[petalas]

Summary

A universal seven-source connector with four arbitrary dirty roots must repeat a normalized source axis. This is a scoped obstruction with an exhaustive finite certificate, produced by Nick Petalas. No new kappa or selected-frontier change.

seven distinct axes + the full-mask output
  -> an affine cube with one point omitted
  -> 30 codes x 5,040 source orders
  -> at least 22 mandatory masks absent in every case

The deficit 22 is attained by four reduced pairs. It is sharp for the mandatory-mask test, not a sharp total-output capacity. The original transfer-reduction objective remains open; this contribution excludes a distinct-axis route toward it and stops at that first proved step.

Only research/seven-source-distinct-axis-obstruction/ is added. Start with the proof and reproduction notes.

Evidence

Before, Mason Hale's PR2282 leaves the four-root transfer tariff open, with conorholds' 56-X star as an upper bound. After, every universal minimum-incidence program must have an axis repetition, even when arbitrarily many scalar binary root frames and all physical read ports are granted.

The two code generators, mandatory-support constructions and word-difference engines agree on every one of the 151,200 missing-mask bitsets. The secondary domain generator examines all 11,811 three-dimensional binary RREF spaces. Both methods give thirty codes, 57 mandatory masks per code, minimum deficit 22 and four minimum-deficit pairs. The generated census digest is f5c200672ca724d968454e2cb3e7de2503a4cbf0f70c0a828a55ca120251eb27.

Local CPython 3.12.15, macOS arm64, standard library:

• Warning-strict normal and optimized direct commands pass, each in under one second locally. These are CI-budget observations, not a performance claim.
• Both registered commands, metadata/source pins, committed bytes/modes and declared source history pass at 92f106ba0afb732a4a16d760b0bba4827f18bc7f.
• Fourteen rotation and 21 transposition controls, the repeated-axis positive control, two invalid-source-word rejections and four false-variant boundaries pass.
• Official export integrity and both read-only, Git-free, empty-PATH replays pass, with identical receipts and all nine export files unchanged in bytes and modes.
• Ten separate actual-file fault probes reject in normal/optimized modes: two changed source documents, a false deficit, interval OR in place of XOR, and allowing the full codeword in the mandatory-mask test.
• Selected metadata bindings and the card's 945-pairing positive control pass. No predecessor scientific census is claimed as this contribution.

From the repository root:

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

Another CPython 3.12 executable may replace the local path. Expected direct status is PASS_SEVEN_SOURCE_DISTINCT_AXIS_OBSTRUCTION; the runner adds PASS_REGISTERED_RESEARCH_PACKAGE. Receipts are generated and bind all package files.

Credit Arham Tahir / PR2795 for the root-code and all-ones interval reduction, Mason Hale / PR2282 for the question and root-minimum theorem, conorholds / PR2182 for normalized axes and the star, Ross Richardson / PR934/943, Douglas Colkitt / PR1185 and their retained connector/common-factor/compiler lineage. These mathematical premises and the existing construction retain their credit; their censuses and physical invoices are not audited here. Classical binary code geometry is not claimed as new.

Advance claim, narrowed finding. Main was refreshed at 7c49fe32c55de02c2c873655c804b16e4c3fef0a, priority revision 8, selected PR6030. The changed card scope and the exact retained document pins are recorded in TASK.json and SOURCES.json.

Limitations and unrun obligations

The theorem fixes seven immutable sources, four arbitrary dirty roots, scalar binary root frames, unobserved outputs, and exactly two complete calls per source and output map. Repeated axes, extra calls, source mutation, output feedback, clean roots, matrix-valued root changes and nonlinear updates are outside the exclusion. The 105-output upper bound following from the deficit is not claimed attained.

No shorter transfer word, global transfer minimum, physical supplier, native realization or favorable complete physical invoice was established. Selected scientific cold replay, formal-kernel proof and independent human review were not run or claimed. All five selected framework assumptions remain. Every registered local obligation was run.

Open next questions

• Can a repeated-axis four-root program beat 56 paid XORs at minimum map incidence? Start with one complete frame/source/readout itinerary and charge every physical port and restoration.
• Can a structural interval proof replace this finite census? Start with its 57 mandatory supports and double-permutation words; no uniform argument is supplied here.

Related open work

No other open PR was found studying this exact four-root, seven-source distinct-axis domain. Nearby connector contracts differ:

• PR4079 studies seven-source masks of weight at most four with a one-root source-word boundary; this result requires the full mask set and paired map incidences on four roots.
• PR5990 studies a five-source fused two-root readout tariff; no fused readout is granted here and its tariff is not recomputed.
• PR6568 studies unsigned composite-characteristic capacity via closed walks; the coefficient alphabet and map multiplicities differ.

No extra computations compared another PR's results. Sparse notes, arbitrary historical diffs and unpublished work remain overlap limits.

The completion refresh inspected all five open account PRs created since the advance CLAIM, including this PR. The four others, PR6600 on Toom-3 interpolation, PR6601 on a one-query triangular carrier, PR6602 on rounded inverse-oracle error and PR6604 on nested-border precision, study different objects. None computes this distinct-axis census or its mandatory-mask deficit. No shared-quantity disagreement was identified, and no extra computation rechecked another contribution.

CI notes

Both hosted checks, plan and replay (research/seven-source-distinct-axis-obstruction), passed at exact head 92f106ba0afb732a4a16d760b0bba4827f18bc7f in run 41628425849. The completed checks were read once; run metadata confirms the matching head and successful conclusion. Hosted replay executes both registered warning-strict normal and optimized census checks and the package/source bindings. All registered and publication checks also passed locally. This is finite certificate replay, not independent scientific acceptance or formal-kernel verification.

Merge Danger

Door: two-way. Blast radius: isolated. The six-file package can be removed without changing shared code, predecessor artifacts or selected records.