The factor that appears in every horizon temperature is the seam constant itself. Black holes, de Sitter and Unruh therefore share one thermal grammar.

Temperature, entropy, power and lifetime all read off c₃, with the Hawking power denominator carrying the compiler fingerprint 1920 = |W(D₅)| (the Weyl group order of D₅). The temperature is not put in by hand: the stationary exterior modular flow Δ^{it} = e^{−2πtK_H} (Bisognano–Wichmann / Tomita–Takesaki) makes the outside state KMS at inverse temperature 2π, so T_H = κ/(2π) — and that 2π is the seam unit 1/(4c₃), reproducing T_H = c₃/M (the seam = horizon modular identification ties to [ρ,Λ_Σ] = 0). The same normalisation is now MEASURED on the reconstructed free seam OS quotient (SEAM.THERMAL.KMS.01, v526): detailed balance gives β = N clock steps at both levels, hence β_angle = 2π and T_seam = 4c₃ — temperature joins geometry and anomaly as the third leg of c₃ ([C]-typed reading: seam euclidean circle = thermal circle of the reconstructed horizon dynamics; the entropy-fraction bridge to the Nariai ledger honestly does not close). The induced R + R² scalaron then corrects the area law to the Wald entropy S_W = (A/4G)(1 + R_h/3M_s²), an exact consequence of f(R) = R + R²/(6M_s²); the leading A/4G is the c₃ area law (1/4 = 1/|μ₄|). [E] for the identities; the black-hole/modular identification is [C].

The Page time is a fixed fraction of the evaporation time, and the scrambling time carries the second fingerprint |μ₄| = 4. The Page-recovery kernel decays at the same λ₂ = (2/3)⁶ that sets the SM flavor gap.

The de Sitter entropy and the cosmic-birefringence angle are the same seam readouts; v_GW = c follows with no measurable dispersion. The defect reading of the black-hole interior: in compiler units it is not a curvature blow-up but the seam attractor — the same gapped transport whose sub-leading eigenvalue is λ₂ = (2/3)⁶ drives φ → φ_⋆ (dφ/dt = 0), so 'ρ → ∞' is replaced by a fixed point; information returns through the same Page-recovery channel; and the end state is a holographic Planck-scale floor (S_BH = A/4, one cell per |μ₄| = 4 Planck areas), not a point. A [C] structural reading — the old RN/torsion-charge metric is not resurrected, it is superseded by the Nariai/seam = horizon anchor.

Put a black hole into the de Sitter bulk: at the maximal (Nariai) mass the horizon cubic has roots (1,1,−2) — exactly the traceless projection of the anchor a = (1,1,2) — and the total entropy bound is exactly the Koide branch value 2/3 = |ℤ₂|/N_fam (each horizon carries S_dS/3). The interpolation is (x²+1)/Φ₃(x) with the N_fam cyclotomic; the three-root entropy total |ℤ₂|·S_dS is conserved for every mass; the mass line is itself a split double cover whose deck involution is the horizon swap; and evaporation always flows away from the anchor point — the same repeller/attractor orientation as the flavor relaxation. Six independent landings on already-load-bearing atoms, zero free parameters; the carrier-in-the-bulk reading stays [C].

The flavor relaxation is the gradient flow of a cubic potential whose critical points are exactly the two branch points, with stationary curvatures ±Δ (the transfer gap) and a constant Lyapunov rate Δ. The SdS entropy functional has the Nariai/anchor point as its unique stationary point with curvature 2/9 = |ℤ₂|/N_fam², and evaporation ascends the entropy away from it. Both sectors flow away from an anchor-stationary configuration with grammar-constant curvatures; reading this as one variational principle of the seam stays [C], with the disanalogies recorded honestly.

The SdS horizon cubic is uniformized by angle trisection (r = 2cos θ turns it into cos 3θ = −3m; the ℤ₃ trisection deck is the triality of coker Q = ℤ/N_fam). In the centered angle the mass is a pure cosine, m = cos(ψ)/N_fam, and the entropy collapses to ONE cosine of glue atoms with canonical curvature (2/3)³ at the anchor — the Koide constant to the family power. The invariant slope dσ/dm at Nariai is −8/9 = −rank E₈/N_fam². The flavor invariant is a rate, (2/3)^{2N_fam} per transport step; the gravity invariant is a curvature, (2/3)^{N_fam}: same base, exponent ratio |ℤ₂|. The gravity-side clock asked for here has since been constructed (v124–v133, sections below): one clock, two known geometries — the identification reading stays [C].

The classical half of the clock question is pure GR: linearizing around the Nariai geometry dS₂×S², the static mode φ(ρ) = ρ solves the static-patch equation exactly with m² = −2Λ = −|ℤ₂|Λ — the exact SdS family itself pins the modulus mass (Ginsparg–Perry tower: exactly one negative mode). In Hubble units the clock's characteristic polynomial is (λ−1)(λ+2) — the anchor quadratic: its eigenvalues are the distinct anchor roots, and the Nariai cubic factors as (t−1)·χ_clock. The anchor appears a third time: configuration roots, curvature base, clock spectrum. The honest (2/3)-test is negative for the classical clock (integer eigenvalues); the quantum clock — the one-loop conversion of curvature into rate — was the remaining [C] and is resolved by the resummed-clock chain below.

