Original ledger status
CELEST.WP1.01
WP1 OF THE CELESTIAL-HOLOGRAPHIC CONTRACT EXECUTED (2026-07-20; CELEST.SEAM.01 work package 1, verdict B): the E8 mu4-glue grading (v128) IS the flat Z4 monodromy of the glue-equivariant celestial chiral algebra on the A3 ALE space C^2/Z4 -- the Bittleston-Homans-Sharma CCA construction (arXiv:2305.09451, JHEP 09 (2023) 008; the Z2/Eguchi-Hanson case) refined to Z4 with a Kronheimer-Nakajima flat connection at infinity. Sympy exact throughout. [E] INNER GRADING / FLAT MONODROMY: h = (2,2,2,2,2;0^4) gives <alpha,h> = glue class mod 4 for ALL 240 roots => glue = Ad(exp(2 pi i h/4)), an order-4 torus element = a flat Z4 monodromy; the A3-side detector h' = (0^5;1,1,1,-3) reads the SAME class -- the glue charge is the diagonal (1,1) of the discriminant group Z4 x Z4 (the v92/v125 Lagrangian glue); Z2 halfway: 120 = SO(16), 128 = spinor (v125 sub-Q {0,2}). [E] SPATIAL SIDE: C^2/Z4 under (z1,z2) -> (i z1, i^-1 z2) IS the A3 singularity XY = Z^4 (invariant ring exact; Hilbert series (1+t^4)/((1-t^2)(1-t^4)); Molien table verified; conjugation symmetry N[d][1] = N[d][3]). [E] EQUIVARIANT SECTOR CLOSES: the glue-equivariant SDYM(E8) modes (j + m = 0 mod 4) form a Lie subalgebra with D[d] = 60(d+1) even / 64(d+1) odd -- uniform per parity ONLY because dim g_j = (60,64,60,64) (the v128 dims are the consistency condition); zero modes (d=0) = g0 = carrier D5+A3+Cartan = 60; asymptotic density 62/248 = 1/4 = 1/|Z4|; EH/Z2 halfway towers 120/128. [E] CHARACTER: Theta_E8 = sum of the 4 glue-coset thetas (shell 1 = (52,64,60,64) from the LATTICE, independent of the root construction); the 4 sector characters Theta_Cj/eta^8 sum EXACTLY to chi_(E8)_1 = 1+248q+4124q^2+34752q^3 (v377 series); sector weights h_D5 = (0,5/8,1/2,5/8), h_A3 = (0,3/8,1/2,3/8) = the v92/v125 discriminant form (5x^2+3y^2)/8 mod 1; glue diagonal h = (0,1,1,1) INTEGER = v125 isotropy = the extension to (E8)_1 is local. [E] CRITICAL CORRECTION (why verdict B): the A3 deck diag(i,i^-1) induces z -> -z on the celestial sphere (projective order 2, the sheet flip) -- NOT the order-4 clock z -> iz; any SU(2) lift of the clock has order 8 (spin group Z8, would quotient to A7); exact bridge (spin clock)^2 = deck, |Z8| = 8 = 2|mu4| (the c3 = 1/(8 pi) winding integer); the order-4 clock IS realised as the U(2) phase diag(i,1) (order 4, fixed {0,inf}, free mu4 orbit -- all v180 properties; normalises the deck, det = i rotates the holomorphic symplectic form by the mu4 generator -- Kaehler, not triholomorphic). [E] GRAVITY SIDE: clock-invariance selects from the versal A3 family XY = Z^4 + a2 Z^2 + a1 Z + a0 EXACTLY the 1-parameter family XY = Z^4 + a0; its 4 branch points are ONE mu4 orbit with cross-ratio 2 -- the seam marks (v179 clock orbit; v168/v214 pillowcase j = 1728). [E] NEGATIVE CONTROLS: false spatial action diag(i,i) killed 3 ways (det = -1 not in SL(2,C); Poisson closure fails 14/14; grades unsymmetric); false glue (60/64 swap) breaks additivity on 3112/6720 root pairs; rigidity: exactly {id, j -> -j} = Aut(Z4) of 24 relabelings are additive. [C] the clock-deck identification is a NAMED extra identification (clock^2 = deck on the sphere, sheet-Z2 spin bookkeeping) -- verdict B, not A. [O] structural arithmetic ONLY: no celestial duality is constructed; CELEST.SEAM.01 (WP2-WP5) stays a research contract; SEAM.EQUIV.01 stays [O], untouched. No gate closes, no marker moves.
