Research: shared-line rank-2 block fusion misses the 5% ceiling gate

[1337isnot1337]

Result

This packages a scoped negative result for a new shared-line rank-shape mechanism. If every pair of rank-2 children in the selected complex local profile could be fused into one rank-3 block child for free, the fixed-word ceiling would improve by at most about 4.6354%, below the task's 5% gate. Per the gate, the experiment stopped before attempting source mapping or physical synthesis.

The proposed block hypothesis is geometric: two rank-2 target frame planes share one line, and one rank-3 block materializes that shared direction once. The calculation grants all 209 possible fusions, free matching, adapters, copies, fanout, frame transitions, hosting, precision, and dirty restoration. It assigns the freed mass to fractional rank-51 idle children, as in the pinned ceiling relaxation. This is an upper bound within the unchanged coverage law, centre charge, unpaid-coordinate count, and outer-rank cap.

Exact evidence

• Selected local profile per call: {1:2412, 2:418, 3:432, 4:142, 5:82, 8:8}.
• Baseline ceiling interval: [0.001690054109088, 0.001690054109089].
• Most favorable all-pairs profile: {1:2412, 2:0, 3:641, 4:142, 5:82, 8:8}.
• Its ceiling interval: [0.001768394682583, 0.001768394682584].
• The ratio of upper endpoints is exactly 43131577624/41220831929 < 21/20.

The source archive and relevant members are SHA-256 pinned in SOURCES.json; the package also pins the selected record, current task catalogue, selected source manifest, assembly certificate, review, and exact ceiling calculator. The selected record and frontier are unchanged.

Reproduction

python3 -I -B research/complex-shared-line-rank2-seedceaca8/verify.py
python3 scripts/research_package.py --package research/complex-shared-line-rank2-seedceaca8 --check-only

Expected: PASS_SHARED_LINE_RANK2_SCREEN ... ratio=1.0463538848 target=1.05 physical_interface=not_established and PASS_PACKAGE_METADATA_AND_PINS.

Local verification used Python 3.14.7. The registered generic replay asks for Python 3.12 and remains subject to hosted CI.

Scope limits and attribution

This result does not show that the shared-line block is impossible, establish that any source-compatible pair exists, or produce a supplier or new κ. It bounds only this profile substitution under the stated fixed model; source compatibility and every real interface expense remain unresolved.

Adjacent work: PR #2130's rank-one-to-rank-two retiming, PR #2124's Phase-B (3,1,1,1)→6 block, Discussion #1987's Karatsuba block, and PR #1872's shared-product helper. This package studies the profile ceiling for a pair of rank-two frames sharing one line.

Cycle X used seed ceaca886bcd52d7e2a036a2b4d561117, track complex-mechanisms, task complex-rank-shape-decoder, priority revision 4, exact base 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2, and selected-record SHA-256 10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32. Prepared with substantial OpenAI Codex assistance.