.Section-by-Section Structure, Claims, Dependencies, and Status
2026-01-16
One-Sentence Summary. A complete logical map of the Maxwell Universe Research Program, organizing its output documents by sections, claims, dependencies, and production status.
Abstract. This document provides a systematic, section-by-section map of the Maxwell Universe Research Program. Each output document is identified by its title and production status (published with DOI or in preparation). For every major section, we list its key claims, logical dependencies, consequences for later documents, and current status. The purpose is to preserve conceptual continuity, make dependencies explicit, and provide a stable reference point for extension and critique.
Keywords. Maxwell Universe, research program map, continuity equation, divergence-free flow, electromagnetic foundations, topology, minimal dynamics
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:
DOI: https://writing.preferredframe.com/doi/10.5281/zenodo.18209801
Establishes that effective propagation speed is not a primitive constant, but an emergent property of electromagnetic 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.
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.
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.
DOI: https://writing.preferredframe.com/doi/10.5281/zenodo.18249258
Shows how closed electromagnetic energy flow produces string- and membrane-like structure without introducing new objects.
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.
Key claim Closed divergence-free flows on a torus
enforce integer winding numbers .
Depends on - Topology of the torus - Divergence-free tangent flows
Enables - Discrete global classification - Topological stability
Status Resolved.
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.
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.
DOI: https://writing.preferredframe.com/doi/10.5281/zenodo.18249230
Derives inertial mass from geometry and circulation alone.
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.
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.
Key claim Inertial mass measures momentum trapped in circulation.
Depends on - Previous decomposition
Enables - Mass without matter
Status Resolved.
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.
DOI: https://writing.preferredframe.com/doi/10.5281/zenodo.18269184
Clarifies how vector fields arise from scalar energy descriptions without adding new primitives.
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.
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.
Key claim 
represent energy content and flow; 
are one possible encoding. Dynamics must not be
conflated with representation.
Depends on - Degree-of-freedom counting
Enables - Avoidance of false derivations
Status Resolved.
Key claim Given with
, at least one pair exists reproducing them.
Depends on - Algebraic constraints - Energy and flux definitions
Enables - Field reconstruction - Interpretation of polarization
Status Resolved.
DOI: https://writing.preferredframe.com/doi/10.5281/zenodo.18264435
Explains why Maxwell’s equations appear as the minimal evolution law compatible with divergence-free transport.
Key claim Continuity constrains accounting, not motion.
Depends on - Definition of continuity
Enables - Need for a dynamical closure
Status Resolved.
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.
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.
Key claim Curl, circulation, and knots coexist only in three dimensions.
Depends on - Differential geometry - Knot theory
Enables - Dimensional selectivity
Status Resolved.
DOI: https://writing.preferredframe.com/doi/10.5281/zenodo.18272625
Fixes terminology and prevents conceptual regression.
Status Resolved, authoritative.
DOI: https://writing.preferredframe.com/doi/10.5281/zenodo.18274175
Defines stance, scope, and boundaries of the program.
Status Resolved.
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.