[petalas]

Summary

Scoped proof with finite corroboration: a common dyadic reader can fail across four reversible cuts even though every proper subfamily admits one. No new kappa is claimed.

For D = Z[1/2], use source-response matrices M_i=e_i e_i^T on two source and two dirty helper coordinates, with e_i=(1,0),(0,1),(1,1),(1,-1).

each individual cut          unit-pairing capacity 1
every proper cut subfamily   one common reader a, with a M_i b_i = 1
all four cuts                no common a, even with arbitrary dyadic b_i

Modulo three, the four kernels cover every reader row. For some cut, a M_i b lies in 3D for every b, so it cannot be a unit. Explicit dyadic witnesses attain every proper subfamily. A listed 14-ADD scalar word visits all four responses and restores every incoming coordinate. Over Q the common reader (1,2) works, with one source column using a denominator three.

This supplies a deletion-minimal temporal compatibility counterexample. Four is not claimed to be the smallest possible obstruction among all matrices. A fixed invertible helper basis and cut-dependent unit rescaling do not escape it; changing readers or the coefficient ring changes the contract.

The contribution was produced by Nick Petalas. Credit Ali Romman's PR5615 single-cut unit-pairing background, PR5602/5611/5599, PR5115 and their retained helper/native/controller/compiler lineage. Projective-line covering and reduction modulo a prime are classical. No predecessor numerical result or verifier was audited or replayed.

Advance CLAIM. Base canonical main a5bff3bf133e482541c09eba4e773884bdb2b1b7, priority revision 8. The source-binding baseline passes and resolves selected conditional kappa .003125804. Live overlap, merged/main searches and reservations were refreshed before committing; the documented coverage does not include unpublished work.

Evidence

• Before: cutwise normalization alone leaves a temporal reader obligation. After: the written proof excludes a common reader in this explicit family, despite compatibility on every proper subfamily.
• All 14 nonempty proper subfamilies, 28 normalizations, 81 residue reader/source pairs, 198 dyadic reductions, five symbolic 4-by-4 prefixes, 625 dirty incoming states and 17,500 scalar updates pass. All 37 controls pass, including deletion and sign mutations of each of the fourteen gates.
• Warning-strict isolated normal and optimized checks produce identical stdout and generated hash-bound receipts on CPython 3.12.15/macOS. Local durations were 0.023059 and 0.025796 seconds; these establish bounded checks, not a performance comparison. Both commands are registered separately with 60-second limits.
• Registered replay, metadata and source pins pass. Exact committed bytes, executable modes and declared source history pass at 8fee704ce85d346aaac08e3d217373d7011a8b13.
• Official export integrity passes. Both direct modes pass in a read-only Git-free export with empty PATH; all six exported files, including its manifest, retain their hashes. Receipts are generated from execution and bind all five package files. No hand-written receipt is included.

Exact reproduction from the repository root:

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

Another CPython 3.12 interpreter path may replace the absolute local path. Only the standard library is used. Expected markers include PASS_COMMON_READER_CUT_OBSTRUCTION, PASS_REGISTERED_RESEARCH_PACKAGE and PASS_RESEARCH_COMMIT_BYTES.

Limitations and unrun obligations

The contract concerns the coefficient response h_i=h_in+M_i x under one fixed physical reader. Its observation still contains arbitrary incoming dirt. The source-response matrices are not asserted to be the full eligible prefix/suffix pairing matrices of an actual P104 helper split. The reversible scalar trajectory alone supplies no free dirty read or productive target.

Actual selected-word installation, native charts/maps, owned delivery, dirt cancellation, physical reader-rebasing tariffs, precision/growth, storage, compiler and the complete paid/target invoice remain unproved. No source-bound supplier replay, selected scientific replay, Lean, Docker, supplier admission or complete multiplication theorem was run or claimed. The selected frontier and its five framework assumptions remain unchanged. Independent human and formal proof-kernel review are unclaimed.

Open next questions

1. Find a nominated physical helper trajectory with a fixed-reader residue obstruction. First derive its literal response matrices in one physical basis; native/helper eligibility and a consumer contract are the missing prerequisites.
2. Determine the least fully charged reader-rebasing cost for this trajectory under a specified physical alphabet. First specify entrance, exit and restoration, then price an explicit two-reader schedule. No physical tariff has been assigned here.

Related open work

Completion refresh found no open account PR created since the advance CLAIM. No inspected open PR studies these four source-response matrices or this fixed-reader feasibility question. No additional predecessor computations were run.

• Conditional κ 0.00309871 from a prepared P104 split helper #5606 remains open and prepares a particular physical P104 helper with its productive debit charged. This synthetic compatibility obstruction does not construct or price that helper.

Previously listed adjacent PRs #6222 and #6214 are now merged. PR6222 concerns joint parallel banks at one common cut with arbitrary joint row/column choices; this result fixes one row across several chronological source responses, so neither computes the other's quantity. PR6214 audits the PR6144/6167 P104 words and their bills; this result neither replays those words nor computes their kappas.

CI notes

Both hosted checks passed at exact head 8fee704ce85d346aaac08e3d217373d7011a8b13 in run 40965015940: plan and replay (research/common-reader-cut-obstruction). The completed checks were read once and both report pass. The PR has since been merged by a maintainer.

Hosted replay certifies the registered normal and optimized finite checks at this head. The local metadata/source pins, committed-byte/mode/source-history checks and read-only Git-free export checks listed above also passed. No CI failure remains to report. These checks do not supply independent human or formal proof-kernel acceptance, physical supplier admission or a new kappa.

Merge Danger

Door: two-way.

Blast radius: package. Five new files and opt-in replay only. Shared code, pinned predecessors and the selected record are unchanged.