[petalas]

Summary

Scoped proof with finite corroboration. For the complete fixed PR2484 112-port mask, give every port width d>=1 and add arbitrary nonnegative excess e_p only on the 44 ports T of its separated 22-plane set Q. The exact minimum fitting rank over every field is

full-mask minimum query dimension = 49d + sum_(p in T) e_p

Arbitrary rectangular ordered free blocks cannot beat this floor. A support-wise encoder/decoder attains it on the full mask. The first instance has width two at port 0 and width one elsewhere: a 113-by-113 full fit with exact minimum rank 50.

This answers one restricted family of Tekalign's #3362 Open next question 1, full unequal-width 112-port attainment. Sagar Thakrar/#2484 supplies the 49-support partition and Q/C5 witness; ywz65/#2541 supplies the all-field uniform block theorem. The new step is the full-mask lift for all 44 independent excess widths. Credit Tekalign/#3362, ywz65/#2471, Cinna Davis/#1825, Adam Gall/#1889, ctoth, Philippe Van Velzen and the retained P112 lineage. Those are cited premises, not audit or replay deliverables. This contribution is produced by Nick Petalas.

Only research/full-mask-separated-excess/ is added. No new kappa or selected-frontier change. Advance claim.

Evidence

Before, #3362 leaves full unequal-mask attainment open. After, PROOF.md proves the matching full-mask lower and upper bounds for this restricted family.

• All 50 new nonuniform full-mask constructions pass every forced identity and ordered zero block. Literal elimination gives the predicted ranks in all 150 checks over F2, F3 and F101. Cases include each of the 44 single-port increases and larger patterns with independent invertible port charts.
• A 201-bit base-width compressed recipe and ten invalid-input, forbidden-block, identity, charge and expansion-bound controls pass. The written proof supplies the universal quantifiers; the finite checks do not enumerate all fittings.
• Warning-strict normal and optimized direct commands pass on CPython 3.12.15/macOS arm64, timed at 0.228 seconds each on the committed export. Registered replay passes, including both commands. Source hashes and generated package/proof-bound receipt are checked.
• All 12 declared committed files pass the committed-byte/source-history preflight. The official committed export passes integrity checking. Normal and optimized Git-free replays pass; changed proof, false receipt and changed source controls are rejected, and exported bytes are restored unchanged.

From the worktree root:

/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -W error -B research/full-mask-separated-excess/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -O -W error -B research/full-mask-separated-excess/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/research_package.py --package research/full-mask-separated-excess
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/check_research_commit.py --package research/full-mask-separated-excess --check-source-history

Expected scientific marker: PASS_FULL_MASK_SEPARATED_EXCESS matrices=50 field_ranks=150 controls=10. Use an installed CPython 3.12 path elsewhere. Standard library only.

Limitations and unrun obligations

The widths outside T remain exactly d. This is linear query-vector capacity for one fixed strict mask, not a native COPY tariff, frame schedule, dirty-state program, hosting, precision/tape bound, paid supplier or complete multiplication theorem. The credited Q/C5 and partition premises remain dependencies. Independent human and formal proof-kernel review are unclaimed. No full selected cold replay, Lean or Docker run was performed.

Canonical main remained 624de9dc66858af0945e5f8a0942488d62280d43. The refreshed cached scan covered 435 open PRs and 3976 Discussion records, but only 129 of 6319 inventoried local notes. Full-main distinctive README and merged-term searches supplement that incomplete sparse coverage. Arbitrary diffs and unpublished work remain limits; the search is not a novelty certificate.

Open next questions

• Can an increase at a C5 port or one of the other 58 ports also attain the principal lower bound on the full mask? Start with one changed width and a complete fitting construction or stronger obstruction.
• Can this unequal query construction improve a fully charged native consumer? First bind charts and pay every read, copy, frame change and restoration.

Related open work

• Prove exact unequal-width query capacity on bipartite masks (no new κ) #4909 proves exact unequal-payload capacity for bipartite masks. This fixed mask contains a C5 and is outside that theorem; no shared new number is compared.
• Research: actual Turyn profiles have asymmetric block rank 9d (no new kappa) #1037 studies asymmetric block-fitting rank on Turyn profiles. Its geometry and characteristic scope differ from this fixed 112-port mask.
• Non-dense fitting B: every E8 term with x·y ≠ 0 has rank ≥ 9; square root-code floors E8 ≥ 72, P112 ≥ 64, P104 ≥ 56, D4 ≥ 12 for any fitting B (no κ claim) #3045 studies sparse fitting pairings and root-code COPY floors. Those tariffs and mask constraints differ from the query dimension here.
• Add exact complex rank-16 block decoder screen #3895 screens rank-16 product-root decoder blocks with a different growing label space; it supplies no full fit for this fixed mask.
• Add exact dirty-input coefficient audit for P112 tetrad block #3916 studies the coefficient and dirty-helper boundary of a P112 tetrad block. This result supplies query rank and leaves dirty realization open.
• Conditional kappa 0.001467289440740487: rank-sector factory on 112 ports #473 studies a 112-port rank-sector supplier and complete paid profile. This restricted block-fitting theorem neither reprices it nor computes its kappa.
• Conditional kappa 0.001467289440740487: rank-sector factory on112 ports #527 separately packages that rank-sector composition; its supplier contract is different and is not a dependency.

The completion refresh inspected all 81 open PRs on this account, including this PR and nine other submissions created since the CLAIM at 2026-10-22 23:40:20 UTC. Only #4909 shares the fitting-rank quantity, on the distinct bipartite domain described above. None reports the same restricted P112 value, and no additional scientific computations were run to compare those submissions.

CI notes

Both hosted checks passed at exact head a52acfd545be3e50a560b133e4349e4f3eb7c425 in run 39873970438: planning in 4m56s and registered package replay in 1m6s. Run metadata confirms the matching head, completed status and successful conclusion. The checks were read once at completion.

The registered replay runs both warning-strict normal and optimized commands. Local committed-byte/source-history and Git-free export checks also passed. Hosted replay certifies execution of these bounded checks; independent human and formal proof-kernel review remain unclaimed. No CI failure was observed.

Merge danger

Reversible. Seven files in one isolated opt-in research package. Shared code, frozen inputs and the selected result are unchanged.