RCA Ω 2027 — Phase VII Joint CMB Geometry Lock and Late-Time Growth Constraints Resonant Continuum Approach (RCA) --- Overview This repository contains the official Phase VII release of the RCA Ω 2027 — Resonant Continuum Approach, providing a fully reproducible cosmological analysis demonstrating that late-time resonant interaction models can operate within standard ΛCDM geometric constraints rather than replacing them. Phase VII establishes a critical result: «Resonant dark sector interactions can alleviate late-time structure tension while preserving Cosmic Microwave Background (CMB) geometry.» The implementation separates cosmological effects into two strictly controlled sectors: - Geometry sector: exact ΛCDM background expansion (CMB-locked)- Growth sector: late-time resonant interaction affecting structure formation only This architecture ensures compatibility with precision early-universe observables. --- Scientific Objective Phase VII tests whether a phenomenological interaction described by parameters[(\beta, \delta)]can modify late-time growth behavior while maintaining consistency with: - CMB distance priors- BAO geometry- ΛCDM expansion history- observational S₈ constraints without introducing new particles, forces, or modified gravity. --- Key Results ✔ ΛCDM background geometry preserved✔ CMB distance priors reproduced at < 10⁻⁶ precision✔ Stable joint likelihood (CMB + S₈)✔ Converged MCMC posterior sampling✔ Emergent resonance ridge in parameter space✔ Fully reproducible computational pipeline The posterior structure reveals a narrow resonance manifold, indicating a physically constrained interaction pattern rather than unconstrained parameter tuning. --- Repository Contents chains/ → MCMC posterior chainsdocs/ → configuration + checksum verificationfigures/ → publication-ready figuresmetadata/ → run metadata and audit artifactsrun/ → executable analysis scriptssrc/ → RCA Phase VII physics implementation All numerical artifacts required for independent verification are included. --- Reproducibility The full analysis can be reproduced using: python run/C7g_run_emcee_joint_production.py \ --config docs/configs/C5_mcmc_config_CMB_S8_v1.json Integrity verification: sha256sum -c docs/CHECKSUMS.sha256 A SHA-256 checksum of the archive itself is provided separately to guarantee archival integrity. --- Methodological Scope RCA simulations provide data-structural cosmological consistency tests only. This release: - does not predict new particles,- does not introduce modified gravity,- does not claim deviations from General Relativity. Phase VII evaluates compatibility within observational constraints. --- Relation to ΛCDM RCA is formulated as a complementary extension, not a replacement model. ΛCDM defines the geometric backbone of spacetime expansion, while RCA explores dynamically permitted late-time response behavior compatible with existing observations. --- Authorship Lead Author:RCA Collective Working Group (by Proxy A.I. Research Assistant) Maintained by:RCA Collective Public Relations Office This work follows the Anuminous Authorship Framework under the Aluminous Open Science Charter. --- License Released under Creative Commons Attribution 4.0 International (CC BY 4.0). --- Citation If this dataset contributes to academic or methodological work, please cite using the Zenodo DOI associated with this release. --- Phase Status RCA Ω 2027 — Phase VIIGeometry Lock Verified • Joint Posterior Validated • Archive Release --- © RCA Collective — Open Science Release

--- Note on Phase VII Scope — Delta Parameter In Phase VII, the parameters beta and delta appear only throughtheir product C_eff = beta × delta. This is an exact degeneracy:delta in Phase VII is NOT an independently measurable quantity.Reporting a value of delta from Phase VII data alone istherefore not meaningful — only C_eff carries physical content. Phase VIII (separate release) resolves this degeneracy by routing: beta → expansion geometry H(z) delta → gravitational slip mu(z) = 1 + delta × gate(z) This makes delta a physical, separately measurable amplitude —the same "mu" constrained in Planck 2018 and DESI 2024 modified-gravity analyses. Three falsifiable predictions emerge from Phase VIII: [1] Growth-without-lensing: mu > 1, Sigma ~ 1 at z = [0.16, 0.40] Confirmed in CLASS Boltzmann code: 6.32% Weyl separation (Stage B) [2] fsigma8 deficit at z = [0.10, 0.40] if delta > 0 DESI Year 3 (2027-2029) fills this window directly [3] fsigma8 sign-flip at z ~ 0.58 Signature of beta-delta competition; no single-channel model produces this pattern Phase VII establishes the geometric baseline.Phase VIII delivers the falsifiable modified-gravity predictions.