Preprint · Release 07

Phase-Flux Field (PFF): Axiomatic Substrate for Wave Confinement Theory — Zero-Wave Invariance, Finite-k Lyapunov Band-Pass, Shell Quantization, and D4 to Continuum

Richard J. Reyes

Independent Researcher · September 8, 2025 · 10.5281/zenodo.17578766

CategoryPrimary WCT foundation Research statusFoundational proposal

Abstract

Phase-Flux Field defines a pre-WCT substrate in terms of observable energy density, flux, and phase. The work develops conservation and causal-flow constraints, a finite-wavenumber Lyapunov band-pass, shell quantization, a zero-wave invariant state, and a D4-to-continuum construction.

Plain-language overview

Research question

What minimal, observable substrate of energy density, flux, and phase can serve as an axiomatic basis for Wave Confinement Theory?

Main contribution

  • Defines a pre-WCT substrate in terms of observable energy density, flux, and phase.
  • Develops conservation and causal-flow constraints and a finite-wavenumber Lyapunov band-pass.
  • Constructs shell quantization, a zero-wave invariant state, and a D4-to-continuum limit.

Evidence type

Analytical derivation

Current limitations

This is an axiomatic foundational construction within an evolving framework; its physical correspondence remains to be tested.

Research assets

Read & download
Zenodo record (manuscript and files)
Research program hub
geometry_of_resonance — equations, manuscripts, and simulations

Related works

Verification and traceability

This section is generated from the canonical publication traceability registry. Empty fields are reported rather than inferred.

Claim IDs
Equation IDs
SymPy audit
Lean coverage
Assumptions
None registered
Formalization
PARTIAL
Empirical state
NOT_TESTED_AS_A_PHYSICAL_SUBSTRATE
Independent replication
NONE_RECORDED
Repositories

Explicit falsifiers

  • The declared substrate fails conservation, causal-flow, or finite-band predictions under a frozen implementation.

Open obligations

  • Formalize the full continuum axioms and connect the substrate to calibrated physical observables.

Recommended citation

Reyes, R. J. (September 8, 2025). Phase-Flux Field (PFF): Axiomatic Substrate for Wave Confinement Theory — Zero-Wave Invariance, Finite-k Lyapunov Band-Pass, Shell Quantization, and D4 to Continuum. Zenodo. https://doi.org/10.5281/zenodo.17578766

Machine-readable identifiers

DOI
10.5281/zenodo.17578766
Zenodo
https://zenodo.org/records/17578766
Local metadata
https://rickyjreyes.github.io/publications/phase-flux-field.html
Author
ORCID 0009-0005-5975-8718

This landing page provides accessible summaries and citation metadata for an archival preprint. The authoritative manuscript and downloadable files are maintained on the Zenodo DOI record. Wave Confinement Theory is an evolving independent framework; claims should be evaluated according to the derivations, simulations, experiments, data analyses, assumptions, and limitations stated in the paper itself.