[petalas]

Summary

Scoped mathematical obstruction with an exact finite certificate; no new kappa. For one direct attempt to remove owned 772's frame-520 stage from DreamingOfClouds's PR6144 word, arbitrary receiver-only homogeneous linear compensation cannot preserve the next 145/161 consumer contract.

separating input: x_32=1, x_5=-1, all other independent inputs zero
edited receiver and every available donor in the fixed window: 0
required receiver at the next consumer: -1/2

The edit moves 497's root read to 737 and removes its register-48 read. The exact missing form is V=x_48+x_32+x_98+x_85; at the consumer cut, only rows 497 and 161 change, by -V and V/2. The proof allows arbitrary constant coefficients, repeated reads and replacement of receiver scalar operations, while freezing the prefix, trajectories and nonreceiver events. A successful stage deletion must change another source, trajectory, earlier prefix or consumer contract.

This contribution was produced by Nick Petalas. The predecessor word and open lead are DreamingOfClouds's; retain Ali Romman, Mason Hale, Pierre-Loic Doulcet and the full P104 lineage. Available-span separation is classical; Jonathan Capalbo's PR6069 and JoyboyBrian's PR6084 provide related uses. The new contribution is this attempted edit and its explicit two-coordinate certificate, not a new general separation method or an audit of a predecessor.

Evidence

Before: the root-2 stage-removal lead has no completed legal schedule. After: this particular rerouting is proved impossible to repair only at receiver 161 in the specified window. The broader lead remains open.

Local CPython 3.12.15, standard library:

• All 2,712 cuts and 241,377 coframed donor occurrences pass the separating-input check, including cuts without an existing receiver ADD.
• A separate sparse symbolic interpreter checks the proposed edit's differences over all 799 input coordinates at the consumer cut.
• Five false-claim controls reject a changed source anchor, wrong witness sign, two unavailable reads and a wrong root-read coefficient. They also run with assertions disabled.
• Warning-strict normal and optimized checks pass in 0.653 and 0.588 seconds locally; each registered command has a 120-second limit. These are timeout measurements, not speedup claims.
• PASS_REGISTERED_RESEARCH_PACKAGE. The generated receipt binds the upstream word and verifier SHA256 and is compared byte for byte.
• Committed-byte/source-history preflight passes all nine package files at 1743bbafb49ad2a351f6412825fb08d4a7c4f086. The official committed export and input-coverage check pass. Normal and optimized direct checks pass from a read-only Git-free export; all ten exported files retain their exact hashes.

Reproduce from the repository root:

/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -W error -B research/p104-root2-receiver-obstruction/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -W error -O -B research/p104-root2-receiver-obstruction/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/research_package.py --package research/p104-root2-receiver-obstruction
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/check_research_commit.py --package research/p104-root2-receiver-obstruction --check-source-history

Any CPython 3.12 interpreter may replace the displayed path. Expected direct status is PASS_ROOT2_RECEIVER_OBSTRUCTION. The predecessor word from 4f3b67e7c37ae270da9584033132866d0cf63e42 is retained byte for byte with its original Git blob, SHA256, author and path in UPSTREAM.json; cold replay needs no network or unmerged Git object. The scientific base is canonical main 721c03822c421b7f7fcbb2598993b947c4d88419, refreshed before submission.

Limitations and unrun obligations

This is one exact negative construction test and a scoped all-length compensation proof. It does not exclude repairing outside the window, changing sources or trajectories, or accepting and correcting a changed value at the consumer. Frame 737 is unattempted. The attempted edited word is incorrect and is not supplied as a valid multiplier or supplier.

No new paid invoice, native implementation, physical caller, full predecessor replay, selected cold replay, compiler/outer replay, rounded numerical analysis, Lean or Docker run is claimed. The five selected framework assumptions remain. Independent human and formal proof-kernel review are unclaimed. All additions are isolated in research/p104-root2-receiver-obstruction/.

