Unity–Photon Duality (UPD): Technical Series

0. UPD Series Overview (Front Matter PDF) TitleUnity–Photon Duality (UPD): Series Overview AbstractThis document summarizes the Unity–Photon Duality (UPD) research program and outlines the dependency structure of the full technical series. It introduces the core axioms, structural assumptions, and derivational philosophy behind UPD, and provides a guide to the logical ordering of all UPD sector papers: foundations, quantum/measurement, particle sectors, macroscopic physics, relativistic structure, gravity, and string-theoretic reductions. The overview serves as the front matter for the Zenodo UPD Collection. KeywordsUnity–Photon Duality, axioms, overview, derivational structure, research series AuthorsCrane Wesson Communitiestheoretical-physics; mathematical-physics Version1.0 NotesFront-matter summary for the UPD Zenodo collection. 1. Axiomatics of Unity–Photon Duality 📄 File: UPD_Axioms.pdf TitleAxiomatics of Unity–Photon Duality: Minimal Core, Derived Consequences, and Emergent Structure AbstractUnity–Photon Duality (UPD) is formulated from a minimal core of independent axioms—unity, quadratic tension, quartic stiffness, and recursive self-consistency—supplemented by structural assumptions enforcing locality, Ad-invariance, and the absence of background tensors. All higher-level phenomena used in UPD (emergent metric, virial scale, Wess–Zumino topology, constitutive closure, anomaly constraints, hyperbolic well-posedness, and minimal electroweak pinning) are rigorously derived as theorems. This paper establishes the foundational backbone of the entire UPD program. KeywordsUPD, axioms, emergent metric, Maurer–Cartan current, quartic commutator, Wess–Zumino, virial scale, anomaly cancellation AuthorsCrane Wesson Communitiestheoretical-physics; mathematical-physics Version1.0 NotesPrimary foundational document of the UPD series. 2. Emergence of the Constitutive Law H = Z₀⁻¹⋆F 📄 File: Emergence_of_Constitutive_Law.pdf TitleEmergence of the Constitutive Law H = Z₀⁻¹⋆F from the UPD Quadratic Action AbstractUsing only the UPD axioms A1–A3 and structural assumptions S1–S4, all allowable metric-built linear maps between two-forms are classified. Variational admissibility prohibits skewon terms; parity excludes axionic terms; absence of background tensors restricts spacetime contractions to the emergent metric. The unique surviving constitutive law is H = Z₀⁻¹⋆F. The result predicts a single light cone, no vacuum birefringence, and electromagnetic impedance as a geometric consequence of the unity field. Keywordselectromagnetism, constitutive law, Hodge dual, vacuum impedance, UPD, no-birefringence AuthorsCrane Wesson Communitieselectromagnetism; mathematical-physics Version1.0 NotesBase layer for the fine-structure constant relation in the gravity paper. 3. Unity–Photon Duality: A First-Principles Derivation of the Born Rule 📄 File: UPD__The_Born_Rule.pdf TitleUnity–Photon Duality: A First-Principles Derivation of the Born Rule AbstractThe Born rule is derived without quantum postulates using UPD’s axioms, the emergent positive quadratic energy norm, WZ-induced complex structure, and detector latching semantics. A complete resolution-of-identity emerges from refinement invariance and hyperbolicity. Action-optimal transport yields Cartan alignment in detector intake layers, giving Born-rule statistics even for massive non-coherent electron folds. KeywordsBorn rule, detector latching, Wess–Zumino, complex structure, probability, UPD AuthorsCrane Wesson Communitiesquantum-foundations; theoretical-physics Version1.0 NotesIncludes Y* appendix for the electron sector. 4. Heisenberg Position–Momentum and Energy–Time Inequalities 📄 File: Heisenberg_inequalities.pdf TitleHeisenberg Position–Momentum and Energy–Time Inequalities from the UPD Axioms AbstractA Born projection on the unity field produces scalar amplitudes with H¹ control from the quadratic tension. Sharp Fourier inequalities yield ΔxΔk ≥ n/2 and ΔtΔω ≥ 1/2, calibrated to ΔxΔp ≥ ℏn/2 and ΔtΔE ≥ ℏ/2 by the universal phase-energy scale of the null sector. Both bounds reflect second-order virial curvature. KeywordsHeisenberg bound, Fourier analysis, virial curvature, UPD AuthorsCrane Wesson Communitiesquantum-foundations; mathematical-physics Version1.0 NotesCompanion to the Born Rule paper. 5. Unity–Photon Duality: Electron as a Degree-One Fold 📄 File: (user-supplied electron model PDF) TitleUnity–Photon Duality: Electron as a Degree-One Pinned Fold on the Electroweak S³ Target AbstractThe electron is constructed as a degree-one electroweak fold stabilized by the quadratic–quartic virial balance on the S³ electroweak coset. The model yields mass, charge −1, g = 2 at tree level, and correct spinorial monodromy (odd WZ level). The geometry fixes the rest-energy gap without explicit Yukawa parameters. Keywordselectron model, electroweak S³, virial scale, g-factor, WZ spinorial monodromy, UPD AuthorsCrane Wesson Communitiesparticle-physics-theory; theoretical-physics Version1.0 NotesPart of the UPD particle-sector block. 