TriPhase Physics Framework: A Wave-Mechanics Foundation Based on Three Axioms

ABSTRACT This Zenodo deposit releases the TriPhase Physics Framework (V16) as a textbook-style reference plus its supporting audit artifacts: the Framework document, the Master Matrix workbook (source-of-truth), the Matrix PDF snapshot, the complete Derivative Chain, a Referee Statement, Known Limitations, Changelog, and citation instructions. TriPhase is a wave-mechanics modeling framework that organizes a family of constant-relations and dimensional linkages under a single auditable derivative chain. V16 adopts standard electromagnetic notation and treats three observed vacuum properties---vacuum permittivity (epsilon_0), vacuum permeability (mu_0), and vacuum impedance (Z_0)---as stated reference quantities for comparison. METROLOGY NOTE (SI 2019): In the post-2019 SI, mu_0 and epsilon_0 are not defined exact constants; they are derived metrologically from measured alpha and other defined constants. This work treats epsilon_0, mu_0, and Z_0 as physically meaningful vacuum response parameters and states which numerical values are adopted for comparison. This is a modeling choice, not a claim about SI conventions. THE DERIVATION PRINCIPLE: All derived quantities trace back to the three observed vacuum properties through explicit derivation chains. No circular dependencies. The error percentages reported are always from the axiom (epsilon_0, mu_0, Z_0) derivation path. FROM THREE OBSERVED VACUUM PROPERTIES, THE FRAMEWORK DERIVES: * Speed of light: c = 1/sqrt(epsilon_0 * mu_0) --- structural identity* Vector Frame Imperivity: vf_0 = 1/epsilon_0 = 1.129 × 10^11 m/F --- explains why G is small* Fine-structure constant: alpha^-1 = 137.036 --- phase closure derivation, error: -0.000063%* Proton/electron mass ratio: m_p/m_e = 1836.156 --- triangular number structure, error: 0.0002%* Gravitational constant: G = c^4 * 7.5 * epsilon_0^3 * mu_0^2 ≈ 7.5/vf_0 --- direct vacuum derivation, error: -0.50%* Weinberg angle: sin^2(theta_W) = q/p^2 = 2/9 from (q,p)=(2,3) error-correcting code, error: 0.30%* Electroweak mass ratios: mZ/mW = 3/sqrt(7) (0.061%), mH/mW = sqrt(17/7) (0.039%), mH/mZ = sqrt(17)/3 (0.10%)* Higgs self-coupling: lambda = 17*g2^2/56 (0.35% match to measured)* MOND acceleration: a_0 = 3*c*H_0/17 --- three-phase geometry, error: 0.08%* Dark energy equation of state: w_0 = -5/6 = -0.833 --- quadrature partition, error: 0.6% The Master Derivative Chain contains 710 embedded Python calculations across 49 derived targets x 18 mathematical frameworks (508 pages). Each calculation is independently runnable and verifiable. VERIFICATION SCRIPTS: All 864 standalone Python derivative scripts (48 targets x 18 frameworks) are publicly available at:https://github.com/triphase-physics/triphase-v16/tree/main/Derivatives All numerical comparisons and error percentages follow the Master Matrix (S1) reference conventions. COMPARISON RULE: Error percentages are comparisons between TriPhase-derived quantities and reference values used solely as calibration checks. Internal derivations do not require agreement with measured constants and are not adjusted to enforce it. CLAIM TAGS: To support review, every major claim is tagged:* (D) derivation/identity --- obtained from axioms without importing target measured constants* (D*) derivation with discrete selection --- includes explicit selection rule* (C) consistency/closure check --- uses measured constant as input* (H) hypothesis/prediction --- requires external validation* (DH) derived hypothesis --- derived from axioms but represents hypothesis about vacuum property REVIEW METHOD: Matrix-first audit is recommended:1. Select a row in the Master Matrix (S1)2. Follow the cited derivation path in the Derivative Chain (S3)3. Verify dimensional consistency and each algebraic step4. Recompute numerical values using stated reference values5. Evaluate whether the claim tag is appropriate REVISION HISTORY Versions 1-9 (2024-2025): Working drafts consolidating notation, derivation workflow, and validation tables. Version 10 (Dec 2025): First peer-review-style draft format; expanded explicit calculations and multi-branch convergence presentation. Version 11 (Dec 2025): Expanded ground frequency anchor framing and worked calculations across convergent branches. Version 12 (Dec 2025): Formalized driver/response language and derivative-chain presentation; expanded convergence methodology and claim-tag discipline. Version 13 (Dec 2025): Editorial correction of causal-language drift (driver vs response) without changing underlying math. Version 14 (Dec 2025): Expanded primitive wave-property definitions; expanded particle sections and supporting appendices. Version 15 (Jan 2026): Release-package consolidation:* Notation lock across documents* Standardized claim tags (D/D*/C/H)* Cross-document alignment (Framework, Matrix, Derivative Chain, Referee Statement)* Expanded Known Limitations and sensitivity points* Referee-appropriate language throughout* Updated changelog/citation guidance for Zenodo baseline publication Version 16 (Mar 2026): Full framework upgrade to epsilon_0, mu_0, Z_0: PRIMARY CHANGE - Incorporate three anchors into full framework:* Peer review papers (REV3) used epsilon_0, mu_0, Z_0 as anchors* V16 upgrades the full framework (textbook, derivations, support files) to match* All derived quantities now trace to three observed vacuum properties P_v CIRCULAR DEFINITION FOUND AND REMOVED:* REMOVED: P_v (vacuum pressure) as intermediate quantity --- units were NOT Pascals* ADDED: Direct G derivation: G = c^4 * 7.5 * epsilon_0^3 * mu_0^2* ADDED: Vector Frame Imperivity (vf_0 = 1/epsilon_0 = 10^11 m/F) --- explains why G is small* ADDED: (DH) claim tag for derived hypotheses* CORRECTED: G error from -0.094% to -0.50% (TriPhase underpredicts measured G) WEINBERG ANGLE AND ELECTROWEAK SECTOR (NEW IN V16):* Weinberg angle derived: sin^2(theta_W) = q/p^2 = 2/9 from (q,p)=(2,3) error-correcting code (0.30% error)* (q,p)=(2,3) arises from [111] crystalline projection of (epsilon_0, mu_0, Z_0)* Unitarity proof: q = p-1 is FORCED (not a free parameter)* Electroweak mass ratios: mZ/mW = 3/sqrt(7) (0.061%), mH/mW = sqrt(17/7) (0.039%)* Higgs self-coupling predicted: lambda = 17*g2^2/56 where 56 = 8x7 (0.35% match)* 7 = qp+1 and 17 = qp^2-1 are Eisenstein primes from the (q,p) algebra DERIVATIVE CHAIN EXPANSION:* 710 embedded Python calculations (49 derivatives x 18 mathematical frameworks)* 508-page Master Derivative Chain PDF with runnable calculations in each box* Each framework box shows: formula + mechanism + independently verifiable calculation TERMINOLOGY UPDATE:* REPLACED: "Elastance" terminology with "Imperivity" (vf_0)* RENAMED: old vf_0 (rigidity 10^42) to vf_r* Imperivity = reciprocal of permittivity (like reluctivity = 1/permeability) CONTACT Christian Ronald FuccilloMagnetic Innovative Solutions LLCmis@misolutions.co.siteResearchGate: https://www.researchgate.net/profile/Christian-FuccilloGitHub: https://github.com/triphase-physics