[petalas]

Summary

Remove the cell-locality premise from PR3560's two residual reader bounds. Closure cells may cross full-basis orthogonal blocks and have arbitrary positive size; block dimensions may be odd. The proof is self-contained for the fixed VVV/MMM query families, over every field of characteristic different from two and with arbitrary ambient readers.

n_k = binary dimension present in exactly k target groups
original D = n_1 + 2n_2 + 3n_3
VVV bill >= D + n_2
MMM bill >= D + n_1 + n_2
strict crossing example: D=6, VVV minimum=7, MMM minimum=9

Crossing cells correlate choices across blocks, so the block bounds need not be attained together. The exact 7-versus-6 example proves this distinction. General nonreducing spans, partial block bases, characteristic two, arbitrary-query classification and physical supplier costs remain open. No kappa or selected-frontier change is claimed.

Package research/p112-cell-crossing-residual-floor contains proof, exact fixtures/results, two checkers, optimized CLI controls and replay metadata. PR3560's exact proof is retained under COMPARISONS with origin commit/path/blob/SHA256 solely as handoff context. All mathematical lemmas used here are proved in the new note, and the runtime has no external scientific input or foreign Git-object requirement. Credit retains PR3560, PR3549/3538, Philippe Van Velzen, Arham Tahir, Tekalign/PR3370 and the P112/E8/native/compiler lineage.

Evidence

• Before: PR3560 excludes planes crossing blocks. Its full arbitrary-query result is not reclassified here.
  After: The new written residual proof permits crossing cells and odd dimensions. A two-port crossing example has exact VVV minimum 7, strictly above its general lower bound 6.
• Two separate implementations agree on all 6,660 assignments, complete four-charge streams, histograms and minima across ten fixtures. The separate checker verifies 3,896 integer and 11,688 gauged F3/F5/F7 actual operator entries.
• Six malformed contracts and two corrupted result records reject through both optimized real CLIs with their intended diagnostics. Sixteen restored runs and two initial positives pass. Geometry faults update fixture hashes so authentication cannot mask a missed contract check.
• At exact commit 51f4425e91f39c6e966007f1ab0ec9172653d83d, CPython 3.12 registered replay, metadata/pins and committed-byte/source-history checks pass. Applicable Ruff and formatting checks passed before commit on the identical final code bytes. All three actual scientific/control commands pass in the 13-file Git-free committed export with PATH=/nonexistent. Source/export hashes, ownership and distinct inode identities stay unchanged.

python3.12 -Werror -B scripts/research_package.py --package research/p112-cell-crossing-residual-floor
python3.12 -Werror -B scripts/check_research_commit.py --package research/p112-cell-crossing-residual-floor --check-source-history

Canonical investigation and original claim. Independent human/formal acceptance, hosted CI, selected full cold replay, native acquisition/coefficient/frame/restoration, hosting/precision/stock, compiler/all-size admission and complete supplier/consumer/outer obligations are unclaimed.

Merge Danger

Door: two-way

Blast Radius: package

Only a new isolated research package is added. Frozen predecessors, canonical sources, shared code and the selected frontier are unchanged.