The Alemoh-Obidi Correspondence (AOC): Continuation of the Theory of Entropicity (ToE) Living Review Letters Series, Letter IC of the Alemoh-Obidi Correspondence (AOC) on the Foundations and Formulation of the Theory of Entropicity (ToE)
Section 10 — The Entropic Probability Conservation Law and the Entropic CPT Law covers the full mathematical architecture across six subsections:
10.1 traces probability from Kolmogorov's 1933 axioms and Born's 1926 postulate through to its ToE derivation as a conservation law, including the Hilbert-space decomposition H_tot = H_o ⊕ H_e (Eq. 20), the combined unitary–entropic evolution operator U_ToE(t) = e^{−iHt} e^{−Ct} (Eq. 21), and the full derivation of P_o(t) + P_e(t) = 1 (Eq. 27) — with detailed analysis of why this is structurally distinct from Kolmogorov normalization, how it connects to the Born rule as a limiting case, and its role as the microscopic mechanism of decoherence, irreversibility, and classicality.
10.2 presents the Entropic CPT Law with the formal transformation rules for C, P, and T acting on the entropic field S(x) (Eqs. 29–33), the physical mechanism of CPT violation through weakening of Lorentz invariance, locality, and spin-statistics at extreme entropic gradients, implications for baryogenesis via early-universe entropic CPT violation, and experimental signatures accessible to next-generation precision tests.
Section 11 — The March–April 2026 Correspondence reconstructs three interconnected themes across seven subsections:
11.1–11.3 cover Alemoh's cosmic expansion question (March 12, 2026), the two-sector Obidi Action architecture (LOA + SOA, Eq. 36), and the dynamic boundary governed by the entropic coherence length and spectral curvature scale (Eqs. 37–38).
11.4–11.7 cover the entropic interpretation of entanglement — formation as topological transition M_A ⊕ M_B → M_AB (Eqs. 39–40), the dual geometry of spacetime distance versus entropic relational distance (Eqs. 42–43), the stability question with coherence strength Γ_AB(t) and decoherence thresholds (Eqs. 44–45), the two-sector Obidi Action for entangled systems (Eq. 49), and Daniel Moses Alemoh's foundational contributions to crystallizing these structures.
Equations run from (20) through (53), showcasing the mathematical structures and internal consistency of the ToE axioms, the Obidi Action, and the entropic field formalism established in the Theory of Entropicity (ToE).
References and Errata
| Ref | Author/Work | Location |
|---|---|---|
| [40] | Kolmogorov, Grundbegriffe (1933) | §10.1 |
| [41] | Born, Zur Quantenmechanik der Stoßvorgänge (1926) | §10.1 |
| [42] | von Neumann, Mathematische Grundlagen (1932) | §10.1 |
| [43] | Gleason, Hilbert space measures (1957) | §10.1 |
| [44] | Zurek, decoherence/einselection (2003) | §10.1.6 (corrected from erroneous [1, 2]) |
| [45] | Lindblad, GKSL master equation (1976) | §10.1.2 |
| [46, 47] | Lüders (1954) and Jost (1957) | §10.2 intro |
| [47] | Jost, Wightman axiomatic proof (1958) | §10.2.1 |
| [48] | Wu et al., parity violation (1957) | §10.2.1 |
| [49] | Christenson, Cronin, Fitch, Turlay, CP violation (1964) | §10.2.1 |
| [50] | BASE Collaboration; CPLEAR Collaboration | §10.2.1; §10.2.5 |
| [51] | ALPHA Collaboration | §10.2.1; §10.2.5 |
| [52] | Sakharov, baryogenesis conditions (1967) | §10.2.4 |
| [53] | Cohen & Kaplan, spontaneous baryogenesis (1987) | §10.2.4 |
| [54] | Maldacena & Susskind, ER=EPR (2013) | §11.5 |
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