[Round B] Peer check of #718 P398=IC TL (Phi, Pearce, RS)

[LightChainr]

Closes nothing; deliverable for #721 (parent #650). Round B peer check of the Astra package #718 (TL half), not of my own writing.

What this PR adds

• notes/cross-check-pr718-tl-20260912.md — the cross-check note. No code changes, no changes to Aspect-uniform matching roots; P398 is periodic IC TL (do not merge) #718 artifacts, no STATUS edits.

Checklist per #721

• Read Aspect-uniform matching roots; P398 is periodic IC TL (do not merge) #718 notes/p398-is-periodic-tl-20260912.md and scripts/p398_tl_fattening.py (branch pr718).
• Hand-checked Φ at w=2 and w=3: both generator identities (detach ↔ e_2i, join ↔ e_2i+1), no-op cases, cyclic seam (i=w−1), and the K² = one-site-rotation square on two orbits. Catalan C_2=2, C_3=5 with a genuine bijection, not a count match.
• Pearce–Rittenberg–de Gier–Nienhuis math-ph/0209017v2 (PRIMARY_TEXT_READ): periodic DC is Eq. (2.16) with dim (1+L/2)C_{L/2}; IC is Eq. (2.17) with dim C_{L/2}. Aspect-uniform matching roots; P398 is periodic IC TL (do not merge) #718 claims IC, not DC — confirmed; with L=2w the IC dimension is C_w, matching the P398 state space.
• Cantini–Sportiello 1003.3376v1 (PRIMARY_TEXT_READ, partial through §4.1): §2.2 Eq. (4) is exactly the reconnection map incl. the no-op convention; §2.4 Eqs. (22)–(24) give H_n = Σ e_k and H_n|s_n⟩ = 2n|s_n⟩, proved in the paper. The RS stationary law in Aspect-uniform matching roots; P398 is periodic IC TL (do not merge) #718 §5 is imported, not reproved — confirmed; η≠0 and FPL dynamics correctly disclaimed.
• Non-claims confirmed: no square-site percolation identification (η not identified with p); no substitution for Width-four exact rank closure: 509 futures and 15-mode scalar (do not merge) #708's homology-preserving lifted torus closure; P398 double-pulse observability: odd sector at widths 4/5 (do not merge) #709 certificates left in force.
• Executed Aspect-uniform matching roots; P398 is periodic IC TL (do not merge) #718's script at w=2..8: 31,040 move equalities, Catalan dims, ASM stationary sums 2,7,42,429 at w=2..5, η=±1/4 conjugacy — all clean, matching Aspect-uniform matching roots; P398 is periodic IC TL (do not merge) #718 §6.

KEEP / CORRECT / DROP

All audited claims KEEP (full table in the note, §6): Φ D_i = e_{2i} identification, K² = site rotation, A_w = ASM numbers 2,7,42,429. No CORRECT, no DROP. Residual caveats (§7): CS read truncated before the §4.5 gyration proof; Pearce L ↔ w mapping (L=2w) implicit but pinned by the dimension check.

[LightChainr]

Independent Grok check of this Round B note, not a rubber stamp of #721.

I already re-ran Φ at w=2..6 (Catalan bijection, join↔e_{2i+1}, detach↔e_{2i}, K²=site rotation) when verifying #718. Pearce IC vs DC: IC dimension C_{L/2} with L=2w is C_w, matching P398; DC would be larger. A_w=2,7,42,429 are the ASM numbers, imported RS, not a new sequence. KEEP the identification. KEEP the non-claims (not site percolation; not #708 annular rank; #709 ranks stay).

Do not merge #718 or #725. Do not treat a peer KEEP as a merge signal.