A registered result in its source context

CCC.SEAM.KINEMATICS.01

Original ledger classification: Certified kinematics dictionary [E] (fine types Identity/Formal (Moebius/D_4 algebra, Stinespring isometry, Hopf equivariance, commutant dimensions, symbolic Einstein/Weyl checks, KMS/detailed-balance identities, Theta-reality censuses -- exact on corpus objects) and Numerical (linking integrals, Obata scans, band arithmetic pinned); the CCC/cyclic READING itself stays [C] and is NOT upgraded; WOIT.OS.TWISTOR.01 stays [O] with all kill tests live)

Original claim text

THE CCC CROSSOVER KINEMATICS DICTIONARY [E] (rounds DL-DLV, notes 2026-08-24; promoted 2026-08-24). EXACT (v957; six probes 28/28 + 29/29 + 18/18 + 21/21 + 14/14 + 7/7 embedded byte-exact, hashes pinned): (1) Penrose's reciprocal gauge Omega*tau(Omega) = -1 is the element tau = rho^2 sigma of the proven mu_4 Moebius stabiliser D_4; tau reverses the clock (= the Z_2 sheet parity), swaps the aeon poles {0, inf}, fixes +-i; the crossover locus |Omega| = |tau(Omega)| is the unit circle carrying all four marks. (2) The clock alone leaves exactly one constant-curvature conformal modulus on the 2D seam and the reciprocal Z_2 kills it (Liouville-exact; so(3,1) commutant dims 2-with-1-boost / 0). (3) The v221 transport is CPTP not unitary; its Stinespring isometry is explicit (V^dag V = 1_3), ||T^n - P_star||_2 = (2/3)^{6n} exactly, the global overlap is invariant and the environment retains full distinguishability -- the entropy reset of the cyclic reading is a REDUCED CHANNEL, no information destroyed. (4) The kinematic uplift: stereographic(Hopf(v)) = z1/z2 exactly; the v492 deck acts freely, so the crossover X = S^3/Z_4 is the smooth lens boundary of the corpus A_3 ALE; clock and reciprocal lift normalise the deck and descend; the four marks lift to four Hopf fibre circles paired into the two Z_2 sheet orbits with Gauss linking 1; the so(4,1) deck-commutant is 4-dimensional, ALL Killing, boost content 0 (infinitesimal Yamabe rigidity with no extra condition; global uniqueness on the explicit Obata boost family, 200-axis scan bounded below); the inversion x -> x/|x|^2 is a conformal involution of the cone C^2/Z_4 fixing the unit lens pointwise and swapping the aeon ends; the Lorentzian bridge (1/cos^2 T)(-dT^2 + g_{S^3}) is Einstein R_ab = 3 g_ab (symbolic Ricci) with a spacelike round-S^3 crossover and Omega_hat*Omega_check = -1, Omega_check = -cos T vanishing to first order. (5) KMS/modular closure at the free level: detailed balance exact, spec(-ln T) = {0, 6 ln(3/2), 6 ln 3}, T = e^{-H_mod}, OS Gram PSD; the v526 normalisation beta_angle = 2 pi = 1/(4 c3) equals the Gibbons-Hawking normalisation on the crossover fibre. (6) Holonomy dictionary: pole strings carry the full mu_4 monodromy (chi(D) = i), every seam string carries exactly the 2-torsion chi(D^2) = -1 = the v522 GSO/fermion-parity wrap (typed [C] structural correspondence). (7) Selector necessity: the admissible reflections of M(delta) close to D_4 iff delta = pi/2 (the clock factorises into admissible reflections only at mu_4); at Majorana operator level with fermionic signs the clock-axis cuts are Theta-real ONLY at k = 4 and asymmetric couplings break reality -- the uniqueness half of the v534 selector is DERIVED as a Theta-reality necessity (survival + coupling sign stay v534's nonperturbative toy facts, cited; reality is sign-blind, checked). (8) The frozen Gate-6 kernel: two decay modes ln(729/64) and ln(729) (ratio 2.709511), frozen defect-class overlap table, disc radius theta_max = eta_rec/(eta_0 - eta_rec) ~ 1.16 deg, kappa derived from the v526 KMS normalisation up to a declared convention band (u_rec <= 8.3e-5, contrast <= 3.3e-4): the template degenerates robustly to the sharp causal top-hat disc -- feeds the preregistered search experiments/ccc-crossover-disc (no CMB data touched).

Original classification detail

Kinematics certified [E]: reciprocal-in-D_4 + conformal rigidity (2D needs tau, 3D automatic) + Stinespring reduced-channel reset + lens-crossover uplift + KMS closure (tick = e^{-H_mod}) + holonomy dictionary (seam strings = GSO 2-torsion) + selector-uniqueness necessity + frozen top-hat kernel; the cyclic/CCC reading stays [C]; the dynamics stay WOIT.OS.TWISTOR.01 [O]

Dependencies as recorded

QGEO.CONF.01 (the seam premise); v221 (transport); v492 (deck/clock, A_3 ALE); v519/v521/v522 (Theta, side-blindness, GSO wrap); v526 (KMS normalisation); v529/v534 (straddle law + selector, cited); VGEO.TORSOR.01 (unit calibration untouched); rounds DL-DLV