Recorded status: Formal/Identity [E] (exact Z4-orbifold/character/spin arithmetic, sympy, negative controls) + [C] (the named clock^2 = deck identification, verdict B) + [O] (celestial programme; SEAM.EQUIV.01 unchanged)
Dependencies, status detail and source
Canonical status: WP1 [E]/[C]/[O]: E8 mu4-glue = inner order-4 torus element = flat Z4 monodromy on the A3 ALE; equivariant SDYM(E8) sector closes (60/64 towers, zero modes = carrier, density 1/4); (E8)_1 character = sum of the 4 glue sectors, weights = discriminant form; clock = U(2) diag(i,1), clock^2 = deck (Z8, 8 = 2|mu4|); clock-invariant deformation XY = Z^4 + a0, branch points = one mu4 orbit, cross-ratio 2; negative controls + Aut(Z4) rigidity; verdict B; SEAM.EQUIV.01 stays [O]
Dependencies: CELEST.SEAM.01; SEAM.EQUIV.01; E8.GLU.01; v92; v125; v128; v168; v179; v180; v214; v377
Scripts: v492_celestial_z4_orbifold.py
Location: tfpt_research_contracts
Original CSV, line 555Original ledger status
CELEST.SEAM.01
THE CELESTIAL-HOLOGRAPHIC RESEARCH CONTRACT (2026-07-20; the fourth research contract alongside CONTRACT.U.01, CONTRACT.G.01 and CONTRACT.F.01): HYPOTHESIS (as corrected by WP1) -- the seam is the glue-equivariant Z4-orbifold sector of the celestial chiral algebra on the A3 ALE space C^2/Z4; the mu4 clock is the Kaehler U(2) phase diag(i,1) whose square is the deck group (spin bridge Z8, 8 = 2|mu4| = the c3 = 1/(8 pi) seam winding integer); the associated twistorial bulk is the SELF-DUAL sector of TFPT gravity. TYPING / NON-CIRCULARITY: admissible inputs = the finite seam/glue data (v92/v125 glue, v128 graded hull, v168/v214 pillowcase, v180 clock) + the WP1/WP2 [E] arithmetic (v492/v493); NOT admissible as input: the continuum existence of the holomorphic (E8)_1 net on the seam (exactly the SEAM.EQUIV.01 target -- assuming it would be circular); scope = the self-dual sector only, never full Einstein gravity (the v358/v359 entanglement-equilibrium route and GRAV.ENTROPIC.ACTION.01 are separate statements about the full equation). WORK PACKAGES: WP1 DONE (v492, verdict B -- match under the one named identification clock^2 = deck); WP2 DONE (v493, verdict B -- both targets landed and SHARPENED: a0 = pure seam SCALE, the tau = i pillowcase shape frozen (I = 12 a0, J = 0 identically, j = 1728 for all a0); the 3 spheres carry the 3 nontrivial mu4 characters, the clock = Coxeter element of W(A3) = the Picard-Lefschetz monodromy of the family, surviving direction = the chi_1-Fourier diagonal; BHS Z2 -> Z4 transfer with corrections linear in a0, grade-conserving, a0 <-> the c^2 slot); WP3 DONE (v495, verdict B -- exact arithmetic alignment EXISTS: lambda_e8 = 6 (unit-trace) resp. 1/10 (adjoint-trace), (kappa/c3)^2 = 12 = |mu4| N_fam resp. 1/300, the Okubo coefficient 5/(2(dim+2)) DERIVED for all 8 algebras with a sharp sl4 negative control and the closed form lambda~^2 = h_vee + 6 across the Deligne series; BUT the look-elsewhere battery shows the alignment format passes 8/8 -- ZERO selectivity; only g_car = 5 | h_vee is e8-selective (1/8), lambda-integrality 2/8 shared with sl3, the isolating conjunction POST HOC: the c3-connection survives as convention-level compatibility + genuine lambda-arithmetic, NOT as e8-selective evidence -- alignment survives, selectivity does not); WP4 DONE (v496, verdict B(ii) -- the (E8)_1 character is NOT a conformal block of the E8[C^2] S-algebra in its own jet grading, the mismatch localised THREE ways (spin unbounded below; growth n^{2/3} vs n^{1/2}, Meinardus poles s = 2 vs 1; the level-2 null ideal deletes exactly 27000 = 30^3 = h_vee^3 with no jet analogue), BUT the boundary/period reading holds exactly at the current stratum (zero modes = 60 = C0 currents, jet slice cycles (60,64,60,64), one mu4 period sums to 248, glue weights (0,1,1,1) integer) -- the SAME MMST scaling-limit structure as SEAM.EQUIV.01 (v336/v449): the character is a boundary/limit SHADOW of the S-algebra, the constructive limit question goes to WP5); WP5a DONE (v497, 2026-07-21 -- 'the null ideal from the limit': the