A registered result in its source context
Original ledger classification: Formal/Identity [E] (exact Okubo/Killing/lambda arithmetic for all 8 algebras, Fraction/sympy, sl4 negative control, look-elsewhere battery) + [C] (the convention typing of the 8 pi and sqrt 3; the alignment reading with the look-elsewhere caveat, verdict B) + [O] (celestial programme WP5; SEAM.EQUIV.01 unchanged)
Recorded statement: WP3 OF THE CELESTIAL-HOLOGRAPHIC CONTRACT EXECUTED (2026-07-21; CELEST.SEAM.01 work package 3, verdict B; the pre-registered 'alignment test only'): the Green-Schwarz axion coefficient lambda_g of celestial/twistorial SDYM (Costello,…
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Paper context: Research contracts
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CELEST.WP3.01
Original ledger classification: Formal/Identity [E] (exact Okubo/Killing/lambda arithmetic for all 8 algebras, Fraction/sympy, sl4 negative control, look-elsewhere battery) + [C] (the convention typing of the 8 pi and sqrt 3; the alignment reading with the look-elsewhere caveat, verdict B) + [O] (celestial programme WP5; SEAM.EQUIV.01 unchanged)
Original claim text
WP3 OF THE CELESTIAL-HOLOGRAPHIC CONTRACT EXECUTED (2026-07-21; CELEST.SEAM.01 work package 3, verdict B; the pre-registered 'alignment test only'): the Green-Schwarz axion coefficient lambda_g of celestial/twistorial SDYM (Costello, arXiv:2111.08879, eq. 1.2.4: kappa = lambda_g/(8 pi sqrt 3)) against the TFPT seam constant c3 = 1/(8 pi). Exact arithmetic throughout (Fraction/sympy, 25 checks). [E] OKUBO IDENTITY DERIVED, NOT QUOTED: Sum_alpha <alpha,x>^4 = [5/(2(dim g+2))] (Sum_alpha <alpha,x>^2)^2 as an exact polynomial identity for ALL 8 algebras on Costello's list (sl2, sl3, g2, so8, f4, e6, e7, e8; e6/e7 carved out of the v492 E8 root set) -- 'no independent quartic Casimir'; NEGATIVE CONTROL: sl4 (which HAS one) fails the proportionality (5/32 on s0^4 vs 3/32 on s0^2 s2^2) -- the list is sharp. [E] Killing normalisation Sum <alpha,x>^2 = 2 h_vee <x,x> exact (h_vee = 2,3,4,6,9,12,18,30); Deligne dimension formula dim g = 2(5h_vee-6)(h_vee+1)/(h_vee+6); CLOSED FORM lambda~^2 = 10 h_vee^2/(dim+2) = h_vee + 6 EXACTLY (8,9,10,12,15,18,24,36) -- fixes Costello-Paquette eq. (1.5); fundamental Dynkin indices i_R = (1,1,2,2,6,6,12,60) from explicit weight systems. E8: lambda~ = 6 (unit-trace) and lambda_fund = 1/10 (adjoint-trace) EXACT. Cross-checks: Costello's sl2 = 8, sl3 = 9 reproduced; HIS PRINTED lambda^2(so8) = 3/2 is a factor-2 slip (his own weight content gives Sum w^4 = 192, not 96: lambda^2 = 3, Okubo-consistent 12/4). [E] ALIGNMENT: (kappa/c3)^2 = lambda^2/3 = 12 = |mu4| N_fam (unit-trace) resp. 1/300 (adjoint-trace), both EXACT anchor rationals; kappa/c3 ITSELF is IRRATIONAL (2 sqrt 3 resp. 1/(10 sqrt 3)) -- the pre-registered 'lambda/sqrt3 rational?' reading FAILS, only the SQUARED alignment holds; anchor decomposition h_vee = 30 = |Z2| N_fam g_car (all three TFPT atoms once, squarefree), phi(30) = 8 = rank(E8), dim+2 = 250 = 2 * 5^3, lambda~ = 6 = |Z2| N_fam, lambda_fund = 1/10 = 1/(|Z2| g_car). [E] LOOK-ELSEWHERE (the HARD FENCE -- alignment != selection): the alignment test AS SUCH passes 8/8 (ZERO selective power for e8), h_vee {2,3,5}-smoothness 8/8, lambda~-integrality 2/8 (sl3 + e8), lambda_fund-rationality the same 2/8, phi(h_vee) = rank 4/8, phi(h) = rank 5/8; the