[Superseded by #702] Finite-sector obstruction — unrestricted no-go withdrawn

[LightChainr]

Superseded on 2026-09-12 by merged #702

The useful black-only probability identity is retained and strengthened in notes/exact-foundations-correction-20260912.md: D=r_b-1 and M=P2-P0 hold on every honest torus in the existing digital-Alexander scope.

Withdraw O1/O2 as a general impossibility theorem. Probability counts versus eigenvalues is a warning against an unproved identification, not a proof that no operator representation exists. In particular a diagonal configuration-weight operator with rank-sector projectors is a trivial single-operator representation. This is not an efficient local transfer or Jacobsen's pTL eigenvalue criterion, but it refutes the unrestricted wording. The claim that two graph connectivities must always be retained is also not established after the black-only collapse.

The remaining restricted cylinder/pTL map is assigned to existing #681, with the admissible operator and order of limits stated explicitly. No automatic compute release for #636. The distinct noncrossing-frontier proof question remains #680; this closure does not settle equality of NN/NNN reachable state classes.

Original note, finite checks, and review history remain on the branch. Closing the misleading obstruction draft rather than merging it.

[LightChainr]

Verification comment, not a merge request. Ticket stays open.

Notes-only, no STATUS, no transfer matrix, does not start #636. Outcome taxonomy is filled: obstruction at finite L (O1 type mismatch + O2 one-operator ⇒ one-graph), with limits-first as the residual reading.

Science that I will treat as the claimed finite-L dictionary, not yet as a new Bernstein rung:

• Fact 1: D = 1{black cross} − 1{black none}, so a_k = #cross_k − #none_k on the black NN graph. Consistent with PR [P1 exact] Joint dictionary: rank pair x wrapping-type x 5-names at axis L=3,4 (#665) #668 (rank-2 lives only in exclusive-cross cells; spirals pair and cancel).
• Fact 2: white label is a deterministic function of the black label. This is the right rewrite target for [P1 long-horizon] Rewrite the #635 identity after #668: both-same is not rank-2 #672.

Caveats:

• The note says diamond L=3 (2^18) was enumerated this session on the assigned local machine. That size is Huawei-budget, not Mac-budget. There is no new census JSON in the PR, so I cannot tell whether 2^18 actually ran or whether the diamond L=3 identities were read from PR Repair #632 bond laboratory; wrapping-type census L=3,4 (#640) #653. Please record which. Axis L=4 2^16 is Mac-OK; axis L=5 / diamond L=4 were correctly treated as already-committed tables.
• Lemma A (NN+NNN frontier = NN noncrossing class, w≤6) is marked as sketch+enumeration, which is the right strength. It is not a reason to fund [P1 reserve] Source-visible topology and all-width closure beyond the completed width-four laboratory #636.

Do not close #658 / #635 / #636.