[petalas]

Summary

Scoped proof with a finite structural certificate; no new kappa. On the exact PR6345 word, changing both endpoints of all 42 one-step helpers cannot enable any single intermediate-stop deletion while every other epoch outside those helpers stays fixed and scalar order is retained. All 2,660 stops have a direct ADD/COPY contact with a fixed partner: 2,654 public stops and six owned stops.

fixed partner at U -> contact forces a visit to U
replace A -> U -> C by A -> C -> contact cannot use its required chart

The merged transport may be placed at any intervening cut. Helper endpoint choices may be arbitrary binary subspaces, beyond the published native catalogue. This answers a bounded version of PR6345's second Open next question with a stronger simultaneous helper relaxation. It is a new source-bound obstruction, not an audit of the predecessor's word, invoice or root.

The result, proof and verifier were produced by Nick Petalas. Credit DreamingOfClouds for PR6345 and the question, Ali Romman for PR6167, DreamingOfClouds for PR6144/6143, and the retained P104/native/caller lineage. Ali Romman's PR5590 already proves the older PR5580 fixed-contact price floor; common-chart equality is inherited syntax. This package supplies the new complete fixed-partner certificate on the different PR6345 word while helper contact charts may vary.

Evidence

The primary epoch index generates one direct-contact witness per stop. A separately implemented streaming checker discovers the complete candidate set and checks every witness, event operand, epoch identity, common chart and fixed-partner condition. Exact binary spans distinguish each stop from its two neighbors. Ten semantic rejection controls and two positive toy controls pass under normal and optimized Python.

From the worktree root, using CPython 3.12.15 and its standard library:

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

Both direct commands pass locally in 0.068 and 0.073 seconds respectively, below their 120-second registered budgets. These are individual check durations, not performance benchmarks. The registered runner reports PASS_REGISTERED_RESEARCH_PACKAGE. The committed-byte/history preflight passes all nine package/input files and source ancestry at 1a2ef236d5aeb255af441804a9e37c4aeb350204. Direct output is PASS_P104_RESPAN_STOP_OBSTRUCTION, with 2,660 witnesses, 42 helpers, ten semantic rejections and two positive toys.

Optional --receipt /absolute/path/outside/checkout/receipt.json generates all contact witnesses with input/payload/package hashes. Witness SHA256 is fbb7f8462f25732d63e422ef831dc311ad112f818f10fb6c1bc6b9dc39aa7dfd. No receipt was hand-written. Exact Git/SHA256 pins are in SOURCES.json; the source word is already on canonical main 7c49fe32c55de02c2c873655c804b16e4c3fef0a. Sparse checkouts must materialize research/p104-frontier-symmetric-ladders.

Limitations

This is a fixed-schedule, single-stop obstruction. Moving a helper MOVE across contacts, changing another non-one-step epoch, changing scalar operations or inserting transports leaves the model. It is not a classification of optimal assignments or a global price ceiling. No numerical price, supplier admission, new kappa or complete multiplication theorem is claimed. The five inherited framework assumptions remain. Full native, caller, compiler, precision/tape and all-size replays were not run because they do not supply the necessary chart implication used here. The two implementations are by the same contributor; independent scientific and proof-kernel acceptance remain unclaimed.

Open next questions

• Jointly change a stop and its blocking partner epoch, then check every other contact and the complete paid/productive bill.
• Move one helper's unique MOVE across scalar contacts, preserving every arbitrary input, and price the resulting explicit program.

These are follow-on ideas, not constructions supplied by this package. TASK.json records their first steps and blockers.

Related open work

• Lift four P104 helper inputs: conditional κ 0.003129111 #6349 lifts four helper inputs on a different PR6167 descendant with changed basis corrections and scalar delivery; this fixed-schedule obstruction does not transfer to it.

• Compose native input lifts with the query tree at conditional κ 0.00314980 #6350 composes those input lifts with a tree caller; this package does not change or compare caller invoices.

• Contract nine native helper outputs at conditional κ 0.00315057 #6353 contracts nine helper outputs using joint bases and new owned operations, outside this move class.

• Independently audit PR6353 rational joint basis and public boundary #6355 audits PR6353's rational public boundary, which is a different source and obligation.

• Independently recount PR6353 recursive invoices and fixed-saving margin #6359 checks PR6353's formal invoice; no invoice is computed here.

• Independently check four frame1094 native matrices #6360 checks PR6353 native matrices; native synthesis is not part of this contact obstruction.

• Independently verify the fixed balanced caller Laurent endpoint #6361 checks the fixed caller endpoint; the local stop domain here is independent of that caller.

• Conditional κ = 0.00315087 (+3.0e-7 over #6353) #6372 changes a joint contact block and transport ranks on PR6353, outside the fixed PR6345 schedule.

• Conditional κ = 0.00315120 (+3.3e-7 over #6372): three shared-carrier input lifts #6375 shares input-lift carriers on PR6372 with changed preparation and delivery; this theorem does not exclude that mechanism.

• Independently audit PR6372 two-anchor scalar boundary and endpoint #6376 audits PR6372 scalar endpoints, a separate fixed word and review scope.

• Certify PR6375 matched profiles and unique relative-tariff threshold #6378 checks PR6375 formal profiles and a tariff switch; this package neither computes nor compares that quantity.

• Two successor hand-offs on the P104 word: conditional κ 0.0030428242 #5553 splits helpers by successor hand-offs on an older word, changing the helper inventory rather than this fixed single-stop move.

• Conditional κ 0.00309871 from a prepared P104 split helper #5606 prepares a split helper as owned storage, changing the arbitrary-input contract and scalar program.

• Explore joint frame retiming after carried swaps (ongoing; no new κ) #4993 explores coordinated retiming on carried-swap paths; multiple changing epochs are outside the present obstruction.

• Prove the exact nineteen-leaf query-tree topology optimum (no κ) #6380 optimizes query-tree topology with the native word fixed; it changes a separate caller layer.

• Prove a paid-rank floor of 22 for three-carrier rank-two tails #6386 gives a paid-rank floor for a three-carrier merge with a rank-two tail on PR6030; joint relay changes are outside this single-stop PR6345 move.

• Prove exact tariffs for carriers visiting distinct entrance lines (no κ) #6388 gives exact tariffs for a carrier visiting several prescribed entrance lines; it studies route cost rather than fixed scalar-contact stop deletion. No numerical quantity is compared.

CI notes

Both hosted checks, plan and replay (research/p104-respan-stop-obstruction), passed at head 1a2ef236d5aeb255af441804a9e37c4aeb350204 in run 41511133311. The checks were confirmed with gh pr checks 6381 --repo CrocSwap/integer-mult-bounds. Local registered replay and committed-byte/source-history checks also pass.

The post-claim open-PR refresh added #6386 and #6388 as related work. They concern different quantities, and no extra computation was run to compare them. The advance claim is retained.

Merge Danger

Door: two-way. Blast radius: isolated research package. The change adds seven files and modifies no existing scientific source, shared verifier or selected-frontier record.