[petalas]

Summary

P112 Lemma N, separate deletions for each direction
4 lines: retained upper bound of two directions
5 lines: explicit independent triple, each needing exactly five
common deletion union: eight lines, not five

Adds only research/p112-seven-flat-five-line-boundary/: literal witness, proof, two exact checkers, receipts and registered replay. This makes the independent-deletion allowance sharp relative to the retained four-line theorem.

Credit DreamingOfClouds/PR3154 at 708f0ad8928c383de8294aea3c126e9461d2066d, the SMALL2/Pencil lineage, and Nick Petalas' retained E8/P112 geometry. Exact pins and the predecessor excerpt are included. Canonical investigation and scope correction.

Evidence

• Before: the complete source audit showed that the initial 2,7^7 target was already covered. Neither that profile nor the discarded two-line census is counted as new.
• After: a rational minor of 16 proves three independent directions. Each has one unique completion among all 43,435 seven-spaces within five deletions. A separate lattice/label reconstruction checks all 66,045 four-deletion subsets per direction; every subset leaves rank at least eight, while five deletions leave rank seven.
• Registered CPython 3.12.15 replay and all 15 behavioral controls pass. The exact committed Git-free export passes both checkers and all controls read-only under CPython 3.13.5 with -OO -W error. Ruff, formatting, warning-strict compilation, export integrity and all 13 publication-byte checks pass locally.

Reproduce with python3.12 -B scripts/research_package.py --package research/p112-seven-flat-five-line-boundary.

The global four-line upper bound remains inherited, not replayed here. The witness does not refute a common-five-line theorem. No new historical profile exclusion, full C5, decoder floor, supplier or kappa claim. Evidence is author-checked, not independent human or proof-kernel review.

Merge Danger

Door: two-way

Blast Radius: research

One isolated package and unchanged declared geometry input. No selected-frontier, shared-code or frozen-input changes. Canonical main was refreshed at 463113d675af7410ac91d53a4fed51ec6494eb9a, priority revision 6.