It from I: External Phenomenology 2 -- The Parameter Ledger

As a direct quantitative sequel to "It from I: External Phenomenology", this paper resolves the primary open analytical problems posed in that work, demonstrating that key empirical parameters of the Standard Model and ΛCDM cosmology emerge from the finite observer algebra M_2(C) ⋊_γ Z_3 and its macroscopic Type III_1 Kubo-Martin-Schwinger (KMS) continuum limit. First, by evaluating Jacobson's Entanglement Equilibrium across the background volume entropy of the emergent KMS vacuum, we integrate the covariant elastic strain induced by baryonic matter to derive Verlinde's galactic scaling relation, M_D^2(r) = (c H_0 / 6G) r^2 M_b(r) (a_0 = c H_0 / 6 ≈ 1.09–1.18 × 10^-10 m/s^2), obtaining the 1/6 prefactor directly from horizon thermodynamics and d = 3 volume-entropy dilution. Second, we show that global boundary crystallization and renormalization group flow across the 2-dimensional cosmic horizon (B_cosmic) initialize phase-coherent superhorizon perturbations with spectral tilt n_s = 1 - 2/N_*. Across the radiation-era KMS thermal baseline (N_* ≈ 62–68), this yields n_s ≈ 0.968–0.971, consistent with Planck 2018 and joint Planck+ACT DR6+DESI measurements without invoking inflation. Third, an internal dark parity Z_2^dark splits the right-handed neutrino sector into a stable Z_2^dark-odd Planck-mass dark matter singlet (NR,1, MR,1 = a_min-1/2 = M_P) and two Z_2^dark-even seesaw partners (NR,2,3). We calibrate the relic abundance of NR,1 via non-relativistic KMS modular freeze-out at crystallization (x_init = M_P / T_init ≈ 65.9), establish its macroscopic convergence with primordial black hole remnants arrested at a_min, and derive the Entanglement Equilibrium action segregating the dark sector between cosmological scales and galactic disks. Fourth, we show that Entanglement Equilibrium absorbs ultraviolet radiative loop shifts to the electroweak hierarchy into the renormalized second moment of the spectral action test function. Finally, we diagonalize the 3 × 3 Holstein-Peierls fermion mass matrices on the internal Z_3 fiber in powers of the lepton-derived staggering constant ε = √(m_μ / m_τ) ≈ 0.244. Evaluating the Floquet-averaged gauge operators per color channel (g_2^(d) = 1/3, g_2^(u) = 1/12) reproduces the Georgi-Jarlskog mass relations (m_b(UV) = m_τ(UV), m_s(UV) = m_μ(UV)/3), the light-quark mass inversion (m_u < m_d) required for proton beta decay stability, the Wolfenstein CKM hierarchy (|V_us| ~ ε, |V_cb| ~ ε^2, |V_ub| ~ (1/3)ε^3), an O(1) Dirac CP phase δ_CP, and the parametric Jarlskog scale J ~ (1/3)ε^6 sin(δ_CP). In the neutral lepton sector, a 3-link Peierls loop holonomy screens the Z_2^dark-even Majorana mass of NR,2,3 to M_seesaw = ε^6 κ2,3 M_P ≈ 6.05 × 10^14 GeV (ε^6 M_P ≈ 2.57 × 10^15 GeV), yielding a rank-2 seesaw with a vanishing lightest mass (m_lightest ≈ 0). Conditioned on a phenomenological tribimaximal neutrino baseline and a delocalized m_2 / m_3 = ε / √2 scaling ansatz, this yields Normal Mass Ordering (m_1 ≈ 0), a reactor angle sin(θ_13^PMNS) = c̃_12^(l) ε / √2 ≈ 0.148, a solar sum rule phase δ_PMNS ≈ 97°–105°, and Δm_21^2 ≈ 7.47 × 10^-5 eV^2 (Σm_ν ≈ 0.059 eV). Together, these results organize the ~26 constants of the Standard Model and ΛCDM into a three-tier Parameter Ledger of parameter-free structural predictions, parametric scaling laws, and foundational boundary inputs.