Preprint · Release 06
Hard Upper Bound on Spatial Dimensionality in Wave Confinement Theory
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.
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Verification and traceability
This section is generated from the canonical publication traceability registry. Empty fields are reported rather than inferred.
- Claim IDs
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- 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
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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.