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Zenodo
2026
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| Online Access: | https://doi.org/10.5281/zenodo.19037166 |
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Table of Contents:
- <h2>GRUT-RAI v2.0 — Phase IV Canonical Build</h2> <p>This release synchronizes the GRUT-RAI codebase with the completed Phase IV foundational closure pass. Phase IV deepened the derivational and structural basis of the Phase I–III effective framework without replacing it.</p> <h2>What's New in v2.0</h2> <p><strong>Action-Principle Landscape</strong></p> <ul> <li>Local–conservative–first-order trilemma identified and documented</li> <li>Three action routes classified: Route A (overdamped parent), Route B (Galley doubled-field), Route C (nonlocal retarded — leading structural parent)</li> </ul> <p><strong>Route B: Galley Doubled-Field</strong></p> <ul> <li>Physical-limit-derived T^Φ_{μν} from Galley doubled-field formalism</li> <li>de Sitter-like w = −1 steady-state structure documented</li> <li>Non-attractor truncation result: Φ_- is not a dynamical attractor; physical limit CTP-enforced</li> </ul> <p><strong>Route C: Nonlocal Retarded Parent</strong></p> <ul> <li>Exact recovery of first-order relaxation law from exponential kernel</li> <li>Markov property: local auxiliary-field reduction confirmed exact</li> <li>Functional-derived stress-functional T^Φ_{μν} converges with Route B physical limit</li> <li>Perturbative metric-variation commutation test around FRW: source and kernel channels commute exactly; lapse channel commutes in proper time</li> </ul> <p><strong>Strong-Field Lapse</strong></p> <ul> <li>Lapse-correction ODE derived from Route C metric-variation pass</li> <li>Bounded correction across compactness range</li> <li>Self-healing at equilibrium: source term Ψ(X − Φ) → 0 at force balance</li> <li>Endpoint law R_eq/r_s = 1/3, Phase III status ladder fully preserved</li> </ul> <p><strong>Effective Lapse Derivation</strong></p> <ul> <li>Exact algebraic result: Φ_barrier/Φ_grav = 1/(1+β_Q) at endpoint</li> <li>β_Q scan: 1→1/2, 2→1/3, 3→1/4 — α_vac coincidence is parametric, not fundamental</li> <li>Three-level distinction: exact barrier ratio | constitutive-derived proxy | unresolved true metric lapse</li> </ul> <p><strong>Tensorial Roadmap</strong></p> <ul> <li>Scalar closure confirmed sufficient for all Phase III results</li> <li>Tensorial extension paths classified (scalar-only, scalar+anisotropic, rank-2)</li> </ul> <p><strong>Repository Health</strong></p> <ul> <li>Final freeze: 1222 passed, 3 skipped, 5 warnings (pre-existing), 0 failures</li> <li>Progressive totals: 614 → 676 → 750 → 846 → 963 → 1093 → 1222</li> </ul> <h2>Scope and Limitations</h2> <ul> <li>Phase III endpoint law (R_eq/r_s = 1/3) and status ladder fully preserved</li> <li>Route C is the strongest structural parent, not a complete solved final ontology</li> <li>T^Φ_{μν} is constitutive/effective; first-principles action-level derivation remains open</li> <li>Sub-horizon metric-to-lapse mapping remains unresolved</li> <li>Nonlinear self-healing beyond first perturbative order untested</li> <li>Doubled-sector ghost/pathology (Route B) remains unresolved</li> <li>Post-Phase-IV extensions (consciousness, particle sector, broader unification): frontier memos only</li> </ul> <p><strong>Phase IV foundational closure pass is complete. Remaining unresolved issues are sharply localized to deeper first-principles and sub-horizon metric questions.</strong></p> <h2>Related Manuscripts</h2> <ul> <li>Phase IV paper: DOI pending (Zenodo)</li> <li>Phase III paper: DOI 10.5281/zenodo.18986085</li> <li>GRUT-RAI v1.0: DOI 10.5281/zenodo.18993690</li> </ul>