[vectorsss]

PR620’s archived ADE screen labels the complement of two orthogonal E8 roots as E6. That construction has 30 root lines and type D6. This companion constructs the A2 complement, checks its 36-line E6 geometry exactly, and recomputes the exceptional-root census without external dependencies.

The certificate includes every-pair reflection closure (20,565 checks), simple-root bases, Cartan determinants and Dynkin arms, and exact rational and binary ranks. Corrected E6 has h=6, v=36, rank_F2(J+G)=7 and the original full-rank-totals proxy x=7/6. Its proxy deficit remains negative. This is a research correction, with no new κ or universal decoder exclusion claim.

All original PR620 bytes and historical review receipts are preserved. Changes are confined to research/exact-ade-census/; source attribution, the archived script hash, background reference and substantial OpenAI Codex assistance are recorded in its README.

Validation:

• Four regression tests pass, including rejection of incomplete, duplicate and zero-root sets and a rational-versus-binary rank control.
• Normal and isolated optimized (-I -O) certificate replays pass using only Python’s standard library.
• Replacing the E6 selector with the archived orthogonal-pair selector is rejected by the regression test (30 != 36).
• Independent code/mathematics review found no issues; git diff --check passes.
• Full make verify was attempted with the system Python 3.9: it passed the first two community arithmetic checks, then stopped in the unchanged scripts/structured_bulk/complex.py because int.bit_count() requires a newer interpreter. No full-suite pass is claimed.

Reproduce from the repository root:

python3 -B research/exact-ade-census/test_census.py
python3 -B -I -O research/exact-ade-census/census.py --check research/exact-ade-census/RESULTS.json

[Mister-Meeseeks]

Thank you @vectorsss. This contribution is now retained on main in the scoped 100-PR review and contributor credits.

Contribution: Correction of the archived E6 exceptional-root census.

Review and limits: Two orthogonal roots leave D6, while the A2 complement gives E6. Exact census and controls correct the research record without asserting a decoder-wide impossibility.

The complete original source, notices and relevant execution evidence are retained through the pinned source archive. The review distinguishes fresh local runs, source-bound historical Linux CI and prior exact-head review; it does not claim 100 fresh full mathematical audits. Closing this historical PR as reconciled. This preserves parallel and cumulative credit without replacing the selected frontier or promoting priced research targets to completed constructions.

Reviewed head: 11a7cc98f8a9ef5192720bc37b45cf2c8369777a. Publication: 64039f1bd3b6a523b96083fd858ad040a75e3030.