boundary limit made a PRECISE coefficientwise limit via the chi_w family with stabilisation threshold w = n+1 (w = 2 = the chiral jet grading); the null ideal DERIVED from root data, Sym^2(248) = 27000 + 3875 + 1 with 27000 = h_vee^3 by Freudenthal + Weyl + peeling; quotient 31124 - 27000 = 4124 = the independent mu4 theta-split sector sum; SO(16)_1 negative control: four blocks, 5304 != 14^3, h = 1/2 breaks one-block fusion; the celestial route now has the SAME two-step shape as MMST -- limit + maximal ideal -- with the ideal quantitatively fixed); WP5b DONE (v498, 2026-07-21 -- 'the singular vector as an operator', SUCCESS on the preregistered criteria: |s> = (E^theta_{-1})^2|0> constructed EXPLICITLY in a machine-built Chevalley/Frenkel-Kac basis (cocycle asymmetry on all 57600 pairs, SGN = -1 forced by Jacobi, kappa derived), J^a_1|s> = 0 for all 248 generators with case tally 190/57/1 (exactly one case sees k), level dial 2(1-k): the deletion object exists ONLY at k = 1 and not in the centerless loop algebra; mu4: j(theta) = 1 (h-adapted chamber), clock phase i^2 = -1, class(2 theta) = 2 sheet-even, 8 quarters = q^2, expressible in the sector-C_1 equivariant variables (KILL branch not triggered); U(g)|s> = V(2 theta) = 27000 = h_vee^3 with the direct g_0-orbit BFS matching Freudenthal through depth 4, quotient 4124 = sector sum; controls: the 248-current state and generic level-2 states NOT singular, the cube at k = 2 (generic Kac mechanics, honestly typed), D8 has the singular vector too but h = 1/2 breaks one-block fusion -- one-block closure stays E8/mu4-specific; HANDOVER to WP5c: in the twisted quarter-slot moding two C_1 modes never sum to 8 quarters (minimum 6 = q^{3/2}) -- the per-period dictionary (v496), not the per-slot identification, carries |s> to q^2); WP5c DONE (v500, 2026-07-21 -- 'the GNS limit state', SUCCESS on the preregistered criteria: the quasi-free family omega_w (affine k=1 vacuum on the currents via the machine-determined compact anti-involution theta(e_a) = -e_{-a}, unique on all 61504 basis pairs, + x^{wr}-contracted radial oscillators) is positive for every finite w and stabilises EXACTLY at the WP5a threshold (omega_w = omega_inf mod x^{N+1} for w >= N+1, sharp at w = N); GNS(omega_inf) levels (1, 248, 4124) via the FULL exact 9361-block level-2 Gram: rank 4124 = chi_2, kernel 27000 = V(2 theta) weight by weight (Freudenthal on all 9361 weights), every block PSD, rank table per Weyl orbit (0,0,1,8,44), h.w. norms (3844,49,2,0); the clock descends to GNS with level-2 rank split (1036,1024,1040,1024) = the per-period lattice theta-split -- the two-routes identity at the STATE level; |s> IS the zero vector of GNS(omega_inf), resolving the WP5b S4.10 twisted-slot tension; CCR obstruction: NO w-uniform damping state exists -- the family formulation is necessary AND the family exists, KILL not triggered; controls: k=2 keeps everything, k=0 has no current layer, D8 gives 2076 = one block of four, wrong family erases the 248 layer 710955 != 248, no damping keeps 897266 != 248); WP5d-alpha DONE (v501, 2026-07-21 -- 'the two-interval index from the lattice', the mu = 1 indicator chain PASSES: fermionic two-interval MI extensive (c fit 0.5000, max |F| = 6e-5 at N = 512, falling with N -- the mu = 1 reference), the sector-summed orbifold prescription pays exactly one classical bit with the 16-layer seam carrier saturating Delta_2 = ln 2 to machine precision (1.1e-15 at N = 512), so [F : F_even] = 2 and mu_gauged = 4 = the v490 parity census (two independent lattice witnesses); complementary-pair budget <= ln 4 = ln mu(SO(16)_1) as a double-limit statement + the orbifold duality-failure witness D(E) != D(E'); condensation arithmetic anchored at both ends: det Cartan(D5) x det Cartan(A3) = 16, KLM/Longo-Rehren 16/4^2 = 4/2^2 = 1, Sigma d^2 = (4,4,1), theta_v = 1 exactly at nu = 16 (rivals != 1) => mu = 1 after condensation, preregistered KILL 'mu-offset != 0 after condensation' NOT triggered; controls: nu = 1 offset non-removable, trivial phase all zero, wrong sector