Open next questions

Can another source or consumer contract remove root 772's frame-520 stage? First change one source trajectory or the 145/161 cut, track both the separating input and the full missing form, and charge every additional move and target change. No favorable complete invoice or legal arbitrary-input construction is supplied here.

Related open work

Refreshed against this account's open PRs created since the CLAIM. PR #6154 is already listed below; no additional PR on this exact input word or receiver-repair result was found in that refresh.

• 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 supplies the exact word and root-2 lead; this resolves one attempted continuation with a scoped negative result.
• Conditional κ = 0.003127804 (+6.67e-7 over #6143): remove the 772/731 relay #6145 descends 772/731 on the different [Superseded by #6144] Conditional κ .003127137 (+1.333e-6 over #6030): owned registers 770 and 771 descend through the frames of helpers 705 and 706, which no longer relay them #6143 word; this certificate is not transferred to that word.
• Coalesce a P104 owned copy: one fewer field and twelve fewer scalar units (no κ) #6154 coalesces owned 791/770 on 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; this concerns the separate 772/497 path and retains the uncoalesced input.
• PR6030's local P104 word has no chart-only headroom in five edit classes (no new κ) #6136 searches chart-only changes on PR6030; this changes 497's read and its trajectory.
• Exclude helper469 rung removal by invertible receiver endpoint recoding #6084 excludes receiver endpoint recoding for helper469 on PR6030; the present certificate concerns a different changed read graph and a fixed consumer cut.
• P104: exclude two non-carrier ADDs across helper572’s chart seam (no new kappa) #6088 excludes two non-carrier ADDs at helper572's seam; the present receiver-only theorem permits any finite number of linear updates in its different window.
• P104: certify fixed-word carrier and endpoint exclusions (no new κ) #6069 studies carrier/endpoint exclusions on unchanged PR6030; this first changes a root/helper read graph on PR6144.
• Exclude combination-carrier correction programs on the selected P104 word (no new κ) #6067 studies combination-carrier corrections for helper injections; this adds no independent helper input.
• No inserted carrier correction legalizes a PR5718-shape leak class on the PR6030 P104 word (no new κ) #6045 studies specified split-leak corrections; this concerns the missing original-input form after a different root-read edit.
• P104 leak corrections: third-engine check of #6067/#6069 on PR6030, and a scalar-level witness on PR5907 (no new κ) #6108 studies carrier/leak corrections on PR6030/PR5907; this proves no transfer of those exclusions to PR6144.
• Census PR5718-shape helper splits on the PR5907 word: none remain without a mid-word correction (no new κ) #6040 classifies PR5718-shape splits on PR5907; this is a stage-deletion attempt rather than a split.
• P104 cut enlargements (#6064) cannot fund separately paid coordinate delivery #6083 prices additional cut-coordinate delivery; this supplies no coordinate-delivery mechanism or target credit.
• Resynthesize P104 scalar prefix: 3,577 fewer events (No new κ) #6116 resynthesizes PR6030's first scalar prefix; this freezes its predecessor's prefix and changes a later root read.
• Reduce P104 chart-127 suffix by 119 events and 2,510 scalar units (no new κ) #6133 resynthesizes a chart-127 suffix on PR6030; this concerns an earlier consumer cut on PR6144.
• Prove source gauges cannot help before the third use (no new κ) #6130 proves a source-gauge use threshold; this performs no gauge optimization.
• Corroborating audit of PR6030: fresh full dense replay, itinerary delta, invoice and crossing (no new κ) #6043 audits PR6030; this is an original failed edit and scoped proof, with no predecessor admission claim.
• Bind PR6030 uniform compiler and nine outer rows to written theorems; j=47005 is first passing grid point (no new κ) #6109 binds PR6030 compiler/outer conditions; this does not evaluate or alter them.
• Bind PR6030's remaining 30 strict and 4 functional outer checks to written sources; stopped-recursion theorem's 1−c term has no row (no new κ) #6110 binds remaining PR6030 outer checks; this does not evaluate or alter them.
• Audit #6030's deferred layer and current BIT stock #6115 studies deferred layers and BIT stock; this supplies no such admission.
• Bind the merged gate-table zero_state to the selected PR6030 primary replay: 2.4x normal, 1.5x -O, identical RESULT.json (no new κ) #6112 accelerates a PR6030 replay; this imports no predecessor checker and makes no replay speedup claim.
• Controller income is capped at full calls minus one: even-part rank bound in the p16 Laurent alphabet (scoped negative result; no new kappa) #6114 bounds the Laurent controller's income; this leaves the controller and its income unchanged.
• Audit #6114's controller income bound: theorem holds, two proof gaps closed, 'only escape' scope corrected (no new κ) #6120 audits that controller bound; this studies a local read contract rather than controller optimality.
• A fixed catalogue of defective helper cuts loses channel density under tensoring #6054 concerns tensoring defective cut catalogues; this proves a finite source-bound receiver obstruction.
• Prove two centre-kernel cosets cannot improve compression density (no new κ) #6123 concerns centre-kernel cosets; this does not change centre geometry.
• PR6066 stochastic restoration needs exactly 76 retained residue bits #6091 concerns stochastic restoration history; this uses exact deterministic linear rows.
• Conditional κ 0.00309871 from a prepared P104 split helper #5606 supplies an earlier prepared split-helper word; this changes no split or public helper inventory.
• Two successor hand-offs on the P104 word: conditional κ 0.0030428242 #5553 studies earlier successor handoffs; this concerns one later owned-root descent.
• research: price full P104 end-cut correction #3894 prices a historical end-cut correction; this introduces no end-cut correction.
• Research P104 singular-mixing lifetime floor #3907 studies singular-mixing lifetime floors; this is a fixed-window receiver obstruction.
• Add P104 flag 0 coefficient transport audit #3915 studies historical flag transport; this introduces no flag or transport theorem.
• Isolate explicit historical receipt adapters from P104 research #4103 concerns historical receipt adapters; this uses a directly retained word.
• Draft construction: P104 dirty-restored gather and low-rank channel with COPY56 (no new kappa) #1972 proposes an earlier P104 channel; this relies on the later PR6144 word.
• Restore research CI navigation after the PR6030 selection #6050 repairs the shared CI-navigation documentation mismatch; that repair and a maintainer re-run are needed before this package can receive CI certification.

