[petalas]

Summary

 fixed two-indicator target, actual complete-plane rectangular reader tariff
- independent triples, pair-span lists, or one common external star
+ any at-most-four-term factorization, arbitrary external directions on both sides
 sharp pair floor m_A + m_B over every field and even orthonormal partition

This closes PR3472's four-query continuation. The new rank-three/rank-three case transfers the four queries and two distinguished targets to GF16 through a complete nine-type six-point incidence classification. All original source and reader zeros survive. The expanded identity then gives the sharp bill. Original terms attain equality, so disjoint pair replacements retain literal P112 total 224.

Only research/p112-four-term-reader-floor/ is added, with the self-contained proof, exact incidence templates, unchanged attributed fixture, source pins, receipt, two arithmetic implementations, actual CLI controls and replay instructions. No supplier, new kappa or selected-frontier update is claimed.

Evidence

• Before: the dependent four-term case with external vectors on both sides remained open. After: the six-point transfer closes it, including arbitrary coefficients, characteristic, outside cancellations, zero terms and repetitions. A seven-point non-Fano example explains why this proof does not automatically extend to five terms.
• Primary checks cover 352 labeled incidence configurations, 330 rational configurations, 21,120 source/reader requests, 256 degenerate requests, 150,528 literal operator entries and all 50,176 expanded-I224 entries. The separate GF256/F3/F5/F7 implementation checks 990 configurations, all 63,360 subset ranks and 63,360 requests, coordinate Gram bills and 225 boundary controls. These corroborate the written universal proof; fixture bills are not global search minima.
• Registered CPython 3.12.15, final committed Git-free optimized CPython 3.15.0, six actual optimized CLI corruptions, the stated Ruff correctness profile/formatting, and exact final committed-byte/source-history checks pass. Source/export receipts bind 877ea00e462a4d306babb9867651d9fd9a1f74b1.

# Set TMPDIR to a private existing external directory.
python3.12 -Werror -B scripts/research_package.py \
  --package research/p112-four-term-reader-floor
python3 -Werror -B scripts/check_research_commit.py \
  --package research/p112-four-term-reader-floor --check-source-history

Canonical source and submission refresh remain 6f100d4bb5083f8c35d96fd95a539811c62f245c, priority revision 6. Public proof comparisons have exact head/blob/SHA receipts separate from ancestry pins. Replay needs only the retained package and its one declared canonical input. Credit Tekalign/PR3370, Philippe Van Velzen/PR3345, PR3398/3414/3463/3472/3475, ctoth and the retained P112/E8/native/compiler/supplier lineage. Scope, sources and full limits are in README.md, PROOF.md and VALIDATION.md.

Independent human and formal proof-kernel review are unclaimed. Five-term synthesis, changed matrices, larger target blocks, native acquisition/coefficients/frames/restoration, hosting, stock, precision, all-size/compiler and outer transfer remain open. Selected cold replay, Lean, Docker and hosted CI were not run.

Merge Danger

Door: two-way

One isolated opt-in research package. Frozen predecessor bytes and existing verifiers are unchanged.

Blast Radius: research

Archiving the result does not admit a supplier or change the selected frontier.