Original ledger status
FR.KOIDE.04
Koide RG attractor is FORCED, not postulated [I] + ONE [P] identification (sharpens FR.KOIDE.01/02/03 via the v81 double cover): a branch-divisor-preserving Moebius map of the pencil line that fixes BOTH branch points q=2 (Koide) and q=5 (carrier) is, in the cross-ratio coordinate rho=(q-2)/(5-q), EXACTLY rho->mu*rho, hence UNIQUE once mu is fixed [I]. The multiplier is NOT a new input: mu=(2/3)^6 is the subleading eigenvalue lambda2 of the THEORY'S OWN unique gapped boundary transfer operator (v54/v56, spectrum {1,(2/3)^6,(1/3)^6}, gap 6 log(3/2)>0), and the Koide branch x=-2/3=-|Z2|/N_fam IS its cusp weight 2/3={0,1,|Z2|}/N_fam; carrier q=5 -> Koide q=2 under the deck period q->q-N_fam (shared cusp class 2/3). With mu=(2/3)^6 the unique map is the integer Moebius map F(q)=2(569q-3325)/(665q-3517), F(2)=2, F(5)=5, F'(2)=(2/3)^6<1 (Koide is the ATTRACTOR), F'(5)=(3/2)^6>1 (carrier the REPELLER), so q_n->2 i.e. x->-2/3 at the SAME rate that governs SM flavor and horizon recovery. NET: the three 'structural postulates' for a Koide derivation collapse to ONE physical identification - source->pole transfer = branch-preserving relaxation of the established transfer operator; rate, uniqueness and direction then follow. NOT a closure: the single identification stays [P]
Recorded status: Physical (conjecture sharpened) + Identity [I]
Dependencies, status detail and source
Canonical status: Identity [I] (map uniqueness + multiplier = the established transfer gap) + Physical [P] (the one source->pole identification; no closure)
Dependencies: FR.KOIDE.01; FR.KOIDE.03; FLAV.PENCIL.03; v54; v56; v81
Scripts: v82_koide_attractor_splitting.py
Location: tfpt_4
Original CSV, line 149Original ledger status
HOR.NARIAI.01
THE MAXIMAL BLACK HOLE IS THE ANCHOR (carrier-in-the-bulk surface; Schwarzschild-de Sitter in seam units): (1) NARIAI = ANCHOR - at M_N = 1/(N_fam sqrt(L)) the horizon cubic is t^3-3t+2 = (t-1)^2(t+2), roots (1,1,-2) = the traceless projection of the anchor a=(1,1,2) (coefficients (-3,2) = (-N_fam,|Z2|); cf chi_a = (t-1)^2(t-2), ARCH.CORE.01). (2) the Koide 2/3 IS the Nariai entropy bound: S/horizon = S_dS/N_fam, total = (|Z2|/N_fam) S_dS, deficit S_dS/3; interpolation S_tot/S_dS = (x^2+1)/Phi_3(x), monotone, min at the merge. (3) three-sheet conservation pi sum r_i^2 = |Z2| S_dS for every M. (4) Koide-form quotient of the three roots ranges [3/8,1/2] = the two nonzero SU(4)_1 weights (pure dS -> 1/2 = delta; Nariai -> 3/8 = p2(a)/e1(a)^2). (5) mass-line double cover disc ~ (1-3m)(1+3m): branch +-1/N_fam, separation 2/3; deck = horizon swap (gravitational twin of the sheet Z2). (6) temperature lemma |kappa_b/kappa_c| = (2x+1)/(x(x+2)) > 1: evaporation flows AWAY from the merge - anchor point = repeller, democratic endpoint = attractor (same orientation as the flavor flow, FR.KOIDE.04) [audit]. (7) seam-unit mechanics: dM = c3 kappa dA, Smarr 2c3, Bekenstein 1/(4c3), P_H = c3/(1920 M^2) (=|W(D5)|, HOR.01), lifetime 5120 pi M^3 = 128 g_car M^3/c3 (128 = 2^7 = dS prefactor), Kerr A_ext = M^2/c3 (ratio 1/2 = 1/|Z2|, S_ext: 1/4 = 1/|mu4|), area quantum 4 ln3 = ln(N_fam^4) = ln(disc of the flavor cover) [P as HOR.QNM]. Six independent landings on already-load-bearing atoms, zero free parameters; lifetime/power normalisations are standard photon/geometric-optics conventions (external); carrier-in-the-bulk reading [P]; structure surface, not a measurement surface (M_N today ~1e22 M_sun)
Recorded status: Identity [I] (exact GR arithmetic on compiler atoms) + Physical [P] (bulk reading)
Dependencies, status detail and source
Canonical status: Identity: six atom landings in SdS mechanics; bulk reading [P]
Dependencies: AX.P1.01; ARCH.CORE.01 (anchor); FLAV.PENCIL.03 (cover); FR.KOIDE.04 (orientation); HOR.01; GATE.METRIC.07 (SU(4)_1 weights)
Scripts: v101_horizon_anchor.py
Location: tfpt_horizon_readouts;origin_theory;tfpt_2
Original CSV, line 184