[P1 exact] Joint dictionary: rank pair (r_b, r_w) × wrapping-type 4×4 at axis L=3,4

[LightChainr]

Parent: #650. No Huawei. Axis L=3 is 2^9, L=4 is 2^16 — seconds. Do not run axis L=5 (2^25) on the Mac; if you want L=5, comment NEED_HUAWEI and stop.

Why

We have two exact views of the same configs that have never been crossed:

• rank pairs (r_b, r_w) / (P11, P20, P02) from the repaired bond/site lab (PR Repair #632 bond laboratory; wrapping-type census L=3,4 (#640) #653, exact_rank_census / census-exact.json)
• wrapping-type 4×4 and probe635: M(p) as both-same sector difference — exact at finite L (verdict A, degenerate sectors); #628 bond rank defect fixed #646 5-names (PR Repair #632 bond laboratory; wrapping-type census L=3,4 (#640) #653 / Wrapping-type census: axis L=5 and diamond L=4 (#640, #651) #657)

#660/#662 writes M as a both-same difference. That identity should be checked against the rank pair, not only against collapsed D. In particular: is both-same the same as rank 2? Is both-same × both-same (spiral pairing, 6 configs at axis L=3 k=6; 685360 at axis L=5) rank-1 or rank-2?

Compute

Stream axis L=3 and L=4 (site). For each config record:

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

Emit exact integer joints. Tripwire: collapsing D from this joint must match committed Bernstein at each L; r_b+r_w=2 on site (PR #653).

Deliverable

Notes + JSON tables + draft PR against main. Integers only. No STATUS, no merge, do not close #635/#660.

Mac only. Wait for ASSIGNED_MACHINE.

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

[LightChainr]

ASSIGNED_MACHINE: local

Axis L=3,4 only (2^9,2^16). L=5 is Huawei if ever. Draft PR against main. Integers only. Do not edit STATUS.

[LightChainr]

Delivered: draft PR #668 (branch issue-665-joint-rank-wrap-l3l4, base main). Notes: notes/issue-665-joint-rank-wrap-20260908.md; integer joints in results/issue665-joint-rank-wrap/axis-L{3,4}.json.

Answer to the ticket question: both-same ≠ rank 2; both-same × both-same is pure rank-1 × rank-1 (spirals) — (1,1): 6 at axis L=3 k=6, (1,1): 1120 at L=4 (k=8..12). both-same splits 6 spiral / 91 cross at L=3 and 1120 / 9045 at L=4. Rank-2 appears only in the D-carrying exclusive-cross cells (0,2)/(2,0). Tripwires pass at both L (Bernstein bit-for-bit, r_b + r_w = 2, PR #653 totals reproduced). Integers only. L=5 not run (Mac boundary; NEED_HUAWEI if wanted). No STATUS edit; ticket left open.

[LightChainr]

PR landed: #668

Grok check (no merge, leave open):

• L=3,4 only; Bernstein and r_b+r_w=2 tripwires claimed pass; L=5 not run.
• Answer: both-same is not rank-2. At L=3 it is 6 spirals (rank-1) + 91 crosses (rank-2). both-same × both-same is exactly the (1,1) spiral pairing (6 at L=3, 1120 at L=4). Rank-2 lives only in neither×both=(0,2) and both×neither=(2,0).
• This is the label split notes(#635/#660): the #635 identity against the wrapping-type tables #662 left hanging: 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 is not rank-pure. Any sector reading has to split both-same by rank.

Ticket stays open. Related comment on #660/#662.