6. UPD Neutrino Splittings: A5 Schur Projection & Virial Hierarchy 📄 File: (user neutrino paper PDF) TitleUPD Neutrino Splittings: A5 Schur Projection, A6 Virial Scale, and Testable Hierarchies AbstractNeutrino-sector excitations are constructed using Schur-projected currents and virial balance. L²-integrability of strongly non-abelian hedgehog profiles is established. Distinct virial minima produce natural neutrino mass hierarchies and mixing textures without explicit Yukawa couplings. Keywordsneutrinos, Schur projection, virial scale, L² integrability, UPD AuthorsCrane Wesson Communitiesparticle-physics-theory; theoretical-physics Version1.0 NotesProvides integrability results used in the Born Rule & electron-sector proofs. 7. Quarks as Tethered Folds 📄 File: UPD quark model.pdf TitleQuarks as Tethered Folds in Unity–Photon Duality: Center Vortices, Linear Confinement, Z₆ Fractional Charge, and Mixed-Scale Mass Formula AbstractColor pinning reduces the target to SU(3)/Z₃, enforcing center vortices and linear confinement. Fractional electric charges arise from single-valuedness on the global Z₆ quotient. Combining an electroweak hedgehog endpoint with a color tube yields realistic quark mass scales. Keywordsconfinement, SU(3)/Z3, Z6 quotient, quark masses, center vortices, UPD AuthorsCrane Wesson CommunitiesQCD; particle-physics-theory Version1.0 NotesIncludes numerical cross-sectional ODE solver for tube tension. 8. UPD-Derived Superconductivity & Horizon Mechanics 📄 File: UPD_Superconductivity.pdf TitleUPD-Derived Superconductivity and Horizon Mechanics: Even-Charge Condensation, Josephson Relations, Compactness, and Area Law AbstractThe quartic commutator term forces even-charge condensation (q = 2e) and reproduces London and Josephson relations. The same structure yields horizon compactness, mass-floor bounds, null-energy focusing, and the classical area law. Superconductivity and black-hole thermodynamics are unified under the same UPD variational principles. Keywordssuperconductivity, Josephson, London equations, horizon mechanics, area law, UPD AuthorsCrane Wesson Communitiescondensed-matter-theory; quantum-gravity Version1.0 NotesBridges macroscopic quantum phases and horizon thermodynamics. 9. Relativistic Kinematics from Null-Fold Expansion 📄 File: UPD Relativistic Kinematics….pdf TitleRelativistic Kinematics from Null-Fold Expansion and Pinned Unity-Field Tension AbstractSpecial relativity is derived without prior metric assumptions. Null-fold clocks and their fold-count asymmetry between observers yield the Doppler ratio, Lorentz factor, and E = γmc². Gravitational redshift emerges from spatial variation of the null-fold tick rate, unifying SR and GR behavior. Keywordsspecial relativity, null sector, Lorentz factor, phase flux, UPD AuthorsCrane Wesson Communitiesrelativity; theoretical-physics Version1.0 NotesStandalone SR derivation. 10. Emergent Gravity from Coherent Tension 📄 File: Emergent Gravity from Coherent Tension.pdf TitleEmergent Gravity from Coherent Tension: Axioms, Metric Induction, and Einstein–Hilbert Emergence AbstractThe Lorentzian metric arises from the quadratic UPD principal symbol. Lovelock constraints enforce the Einstein–Hilbert action as the unique local metric sector. A determinant partition law links the gravitational coupling to the unity-field impedance, giving G = (ℏc/Λ²)2π α¹⁶ e⁻δ(α). Newtonian, wave, and FRW limits follow automatically. Keywordsemergent gravity, Einstein–Hilbert, Lovelock, impedance, α¹⁶, UPD AuthorsCrane Wesson Communitiesquantum-gravity; relativity Version1.0 NotesFlagship UPD gravity derivation. 11. Ten-Dimensional Group-Manifold Compactifications Reduce to UPD 📄 File: Strings to UPD.pdf TitleTen-Dimensional Group-Manifold Compactifications Reduce to UPD: Exact Worldsheet and 4D Equivalence AbstractThe WZW worldsheet model on a compact group manifold is shown to equal the effective worldsheet action of a thin, virialized UPD fold. Kaluza–Klein reduction on M₄×K recovers the UPD sigma model with identical Ad-invariant bilinear. Extra dimensions are reinterpreted as internal coset coordinates of U rather than spatial directions. The string tension α′ emerges from virial balance. Keywordsstring theory, WZW model, Kaluza–Klein, group manifold, sigma model, UPD AuthorsCrane Wesson Communitiesstring-theory; mathematical-physics; theoretical-physics Version1.0 NotesPlaces string theory’s exact WZW sector inside UPD as a derived corner. ---A mirror of the UPD Series is available on OSF: https://osf.io/ygdh2/files/