Fractal Resonance Coherence
A living research program connecting entropy, coherence, open-system physics, chaos, measurement, and computation.
Definitions, exact results, model-specific evidence, and conjectures are labeled separately.
FRC 566.001 · canonical relation
dS + k* d ln C = 0
k* is scale-invariant in form; operational registers declare its representation.
Canonical reading path
Technical routeCurrent pillars
The latest living statements of the framework, with stable FRC identifiers and versioned records.
Coherence in Chaos: Diffusion, Localization, and Decoherence in the Standard Map / Quantum Kicked Rotor Family
Entropy-Coherence Reciprocity and the Universal Coherence Condition v2.2
Mathematical Foundations v1.5: Canonical Reciprocity and Status-Labeled Open Problems
Four anchors, four statuses
Formula indexCanonical relation
dS + k* d ln C = 0
FRC 566.001 · physical universality conjectural
Exact von Mises identity
dS / d ln C = −κr
FRC 566.030 · exact for the declared family
Chaos structure functional
Σ = SvM(C) − S ≥ 0
FRC 100.002 · pilot-supported observable
Localization crossover target
t* γC = O(1)
FRC 100.002 · tolerance band still open
Current program
- 01Complete the KAM, quantum, and cross-mechanism gates registered in FRC 100.002.
- 02Test Lambda-Flight criteria across independent physical and computational platforms.
- 03Keep living papers, books, concept DOIs, and machine-readable indexes aligned.
Claim boundaries
Established in scope
Mathematical identities, reproducible computations, and reported negative results.
Under active test
Chaos, localization, boundary, and cross-platform coherence programs.
Conjectural
Universal physical reciprocity, a fundamental Lambda field, and the Born mechanism.