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 ([T^42]^2 impedance + V3/V6 volumetric filtering). Structural Sanitization: Removed non-technical conjecture and corrected numerical alignment for the physical Higgs VEV (v_phys ≈ 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 (L_TI). 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