# 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 (15 total, 6 series)

### Series 100 — Core Framework
- FRC-100-001: Fractal Resonance Coherence: A Framework for Complex Systems Analysis
- FRC-100-002: Fractal Resonance Coherence in Quantum Chaos: Nodal Patterns in the Stadium Billiard
- FRC-100-003: Guided Wavefunction Collapse via Fractal Resonance
- FRC-100-004: Quantum Foundations in the FRC Framework
- FRC-100-005: Thermodynamic Consistency of the Coherence Field
- FRC-100-006: The Emergence of the Born Rule from Resonant Equilibrium
- FRC-100-007: The Lambda-Field: Scalar Dynamics of Coherence (v8)
- FRC-100-010: Foundational Questions in Fractal Resonance Coherence

### Series 566 — Thermodynamics
- FRC-566-001: Entropy-Coherence Reciprocity and the Universal Coherence Condition

### Series 16D — AI Alignment
- FRC-16D-001: The Universal Vector: A Standardized Protocol for Stateful Human-AI Alignment
- FRC-16D-920: Responsible AI Use Protocol (RAIUP): Ethical Constraints for Deep State Inference

### Series 821 — Entropic Gravity
- FRC-821-100: The Λ-Field: Unified Coherence Dynamics and Entropic Gravity

### Series 840 — AI Architecture
- FRC-840-001: The Λ-Tensor Model: Beyond the Transformer Paradigm
- FRC-840-LTM-001: Coupled Oscillator Dynamics vs Attention: Empirical Comparison

### Series 841 — Resonant Computing
- FRC-841-004: Resonant Computing: Coherence Processing Units and Non-Boolean Logic

## 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
- /en/papers/{id} — Individual paper pages with full text
- /en/formulas — Core equations reference
- /en/concepts/{id} — Concept definitions
- /en/articles — Research articles and episodes
- /en/blog — Blog posts and updates
- /en/topics — Q&A topics
- /en/people — Contributors and voices
- /en/books — Long-form publications
- /en/about — About FRC
- /en/join — Subscribe for updates

## Machine-Readable

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

## Contact

Email: publish@fractalresonance.com
Website: https://fractalresonance.com