Independent research at the intersection of geometry, resonance, and the physical world
Published preprints on the ResonanT⁴ framework. All work is open access via Zenodo under CC BY 4.0.
Modular Closure and Transverse Geometry
Defines the ResonanT⁴ admissibility framework based on exact phase closure. Introduces intrinsic modular phase states, locking structure via integer relations, and transverse projection generating apparent motion without dynamics.
Admissibility, Locking, and Phase-Aligned Control
Extends the framework to driven systems. Stability and control relevance arise only when resonance respects admissibility conditions. Introduces closure deficits and phase-aligned control as effective analysis constructs.
Discrete Labels from Exact Phase Closure
Reinterprets discrete quantum numbers as invariants arising from exact intrinsic phase closure. Integer labels emerge from closure conditions on compact phase descriptions without invoking operator quantization.
Cyclic Permutations, Phrase Closure, and Scale Selection on 𝕋³
A cyclic permutation on the three-torus encodes core structural elements of music: phrase closure, polyphonic voice decomposition, intervallic logic, melodic contour, rhythmic variation, and scale selection within a five-parameter construction.
Technical notes and open-source tools derived from ongoing research. Apache 2.0 code, CC BY 4.0 writeups.
ResonanT⁴ is a discrete geometry framework built on exact phase closure on the three-torus 𝕋³.
The framework is documented in full at resonant4.io — interactive visualizer, instrument, and all four papers.
Admissible configurations are defined by exact arithmetic closure: σ(p) = (p·k) mod n. Structure emerges from necessity, not approximation.
The arc-length integral over RT⁴ orbits is the complete elliptic integral of the second kind. Exact closed-form solutions replace numerical methods.
Wherever physics reduces to a large-angle pendulum or elliptic-integral geometry, RT⁴ yields exact solutions: cam profiles, inductor geometries, oscillator calibration, and beyond.
All publications carry Zenodo DOIs. All code is open-source. Results are reproducible. Independent research with no institutional constraints.
The ResonanT⁴ Research and Product Institute is an independent research organization founded by Egils Jakovels. Its focus is the ResonanT⁴ (RT⁴) framework: a structure discovered through computational art that revealed unexpected mathematical depth.
What began as an attempt to build a virtual three-dimensional zoetrope became a formal framework for discrete orbital geometry on the three-torus. The institute exists to explore where this structure applies and to publish those findings openly.
R4RPI operates without institutional affiliation, grant dependencies, or publication paywalls. Research follows curiosity. Results are published as they are validated.