[petalas]

Summary

Full D6 axis, arbitrary ambient binary rank <= 6
  14 axis labels force the entire full-E8 root closure onto the axis
  13 is insufficient: a literal six-space has 13 axis + 7 outside roots

Adds an analytic sharp concentration theorem in research/d6-axis-concentration14. A rank-five section of the 32-root bulk has at most 12 labels, so a six-space outside its seven-dimensional span has at most 13 axis labels. Exact reflection transport covers all 7,560 ordered orthogonal root pairs.

PR3295 owns the earlier finite threshold 18 and its caller result. PR3292 supplies the credited quadratic model. Their exact proof bytes and canonical geometry are retained and authenticated. This improves the concentration threshold; it claims no new common-cut theorem, caller exclusion, scalar factor, supplier or kappa. The full 120-root model is essential.

Evidence

• Before: the rank-six concentration dependency was checked at 18 labels. After: the written analytic proof establishes sharp 14, with an actual 13-label nonconcentration witness.
• Registered CPython 3.12 replay passes all three commands. The primary checks 2,667 bulk sections; separate enumeration checks all 10,795 six-spaces in the canonical fiber span and finds 120 maximizers of size 13. Seven CLI corruption controls and the rank-seven boundary control pass.
• All committed source/input bytes and official archive integrity pass. All three actual commands pass in the regular-only, inode-disjoint, read-only Git-free export on Python 3.12 and optimized 3.13. Ruff and formatting pass. The designated internal read-only peer check found no scoped blocker; its exact receipt is retained in REVIEW.json. The proof, source, witness and mathematical verifier bytes remain unchanged. A later portability correction deletes only the unused os import and required-TMPDIR guard from the test harness; its exact proportional recheck is retained in REVIEW-PORTABILITY.json. The actual affected test passes with TMPDIR absent and process-local scratch confined to the reviewer cache.

python3.12 -Werror -B scripts/research_package.py --package research/d6-axis-concentration14

Base 463113d675af7410ac91d53a4fed51ec6494eb9a, priority revision 6. Canonical main and exact predecessor heads were refreshed before submission. Canonical investigation. Open next questions require an actual caller and complete incidence budget before using the sharper threshold.

Credit Nick Petalas/PR3295/3292/3267, canonical PR3161/3162, David Arias's quadratic model, DreamingOfClouds/PR3154 and the retained E8/P112 lineage including joaqcoo. No historical heavy census, selected cold replay, Lean, Docker, native/physical/consumer/outer admission or human/proof-kernel approval is claimed.

Merge Danger

Door: two-way

Blast Radius: isolated

One new research package and opt-in replay. Frozen sources, shared verifiers and selected science are unchanged. Source authentication is separate from mathematical admission; hosted CI is reported separately.

Publication head 040dd292adfb2eab53c429345b115a6205df5235. All 17 final committed package/input bytes and archive integrity pass. All three corrected-code export scripts passed at 1480e53d6740d27c2b5d9329dc6f4b11c1737717; the final head adds only check metadata and the verbatim portability receipt. All 18 final archive entries are verified, unchanged scientific payloads match the reviewed export, and the actual affected test entry point passes again with TMPDIR absent.