hyconiek/Fractal-Nadsoliton-Theory: Release 4.0 — Ringdown Energy Discovery & Scaling Law

Release 4.0 — Ringdown Energy Discovery & Scaling Law Emergent Gravity, Hierarchical Bayesian Audit & Non-GR Scaling Study Range: QW-1625 → QW-1711 (Phase 6–11) Author: Krzysztof Żuchowski Affiliation: Independent Researcher — Fractal Information Theory Project Release Date: v4.0 (2026-01-01) Previous Stable: v3.9.2 — GWTC-4 Verification 1. Abstract This release marks a paradigm shift in the verification of the Fractal Information Nadsoliton (FIN) framework. Following the inconclusive results of linear propagation tests (Phase 6–7), the investigation extended to higher-order emergent sectors using a dataset of 112 gravitational-wave events (GWTC-3 + GWTC-4). Analysis revealed a coherent, statistically significant excess in the ringdown energy sector (Phase 8), which defies General Relativity predictions. Subsequent parametric localization (Phase 9) and scaling analysis (Phase 10) confirmed a sub-extensive scaling law ($E \propto M^{0.497}$) consistent with the FIN prediction of information content on a holographic horizon. Bayesian model comparison (Phase 11) now strongly favors FIN over GR ($\ln \text{BF} \approx 18$). 2. Key Findings (The "Ringdown Discovery") Phase 6–7: Propagation Consistency (GR Holds) Result: Linear propagation tests (amplitude reweighting, dispersion) show no deviation from General Relativity. Implication: FIN does not manifest as a "massive graviton" or simple modified gravity theory. Phase 8: Coherent Energy Excess Result: Stacking analysis revealed a persistent non-zero energy residual in the ringdown phase. Significance: The signal is coherent (same sign across events), robust to noise injection (up to 55%), and stable across catalog splits (GWTC-3 vs GWTC-4). Phase 10: The Fractal Scaling Law Discovery: The residual energy $E$ scales with final mass $M$ as: $$ E \propto M^p, \quad p = 0.497 \pm 0.084 $$ Theory: This matches the FIN prediction of $p \approx 1/2$, representing the square root of information content (sub-extensive scaling), whereas GR predicts linear scaling ($p \ge 1$). Phase 11: Bayesian Victory Verdict: Formal model comparison yields a Bayes Factor of $\ln \text{BF} \approx 18$ in favor of FIN. Interpretation: This constitutes Strong Evidence that the FIN framework provides a superior description of the ringdown regime than standard General Relativity. 3. Methodology Dataset: 112 Confirmed GW Events (GWTC-3 + GWTC-4). Tools: Hierarchical Bayesian Inference, Importance Sampling, Jackknife Resampling, Null Tests. Integrity: All "Discovery" claims are supported by rigorous systematics checks (null tests, sign-scrambling, selection bias analysis). 4. Conclusion FIN Theory is no longer just "consistent" with observations—it is now actively preferred by the data in the high-energy ringdown sector. The specific scaling law $p \approx 0.5$ provides a unique "fingerprint" of the fractal informational structure of the Nadsoliton. 5. Resources Documentation: TOE_FINAL_DOCUMENTATION.pdf (Updated to v4.0). Evidence: phase10_results.json, phase11_results.json in repository. Official Repository: https://github.com/hyconiek/Fractal-Nadsoliton-Theory