Unified Recursion Theory: A Proportionality Law Linking Energy and Informational Entropy Change

Version: v7.3
Release Type: Consistency, validation, and appendix stabilization update
Status: Public archival update (Zenodo)

Overview

Version 7.3 is an updated internal consistency check up of the Unified Recursion Theory (URT) manuscript across quantum, thermal, biological, and relativistic domains. This release resolves legacy notation issues, clarifies regime-dependent efficiency behavior, and stabilizes all appendices supporting falsification, uncertainty propagation, and cross-domain comparison.

No new empirical datasets are introduced in this release. All numerical results are preserved. Changes are structural, not interpretive.

Key Updates

1. Regime-Consistent λ Framework

• Fully replaced legacy references to a single universal efficiency (λ_c) with a regime-dependent efficiency structure:
  • λ₀ ≈ 0.78: low-stiffness, irreversible asymptote (quantum domain)
  • λ → 1: reversible/conserving limit (thermal equilibrium, relativity)
  • λ → 0: equilibrium midpoint boundary (protein unfolding)
• Explicit regime gating added throughout Appendices B–D.

2. RNA Efficiency Formula Correction (Appendix B.3)

• Corrected RNA efficiency extraction to use entropy (ΔS°) in the denominator, consistent with thermodynamics and the dependency map.
• Removed erroneous ΔH° denominator usage.
• Locked canonical RNA expression at T = 310 K.
• Numerical result unchanged: λ_RNA ≈ 0.25 ± 0.07.

3. Protein Domain Reframing (Appendix B.4)

• Revalidated protein unfolding using published DSC endpoint values.
• Clarified that protein data anchor the equilibrium boundary (λ → 0) rather than testing λ₀.
• Removed overextension of stiffness-suppression claims at the midpoint.

4. Relativistic Domain Clarification (Appendix B.5 & C.4)

• Relativity now explicitly treated as a reversible anchor (λ = 1).
• Entropy-preserving clock evolution clearly separated from compressive regimes.
• Strong-curvature and cosmological extensions deferred to a dedicated cosmology manuscript.

5. Appendix C (Falsifiable Predictions) Cleanup

• Added scope clarification and regime labeling to all predictions.
• Removed strong-curvature cosmological predictions from this manuscript.
• Preserved falsification criteria with explicit regime conditions.

6. Appendix D (Uncertainty & Statistics) Alignment

• Clarified backend temperature normalization as a reporting convention, not a physical assumption.
• Updated aggregation language to reflect regime-specific, not universal, λ values.
• Statistical methodology unchanged and fully compatible with v7.2 results.

Cross-Domain Consistency (Final)

• Quantum (irreversible, low stiffness): λ₀ = 0.782 ± 0.019
• Thermal equilibrium (reversible): λ → 1
• RNA (moderate stiffness): λ ≈ 0.25 ± 0.07
• Protein unfolding midpoint: λ → 0
• Relativistic time dilation: λ = 1

This ordering is now explicit, consistent, and closed.

What v7.3 Is (and Is Not)

• Is: a stabilization, correction, and consistency release
• Is: suitable as a canonical reference version
• Is Not: a reinterpretation of results or a numerical refit
• Is Not: a cosmological or strong-curvature extension

Citation Note

Users are encouraged to cite v7.3 for all discussions of URT efficiency structure, regime dependence, falsifiable predictions, and statistical methodology. Earlier versions remain archived for provenance.

Experimental Context
Contemporary experimental and observational results relevant to Unified Recursion Theory are cataloged and interpreted in a separate, continuously updated URT Experimental Interpretation Ledger (Living Document) (Zenodo DOI: https://zenodo.org/records/17990083). The ledger provides interpretive context only and does not modify, validate, or extend the claims of this paper.

URT PAPER FAMILY

This work forms part of the Unified Recursion Theory (URT) research program, which develops a cross-domain framework for physical evolution based on constrained informational recursion and an energy–entropy proportionality law. Each paper in the series is self-contained, while collectively establishing the theoretical structure across quantum, geometric, biological, cosmological, and particle-level domains.

Related URT works available on Zenodo:

FOUNDATIONAL PAPERS

1. Unified Recursion Theory — Core Framework (URT Core)

DOI: 10.5281/zenodo.17642761
Record: https://zenodo.org/records/17642761

2. Discrete Admissible Regimes in Unified Recursion Theory: Operator Closure, Constraint Topology, and the Necessity of Five Operators

DOI: 10.5281/zenodo.18148192
Record: https://zenodo.org/records/18148193

3. Informational Field Theory in Strong Curvature (IFT-SC)

DOI: 10.5281/zenodo.17850379
Record: https://zenodo.org/records/17850379

4. Dynamical Evolution of the Informational Stiffness Field (ISW Theory)

DOI: 10.5281/zenodo.17860533
Record: https://zenodo.org/records/17860533

RESOLUTION PAPERS (PHYSICAL PARADOXES)

5. Informational Recursion and the Dissolution of the Black Hole Information Paradox

DOI: 10.5281/zenodo.17868662
Record: https://zenodo.org/records/17868662

6. ORM and the Quantum Measurement Problem (ORM)

DOI: 10.5281/zenodo.17881944
Record: https://zenodo.org/records/17881944

BRIDGING / CONSTRAINT PAPER

7. Distinguishability Geometry in Informational State Space

DOI: 10.5281/zenodo.17957062
Record: https://zenodo.org/records/17957062

Provides the geometric foundation for informational state space.
Underpins the emergence of spacetime, efficiency universality, and landscape geometry.

THEORETICAL EXPANSION PAPERS

8. Emergent Spacetime from Informational Recursion

DOI: 10.5281/zenodo.17885555
Record: https://zenodo.org/records/17885555

9. λ-Universality Across Scales (λ-UAS)

DOI: 10.5281/zenodo.17934065
Record: https://zenodo.org/records/17934065

10. Free-Energy Landscape Geometry in Unified Recursion Theory

DOI: 10.5281/zenodo.17940995
Record: https://zenodo.org/records/17940995

BIOLOGY / COMPLEXITY PAPER

11. URT in Biology: Efficiency, Folding Funnels, Replication Fidelity, and Molecular Motor Dynamics

DOI: 10.5281/zenodo.17945209
Record: https://zenodo.org/records/17945209

COSMOLOGICAL EXTENSIONS

12. Cyclic Cosmology from Informational Recursion

DOI: 10.5281/zenodo.17955043
Record: https://zenodo.org/records/17955043

13. Antimatter as Inverse Recursion: Temporal Operator Asymmetry and Matter–Antimatter Imbalance in Unified Recursion Theory

DOI: 10.5281/zenodo.17955043
Record: https://zenodo.org/records/17955625