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CELEST.WP2.01: WP2 of the celestial-holographic research contract CELEST.SEAM.01 -- the clock-invariant deformation XY = Z^4 + a0 of the A3 seam orbifold (geometry, periods/monodromy, deformed algebra; Bittleston-Homans-Sharma Z2 -> Z4 transfer, arXiv:2305.09451). [E] geometry: P(iZ) = P(Z) forces a3 = a2 = a1 = 0 sharply (two-sided: prod(Z - i^k w) = Z^4 - w^4); smooth iff a0 != 0 (disc = 256 a0^3); branch points = ONE free mu4 orbit; cross-ratio 2 / j = 1728 for ALL a0 (quartic invariants I = 12 a0, J = 0 identically) => a0 = pure SCALE, tau = i pillowcase FROZEN -- no shape modulus. [E] periods: Pi = t(i-1)(1,i,i^2), all 3 spheres same volume sqrt(2) t (lockstep); clock on H2 = COXETER element of W(A3) (char x^3+x^2+x+1, eigenvalues {i,-1,-i} = A3 exponents; h(A3) = 4 = |mu4| = N_fam+1); no invariant cycle (det(A-1) = -4); surviving direction = chi_1-Fourier diagonal (1,i,i^2); the clock IS the Picard-Lefschetz monodromy of the family; versal weights (1,2,3,0) = regular mu4 rep. [E] algebra: mode dictionary {w[m,n]: m = n mod 4} <-> {X^p Y^q Z^r: r <= 3}; bracket -4*Nambu(F) anchored at the a0 = 0 orbifold ({X,Y} = 16 Z^3, {Y,Z} = -4Y, {Z,X} = -4X), Jacobi + Casimir exact, uniform clock-degree -1; S-algebra corrections exactly LINEAR in a0 at the Z4 wrap, grade-conserving (no sector leak => the v492 equivariant SDYM(E8) sector deforms consistently); a0 <-> BHS c^2 slot (weight 0); matrix factorisations deform along all orbit splittings, clock fixes exactly the antipodal 2+2 sector (EH/Z2 middle node, 4 = 2 x 2). [E] negative controls: a1 Z => j = 0 (hexagonal); pure a2 Z^2 => stays singular (A1); a2 != 0 => j = 1556068/81 != 1728; grading leak explicit. [C] three named identifications (verdict B): -4*Nambu = THE k = 4 CCA bracket; period = root difference; seam-scale reading via clock^2 = deck. [C] v216 precision typed: given the order-4 clock the deformation freezes the (2,2,2,2) modulus to the square automatically -- relocation of the same order-4 input, no marker move. [O] full twisted-sector OPEs, W(mu) scaling limit for k = 4, splitting-function check, WP3-WP5; SEAM.EQUIV.01 stays [O]. Exact (sympy).

Linked claims

CELEST.WP2.01

Paper sections

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