sum loses the full ln 2; WP5d-beta DONE (v504, 2026-07-21 -- 'split + strong additivity from the lattice', the two remaining KLM legs: strong additivity ALGEBRAICALLY EXACT with the shared boundary Majorana (Even(A) v Even(B) = Even(A u B), GF2 spans full 64/64..1024/1024, matrix rank 32/32; disjoint exactly index 2 = the v501 ln-2 bit, localised at the split point), the entropic touching defect BOUNDED < ln 2 with the Ising 1/4-exponent approach (p = 0.2444 vs 2 Delta_mu = 1/4) while the preregistered U(1)/Dirac control DIVERGES ((1/2) ln Var Q, Klich-Levitov pinned, infinite index) -- bounded-vs-divergent is the lattice discriminator and the quotient net sits on the bounded side; split via the elliptic-nome sigma_k ladder (rate pi K(1-x)/K(x) to 1.3-2.0%, sigma_1 ~ x^{1/2}, trace norm summable) with EXACT orbifold inheritance (C -> -C machine identity + the Lambda^2 C compound -- Longo heredity); Pimsner-Popa E(a) - a/2 = PaP/2 identically, lambda = 1/2 = 1/[F:F_even] with exact integer attainment (16384 + 2048 monomials, 0 violations), lambda_E4 = 1/4 = 1/mu, index consistency exp(Delta) = 2 = 1/lambda_PP over two independent routes: WITH v501 ALL THREE KLM INGREDIENTS of complete rationality -- split, strong additivity, finite mu -- are witnessed on the lattice; the continuum uplift stays [O]: 'finite-group orbifolds of completely rational nets are completely rational' is XU'S THEOREM, cited not claimed -- the proof for the concrete seam quotient net and the interacting condensed (E8)_1 net remains WP5e/Costello-Li); WP5e: alpha stage (CFT-side prefactor + level pinning) executed via v502 (2026-07-21, CELEST.WP5E.ALPHA.01 -- the q^{-1/3} prefactor derived as exact mu4 vacuum-energy bookkeeping (inner clock => shift orbifold theta = 0^8, common -c/24 = -1/3; discriminant form = Casimir via spectral flow AND 16-Majorana free fermions) and k = 1 forced three independent ways (current condition h(J) = k = 1, conformal embedding 47(k-1)(k+266/47) = 0 resp. 128(k-1) = 0, c = 8 <=> 240(k-1) = 0, plus the WP5b singular-vector dial 31124 - 27000 = 4124), with the honest sharpening that glue-h integrality holds for ALL k and fixes nothing); beta stage (equivariant twistor skeleton) executed via v505 (2026-07-21, CELEST.WP5E.BETA.01 -- the Atiyah-Bott/Lefschetz fixed-point skeleton of the inflow exact: denominators (2,4,2), characters (248,0,-8,0) two routes, per-sector Okubo with the RIGID 32 T3 twisted residual, index bridge f(m) = ch2(T_m) with glue defect -78 both routes, level dials k = 1 geometric (current count 240/0/0/0), and the E3 refutation a0 = graviton modulus O(2) NOT the axion O(-2) with the three sphere classes filling the three twisted axion slots; the preregistered kill 'inflow demands a level != 1' does NOT fire on the equivariant skeleton); gamma stage (the sphere-axion pairing check) executed via v508 (2026-07-21, CELEST.WP5E.GAMMA.01 -- an honest rigid NEGATIVE result with certificate: the W(D5) x W(A3)-invariant vertex spaces are exactly dim 2 (quadratics) and dim 5 (quartics), the product of any two invariant quadratics has zero T5/T3 content, so the exchange matrix is rank 2 with rank([M | A_fix]) = 3 and annihilator certificate (Phi_T5, Phi_T3, Phi_P)(A_fix) = (0, 32, 72) -- the three sphere axions CANNOT cancel the rigid 32 T3 residual by quadratic-vertex exchange, rule- and coupling-independently; the slot bijection is untouched and the preregistered level-kill still does not fire); WP5e: alpha (CFT side, v502) + beta (equivariant twistor skeleton, v505) + gamma (exchange no-go, v508) executed; the global BCOV quantisation stays [O] -- the exchange sub-branch is closed by v508; epsilon-2 executed via v509 (2026-07-21, CELEST.WP5E.EPS2.01, 'the CPS level-from-flux dial', verdict B): the one-level statement is now a THEOREM (lockstep from clock invariance -- one mu4 orbit of branch points, |Pi_j| = sqrt(2) t equal on all three spheres, det(A-1) = -4 no invariant flux vector; falsifier Z^4 - Z: 0/24 orderings lockstep), level = 1 carries the new sector-counter dial #prim((E8)_k) = 1 <=> k = 1 (affine marks: (1, 3, 5, 10, 15, 27) for k = 1..6), fluxes (64, 60, 64) with uniformly one quantum per charged current and the naive 'level = total flux' killed by the lockstep test itself; the PT/Z4 back-reaction stays [O]; delta-2 executed via v511 (2026-07-21, CELEST.WP5E.DELTA2.01, intermediate verdict, exact -- the full-tensor ledger: the v508 collapse is confirmed full-tensorially and arity-crossing by the innerness theorem (h in the g0 Cartan, all 15 non-neutral trilinear triples Hom = 0), but the su(4) d-symbol -- the unique symmetric trilinear on e8 -- opens the T3 channel (Q_dd = (1/60)(T3 - P3/4), Phi_T3(Q_dd) = 1/60 != 0), leaving the pairing obstructed only by the weaker certificate {Phi_T5, psi = Phi_P - Phi_T3/4}, psi(A_fix) = 64, and exactly solvable relaxed with c_d = 1920 = |W(D5)|); delta-2 executed via v511 -- the full-tensor collapse is confirmed (innerness), but the cubic d-symbol channel opens T3 with the weaker certificate psi = 64; delta-1 since DECIDED NEGATIVE under the DERIVED measure by v518 (2026-07-22, CELEST.WP5E.DELTA1.01: the derived chiral measure -- blockwise SL(2,Z) covariance solved for, the mu4 multiplier obstruction a CHARACTER (koboundary defects (1,1,1) on all 15 pairs, lambda(gamma) = i^{2B + C/4} on Gamma_1(4)) cancelled exactly by the twisted fibre block f1 f3 = G, NOT by the three sphere axions -- fails all three preregistered testers under both derived solutions chi_4/chi_10, with no (N1, N2) rescue in the positive cone: a genuine KILL on the derived surface, in stated TENSION with the DECLARED completion reading of v516 which delivers the psi = 64 slice and cancels 32 T3 -- both are exact, and which of the two is the true BCOV measure is the named [O]); the pre-v518 state was: the strict holomorphic reading is refuted at the Z2 anchor, the contact term is the modular completion (Harvey-Moore tau-integral) with the forced leading (T5,T3) ratio 4:3 -- the named remaining targets are the tau-integral and the physical justification of the cubic GS term (c_d = 1920; the 1920 = |W(D5)| reading is look-elsewhere-loaded (11/924 vs. 8/924 for the control target 1800) and convention-contingent -- v513; the convention-stable [E] core is c_d = 32 x 60), plus the epsilon-1 O(-2) bulk-axion construction (success: partition function = E4/eta^8 including the q^{-1/3} prefactor FROM THE TWISTOR SIDE; kill: anomaly mismatch at the Costello-Li grade -- neither the CFT-side dials of v502 nor the equivariant skeleton of v505 trigger it). KILL TESTS (pre-registered): (K1) the equivariant structure could have contradicted 52+64+60+64 -- SURVIVED by WP1 AND WP2 (false-glue control: 3112/6720 violations show the test has teeth; WP2 deformation side: no shape modulus survived clock-invariance, no sector leak -- the clock-variant controls fail two independent ways each); (K2) one-loop associativity demanding extra fields TFPT lacks -> contract dies (Costello's axionic mechanism passes E8 at the algebra level; the TFPT field content is the open half); (K3) EVALUATED by WP3 (v495): does NOT fire -- exact alignment exists ((kappa/c3)^2 = 12 resp. 1/300); but its SCOPE IS DEMOTED on the look-elsewhere evidence (the alignment format passes 8/8 across Costello's whole list): compatibility, not e8-selective evidence; (K4) EVALUATED by WP4 (v496): fires only against the exact-block reading -- the sector arithmetic holds exactly, so the contract does NOT degrade to 'E8 is an admissible celestial gauge algebra'; WP4 lands at the boundary-limit reading (verdict B(ii), the SEAM.EQUIV.01 scaling-limit shape). HONEST SUCCESS ESTIMATE: full success (WP5e, constructive holography at the Costello-Li grade) low probability; the partial-findings expectation is now REALISED AND EXCEEDED: WP1-WP4 + WP5a-WP5d all executed with sharp structural results (verdicts B, B, B, B(ii); ALL FIVE constructive WP5 milestones landed -- null ideal, singular vector, GNS limit state, two-interval index, split + strong additivity (both WP5d stages) -- plus the WP5e alpha stage (CFT-side prefactor + level pinning, v502) AND the WP5e beta stage (equivariant twistor skeleton with the honest a0 refutation, v505) AND the WP5e gamma stage (the exchange no-go with certificate, v508) AND the WP5e epsilon-2 stage (the CPS level-from-flux dial with the lockstep theorem and the sector-counter dial, v509); AND the WP5e delta-2 stage (the full-tensor ledger with the innerness theorem and the cubic d-symbol channel, v511); WP5e proper, the global BCOV quantisation, is the single remaining open piece -- narrowed by v508/v509/v511 to the delta-1 tau-integral (since DECIDED by v518, CELEST.WP5E.DELTA1.01: kill under the derived measure, all three preregistered testers fail; the measure tension with v516 is the named [O]), the physical justification of the cubic GS term (c_d = 1920; the |W(D5)| reading look-elsewhere-loaded and convention-contingent -- v513) and the epsilon-1 bulk-axion construction (executed via v514) plus the PT/Z4 back-reaction (M1 executed via v515: the back-reacted Omega_N closed-form with (2 pi i)^2-integral lockstep flux vector and forced source charge 4 = |mu4|; M2+M3 executed via v516/v517 -- the v514 fence M1-M3 is fully worked off: the twisted KS measure (declared completion reading, ch2-weighted) cancels the 32 T3 residual and delivers the psi = 64 slice without the cubic d-channel, and the a0 uplift couples to the centre count on four scales; what stays [O]: the BCOV measure question -- the delta-1 chain itself is DECIDED by v518 (kill under the derived measure, tension with v516 stated) -- and SEAM.EQUIV.TWISTOR.01)) -- the clock^2 = deck correction, the Coxeter/Picard-Lefschetz monodromy, the non-selective GS alignment, the boundary-limit localisation of the character mismatch, the explicit singular vector with its level dial 2(1-k), the limit state with the ideal in its GNS kernel, the entropically measured mu-chain 16 -> 4 -> 1, and the lattice KLM completeness witness (split + strong additivity + finite mu, v501/v504). SEAM.EQUIV.01 stays [O] throughout; nothing here moves it.
Recorded status: Open (research contract; WP1-WP5d executed [E]/[C]/[L] via v492/v493/v495/v496/v497/v498/v500/v501/v504 -- WP5d: alpha (mu-index) + beta (split + strong additivity) executed via v501/v504, all three KLM ingredients witnessed on the lattice, continuum uplift stays [O] (Xu's theorem cited); WP5e alpha stage [E] via v502 + beta stage [E] via v505 (equivariant twistor skeleton; kill not fired) + gamma stage [E] via v508 (exchange no-go with certificate (0, 32, 72); negative result, kill not fired) + epsilon-2 stage [E] via v509 (level-from-flux: the one-level statement is now a THEOREM of clock invariance, the sector-counter dial #prim((E8)_k) = 1 <=> k = 1 pins the level; the PT/Z4 back-reaction stays [O]); + delta-2 stage [E] via v511 (the full-tensor ledger: collapse confirmed by innerness, the cubic d-symbol channel opens T3 with the weaker certificate psi = 64, relaxed solution c_d = 1920 = |W(D5)|); + epsilon-1 stage [E] via v514 (epsilon-1 executed via v514: the O(-2) bulk-axion slot is a construction (equivariant Penrose ledger), lambda-tilde = 6 pinned by three exact ledgers (Okubo / measure cancellation excluding 3 and 12 / flux), and the GH/A3 back-reaction step re-derives the v493 family and the Coxeter clock from geometry -- the quantised BCOV coefficient and the twisted channels stay [O] (M1-M3 preregistered)); WP5e-M1 DONE (v515: M1 executed via v515: the back-reacted Omega_N is closed-form on the A3 twistor family, all S3/Z4 periods are (2 pi i)^2-integral with the lockstep flux vector and clock covariance, and the lens geometry FORCES the source charge 4 = |mu4|; honest fence: integrality alone does not discriminate -- the discriminator is the lockstep phase structure (0/24 on the forbidden family)); WP5e-M2+M3 DONE (v516/v517: M2+M3 executed via v516/v517 -- the v514 fence M1-M3 is fully worked off: the twisted KS measure (declared completion reading, ch2-weighted) cancels the 32 T3 residual and delivers the psi = 64 slice without the