DOI-archived release · 25
Exact Scale-Winding Bijection Between Discrete Scale Invariance and WCT Active-Domain Phase Closure
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 Exact Scale-Winding Bijection Between Discrete Scale Invariance and WCT Active-Domain Phase Closure, listed in the research chronology as , with canonical citation DOI 10.5281/zenodo.22665914 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.22665914
- Zenodo record
- https://zenodo.org/records/22665914
- Source repository
- https://github.com/rickyjreyes/geometry_of_resonance
Abstract
This work formalizes an exact mapping between discrete scale changes in logarithmic coordinates and integer phase winding in the WCT active-domain construction, providing a mathematical bridge between log-periodicity and phase closure.
Plain-language overview
Research question
Can discrete scale invariance be mapped exactly to WCT active-domain phase winding rather than treated only as a phenomenological analogy?
Main contribution
- Derives a scale-to-winding correspondence in logarithmic coordinates.
- Connects discrete scale invariance to active-domain phase closure within the WCT mathematical framework.
Evidence type
Current limitations
The result establishes a mathematical correspondence inside the declared framework; physical realization and cross-domain universality require 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
- MATHEMATICAL_DERIVATION
- Empirical state
- NOT_APPLICABLE
- Independent replication
- NONE_RECORDED
- Repositories
Explicit falsifiers
- A counterexample violates the stated scale-to-winding bijection under the paper's declared assumptions.
Open obligations
- Map the derivation into the canonical equation registry and formal proof layer, then distinguish mathematical equivalence from physical universality.
Recommended citation
Reyes, R. J. (September 8, 2026). Exact Scale-Winding Bijection Between Discrete Scale Invariance and WCT Active-Domain Phase Closure. Zenodo. https://doi.org/10.5281/zenodo.22665914
Citation copied to clipboard.
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.