Transduction Identity: A Unified Geometric Derivation of Fundamental Scaling Constants

Transduction Identity: Scalar-Tensor Unification of Atomic and Galactic Scales Version 12. 0 | Release Note This major revision establishes the Transduction Equivalence Principle (TEP) and provides the first-principles derivation of the W boson mass (Mw) as a terminal verification of the Electroweak Pillar. Key Technical Updates: The W Boson & Bimodal Sampling: Finalized the derivation of Mw ≈ 80. 37 GeV. This update justifies the factor of 1/2 as a requirement of geometric bimodal sampling at the manifold interface. Equivalence Principle Unification: Integrates the Weak Equivalence Principle (WEP) as a consequence of Geometric Sampling Invariance, linking the universality of free fall directly to the metric grain (L). Vacuum Energy Rigor (n=42): Explicitly detailed the dimensional sequestration mechanism, moving from general harmonics to a two-phase suppression model (T⁴2² impedance + V3/V6 volumetric filtering). Structural Sanitization: Removed non-technical conjecture and corrected numerical alignment for the physical Higgs VEV (vₚhys ≈ 246. 22 GeV). Project Overview The Transduction Identity (TI) is a scalar-tensor framework that resolves persistent physical discrepancies by identifying a mandatory geometric residual, ξ = 1/12, at the interface of a 6D conformal background and 4D manifest spacetime. Rather than invoking undetected particles, this work demonstrates that "Dark" phenomena and precision anomalies are manifest consequences of the Manifold Resolution Limit (LTI). I. The Core Identity We derive the fixed matching condition ξ = 1/12 as the required conformal coupling for stable dimensional transition. This single geometric constant governs the scaling of physics from the subatomic to the galactic, acting as a "Universal Suture" between scales. II. The Four Pillars of Validation The Galactic Pillar (MOND): Derives the MOND acceleration floor (a0 ≈ 1. 18 × 10⁻¹⁰ m/s²) as a geometric projection of vacuum curvature, yielding the identity a0 = 1/6 c H0. The Precision Pillar (Leptonic Anomalies): Resolves the muonic g-2 and proton radius discrepancies as Topological Hysteresis (n=7), treating anomalies as manifest noise at the manifold’s terminal resolution. The Electroweak Pillar (Higgs/W Scales): Resolves the Hierarchy Problem via 12th-order symmetry saturation (n=12). This pillar now includes the W boson mass as the manifest energy threshold for stationary transduction. The Cosmological Pillar (Vacuum Catastrophe): Resolves the 10¹²² discrepancy via Dimensional Sequestration (n=42), where bulk potential is filtered through the 42nd-order harmonic of the 6D lattice. III. Falsifiable Roadmap Sync-Lock Deviations: Interpretation of the 2022 CDF W mass outlier (80. 43 GeV) as a local phase-slip or "Sync-Lock" failure at the manifold interface, contrasted with the CMS 2026 stationary average. Local Variance: Correlation between galactic rotation scatter and local Hubble expansion (H0). Precision Floor: A vertex-level geometric contribution to the muonic anomaly (6. 1 × 10⁻¹⁰) independent of QED radiative corrections. Methodology & Transparency Utilizing a multi-model synthetic reasoning workflow (Google DeepMind Gemini & Perplexity. ai), the derivations have been stress-tested against LHC Run 3 and Fermilab datasets. The framework utilizes a "Transduction" model conceptually aligned with communication engineering functional blocks (e. g. , Caleffi et al. , 2025). This approach treats the manifold interface as an active functional operator for scale-dependent information transfer. Contact: pgrant. researcher@gmail. com Concept DOI: 10. 5281/zenodo. 19141222 License: Creative Commons Attribution 4. 0 International