cubic d-channel, and the a0 uplift couples to the centre count on four scales; what stays [O]: the BCOV measure question -- the delta-1 chain itself is DECIDED by v518 (kill under the derived measure, tension with v516 stated) -- and SEAM.EQUIV.TWISTOR.01); the global BCOV quantisation [O] (single remaining milestone -- the exchange sub-branch closed by v508, the epsilon-2 flux dial executed by v509, the delta-2 tensor ledger executed by v511, the epsilon-1 axion slot executed by v514, the M1-M3 back-reaction milestones executed by v515/v516/v517 (the v514 fence fully worked off); named remaining target: the BCOV MEASURE QUESTION -- the delta-1 chain is DECIDED by v518 (CELEST.WP5E.DELTA1.01: kill under the derived measure, all three testers fail; tension with v516 stated), so what remains is which of the two exact measures (the declared v516 completion reading vs the v518 derived chiral measure) is the true BCOV measure; the cubic GS term stays dissolved (psi = 64 delivered by v516, no branch fires under the derived measure, v518)))
Dependencies, status detail and source
Canonical status: Open (research contract): seam = glue-equivariant Z4-orbifold sector of the CCA on the A3 ALE; clock^2 = deck (Z8 spin bridge); twistorial bulk = self-dual sector only; WP1-WP4 + WP5a-WP5d executed (verdicts B, B, B, B(ii); WP5a: null ideal derived, 27000 = h_vee^3, quotient = sector sum = 4124, stabilisation threshold w = n+1; WP5b: the singular vector explicit, J^a_1|s> = 0 on all 248 generators with case tally 190/57/1, level dial 2(1-k), j(theta) = 1, clock phase i^2 = -1), WP5c DONE (v500: GNS limit state omega_inf with the null ideal in its kernel -- level-2 rank 4124, kernel 27000 = V(2 theta) weight by weight, clock split (1036,1024,1040,1024), |s> = the GNS zero vector, CCR necessity of the family), WP5d-alpha DONE (v501: two-interval index -- 16-layer ln 2 plateau at 1e-15, [F : F_even] = 2, mu_gauged = 4 = v490, KLM chain 16 -> 4 -> 1 anchored at both measured ends, theta_v = 1 at nu = 16), WP5e-alpha DONE (v502: q^{-1/3} prefactor = exact mu4 vacuum-energy bookkeeping (shift orbifold, discriminant form = Casimir two ways) + k = 1 forced three ways, glue-h integrality honestly demoted), WP5e-beta DONE (v505: the equivariant anomaly ledger exact -- AB characters (248,0,-8,0), per-sector Okubo with the rigid 32 T3 residual, index bridge f(m) = ch2(T_m) with defect -78 two routes, geometric k = 1 dials, a0 refuted as GS axion (graviton slot O(2)), the three sphere classes = the three twisted axion slots; kill not fired), WP5d-beta DONE (v504: split + strong additivity from the lattice -- Even(A) v Even(B) = Even(AuB) EXACT with the shared boundary point (disjoint index exactly 2 = the v501 ln-2 bit), bounded-vs-divergent entropic discriminator (Z2 deficit < ln 2 with the Ising 1/4-exponent approach vs U(1) divergence, Klich-Levitov pinned), elliptic-nome split ladder with exact orbifold inheritance (C -> -C + Lambda^2 C, Longo heredity), Pimsner-Popa lambda = 1/2 = 1/[F:F_even] and lambda_E4 = 1/4 = 1/mu with integer attainment, index consistency exp(Delta) = 2 = 1/lambda_PP two routes -- all three KLM ingredients witnessed on the lattice; continuum uplift stays [O], Xu's theorem cited), WP5e-gamma DONE (v508: the sphere-axion pairing check -- exchange no-go with certificate: invariant vertex spaces exactly dim 2/5 by Weyl nullspace, product theorem kills every exchange image in the T3 direction, rank([M | A_fix]) = 3 with certificate (Phi_T5, Phi_T3, Phi_P) = (0, 32, 72), naturalness dissolves scale-independently, SO(16)/D8 controls; slot bijection untouched, level-kill still not fired), WP5e-epsilon-2 DONE (v509: the CPS level-from-flux dial, verdict B -- the one-level statement is now a THEOREM (lockstep from clock invariance, falsifier Z^4 - Z: 0/24), level = 1 carries the new sector-counter dial #prim((E8)_k) = 1 <=> k = 1, fluxes (64, 60, 64) with one quantum per current, the naive 'level = total flux' killed; the PT/Z4 back-reaction stays [O]), WP5e-delta-2 DONE (v511: the full-tensor