Controls Engineer · Independent Researcher · Software Developer
Wave Confinement Theory was publicly disclosed by Richard J. Reyes on April 22, 2025. Papers, equations, simulations, experiments, open-data analyses, and computational extensions are organized here with public dates, DOI records, code, and evidence artifacts.
Selected priority & evidence anchors
This is a deliberately selected homepage view rather than the complete audit ledger. It surfaces the most important empirical and prospective records across gravitational-wave, collider, atomic, and neutrino-detector work. The full Priority registry retains the complete dated chronology and validation record.
Training-only selection froze k*=9.6023256 before the 104-event holdout evaluation. The holdout returned ΔD=10.0354 with Monte Carlo p=0.00129987.
The untouched G2 phase-locked holdout returned A=0.9708618 and Δχ²=126.2832 under the declared background. Interpretation remains background-model sensitive.
The public NIST Atomic Spectra Database program tests bin stability, active-domain winding, Poisson-bootstrap nulls, neighboring ions, implementation parity, and baseline sensitivity.
Open NIST recordThe open-data candidate-spectrum analysis tests log-domain residual structure, active-domain winding, Koide-like comb geometry, sideband controls, charm-continuum controls, and veto-window covariance.
Open LHCb recordThe November 20, 2025 study asks whether WCT-motivated log-energy or ghost-mode modulations could survive JUNO energy resolution, smearing, and systematic limitations. It is a falsifiable detectability forecast, not a JUNO observation.
Open JUNO forecastThe research idea
The homepage follows the proposed dependency flow: a chaotic broadband field organizes its first ZW1 fold around the invariant zero-wave reference, Lyapunov basins draw down the field state, finite-wavenumber selection filters the spectrum, a toroidal Phase–Flux grid routes energy and phase subject to causal-flow constraints, eigenmode attractors emerge, and resonant geometry closes into curvature locking.
Illustrative dependency map in the WCT visual language. “Sinkhole” is used here as a visual metaphor for mode-attractor basins; individual stages retain their separate proof, numerical, or proposal status.
Chaotic broadband wave turbulence folds toward a first coherent ZW1 mode in the three spatial directions. The exactly invariant zero-wave state remains the mathematical reference, distinct from the fluctuating field drawn here; the Sobolev n ≤ 3 condition belongs to the boundedness argument in step 03.
Field states are shown moving through a basin of lower 𝓔_WCT[ψ], not merely down a one-dimensional curve. Under the stated gradient-flow assumptions, trajectories descend toward lower-energy attractor structure.
1–3D: the H² embedding controls peaks. 4D: a critical multiscale sequence develops a growing peak despite a bounded H² norm. 5–6D: Gaussian concentration grows supercritical. The n-cube projection shows dimensional geometry, not physical confinement failure.
Broadband Fourier support fades outside the preferred nonzero wavenumber k★, revealing the finite-shell diagram. Quartic selection is illustrated by off-shell attenuation—not by moving wavelengths or integrating the WCT PDE.
Energy density u, flux S, and phase θ are illustrated on a toroidal grid with a central spindle-like flow channel. The full capacity rail represents the null-flow normalization, not a measured flux or a solved PFF state. Phase–Flux paper ↗
Broadband content is visualized draining into competing mode basins—sinkhole-like attractors—while spectral entropy falls and a smaller set of persistent eigenmode-like structures dominates.
Boundary and feedback conditions organize those selected modes into persistent standing structures rather than freely propagating content.
Phase advances around a curved closed path with integer winding. An illustrated feedback correction drives the seam mismatch toward zero while the tangent and osculating circle track local geometry. The decay is prescribed, not a demonstrated WCT stability law.
Equation build-up · registered chain
Scroll through the registered chain. The calculation follows the curve by segment arc length, its Frenet geometry produces \(\sigma(s)\), a declared positive density weight \(w(s)\) changes the measured average, and the constrained phase rail shows whether the displayed loop is perfectly locked or mislocked before the conditional mass map is revealed.
