[P1 exact] Joint dictionary: rank pair x wrapping-type x 5-names at axis L=3,4 (#665)

[LightChainr]

Closes nothing; deliverable for #665 (parent #650). Draft — do not merge.

What

Joint exact census of site configurations at axis L=3 (2^9) and L=4 (2^16), recording for every configuration

(k, r_black, r_white, wrap_black, wrap_white, label5_black, label5_white)

— the rank pair (r_b, r_w) of PR #653's repaired lab crossed with the coarse 4×4 wrap labels and the #646 5-names, for the first time in one table.

• Script: scripts/issue665_joint_rank_wrap_census.py (imports probe635_sector_decomposition.py from PR probe635: M(p) as both-same sector difference — exact at finite L (verdict A, degenerate sectors); #628 bond rank defect fixed #646 onto main, verbatim)
• Integer joints: results/issue665-joint-rank-wrap/axis-L3.json, axis-L4.json
• Notes: notes/issue-665-joint-rank-wrap-20260908.md
• Test: tests/test_issue665_joint_rank_wrap.py (axis L=2,3, seconds)

Answer to the ticket question

both-same is NOT the same as rank 2, and both-same × both-same contains only spirals (rank-1 × rank-1), no rank-2.

	rank-1 (spiral)	rank-2 (cross)
both-same at L=3	6	91
both-same at L=4	1120	9045

• both-same × both-same by rank pair: (1,1): 6 (L=3, k=6) and (1,1): 1120 (L=4, k=8..12). Zero rank-2 involvement — structurally impossible at any L, since r_b + r_w = 2 on site forbids rank-2 on both sides.
• Rank-2 lives exclusively in the D-carrying exclusive-cross cells: neither × both is exactly (0,2) (259 / 36559) and both × neither exactly (2,0) (91 / 9045).
• The 6-count spiral pairing at axis L=3 k=6 (and its L=4 analogue) carries D = 0 and rides inside both × both; the probe635: M(p) as both-same sector difference — exact at finite L (verdict A, degenerate sectors); #628 bond rank defect fixed #646 both-same amplitude rows are therefore not rank-pure — any sector-level reading must split both-same by rank.
• both-two mass 0 at every k at both sizes; dir0 × dir0 = dir1 × dir1 (78 / 9406 each).

Tripwires — pass

1. Bernstein collapse bit-for-bit: L=3 [-1,-9,-36,-78,-90,-36,36,36,9,1]; L=4 committed rung.
2. r_b + r_w = 2 on every configuration, zero violations; PR Repair #632 bond laboratory; wrapping-type census L=3,4 (#640) #653 rank-pair totals reproduced exactly.

Integers only. Axis L=5 (2^25) not run here — NEED_HUAWEI if wanted. No docs/STATUS.md edit; no ticket closed; draft PR, not for merge without review.

Related: #635, #640, #646, #650, #651, #653, #657, #660, #662.