ONLY e8-selective single test is g_car = 5 | h_vee (1/8); the conjunction that isolates e8 (1/8) was assembled POST HOC from correlated sub-tests -- it quantifies where e8 sits, it is NOT a preregistered discriminator. [E] KILL-TEST K3 EVALUATED: does NOT fire (exact alignment EXISTS) but its scope is DEMOTED -- the c3-connection of the celestial route survives as convention-level compatibility + genuine lambda-arithmetic, NOT as e8-selective evidence. [C] TYPED: the 8 pi in Costello's (1.2.4) is the 2 pi convention of the anomaly polynomial (his A.0.10 constant descended to spacetime), NOT an independent occurrence of the seam constant; the sqrt 3 is the anomaly's own (sqrt 48 = 4 sqrt 3 from the twistor box diagram, 48 = 2*4!); WP3 is an alignment yes/no ONLY -- it can never derive c3 from celestial data (contract wording, honoured). [O] WP5 (constructive holography) and SEAM.EQUIV.01 stay [O], untouched. No gate closes, no marker moves.
Original classification detail
WP3 [E]/[C]/[O]: Okubo coefficient 5/(2(dim+2)) derived for all 8 algebras (sl4 control); lambda~^2 = h_vee + 6 closed form; lambda_e8 = 6 resp. 1/10 exact; (kappa/c3)^2 = 12 = |mu4| N_fam resp. 1/300 exact, kappa/c3 irrational; so8 slip flagged; look-elsewhere: alignment 8/8 (zero selectivity), g_car | h_vee 1/8 (e8 only), joint test post hoc; K3 not fired, scope demoted -- compatibility, not e8-selective evidence; verdict B; SEAM.EQUIV.01 stays [O]
Dependencies as recorded
CELEST.SEAM.01; CELEST.WP1.01; SEAM.EQUIV.01; v92; v125; v128; v492; v493
Open the original ledger source, row 558Location recorded in the ledger
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- Research contracts
Sections that explicitly cite this claim
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- Research Contract — CELEST.SEAM.01 (the celestial and twistor continuum route)tfpt research contracts
- Research Contract — CELEST.SEAM.01 (the celestial and twistor continuum route)tfpt research contracts
- Front matter / supportResearch contracts
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
- Research Contract — CELEST.SEAM.01 (the celestial and twistor continuum route)Research contracts
- 2026-07-21 (III) (CELEST.SEAM.01 WP3 [formula in source] WP4 executed and promoted: v495 Green–Schwarz alignment (verdict B, honestly non-selective) [formula in source] v496 character-vs-S-algebra type mismatch (verdict B(ii), boundary-limit shadow); contract now WP1–WP4 done, WP5 ; no gate closes, no marker moves, SEAM.EQUIV.01 untouched)Research changelog; TFPT — Introduction and reading guide
Navigation through a shared verification script
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- 2026-07-21 (XV) ( v505 — WP5e- [formula in source] of CELEST.SEAM.01 ``the equivariant anomaly ledger on twistor space'' promoted as CELEST.WP5E.BETA.01: the Atiyah–Bott/Lefschetz fixed-point skeleton of the one-loop twistor inflow is EXACT — denominators [formula in source] with Dedekind sum [formula in source] , equivariant characters [formula in source] by two routes, invariant Okubo [formula in source] with the twisted sectors NOT reducing and the AB sum leaving the RIGID residual [formula in source] , the index bridge [formula in source] exact with glue defect [formula in source] both routes, the level dials [formula in source] geometric (current count [formula in source] ), and the