Mathematical structure
Canonical equations, explicit assumptions, status labels, symbolic checks, and formal-support mappings define what the theory actually claims.
Controls Engineer · Independent Researcher · Software Developer
A direct entry point to the Wave Confinement Theory research program.
Papers, equations, simulations, experiments, open-data analyses, and computational extensions organized so new readers can find the central idea before entering the full corpus.
ψ
confinement
phase
curvature
topology
22Zenodo releases
2025–2026public research chronology
Openpapers, code, data, and unresolved problems
The research idea
Persistent structure as confined wave dynamics.
Wave Confinement Theory is a proposed geometric wave framework in which localized physical structure arises from sustained oscillation, finite-wavenumber selection, phase organization, curvature feedback, and topology.
01Wave transport
Energy and phase propagate through a field.
02Finite-band selection
A preferred spectral shell suppresses unrestricted growth.
03Resonant confinement
Boundary and feedback conditions organize persistent modes.
04Curvature locking
Phase, geometry, and topology stabilize localized structure.
Research status. WCT is an evolving independent framework, not an established physical theory. Definitions, derivations, simulations, measurements, phenomenology, and speculative extensions are separated so each claim can be evaluated independently.
Visual guide
See the geometry before entering the registry.
The strongest visuals are used as orientation or technical figures, with their evidentiary role stated explicitly.
Boundary: illustrations explain the intended geometry; numerical and empirical claims are evaluated separately.
Where to go
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This website
Accessible plain-language summaries, research-status labels, and publication discovery.
Browse publications -
Machine-readable corpus
Stable equation IDs connected across canonical equations, SymPy, Lean, semantic graph records, and DOI sources.
Explore the corpus -
GitHub research hub
Equations, manuscripts, simulations, and the full technical archive of the program.
Opengeometry_of_resonance -
Zenodo
Permanent DOI records and downloadable releases for every cited paper.
View archived works
Start here
Four papers define the shortest path into the program.
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01
Core overview · Foundational proposal
The Geometry of Resonance
The main statement of WCT and its proposed emergence of mass, force, and effective spacetime geometry.
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02
Axiomatic substrate · Foundational proposal
Phase–Flux Field
Observable energy density, flux, phase, conservation, finite-wavenumber selection, and shell formation.
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03
Mass-locking proposal · Mathematical derivation
Rest Energy from Density-Weighted Loop Curvature
The cleanest formulation of the loop-curvature rest-energy ansatz.
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04
Mathematical stability · Mathematical derivation
Hard Upper Bound on Spatial Dimensionality
The argument that stable curvature-locked confinement is restricted to at most three spatial dimensions.
From theory to technology
A research program with implementation paths.
WCT begins as a mathematical framework, but several branches are being explored as computational, photonic, memory, security, and control architectures. These are proposed application directions, not demonstrated commercial products.
Numerical models
Simulations and diagnostics test finite-band selection, localization, phase organization, persistence, and failure modes.
Implementation concepts
Research branches explore persistent wave memory, drift detection, resonant references, coherent field generation, and related computational structures.
Evidence and IP
Reproducible source, experiments, public-data studies, patent filings, and open technical gaps provide separate paths for evaluation.
Potential application directions
These areas are being investigated as consequences or engineering extensions of the underlying confinement and coherence ideas.
Current boundary: commercial performance, scaling advantage, production-scale hardware feasibility, and independent replication remain open.
Research branches
Theory, experiment, public data, and computation.
01 / Core
Wave Confinement Theory
The central archive for equations, manuscripts, simulations, reading maps, experiments, and the current dependency structure of the program.
geometry_of_resonance →02 / Experiment
Photodiode harmonic state
Raw oscilloscope waveform, FFT analysis, prediction ledger, ratio diagnostics, shuffle nulls, and explicit control requirements.
photodiode →03 / Atomic data
Fe II log-cosine scan
A reproducible line-density scan using public NIST Atomic Spectra Database exports, with Python and R implementations.
NIST analysis →04 / Collider data
LHCb candidate spectra
Log-periodic residual tests, active-domain winding, Koide-like comb geometry, sideband controls, and veto-covariance diagnostics.
LHC analysis →05 / Computation
WaveLock and CurvaChain
Experimental path-dependent commitments, one-time signatures, adversarial audits, and a prototype ledger. Not production cryptography.
Wavelock →06 / Architecture
AI and resonance control
Extensions of confinement and coherence concepts into AI architecture, recursive drift analysis, and diagnostics-driven fusion control.
Browse the publication archive →NIST: NIST is the public data provider only. No NIST endorsement, certification, or validation is claimed.
WaveLock: The current constructions are experimental research prototypes with documented security limitations and unresolved proof obligations.
Latest releases
The newest work, with the full archive one click away.
All releases are authored by R. J. Reyes and linked to their archival Zenodo records.
Bin-Stable Log-Periodic Structure in Public NIST Atomic Line List
A reproducible log-cosine line-density scan over public NIST Atomic Spectra Database exports, with null controls. NIST is the data provider only.
10.5281/zenodo.20435463
Log-Spectral Structure and Koide-Like Winding Geometry in Open-Data B⁰ → K*⁰ μ⁺μ⁻ Candidate Spectra
An open-data search for log-domain residual structure and Koide-like comb geometry, with sideband controls and explicit non-discovery caveats.
10.5281/zenodo.20164333
Recursive AI Drift: A 2025 Prediction Timeline External Validation Audit and Technical Note
An audit of dated 2025 claims against later developments that separates chronology and partial support from direct validation.
10.5281/zenodo.20142976
The complete, searchable archive holds all 22 chronological releases with research-status labels, category and year filters, DOIs, and citation exports.
About
Engineering practice and independent research.
Richard J. Reyes is a controls engineer and software developer working in industrial refrigeration and process automation. His engineering work includes PLC logic, instrumentation, alarms, sequencing, networked HMIs, commissioning, and control-system troubleshooting.
He holds a B.S. in Computer Science from San José State University. His independent research spans nonlinear wave dynamics, mathematical physics, scientific computing, experimental signal analysis, public-dataset studies, computational architecture, and resonance-based control.
- Education
- B.S. Computer Science
San José State University - Profession
- Controls Engineer
Industrial automation - Research
- Independent mathematical physics
Scientific computation - ORCID
- 0009-0005-5975-8718
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