The quantum clock now has a closed form: rate(n) = −p₂ ln(1 − n/N_fam) — the three-level spectrum is forced by the pole at N_fam, and the bend log₃∕₂3 is its n = 2 value. Its weights are the Mehta–Seshadri parabolic weights of the exact anchor residue A₀* (v126); the geometric tail is the standard log-determinant/RPA ring resummation, one tower per hexagon site (v127); the rate is an entropy power law Γ ∝ (S/S_dS)^{p₂} in Gibbons–Hawking form (v129); the exponent p₂ = 2h follows from mode counting plus the Born rule, h = N_fam = half the zero-mode count (v130); the per-mode S^{1/2} is the zero-mode area norm ‖Y₁ₘ‖² = A/(4π) exactly (v131); and the scaling anomaly of the non-zero-mode S² determinant is exactly −2/3 = −|ℤ₂|/N_fam — the Koide constant as a spectral anomaly (v132). The ζ(0) budget computed both ways selects the reduced seam reading: per sector −2/3, total −4/3 = minus the seed gain, while the naive 4d route gives −109/45, no atom (v133). The residue of the clock question is one finite budget — the graviton/ghost heat coefficients on S²×S² [C]. The det-ratio step is since derived within the SdS family: e₂-rigidity gives r_b·r_c = 1 − Δ²/3 exactly, so the non-zero-mode determinant ratio is (1 − Δ²/3)^{4/3} with no first-order term in the horizon split (v144); the finite-weight absorption stays [C] with its obstruction stated sharply. The ring sum is now identified as the Born-squared Gaussian zero-mode integral (variance = area ratio, forced by v131), and the quantum bend log_{3/2}3 is determinant-clean — both Nariai weights share one geometry (v147); the residue is the measure identification plus one reference normalisation.

The Nariai pattern is stored inside the flavor compiler as a dual invariant: d := aᵀR⁻¹ = aᵀL⁻¹ = (−1/2, −1/2, 1), with d·1 = 0, d·a = 1 and (1,1,−2) = −2d. The invariance is structural (Sherman–Morrison): a covector is winding-invariant iff it annihilates R⁻¹1 = (1,1,−1)/4 — the anchor does, while 1, e₁ and the torsion normal n do not (the membership is special). Together (d, n) form the dual normal pair of the flavor boundary: d reads the traceless horizon structure, n reads first-generation torsion. A third, purely algebraic leg of the flavor↔horizon bridge, beside the shared clock spectrum (v126) and the entropy power law (v129) [E]; the bridge reading stays [C].

Audit-level search ansätze, explicitly [O]: black-hole echoes / horizonless compactness (any near-horizon echo amplitude ratio ≤ (2/3)⁶ ≈ 0.0878; the gravastar maximum compactness C = 3/8 turns this into an echo template, experiments/gravastar-compactness); the Page-curve recovery kernel I ~ (2/3)^{6n} as a falsifiable shape; FRB repeaters as a preregistered search interface for the frozen kernel ratios (experiments/frb-tfpt-signatures); the BH HFQPO ladder tooth — the four published 3:2 twin pairs are consistent with exactly 3/2 but the cluster is cheap (anchored selection null 18.5%, XTE J1859+226 breaks universality at +9.2σ) and mapping the relaxation-ladder step 3/2 onto a two-oscillator ratio is non-canonical; the one discriminating target, a third tooth at ν₃ = (3/2)ν_u (661.5/414/252/363 Hz, integer harmonics forbidden), was never targeted by any published search, and the preregistered archival RXTE PCA scan (executed 2026-07, 77 ObsIDs, sanity gate 11/12, injection-calibrated) finds neither the tooth nor the integer control line anywhere — a well-powered null with 3σ limits 0.53–3.06% rms; the preregistered NICER extension (MAXI J1820+070, 2026-07-22, single-QPO rule) adds a second-instrument null_with_sensitivity (anchor 55.03 Hz reproduced at 3.8σ, tooth limit 0.75% rms below the anchor strength, the ~110.6 Hz integer line at 3.82σ below the 4σ threshold — a sub-threshold excess, no hit; AstroSat/LAXPC blocked): the ladder reading is unsupported but not killed, GR resonance stays favored, the channel is dormant (experiments/hfqpo-ladder; even a future tooth hit would be [C] until the mapping is derived); cosmological coupling k = 3 (w_in = −1, experiments/ccbh-dark-energy, contested); and cosmic spin parity (approximate parity, a frontier watchdog, experiments/cosmic-handedness). Hunting grounds, not foundations.