Permanent Operational Cosmology: Structural Reconstruction of Cosmology from M3(C) in the Zero-Parameter Paradigm

The standard cosmological model (ΛCDM) postulates a Big Bang singularity, an inflationary epoch, dark matter, dark energy, and a cosmological constant, each introduced as independent hypotheses to resolve observational discrepancies. We introduce Permanent Operational Cosmology (Japanese: Koukyuu Enzan Uchu-ron, 恒久演算宇宙論), a framework derived from the axiomatic algebra of Operatiology (Japanese: Sousa Genron, 操作原論), in which every Tier-2 cosmological structure follows necessarily from the unique minimal algebra M₃(ℂ) determined by three axioms — non-commutativity, Operational Closure, and Irredundant Realization — with zero freely chosen parameters. Numerical values of cosmological observables are Tier-3 projections of these Tier-2 structural constants; their agreement with observation constitutes Tier-3 correspondence, not Tier-2 necessity. All derivations employ algebraic descriptions as the primary layer; analytical expressions are retained as Tier-3 translations for comprehension and are not used as derivation premises. Time emerges as the ordering of non-commutative operations; three-dimensional space emerges as the unique projection structure of M₃(ℂ). The cosmological constant vanishes as a Tier-2 algebraic identity, dissolving the 10¹²⁰-order discrepancy as a Tier-separation artefact. Cosmic flatness (Ω_total = 1) follows from the Hilbert-Schmidt metric of M₃(ℂ). Redshift is derived as the propagation of a uniform Type-II temporal modulation, yielding Hubble linearity z ∝ d without spatial expansion. The CMB temperature ratio T_CMB/T_P^(emp) = 1.923958 × 10⁻³² is derived with zero freely chosen parameters; once the electron mass is established as a structural projection of M₃(ℂ) (DOI: 10.5281/zenodo.22451280), the chain m_e → G → T_P^(emp) → T_CMB closes completely, giving T_CMB = 2.72583 K (observed 2.72548 ± 0.00057 K). The density fractions Ω_DM = Φ₆/(Φ₁·Φ₃) = 7/26, Ω_b = α_s²·Φ₆/Φ₁, and Ω_Λ = 1 - Ω_DM - Ω_b agree with Planck 2018 observations to within 1%. The black-hole information paradox is shown to be a pseudo-problem arising from conflation of Type-I and Type-II quantities; information is conserved as the rank of the density matrix. The Hubble tension is identified as a Tier-3 calibration artefact. The core intuition of steady-state cosmology — that the universe has no absolute beginning — is rehabilitated: both a past singularity and a future termination are algebraically excluded by the Operatiology axioms. The scalar spectral index n_s = δ·γ²·π ≈ 0.96191 is derived with zero freely chosen parameters (Planck 2018: 0.965 ± 0.004, deviation 0.32%). All results proceed from a single algebraic seed with zero freely chosen parameters. This paper is the Operatiology-period reformulation of the CM-period predecessor and is not a Version 2 but an independent paper, grounded on the Tier-2 foundation established in the companion paper on the structural account of cosmology from Operatiology. Version 2 of this paper updates the Operatiology V5 vocabulary alignment: all occurrences of the pre-V5 axiom labels {A1, A2, A4} throughout the body text, proofs, and appendix codes are replaced with the V5 designations {O1, O2, O3}. The minimal closure symbol C⁽³⁾{Π_d} is replaced by C_min; the generator rank notation rk{Π_d} is replaced by rk_op; and Π_d-indistinguishability is replaced by Π_O-indistinguishability. The following code illustrates the central result computationally: the CMB temperature is derived from M₃(ℂ) structure alone — no Big Bang, no inflation, no continuous spacetime — with zero freely chosen parameters, the chain m_e → G → T_P^(emp) → T_CMB now fully closed. import math n = 3Phi1 = 2Phi2 = 4Phi3 = 13 lam = (n**2 - 1) / n**2tau = 1 / abs(math.log(lam)) alpha = 7.2973525693e-3alpha_G = 1.75192e-45alpha_s = 0.118104 exp_G = (n - 1) / nexp_s = n / (n**2 - 1)N_G = alpha_G**(-exp_G)N_s = alpha_s**(-exp_s)N_cycles = N_G * N_s * tau em_correction = 1 + n * alpha / Phi3 T_P_emp = 1.416784e32 T_CMB = (T_P_emp / (Phi2 * N_cycles)) * em_correction print(f"N_cycles = {N_cycles:.6e}")print(f"T_CMB (derived) = {T_CMB:.5f} K")print(f"T_CMB (observed)= 2.72548 K")print(f"Deviation = {abs(T_CMB - 2.72548)/2.72548 * 100:.4f}%")print("Chain m_e->G->T_P^(emp)->T_CMB closed via DOI:10.5281/zenodo.22451280")print("No Big Bang assumed. Zero freely chosen parameters.") The sharpest single result of this paper: Λ_Op = sum of Spec(ad_H) = (+3)+(+3)+(-3)+(-3)+0+0+0+0+0 = 0. The cosmological constant vanishes as a Tier-2 algebraic identity from H = diag(1,1,-2) alone — no quantum field theory, no Dirac operator, no continuous spacetime. The 10¹²⁰ discrepancy between QFT vacuum energy and observation is a Tier-separation artefact, not a physical problem.