Fourth Law of Cosmological Thermodynamics - Rant-Marusic Law of Conservation of Vacuum Exergy - V_AV Formulation V7.1 Final Unambiguous Edition

Provenance & Acknowledgement: The foundational exergy/anergy matter framework originates from Z. Rant (1956) who introduced the concept of exergy. The present work is a subsequent formulation - the Rant-Marušič V_AV construction V_AV(z)=1/3*B_AV(z)*H0/H(z), B_AV(z)=rho_DE(z)[1+w(z)] - developed from that framework. The distinction between Rant's original framework and the Rant-Marušič construction is made explicit in the attached Fact-check note. This note also provides numerical consistency check for z_c and BAO chain. --- Formulation: V_AV(z) = 1/3 * B_AV(z) * H0/H(z), where B_AV(z) = rho_DE(z) + p_DE(z) = rho_DE(z)[1+w(z)] is vacuum exergy density [J/m3], the available work density of dark energy. Observational anchor DESI DR2 BAO: (D_H/r_d)_obs = 8.632 at z=2.33. B_AV,obs = -5.16e-11 J/m3 is an observational input to V_AV calculation, rather than CPL-derived value. This gives V_AV,phys(2.33) = -4.91e-12 J/m3. Full BAO chain: r_d H0 / c = 0.03306097 → 0.033069 (calibration refined), H0/H(2.33) = 0.2854524 → 0.2855. CPL parameters: w0 = -0.847, wa = -0.516, Omega_m = 0.296, Omega_DE = 0.704, H0,fid = 67.4 km/s/Mpc, transition redshift where B_AV(z_c)=0 and w(z_c)=-1 is z_c = 0.4214876 → 0.4215. Fourth Law - conserved quantity: V_EX = ∫_0^{z_c} |B_AV(z)|/E(z) dz = 1.64847160e-11 J/m3 → 1.65e-11 J/m3. This is total conserved vacuum exergy available from today to z_c. Alternative integral (clarification): I_alt coarse = 0.55e-11 = 5.5e-12 J/m3 (documented coarse procedural value, retained intentionally) I_alt refined = 5.10803825e-12 → 5.11e-12 J/m3 (precision-refined numerical integration) Equality 0.55e-11 = 5.5e-12 is exact. 5.5e-12 is NOT a typo and NOT ordinary rounding of 5.108e-12; they represent different precision levels. Physical consequence of conservation law: Delta H0 = k_phys * V_EX, with Delta H0 = +4.5 km/s/Mpc, k_phys = 2.73e11 (km/s/Mpc)/(J/m3), giving H0 = 67.4 + 4.5 = 71.9 km/s/Mpc as calibration-dependent result. QES signed document V7.1 Final Unambiguous Edition, 8 pages, numerical audit PASS. DOI reserved: 10.5281/zenodo.23108624. This constitutes the proposed Fourth Law: total vacuum exergy V_EX is conserved and converted into Hubble expansion work. Keywords: Fourth Law, cosmological thermodynamics, vacuum exergy, Hubble tension, DESI DR2 # FixNEW / Point-1 - Version Chain & Current Status This document clarifies the finalized version chain for the FixNEW / Point-1 research records on Zenodo to avoid confusion from record numbers. ## Current Canonical Records Latest Point-1 Derivation Record: 23119616 | DOI: 10.5281/zenodo.23119616 - V4 (Current) Current V7.1 Formulation & Supporting Materials Record: 23113019 | DOI: 10.5281/zenodo.23113019 - V2 for V7.1 formulation Both records are current but serve different roles. V4 does NOT replace V2 conceptually - it extends it. ## Verified Zenodo Version Chain Use Zenodo's explicit is new version of metadata, not numerical order, to interpret the chain: | Zenodo ID | DOI | Role | Explicitly New Version Of | | 23108624 | 10.5281/zenodo.23108624 | Earlier / foundational V7.1 formulation | - | | 23113019 | 10.5281/zenodo.23113019 | V2: Finalized V7.1 formulation + fact-check / MetaV7 supporting materials | 23108624 | | 23118905 | 10.5281/zenodo.23118905 | V3: First Correction – Point 1 Derived | 23113019 | | 23119616 | 10.5281/zenodo.23119616 | V4: Latest Point-1 / FixNEW derivation (11-equation formulation) | 23118905 | Chain to cite: 23108624 -> 23113019 [Separate formulation chain] 23118905 -> 23119616 [Active Point-1 derivation / correction chain] ## What Changed Between Versions V2 (23113019) -> V3 (23118905): - Added explicit stress-energy definition from vacuum action - Defined B_AV = 3[V_AV + p_AV] - Added explicit time derivatives - Added Bianchi / first-law step and full conservation chain leading to proposed Fourth Law V3 (23118905) -> V4 (23119616): - Reformulated Point-1 derivation in 11-equation form - States full conservation / integration chain - Proposes relation V_AV + V_EX = const. - Provides falsifiability criterion ## Falsifiability Criterion (V4) V4 makes a stated testable prediction for DESI DR3: z_c = 0.4215 ± 0.02 ## How to Cite If you refer to the formulation and supporting evidence, cite: Marušič, I. R. (2026). V7.1 formulation. Zenodo. https://doi.org/10.5281/zenodo.23113019 If you refer to the Point-1 derivation / FixNEW and its prediction, cite: Marušič, I. R. (2026). Point-1 Derived - V4. Zenodo. https://doi.org/10.5281/zenodo.23119616 For full history, include the intermediate correction: V3: https://doi.org/10.5281/zenodo.23118905 ## Status and Next Steps 1. 23119616 is the latest citable artifact for the Point-1 derivation. 2. 23113019 remains the canonical artifact for the V7.1 formulation. 3. Future revisions will explicitly state which record they supersede and will preserve the Zenodo version link. 4. Scientific validation status: A Zenodo record establishes a public, citable, timestamped research artifact. It does not by itself establish scientific correctness or peer-reviewed acceptance. 5. Next substantive step: Independent reproduction of the derivation and numerical calculations, followed by testing the z_c prediction against DESI DR3 data. --- V4 Zenodo Description (short): V4 - Latest Point-1 / FixNEW Derivation (11-equation formulation) This record (23119616 / DOI 10.5281/zenodo.23119616) is the latest Point-1 derivation record and is explicitly a new version of 23118905 (V3). Version chain: 23108624 -> 23113019 (V2 - V7.1 formulation) -> 23118905 (V3 - First Correction) -> 23119616 (V4 - Current). Role separation: Use 23113019 as the canonical V7.1 formulation and supporting-materials record. Use 23119616 as the canonical Point-1 derivation record. New in V4: 11-equation formulation, full conservation/integration chain including V_AV + V_EX = const., and stated falsifiability criterion z_c = 0.4215 ± 0.02 for DESI DR3. Zenodo establishes a public citable artifact; it does not establish correctness. Next step is independent reproduction and DESI DR3 test.