Add exact E6 sheared-frame cost census

[1337isnot1337]

Result

Adds a scoped exact negative result for an E6 one-extra rank-one decoder family. Starting from the pinned six-term Gram factorization, the search applies each of the 60 signed elementary transvections A = I + epsilon E_ij, then tests the declared 365 projective correction directions and every exact nonzero-lambda breakpoint and complementary interval with fixed dense pairing B0.

Across 330,486 support cells, the minimum raw and fully charged root-unit costs are both 37. There are 26 degenerate six-active cells and 330,460 seven-active cells; none of the seven-active cells reaches 35. A least-cost witness is A=I+E_23, a=(1,-1,1,0,0,1), lambda=1/2, with rank profile (6,0,6,6,6,6,7). This does not establish an unrestricted E6 impossibility, a supplier implementation, or a change to the selected kappa.

Evidence and replay

The package contains the exact derivation, source pins, per-transvection shards, aggregate certificate, task and overlap metadata, and a stdlib-only rational verifier with identity and rejection controls. Local checks passed: --smoke, both shard replays (164784 and 165702 cells), package metadata/source pins, and git diff --check, using Python 3.14.7. Python 3.12 is not installed locally; the registered package workflow is expected to run its declared replay in the repository environment. No CI result is claimed here.

The search stopped at the declared finite family: 60 transvections, 365 directions, exact breakpoints and one rational representative per open interval. It does not cover other six-term factorizations or arbitrary GL6(Q) changes. The cost is algebraic root-unit cost only; source, copy, frame, hosting, restoration, precision, interface and supplier costs are not mapped.

Pins and attribution

• Base/main: 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2
• Contribution head: 24456c7c97752b4f301aa8b3873d3b20b7d1a9ae
• Selected-record SHA-256: 10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32
• Task seed: b401f2874293cab50e88e4bd7068a949; track complex-mechanisms
• Claim: Handoffs and requests for independent checks #1166 (reply in thread)
• Predecessor model/context: merged PR Root-unit decoders: two lemmas, an erratum to #595, and open cases (partial; no κ claim) #1590; Cycle30 fixed-identity family PR Research bounded E6 one-extra frame decoder screen #2240. This changes the six-term basis by elementary transvections.

Prepared with substantial OpenAI Codex GPT-6 assistance in scope selection, exact derivation, implementation, verification and writing. No independent human review is claimed. Apache-2.0.