Publication history: 2026-06-11

Details

• External-review integration (v83) and release hygiene. Manifest --check mode and the release rule; holomorphy pins (E_8)_1 (the unique even unimodular rank-8 lattice theory).
• Sheet diamond and centered form (v94/v95). All four flavor operators are points of one two-parameter surface M(s,t); centered cross R,L=C\mp U, K,F=C\mp V with the cofactor seam normal n=(5,-9,6); documentation pass (“The Sheet Diamond and the Winding Line” in paper 3).
• Horizon/anchor round (v101–v103). The maximal (Nariai) black hole is the anchor: roots (1,1,-2), entropy bound \tfrac23=|\mathbb Z_2|/N_{\mathrm{fam}}; one repeller/attractor orientation in both sectors; trisection normal form (the canonical cosine coordinate).
• Clock/ladder round (v104–v108) + Lean hardening. The classical Nariai clock speaks anchor (\chi_{\mathrm{clock}}=(\lambda-1)(\lambda+2)); machine-pinned residual inventory; first review validation; quantum-clock target made quantitative; Pascal Ladder Theorem (g=2K+1 \Leftrightarrow the closure).
• QBL theorem chain (v109–v113). Sheet-Pairing Lemma; Calderón-sheet selection (a scalar seam datum exists iff the involution is sheet-odd); Quadratic-Transport Theorem (degree exactly 2); Self-Counting Channel (the Pascal closure as an identity); quasi-free kernel (one 2-point kernel determines the whole net, rank =c) — the QBL input merges with the R2/holomorphy premise; communicated across all status surfaces.
• U_{\mathrm{wall}} made exact (v114–v118). Torsion normal form and \delta=\tfrac12 theorem; exact anchor residue A_0^\star (diag =a/|\mu_4|, off-weights (8,0,5)/144); resonance theorem (M_\infty=\mathbf 1\iff a_{13}=0, one gauge orbit); the holonomy is the exact 24-element W(A_3)=S_4; the hypercharge hexagon is the sign-twisted family spectrum with the lepton coefficients as resolvent determinants.
• Second review validation + address pinning (v119–v121). Anchor ratio triad (\tfrac23,\tfrac43,\tfrac53); the 121 audit lemma; the lepton words are the compiler atoms (8,5,3) with divmod-hexagon addresses; R is the unique hexagon matrix with atom margins and \det 8 — the address table carries zero residual information.