Unified Recursion Theory (URT) — Validation Datasets (Quantum, Thermal, Biological, Relativistic)

This archive contains the complete dataset package used to validate the Unified Recursion Theory (URT) across four empirical domains: quantum systems, thermal systems, biological information processes, and relativistic information flow. All data, metadata, processed outputs, and integrity-verification files required to fully reproduce the results reported in the URT v5.6 manuscript are included. The repository is structured to ensure domain-invariant reproducibility and transparent verification of the URT informational proportionality relation: ΔE=λ kBTΔH\Delta E = \lambda\, k_B T \Delta HΔE=λkBTΔH This dataset collection includes: 1. Quantum Validation (a) IBM Fez & Marrakesh Backends (2025) Eight entropy–energy scans from IBM Quantum devices using the revised Phase-2 header structure.Includes raw CSV files, per-row and per-scan λ values, and summary outputs. (b) Harvard Optical-Lattice Gauge-Invariance Dataset Reconstructed traces (57 Hz, 89 Hz, DMRG, QLM) from Harvard Dataverse (DOI: 10.7910/DVN/3RXD).Used to verify Liouvillian continuity and stationary entropy flow. 2. Thermal Validation Shomate-parameter thermochemical tables for: H₂O (steam phase) CO₂ Ar Extracted from NIST JANAF Thermochemical Tables.Processed prediction tables and thermal λ summaries included. 3. Biological Validation (a) Differential Scanning Calorimetry (DSC) Unfolding Lysozyme and β-lactoglobulin enthalpy/free-energy transitions from Seelig & Seelig (IJMS, 2023).Confirms URT reversible boundary (λ → 0). (b) RNA Nearest-Neighbor Thermodynamics Watson–Crick ΔG°₃₇ and ΔH° tables from the Turner04 NNDB dataset.Used to compute λ stability across RNA helix stacking motifs. (c) Viral Evolution Population-Entropy Dataset SARS-CoV-2 long-term passaging dataset (Foster et al., 2025; BioProject PRJNA1018257).Includes variant-frequency tables, SRA metadata, supplementary materials, entropy trajectories, retention indices, and fitted recursion parameters. 4. Relativistic Validation (a) Optical-Clock Gravitational Redshift (Zheng et al., Nature Communications, 2023) Height–dependent frequency-shift data from Zenodo supplementary materials.Includes raw CSVs for probabilities, corrections, redshift gradients, and clock baselines, along with processed URT regression outputs. (b) Landauer Limit – Information Erasure (Nature 2012) Digitized P(Q), Q(τ), and success-probability curves from Bérut et al. (Nature 483).Includes λ(τ) convergence analysis showing approach to the reversible limit λ → 1. Included for Every Validation Domain raw/ — unmodified files from original publications and repositories processed/ — URT-derived tables, λ estimates, regression outputs analysis/ — report.json (methods, settings, equations), SHA256SUMS files metadata.json — provenance, dataset descriptions, integrity notes All raw files include SHA-256 fingerprints for independent verification. The directory structure is: datasets/ quantum/ fez-marrakesh/ harvard-optical-lattice/ thermal/ biology/ dsc_unfolding/ molecular_energetics/ population_entropy/ relativistic/ gravitational_redshift/ landauer_2012/ Reproducibility All computations follow the URT v4.5 reproducibility protocol, with: standardized entropy estimation energy-normalization procedures weighted least-squares regression (HC3 robust covariance) uncertainty propagation as defined in Appendix E of the URT manuscript cross-domain invariance checks for λ These datasets support full reproduction of all empirical validations reported in the URT v5.6 manuscript. License CC-BY 4.0All raw scientific data remain under their original publication licenses; processed URT outputs are released under CC-BY for research and verification purposes.