Illustrative computation on a (2,3) torus knot. κ, τ, arc length, σ, the weighted integrals, and the constrained phase rail are computed from the displayed curve. w(s) is an explicitly declared positive demonstration weight, not measured data. The visual reports the resulting mislock α; the mass relation is shown only as the perfect-lock α=0 limit.
This website
Accessible plain-language summaries, research-status labels, and publication discovery.
Browse publicationsMachine-readable corpus
Stable equation IDs connected across canonical equations, SymPy, Lean, semantic graph records, and DOI sources.
Explore the corpusGitHub research hub
Equations, manuscripts, simulations, and the full technical archive of the program.
Open
geometry_of_resonance
Zenodo
Permanent DOI records and downloadable releases for every cited paper.
View archived worksStart here
Core overview · Foundational proposal
The main statement of WCT and its proposed emergence of mass, force, and effective spacetime geometry.
Axiomatic substrate · Foundational proposal
Observable energy density, flux, phase, conservation, finite-wavenumber selection, and shell formation.
Mass-locking proposal · Mathematical derivation
The cleanest formulation of the loop-curvature rest-energy ansatz.
Mathematical stability · Mathematical derivation
The argument that stable curvature-locked confinement is restricted to at most three spatial dimensions.
Research branches
01 / Core
The central archive for equations, manuscripts, simulations, reading maps, experiments, and the current dependency structure of the program.
geometry_of_resonance →02 / Mathematics
Original results in nonlinear PDEs, spectral and variational analysis, and geometric constraints. Explore mathematical manuscripts, Lean 4 formalizations, reproducible proofs, and the Reyes Problem Repository.
Mathematics → Reyes Problem Repository →03 / Experiment
Raw oscilloscope waveform, FFT analysis, prediction ledger, ratio diagnostics, shuffle nulls, and explicit control requirements.
photodiode →04 / Atomic data
A reproducible line-density scan using public NIST Atomic Spectra Database exports, with Python and R implementations.
NIST analysis →05 / Collider data
Log-periodic residual tests, active-domain winding, Koide-like comb geometry, sideband controls, and veto-covariance diagnostics.
LHC analysis →06 / Collider replication
Cross-period frozen-frequency replication culminating in a prospective fixed-frequency, fixed-phase, fixed-sign CMS Run2016G holdout.
CMS analysis →07 / Gravitational-wave data
Training-only frequency selection followed by frozen GWTC holdout tests and a prospective log-frequency prediction for future catalogs.
GWTC analysis →08 / Computation
Experimental path-dependent commitments, one-time signatures, adversarial audits, and a prototype ledger with documented security-analysis targets.
Wavelock →09 / Architecture
Extensions of confinement and coherence concepts into AI architecture, recursive drift analysis, and diagnostics-driven fusion control.
Browse the publication archive →Inventions and intellectual property
Public, non-enabling summaries connect the filing chronology to related papers, repositories, experiments, and evidence-status labels without publishing confidential application material.
Curvature-regulated commitments, replay verification, protocol binding, attestation, and runtime drift analysis.
Wave-state storage, spectral confinement, readout, reset control, physical cells, arrays, and software emulation.
Optically programmed semiconductor resonance with harmonic readout and oscillator-integration concepts.
Structured excitation, controlled confinement geometry, harmonic stabilization, relocking, and detector feedback.
Latest releases
Recent releases link to DOI records when archived and to their source repositories when archival records are pending.
A progressively constrained CMS sequence from discovery to frozen-frequency replication, cross-period preregistration, and a prospective fixed-frequency, fixed-phase, fixed-sign holdout.
github.com/rickyjreyes/wct-cms
Training-only model selection identifies a stable log-frequency near k ≈ 9.7, followed by frozen holdout tests under two statistical formulations and a preregistered prospective target.
github.com/rickyjreyes/GWTC
A reproducible log-cosine line-density scan over public NIST Atomic Spectra Database exports, with null controls.
10.5281/zenodo.20435463
The complete, searchable archive holds 28 research releases with research-status labels, category and year filters, DOI links where available, source repositories, and citation exports.
About
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.
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