Research bounded E6 one-extra frame decoder screen

[1337isnot1337]

Result

Adds a reproducible, exact screen for one seven-term E6 decoder mechanism: a one-extra rank-one extension of the six-term Gram factorization, with the dense pairing B0 fixed. Across the 36 projective E6 root directions, all 364 projective {-1,0,1}^6 directions in the pinned basis, and all rational lambda support cells, the minimum raw and fully charged Theorem C costs are both 40. This family therefore misses the requested cost-35 target. The result is scoped to this factorization and finite direction alphabet; it does not settle arbitrary seven-term E6 decoders and makes no kappa claim.

The package includes the exact identity, root/basis reconstruction, breakpoint coverage argument, cost certificate, positive fixtures, and negative controls. It preserves the initial root-only screen (566 cells, minimum 42) and records the one bounded pivot to the ternary directions.

Pins and reproduction

• Exact base: 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2
• Cycle 30 seed: 4dd9ff38bfc63aa200c17c947da92d9e; track complex-mechanisms
• Package: research/e6-one-extra-frame-seed4dd9/
• Reproduce: python3 scripts/research_package.py --package research/e6-one-extra-frame-seed4dd9

Checks completed locally:

• Package metadata and source pins pass.
• Exact package verifier passes normally and under python3 -O on Python 3.14.7.
• The predecessor's focused E6 exact baseline check passes, confirming the six-term reference ranks (6,7,6,6,6,6) and cost 37.
• git diff --check passes.

The registered replay hook is configured for Python 3.12, which is not installed in this environment; its wrapper reports that requirement. The declared verifier itself was run directly under the available Python 3.14.7. CI replay remains useful for the configured runtime.

Scope and credit

This differs from the rank-four E6 screens in PRs #2137 and #2232: it uses seven terms and a redundant rank-one frame, holding G and B0 fixed. It builds on merged PR #1590's root-unit model and Theorem C pricing; open PR #2228 separately leaves overcomplete E6 at seven terms open. No physical supplier mapping, changed paid profile, selected-frontier change, or independent human review is claimed. Prepared with substantial OpenAI Codex GPT-6 assistance.