Follow a result back to its evidence.

CELEST.WP5E.M1.01: milestone M1 of the celestial-holographic research contract CELEST.SEAM.01 (WP5e back-reaction programme) -- 'the A3 Omega_N', executed (SUCCESS on the preregistered v514 S8.1 criterion): the back-reacted holomorphic 3-form Omega_N on the twistor uplift of the deformed A3 ALE, with exact periods. Exact sympy, no floats (30 checks, ~1 s). [E] RESIDUE FORM DERIVED: on F = XY - P(Z) all three ambient representatives satisfy dF ^ omega2 = -dX^dY^dZ and pull back to omega2 = dX^dZ/X (Poincare residue, derived not assumed); cover pullback at a0 = 0: omega2 = 4 dz1^dz2 = |mu4| x (flat form) -- the residue normalisation CARRIES the source charge 4; clock diag(i,1): omega2 -> i omega2 (v492 S5 replicated); weight ledger 4+4+2-8 = 2, Omega in O(4) = -deg K_PT; EH anchor 2 = |Z2|; wrong-weight control Z in O(4) breaks three ways (4 != 2, 6 != 4, 5 != 3). [E] THE TWISTOR FAMILY CLOSED: from the four O(2) centre sections q_p(la) = i^p t0 - i^-p t0 la^2 the family is EXACTLY XY = Z^4 + 4 t0^2 la^2 Z^2 - t0^4 (1 - la^4)^2 (e1 = e3 = 0 identically; la = 0 gives exactly the v493 clock family; a2 in O(4) opens only off-seam, a2(0) = a2(inf) = 0); clock lift gamma: (Z, la) -> (iZ, -i la), gamma^4 = 1, Omega -> +Omega (CY-compatible); weight chain 4+4+2-8+2 = 4 = -deg K_PT. [E] OMEGA_N CLOSED + QUANTISED PERIODS: Omega_N = Omega_0 + sum N_p K_p with CPS/Bochner-Martinelli kernels on the centre twistor lines; dK = 0 away from the source, scale degree 0; PERIOD TABLE: boundary S^3/Z4 at the orbifold point (2 pi i)^2 x 1 (minimal invariant charge 4 = |mu4| -- the lens fundamental domain FORCES N in 4Z), deformed phase (2 pi i)^2 x 4, linking S^3 uniformly (2 pi i)^2 x N, per-sphere flux vector (2 pi i)^2 x N (1,1,1) (forced uniform twice over: clock orbit + K4 connectivity), seam-fibre phase vector 2 pi i t0 (i-1)(1, i, i^2); the undeformed Omega_0 carries ZERO quantised 3-flux (all flux sourced); (2 pi i)^2 = (fibre residue) x (transverse residue) (density -sin 2 theta). [E] CLOCK COVARIANCE: Pi_{j+1}(-i la) = i Pi_j(la) for ALL la; the 12 collision nodes sit exactly on the 8 eighth roots of unity (8 = 2|mu4|, the Z8 seam bridge), clock orbits 4+4+4, honest conifold points (Hessian det 512 t0^6, quadric rank 4). [E] KILL PROBE (honest): the forbidden family Z^4 - Z: 0/24 orderings lockstep (vs 8/24), la-support 12 twelfth roots != Z8, no antipodal pairing -- BUT the (2 pi i)^2 quantisation holds there TOO: integrality alone is NOT the discriminator, the discriminator is the lockstep phase structure + the clock forcing of equal fluxes; the v509 dial survives. [E] ANCHORS + CONTROLS: EH/Z2 (2 nodes, charge 2 = |Z2| forced); CPS original (full S^3: every integer N allowed); diag(i,i): Omega_0 -> -Omega_0 (collapse at step zero) while K stays invariant; fractional charges N = 1, 2, 3 excluded. [C] global kernel patching (Green function), Hitchin small resolution, CPS brane dictionary. [O] M2 (twisted KS measure), M3 (a0 uplift), the quantised BCOV coefficient; SEAM.EQUIV.TWISTOR.01 untouched (preparation, not construction). No marker moves.

Linked claims

CELEST.WP5E.M1.01

Paper sections

Source section 1Source section 2Source section 3Source section 4Source section 5Source section 6Source section 7Source section 8Source section 9Source section 10Source section 11Source section 12Source section 13Source section 14Source section 15Source section 16Source section 17Source section 18Source section 19