DOI-archived release · 03
Part I — P vs NP in Curvature-Bounded Wave Computation: A Model-Relative Pᴡᴄᴄ ≠ NPᴡᴄᴄ Separation
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 Part I — P vs NP in Curvature-Bounded Wave Computation: A Model-Relative Pᴡᴄᴄ ≠ NPᴡᴄᴄ Separation, listed in the research chronology as , with canonical citation DOI 10.5281/zenodo.17743607 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.17743607
- Zenodo record
- https://zenodo.org/records/17743607
- Source repository
- https://github.com/rickyjreyes/geometry_of_resonance
Abstract
This work defines a curvature-bounded wave-computation model and studies complexity classes internal to that model. Its separation claim is explicitly model-relative: it concerns P_WCC and NP_WCC under the stated physical and geometric constraints rather than claiming an unrestricted proof of the classical P versus NP problem.
Plain-language overview
Research question
Within a curvature-bounded wave-computation model, do the internal complexity classes P_WCC and NP_WCC separate?
Main contribution
- Defines a curvature-bounded wave-computation model with explicit physical and geometric constraints.
- Establishes a model-relative separation argument for P_WCC and NP_WCC.
Evidence type
Current limitations
The separation is explicitly model-relative to P_WCC and NP_WCC under the stated constraints; the unrestricted classical P versus NP problem is outside the scope of this result.
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
- OPEN
- Empirical state
- MODEL_RELATIVE
- Independent replication
- NONE_RECORDED
- Repositories
Explicit falsifiers
- A polynomial-overhead simulation invalidates the claimed separation under the same encoding, precision, and resource assumptions.
Open obligations
- Specify encoding, precision, update cost, resource bounds, and theorem-level relations to standard computational models.
Recommended citation
Reyes, R. J. (May 7, 2025). Part I — P vs NP in Curvature-Bounded Wave Computation: A Model-Relative Pᴡᴄᴄ ≠ NPᴡᴄᴄ Separation. Zenodo. https://doi.org/10.5281/zenodo.17743607
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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.