ledger -- delta-2 executed via v511 -- the full-tensor collapse is confirmed (innerness), but the cubic d-symbol channel opens T3 with the weaker certificate psi = 64; delta-1 since DECIDED NEGATIVE under the DERIVED measure by v518 (2026-07-22, CELEST.WP5E.DELTA1.01: the derived chiral measure -- blockwise SL(2,Z) covariance solved for, the mu4 multiplier obstruction a CHARACTER (koboundary defects (1,1,1) on all 15 pairs, lambda(gamma) = i^{2B + C/4} on Gamma_1(4)) cancelled exactly by the twisted fibre block f1 f3 = G, NOT by the three sphere axions -- fails all three preregistered testers under both derived solutions chi_4/chi_10, with no (N1, N2) rescue in the positive cone: a genuine KILL on the derived surface, in stated TENSION with the DECLARED completion reading of v516 which delivers the psi = 64 slice and cancels 32 T3 -- both are exact, and which of the two is the true BCOV measure is the named [O]); the pre-v518 state was: the strict holomorphic reading is refuted at the Z2 anchor, the contact term is the modular completion (Harvey-Moore tau-integral) with the forced leading (T5,T3) ratio 4:3 -- the named remaining targets are the tau-integral and the physical justification of the cubic GS term (c_d = 1920; the 1920 = |W(D5)| reading is look-elsewhere-loaded (11/924 vs. 8/924 for the control target 1800) and convention-contingent -- v513)), WP5e-epsilon-1 DONE (v514: epsilon-1 executed via v514: the O(-2) bulk-axion slot is a construction (equivariant Penrose ledger), lambda-tilde = 6 pinned by three exact ledgers (Okubo / measure cancellation excluding 3 and 12 / flux), and the GH/A3 back-reaction step re-derives the v493 family and the Coxeter clock from geometry -- the quantised BCOV coefficient and the twisted channels stay [O] (M1-M3 preregistered)); WP5e-M1 DONE (v515: M1 executed via v515: the back-reacted Omega_N is closed-form on the A3 twistor family, all S3/Z4 periods are (2 pi i)^2-integral with the lockstep flux vector and clock covariance, and the lens geometry FORCES the source charge 4 = |mu4|; honest fence: integrality alone does not discriminate -- the discriminator is the lockstep phase structure (0/24 on the forbidden family)), WP5e-M2+M3 DONE (v516/v517: M2+M3 executed via v516/v517 -- the v514 fence M1-M3 is fully worked off: the twisted KS measure (declared completion reading, ch2-weighted) cancels the 32 T3 residual and delivers the psi = 64 slice without the cubic d-channel, and the a0 uplift couples to the centre count on four scales; what stays [O]: the BCOV measure question -- the delta-1 chain itself is DECIDED by v518 (kill under the derived measure, tension with v516 stated) -- and SEAM.EQUIV.TWISTOR.01), the global BCOV quantisation [O] (the single remaining milestone: Costello-Li uplift -- the exchange sub-branch closed by v508, the flux dial executed by v509, the tensor ledger executed by v511, the epsilon-1 axion slot executed by v514, the M1-M3 back-reaction milestones executed by v515/v516/v517; the named remaining target is the BCOV measure question (the delta-1 chain is DECIDED by v518: kill under the derived measure, tension with v516 stated; the cubic GS term stays dissolved)); kill tests evaluated: K1 survived, K3 not fired (scope demoted -- alignment non-selective, compatibility not evidence), K4 lands at the boundary-limit reading; SEAM.EQUIV.01 untouched [O]
Dependencies: CELEST.WP1.01; CELEST.WP2.01; CELEST.WP3.01; CELEST.WP4.01; CELEST.WP5A.01; CELEST.WP5B.01; CELEST.WP5C.01; CELEST.WP5D.01; CELEST.WP5DB.01; CELEST.WP5E.ALPHA.01; CELEST.WP5E.BETA.01; CELEST.WP5E.GAMMA.01; CELEST.WP5E.EPS2.01; CELEST.WP5E.DELTA2.01; CELEST.WP5E.EPS1.01; CELEST.WP5E.M1.01; CELEST.WP5E.M2.01; CELEST.WP5E.M3.01; CELEST.WP5E.DELTA1.01; SEAM.EQUIV.01; CONTRACT.G.01; GATE.METRIC.01; v92; v125; v128; v168; v180; v214; v492; v493; v495; v496; v497; v498; v500; v501; v502; v504; v505; v508; v509; v511; v514; v515; v516; v517; v518
Scripts: v492_celestial_z4_orbifold.py
Location: tfpt_research_contracts
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