DOI-archived release · 06
Hard Upper Bound on Spatial Dimensionality in Wave Confinement Theory
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 Hard Upper Bound on Spatial Dimensionality in Wave Confinement Theory, listed in the research chronology as , with canonical citation DOI 10.5281/zenodo.17081283 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.17081283
- Zenodo record
- https://zenodo.org/records/17081283
- Source repository
- https://github.com/rickyjreyes/geometry_of_resonance
Abstract
This work develops a three-dimensional stability threshold under the stated WCT H²-confinement and regularity hypotheses. The verified Sobolev result establishes the H²-to-L∞ threshold for integer n≤3; the broader claim that every admissible higher-dimensional confinement mechanism is unstable remains conditional.
Plain-language overview
Research question
In the WCT framework, is stable curvature-locked confinement restricted to a maximum number of spatial dimensions?
Main contribution
- Argues that stable curvature-locked confinement is restricted to at most three spatial dimensions.
- Combines Sobolev control, Lyapunov scaling, entropy localization, topology, and curvature feedback into convergent routes toward the same bound.
Evidence type
Current limitations
The registered E70 claim is CONDITIONAL. Failure of the general H²-to-L∞ embedding route above three dimensions does not by itself prove a universal impossibility theorem for every conceivable WCT confinement mechanism. The archival title and DOI citation are preserved unchanged.
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_APPLICABLE_TO_THE_SOBOLEV_THRESHOLD
- Independent replication
- NONE_RECORDED
- Repositories
Explicit falsifiers
- A valid stable higher-dimensional WCT confinement mechanism that does not require the declared H2-to-L-infinity route falsifies the universal interpretation.
Open obligations
- Prove necessity of the H2 confinement route for every admissible WCT mechanism or retain explicitly conditional wording.
Recommended citation
Reyes, R. J. (August 13, 2025). Hard Upper Bound on Spatial Dimensionality in Wave Confinement Theory. Zenodo. https://doi.org/10.5281/zenodo.17081283
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.