Tension Field Theory: Emergent Electrodynamics and Lattice Gauge Mechanics (Collected Papers I - VI)

This collection presents six mathematical-physics studies of electromagnetic correspondence and gauge mechanics in the dual-phase face-centered-cubic (FCC) model proposed by Tension Field Theory. The papers investigate how specified mechanical degrees of freedom can support electric-flux energy, circulation, dynamical sources, and electromagnetic response, while identifying the assumptions and obstructions that separate mathematical constructions from a physical realization. Paper I derives an elastic-envelope-to-electric-flux mapping in a tethered model and establishes quantum-metric band-projection identities and error bounds. Paper II constructs finite toroidal circulation with a coherent registry core and an anchored annulus, obtaining static response, kinetic coefficients, and transition-action constraints from a common material action. Paper III analyzes shared-throat network assembly and derives nonperturbative monopole-density bounds and random-heat representations for a specified compact U(1) gauge Hamiltonian. Paper IV develops finite open transfers and Gauss-preserving dynamical defect sources under an explicit two-lock registry hypothesis. Paper V derives fixed-source material-reference screening, distinguishes static and radiative coupling normalization, and audits proposed geometric coupling and atomic-spectrum relations. Paper VI extends this analysis to all-sideband virtual-dipole susceptibility, the passive-sign obstruction to one normalization hypothesis, and a conditional electric–magnetic balance with an associated wave-speed shift. It also establishes boundary-layer perimeter scaling, examines the electric Hodge decomposition, and derives subluminal core-current bounds. Signed-shell constructions and a separate Dirac–Gordon–Foldy–Wouthuysen comparison clarify the assumptions behind magnetic-moment and contact-term matching. The completed conditional atomic Hamiltonian reproduces the leading hydrogenic fine-structure coefficients in all 64 retained quantum-number channels through principal quantum number eight. Analytical proofs and computational checks are documented separately in the constituent papers. Results are classified as DERIVED within stated models, PROPOSED constitutive inputs, CONDITIONAL physical correspondences, or OPEN questions. Microscopic parameter selection, physical charge normalization, a compact Coulomb phase for the proposed vacuum, a stable mechanical electron, and a parameter-free determination of the empirical fine-structure constant remain open. Included Papers (Collected Volume, Papers I–VI) Paper I: Mechanical Origin of Electric-Flux Stiffness and Quantum-Metric Wannier Projection in a Tethered Dual-Phase FCC Vacuum Paper II: Coherent-Core Registry, Finite Toroidal Circulation, and Certified Annular Response in a Dual-Phase FCC Vacuum Paper III: Shared-Throat Network Descent, Nonperturbative Monopole-Density Bounds, and Random-Heat Representations in a Dual-Phase FCC Gauge Model Paper IV: Coupled Open-Transfer Registries and Dynamical Defect Sources in a Dual-Phase FCC Model Paper V: Material-Reference Slip Screening, Speed-Matched Fine-Structure Normalization, and Atomic-Spectrum Audit in a Dual-Phase FCC Model Paper VI: Virtual-Dipole Susceptibility Bounds, Boundary-Layer Perimeter Scaling, and Subluminal Core-Current Constraints in a Dual-Phase FCC Model Computational Reproducibility & Verification Archive: Alongside the linked master manuscript PDF, this record includes TFT_Emergent_Electrodynamics_Collected_Papers_Reproducibility_Archive_V1.0.zip, which contains the complete, self-contained Python verification suites, exact rational/interval certificate generators, reference outputs, and manuscript audit scripts for all six papers (requiring only Python 3.10+, NumPy, SymPy, and standard libraries, with no network access required).