# The Maxwell Universe Research Program — A Logical Map This document serves as a **conceptual checkpoint** for the Maxwell Universe Research Program. It does not introduce new results. It does not reinterpret existing ones. Its sole purpose is to **preserve structure**: to record what has been established, how results depend on one another, and where the program remains open. The map is organized **by document**, and within each document **by section**. For each section we record: - the key claim, - its logical dependencies, - what it enables downstream, - its production status. ## Light Speed as an Emergent Property of Electromagnetic Superposition DOI: https://writing.preferredframe.com/doi/10.5281/zenodo.18209801 ### Program role Establishes that effective propagation speed is not a primitive constant, but an emergent property of electromagnetic superposition. ### Maxwell theory and superposition **Key claim** Maxwell’s equations are linear, but physical observables are quadratic. Linearity does not imply non-interaction. **Depends on** - Linearity of Maxwell equations - Quadratic form of energy and phase observables **Enables** - Phase delay without matter - Emergent refractive behavior **Status** Resolved. ### Quadratic observables and phase delay **Key claim** Overlapping electromagnetic fields with different phases produce a total field whose evolution is slower than any individual component. **Depends on** - Definition of electromagnetic energy density - Superposition of phase-shifted fields **Enables** - Effective susceptibility without matter - Self-induced delay mechanisms **Status** Resolved. ### Effective light-speed variation **Key claim** Local effective propagation speed depends on electromagnetic energy density and superposition structure. **Depends on** - Previous sections - Operational definition of phase velocity **Enables** - Refraction without matter - Field-only waveguiding - Basis for later self-confinement **Status** Resolved. ## String Theory Derivation in a Maxwell Universe DOI: https://writing.preferredframe.com/doi/10.5281/zenodo.18249258 ### Program role Shows how closed electromagnetic energy flow produces string- and membrane-like structure without introducing new objects. ### Energy transport in Maxwell theory **Key claim** Energy transport is intrinsic to Maxwell theory through the Poynting vector. **Depends on** - Maxwell equations - Poynting theorem **Enables** - Definition of flow velocity - Flow-first ontology **Status** Resolved. ### Toroidal organization and winding numbers **Key claim** Closed divergence-free flows on a torus enforce integer winding numbers $(m,n)$. **Depends on** - Topology of the torus - Divergence-free tangent flows **Enables** - Discrete global classification - Topological stability **Status** Resolved. ### Tension and inertia from energy flow **Key claim** Localized circulating energy defines effective tension and inertial mass density. **Depends on** - Energy density - Momentum density **Enables** - Mass without particles - Energy–inertia equivalence **Status** Resolved. ### Stability and discrete excitation spectrum **Key claim** Self-induced refraction and periodicity produce stable, discrete modes. **Depends on** - Emergent refraction - Periodic boundary conditions **Enables** - Particle-like persistence - Quantized excitations **Status** Resolved. ## Geometric Inertia: Mass as Trapped Energy DOI: https://writing.preferredframe.com/doi/10.5281/zenodo.18249230 ### Program role Derives inertial mass from geometry and circulation alone. ### Geometry of constrained motion **Key claim** Local propagation at the maximal rate combined with curved paths produces reduced effective translation. **Depends on** - Euclidean geometry - Path length versus displacement **Enables** - Subluminal effective motion without slowing local propagation **Status** Resolved. ### Momentum decomposition **Key claim** Momentum splits into translational and circulating components; only the former contributes to net motion. **Depends on** - Momentum density - Directional decomposition **Enables** - Definition of inertial resistance **Status** Resolved. ### Mass from circulation **Key claim** Inertial mass measures momentum trapped in circulation. **Depends on** - Previous decomposition **Enables** - Mass without matter **Status** Resolved. ### Topological stability **Key claim** Knotted or wound circulation prevents continuous unwinding, stabilizing mass (self-sustaining electromagnetic knots.) **Depends on** - Topology - Integer winding **Enables** - Persistent objects **Status** Resolved. ## Defining Electromagnetic Fields from Continuity and Divergence-Free Structure DOI: https://writing.preferredframe.com/doi/10.5281/zenodo.18269184 ### Program role Clarifies how vector fields arise from scalar energy descriptions without adding new primitives. ### Scalar configurations and spatial flow **Key claim** A single scalar configuration by itself does not define flow; flow is defined by the spatial relation between scalar configurations under continuity. **Depends on** - Continuity equation **Enables** - Necessity of vectorial description **Status** Resolved. ### Divergence-free structure and circulation **Key claim** Locally, divergence-free structure implies curl structure and circulation; globally, topology determines allowed circulation. **Depends on** - Vector calculus identities - Topological conditions **Enables** - Toroidal shells - Circulating energy structures **Status** Resolved. ### Representation versus dynamics **Key claim** $(u,\mathbf{S})$ represent energy content and flow; $(\mathbf{E},\mathbf{B})$ are one possible encoding. Dynamics must not be conflated with representation. **Depends on** - Degree-of-freedom counting **Enables** - Avoidance of false derivations **Status** Resolved. ### Reconstruction lemma **Key claim** Given $(u,\mathbf{S})$ with $|\mathbf{S}|\le cu$, at least one pair $(\mathbf{E},\mathbf{B})$ exists reproducing them. **Depends on** - Algebraic constraints - Energy and flux definitions **Enables** - Field reconstruction - Interpretation of polarization **Status** Resolved. ## Maxwell Electromagnetism as the Minimal Dynamics of Divergence-Free Energy Flow DOI: https://writing.preferredframe.com/doi/10.5281/zenodo.18264435 ### Program role Explains why Maxwell’s equations appear as the minimal evolution law compatible with divergence-free transport. ### Continuity as kinematic **Key claim** Continuity constrains accounting, not motion. **Depends on** - Definition of continuity **Enables** - Need for a dynamical closure **Status** Resolved. ### Failure of gradient-driven dynamics **Key claim** Gradient-driven evolution generically creates divergence and cannot describe source-free transport. **Depends on** - Vector calculus identities **Enables** - Exclusion of algebraic-only evolution **Status** Resolved. ### Curl as minimal divergence-preserving operator **Key claim** Curl-based evolution preserves divergence-free structure identically. **Depends on** - Identity: divergence of a curl vanishes **Enables** - Justification of curl dynamics **Status** Resolved. ### Dimensionality **Key claim** Curl, circulation, and knots coexist only in three dimensions. **Depends on** - Differential geometry - Knot theory **Enables** - Dimensional selectivity **Status** Resolved. ## Canonical Glossary of Terms and Symbols DOI: https://writing.preferredframe.com/doi/10.5281/zenodo.18272625 ### Program role Fixes terminology and prevents conceptual regression. **Status** Resolved, authoritative. ## The Maxwell Universe Research Program DOI: https://writing.preferredframe.com/doi/10.5281/zenodo.18274175 ### Program role Defines stance, scope, and boundaries of the program. ### Key clarifications - Source-free does not deny localized structures. - Charges and currents are configurations, not primitives. - Stability arises from topology, not forces. - Minimal does not mean unique or final. **Status** Resolved. ## Global program status ### Fully established - Refraction without matter - Mass without particles - Stability without forces (stability arising from circulation and topology rather than force balance) - String- and membrane-like structure as effective descriptions - Maxwell dynamics as minimal divergence-preserving evolution - Vector fields arising from scalar relations under continuity ## Closing note This map is a **stability surface**. It preserves what is logically forced, records what remains open, and prevents regression. Nothing here is speculative. Nothing here is implicit. Everything else in a Maxwell Universe builds from this.