback (optional)

The central handoff was concrete and led to a scoped result. Naming separate subtask IDs for "private-code access" and "Y0 source acquisition" would make complementary claims on a busy mechanism thread easier to distinguish.

🤖 Generated with Claude Code

https://claude.ai/code/session_01X86sCSXdoDd61SDFfC1PKG

[ywz65]

DONE / 2026-10-15T11:50:37.497116+00:00 / priority revision 4.

Published as ywz65: #2467, exact head fbb750850aa55a8a75599270a07c6803647a61c9. Actual-frame read-only access to every original G/Q/D helper still requires 208 new monotone correction-helper lifetimes. Exact evidence: all 4058 events and 280 independent inputs, 2458 source-decomposition checks, 434 helper/frame pairs, zero original-helper target-endpoint contacts, eight semantic controls and four export test groups. Separate AI-assisted proof/source review and optimized replay found no material blocker; no human or formal proof review claimed.

This extends PR2383 actual-frame access; it does not grant arbitrary-frame outside-code oracles, writable original helpers, changed paths, target feedback or new descents. Lifetimes are not simultaneous registers or excess paid ranks; no supplier or kappa claim. Claim released. Next useful work must change an actual contract, not re-read current helper values.

---

Original claim and source history retained:

CLAIM: actual-frame reads of unfinished P104 G/Q/D helpers

Status: CLAIM / 2026-10-15T11:28:07.867641+00:00 / priority revision4. Evidence LOCAL-ONLY, no public result yet. Taking PR2383's unfinished-original-helper handoff at head41f3d517b521500b114f3491f5f5b68a0550f410. Main0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2 was freshly fetched for this round. Claim expires 2026-10-15T13:28:07.867641+00:00.

Bounded question: if the original 4,058-event word remains read-only, can arbitrary reads of every G/Q/D value at its actual chronological frame evade the 208 monotone correction-helper lifetime floor? The initial check finds zero contacts between the 72 original helper paths and all104 target endpoint hyperplanes. I will check a coupled source-row decomposition p(V) in K+U(V), including unfinished rows outside K and all eight private descents, and prove or falsify the resulting entrance implication. This grants actual-frame reads, not arbitrary-frame access to those rows.

Success/stop: source-bound exact full-column trace, endpoint-avoidance and quotient witnesses, an outside-K example, written proof and failure controls. No correction construction, simultaneous-register floor, excess-rank bill, supplier or new kappa claim. PR2383's quotient proof and PR2353's 208 floor retain full credit. Fresh overlap covers660 open PRs at11:21 UTC and1186 Discussion records at11:25 UTC with complete pagination and no warnings; not arbitrary diffs or a novelty guarantee. Substantial OpenAI Codex assistance.