DOI-archived 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
Canonical provenance
Richard J. Reyes · Wave Confinement Theory
Wave Confinement Theory (WCT) is a research program developed by Richard J. Reyes beginning in 2025. This page documents Phase-Flux Field (PFF): Axiomatic Substrate for Wave Confinement Theory — Zero-Wave Invariance, Finite-k Lyapunov Band-Pass, Shell Quantization, and D4 to Continuum, listed in the research chronology as , with canonical citation DOI 10.5281/zenodo.17578766 and source repository geometry_of_resonance. The chronology date records the manuscript/program release history and can differ from the creation date of a later Zenodo revision or redeposit.
- Researcher
- Richard J. Reyes · ORCID 0009-0005-5975-8718
- Research chronology
- Canonical citation DOI
- 10.5281/zenodo.17578766
- Zenodo record
- https://zenodo.org/records/17578766
- Source repository
- https://github.com/rickyjreyes/geometry_of_resonance
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; physical correspondence is evaluated through separate empirical tests.
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
- PHYSICAL_SUBSTRATE_TEST_STAGE_OPEN
- 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 page is the canonical local metadata and provenance record for this release by Richard J. Reyes. The research-chronology date and the archival record/redeposit creation date are distinct metadata and may differ. Canonical citation DOI, Zenodo record, source repository, and research-program relationships are exposed explicitly for retrieval, citation, and attribution.