Width-three exact closure and width-four topological memory (do not merge)

[LightChainr]

Draft. Do not merge. Refs #681, #636, #706, #650. Additive after merged #705 (eb89e942).

What

Width-three square-site torus, periods (3,0),(0,m), m≥2:

• configurationwise r = 1_F + 1_V (full row + every interface overlaps);
• M_{3,m}(p) = tr(T(p)^m) - (1-p^3)^m with a 7-state local row transfer;
• tr(T^m)=tr(B^m)+2 tr(C^m), multiplicity two is ordinary/semisimple;
• cylinder sextic p^6-3p^5-5p^4-4p^3+p+1=0, unique root in (0,1)
q_3=0.58888069991785… = Jacobsen 2015 Table 2 n=3. Not a new p_c.
• every finite p_{3,m} < q_3, with explicit subleading displacement.

Width four is a new representation question. Prefixes [13,5] and [7,5] have
the same occupation count, frontier mask {0,2}, ordinary partition {{0,2}},
and no existing winding, same weight p^5(1-p)^3, but lifted displacements
-2 vs +2. Common suffix [13,0] gives ranks 0 and 1. Occupancy +
ordinary partition + wrapping flag cannot preserve continuation. This is a
scoped insufficiency, not the withdrawn #675 no-go.

Also archives the already-completed #706 transport-order job (not a new MC)
and a proposed re-scope of existing #636 (no new issue).

Independent Grok check (not the bundle script)

Spanning-tree winding rank (the exact_torus_enum method, rectangular periods),
not width3_cylinder_exact.ambient_rank:

• identity r=1_F+1_V fails on 0 / 299,584 configs (3×2 through 3×6);
• 3×3 Bernstein [-1,-9,-36,-78,-90,-36,36,36,9,1] matches the known square rung;
• M_{3,m}(1/2) equals tr(T^m)-(1-p^3)^m for m=2..6 to machine zero;
• [1,5,4,5] has r=0 vs naive 1; [11,14] has r=2 vs naive 1;
• [13,5,13,0] → r=0, [7,5,13,0] → r=1; open lifts -2 vs +2;
• uniqueness of q_3 via s=p/(1-p): (1+s)^6 P(s/(1+s)) = 1+7s+20s^2+26s^3+8s^4-14s^5-9s^6 has one Descartes sign change.

Seven local tests pass after git apply on current main. Full-repo CI was not run for this patch. #706 CI is a different check.

Out of this PR

• Do not re-dispatch [P1 CPU / existing data] After #702: within-model quantile-shape symmetry and full-vector finite-size motion #622 / [Completed bounded delivery] Exact width-two torus/cylinder bridge and the finite-length correction #681 as the same analysis.
• Do not start a weighted transfer engine or GPU job.
• [P1 proof / bounded CPU] Observable spectral remainder and width uniformity after the exact n=2 bridge #636 next step is the attached width-four annular/lifted closure brief, on the existing issue.

No docs/STATUS.md edit.

[LightChainr]

Do not merge. Independent Grok check is in the PR body: spanning-tree winding rank, not the bundle’s ambient_rank, on all 299,584 configs of 3×2–3×6 (zero identity failures); width-four ranks and lifts reproduced; q_3 uniqueness via the s-transform polynomial 1+7s+20s^2+26s^3+8s^4-14s^5-9s^6 (one Descartes sign change). Seven local tests passed after apply on main@eb89e942. Full-repo CI not run for this patch.

[LightChainr]

Width-three argument stands (this PR’s own CI 34689086221 is a different check from the new patch). Width-four sufficiency is draft #708, not a rewrite of this PR. Do not merge either.