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[P1 long-horizon] Rewrite the #635 identity after #668: both-same is not rank-2 #672
Description
Parent: #650. Follow-up to PR #662 (from #660) and PR #668 (from #665). Notes-first. Mac-only.
Why this ticket exists
PR #662 wrote wrapping-form A treating both-same as the rank-2 (cross) class, then mapped it onto coarse both. PR #668's joint census killed that identification:
both-same= rank-1 spiral ⊎ rank-2 crossboth-same × both-sameis exactly(r_b, r_w) = (1,1)(6 at L=3, 1120 at L=4)- rank-2 lives only in exclusive-cross cells:
both × neither = (2,0)andneither × both = (0,2) - collapsed
a_k = \Delta#(both-same)still equals Bernstein because spirals cancel, not because everyboth-sameevent is a cross
#662 is therefore a correct numerical identity with a wrong dictionary. Rewrite the identity so a later reader cannot confuse the two.
Questions
- Write wrapping-form A' in the joint
(rank pair × wrap × 5-name)language of [P1 exact] Joint dictionary: rank pair x wrapping-type x 5-names at axis L=3,4 (#665) #668, with D-carrying cells named as exclusive crosses. - State the spiral-cancellation lemma that makes
\Delta#(both-same) = a_kstill true. Prove it from the L=3,4 integers, or mark it a conjecture for all L. - Does A-continues ([P1 exact] Does both-two acquire mass at axis L=5? Structural caveat on #635 A #651, axis L=5 / diamond L=4,
both-two = 0) survive the rewrite, or did it secretly depend on the wrong dictionary? - Do not fund [P1 reserve] Source-visible topology and all-width closure beyond the completed width-four laboratory #636. If the rewritten identity still does not need a transfer matrix, say so.
Constraints
- Read PR notes(#635/#660): the #635 identity against the wrapping-type tables #662, [P1 exact] Joint dictionary: rank pair x wrapping-type x 5-names at axis L=3,4 (#665) #668, probe635: M(p) as both-same sector difference — exact at finite L (verdict A, degenerate sectors); #628 bond rank defect fixed #646, 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 notes/JSON. Do not re-enumerate L=4. Dumping the 6 L=3 spiral configs (
2^9) is Mac-OK if you need occupancy lists. - Axis L=5 joint census is
NEED_HUAWEI; do not run it. If you need that rung, commentNEED_HUAWEIand stop. - Integers only in exact artifacts. No
docs/STATUS.md, no merge, do not close [P1 long-horizon] Is M(p) the difference of two topological sector amplitudes? Prove or kill the map before anyone builds a transfer matrix #635 / [P1 long-horizon] Write the #635 identity against the wrapping-type tables #660 / [P1 exact] Joint dictionary: rank pair (r_b, r_w) × wrapping-type 4×4 at axis L=3,4 #665.
Deliverable
notes/issue-635-identity-rewrite-YYYYMMDD.md + draft PR against main.
Wait for ASSIGNED_MACHINE.
Activity
LightChainr commentedon Sep 8, 2026
Notes-first rewrite of wrapping-form A after the #668 dictionary. No Huawei. No L=5 joint census. Draft PR against main. Do not edit STATUS. Do not merge. Do not close #635/#660/#665.
LightChainr commentedon Sep 8, 2026
Read PR #675 (
notes/sector-obstruction-20260908.md) before rewriting A. Claimed finite-L dictionary is nowM_L = A^{cross}_{NN} − A^{none}_{NN}with white labels a deterministic function of black labels. Combine that with PR #668 (spirals =both-same×both-same=(1,1)). Still do not fund #636. Still no L=5 joint census on the Mac.LightChainr commentedon Sep 8, 2026
Draft PR: #676
Notes-first rewrite of the #635 identity in the #668 joint language (
notes/issue-635-identity-rewrite-20260908.md):neither × both = (0,2)(−1) andboth × neither = (2,0)(+1);both-same × both-sameis(1,1)pure spiral, D = 0 (6 at L=3, 1 120 at L=4).Integers only; no
docs/STATUS.mdedit; #635/#660/#665 left open.LightChainr commentedon Sep 8, 2026
PR: #676
A′ rewrite landed as notes. Ticket stays open. Not merging. Local clone removed after the branch was on origin at
0bb6ca5.