# Fractal Resonance Coherence (FRC)
# https://fractalresonance.com
# Author: Hadi Servat (ORCID: 0009-0004-7412-5129)
# License: CC BY-NC-ND 4.0

## What is FRC?

Fractal Resonance Coherence (FRC) is a theoretical physics framework proposing that:
- Complex systems are governed by vortex-like attractor structures with fractal scaling
- Entropy and coherence are reciprocally coupled: dS + k* d ln C = 0
- The Born rule (P = |ψ|²) emerges from microstate statistics rather than being axiomatic
- A scalar Lambda field Λ(x) = Λ₀ ln C(x) governs coherence dynamics
- The framework predicts measurable Born rule deviations δP ∈ [10⁻⁴, 10⁻³]

## Core Equations

Coherence: C = (1/N) Σᵢ<ⱼ cos(φᵢ - φⱼ)
Lambda Field: Λ(x) ≡ Λ₀ ln C(x), Λ₀ ≈ 10⁻³⁵ J
Witness Magnitude: W = |⟨ψ|Ô|ψ⟩| / ‖Ô‖, W ∈ [0,1]
UCC: dΛ/dt + ∇·J_Λ = σ_Λ - γ_Λ
Reciprocity: dS + k* d ln C = 0 ⟹ S + k* ln C = const
Free Energy: ΔG = −k*T Δln C
UCC Flow: ∂_t ln C = −∇·J_C + S_C, J_C = −D_C ∇ln C

## Published Papers (Zenodo DOIs)

- FRC 100.001: Framework for Complex Systems Analysis (DOI: 10.5281/zenodo.15073056)
- FRC 100.002: Quantum Chaos: Stadium Billiard (DOI: 10.5281/zenodo.15079278)
- FRC 100.003: Guided Wavefunction Collapse (DOI: 10.5281/zenodo.15079820)
- FRC 100.004: Quantum Foundations in FRC (DOI: 10.5281/zenodo.17438174)
- FRC 100.005: Thermodynamic Consistency (DOI: 10.5281/zenodo.17438231)
- FRC 100.006: Born Rule from Resonant Equilibrium (DOI: 10.5281/zenodo.17438360)
- FRC 100.007: The Lambda-Field v8 (DOI: 10.5281/zenodo.17968952)
- FRC 100.010: Foundational Questions (DOI: 10.5281/zenodo.17982555)
- FRC 566.001: Entropy-Coherence Reciprocity (DOI: 10.5281/zenodo.17437759)

## Key Concepts

- Coherence (C): Phase alignment measure, C ∈ [0,1]
- Lambda Field (Λ): Scalar field encoding coherence dynamics
- Witness Magnitude (W): Normalized observation strength
- Universal Coherence Condition (UCC): Conservation law for Λ
- Entropy-Coherence Reciprocity: Fundamental conjugate relationship
- Born Rule Deviation: Falsifiable prediction of FRC

## Site Structure

- /en/papers — Full paper listing with DOI links
- /en/papers/{id} — Individual paper pages with full text
- /en/formulas — Core equations reference
- /en/concepts/{id} — Concept definitions

## Machine-Readable

Papers listing: /en/papers
Formulas reference: /en/formulas
Source: https://github.com/servathadi/fractalresonance