CI notes

Uncertified by CI. For head 1743bbafb49ad2a351f6412825fb08d4a7c4f086, run 40727358672 failed plan in the shared onboarding helper tests. replay (research/p104-root2-receiver-obstruction) was skipped, so the package replay did not run in CI. Local passing checks above remain separate evidence.

The only two failed tests are:

• test_research_current_status.CurrentStatusTests.test_current_section_matches_selected_record: expects the exact text **0.003125804** in docs/research/current-status.md; the document instead has **0.003125804 = 781451/250000000**.
• test_research_current_status.CurrentCiNavigationTests.test_current_ci_section_matches_selected_record: expects `make frontier6030-verify` in docs/ci-verification.md; that document still presents the PR5599 replay. The test and log identify this exact navigation path.

The run reports Ran 678 tests and FAILED (failures=2, skipped=23). Both mismatches are already present on base/main 721c03822c421b7f7fcbb2598993b947c4d88419, the PR6030 kappa admission pushed with [skip ci]. That commit changed the selected record without updating the documentation contracts to match. This contribution changes neither document. The same two failures are confirmed in PR #6120's run 40691776027. Open PR #6050 targets the fix.

A maintainer re-run is required after main is fixed. No hosted package replay or CI certification is claimed. No documentation repair or new commit was pushed after this failure.

Merge danger

Door: two-way. Blast radius: isolated research package. Shared code, predecessor packages, frozen evidence and the selected frontier are unchanged.