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
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
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
- 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
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Machine-readable identifiers
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.