honest E3 REFUTATION: [formula in source] fills the GRAVITON slot [formula in source] , NOT the axion slot [formula in source] — the three sphere classes fill the three twisted axion slots instead; the preregistered kill (``inflow demands a level [formula in source] '') does NOT fire on the equivariant skeleton; WP5e: [formula in source] (CFT side, v502) [formula in source] [formula in source] (equivariant twistor skeleton, v505) executed, the global BCOV quantisation stays ; Wolfram extension [formula in source] (verified engine run); SEAM.EQUIV.01 stays , no marker moves)Research changelog; TFPT — Introduction and reading guide
- Front matter / supportResearch contracts
- 2026-07-21 (IV) (Wolfram engine reactivated — the deferred second-path mirrors VERIFIED: base [formula in source] [formula in source] extension [formula in source] ( [formula in source] , the 16 mirrors accumulated since 2026-07-14 now counted); GATE.WOLFRAM.01/02 and all counter surfaces synced; no gate closes, no marker moves)Research changelog; TFPT — Introduction and reading guide
- The celestial and twistor continuum routeinput 5 tfpt 3 e8 audit bootstrap
- 2026-07-21 (VIII) (Editorial: dedicated celestial-route section in Paper 3 [formula in source] website mirror — the scattered celestial sentences consolidated into one coherent six-step section; no new scripts, no status changes, no marker moves, SEAM.EQUIV.01 untouched)Research changelog; TFPT — Introduction and reading guide
- Front matter / supportResearch contracts
- The celestial and twistor continuum routeE8 audit and bootstrap
- The celestial and twistor continuum routeinput 5 tfpt 3 e8 audit bootstrap
Registered verification modules
- v495_celestial_wp3_gs_alignment.pyRegistered verification module · frontier
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CELEST.WP3.01: WP3 of the celestial-holographic research contract CELEST.SEAM.01 -- the Green-Schwarz axion coefficient lambda_g of celestial SDYM (Costello, arXiv:2111.08879) vs the TFPT seam constant c3 = 1/(8 pi); the pre-registered 'alignment test only'. [E] Okubo identity DERIVED, not quoted: Sum <alpha,x>^4 = [5/(2(dim+2))] (Sum <alpha,x>^2)^2 exact for all 8 algebras on Costello's list (e6/e7 carved out of the v492 E8 root set); sl4 negative control fails (5/32 vs 3/32). [E] Killing = 2 h_vee <.,.>; closed form lambda~^2 = 10 h_vee^2/(dim+2) = h_vee + 6 over the Deligne series; Dynkin indices (1,1,2,2,6,6,12,60); E8: lambda~ = 6, lambda_fund = 1/10 EXACT; Costello cross-checks sl2 = 8 / sl3 = 9; so8 slip flagged (exact 3, printed 3/2). [E] Alignment: (kappa/c3)^2 = lambda^2/3 = 12 = |mu4| N_fam resp. 1/300 exact; kappa/c3 itself irrational (2 sqrt3); anchors h_vee = 30 = |Z2| N_fam g_car, phi(30) = 8 = rank, lambda~ = |Z2| N_fam, lambda_fund = 1/(|Z2| g_car). [E] LOOK-ELSEWHERE (hard fence, alignment != selection): alignment 8/8 (zero selectivity), smoothness 8/8, lambda-integrality 2/8 (with sl3), phi(h_vee) = rank 4/8; only g_car | h_vee is e8-selective (1/8); the isolating conjunction is post hoc. [E] K3 does NOT fire but is scope-demoted: compatibility + lambda-arithmetic, NOT e8-selective evidence. [C] the 8 pi is the anomaly 2 pi convention, the sqrt3 the box diagram's sqrt48 -- WP3 can never derive c3. [O] WP5 + SEAM.EQUIV.01 stay [O]. Verdict B. Exact (Fraction/sympy).
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