Cyclical Causal Automata (CCA) Research

Status: Peer-Review Ready (Version 7.9 — Strategic Submission Build)

Scientific Basis: Tensor Effective Field Theory / Information Cosmology

Target Journals: JCAP / Physical Review D

Author: Alexey Lukin

🌌 Overview

This repository presents the theoretical framework for the CCA Framework, identifying Dark Matter as the emergent gravitational backreaction of causal history archival in a discrete substrate.

By treating the "Archival Burden" as a generally covariant tensor field coupled to the local scalar curvature $R$, the model derives observed galactic dynamics and local dark matter densities from first principles. This approach effectively unifies Information Theory with General Relativity.

🧬 Key Theoretical Pillars (v7.9)

1. Tensor Effective Field Theory ($T_{\mu\nu}$)

We have derived the archival stress-energy tensor $T_{\mu\nu}^{archival}$ from the variation of the archival action. We provide a mathematical proof that the archival "ghost" satisfies the dust-like equation of state ($w = p/\rho \approx 0$) in the late-time limit, making it a viable Cold Dark Matter (CDM) candidate.

2. Local Diffeomorphism Invariance

The model ensures coordinate independence by coupling the archival intensity $\mathcal{I}(x)$ to the local scalar curvature $R$:

$$\mathcal{I}(x) \equiv \frac{\gamma_{\mathcal{A}}(x)}{\sqrt{R/6}}$$

This formulation makes the "Information Intensity" a true scalar field, allowing for a rigorous treatment within General Relativity.

3. Quantitative Bullet Cluster Resolution

The CCA framework resolves the Bullet Cluster lensing offset through an entropy-to-mass gradient. Since stars emit significantly higher entropy flux per unit mass than diffuse gas ($\dot{s}{stars}/\dot{s}{gas} \approx 10^2 \text{--} 10^3$), the archival mass remains anchored to collisionless stellar populations, matching observational lensing maps.

4. The "Killer" Prediction: Post-Starburst (E+A) Excess

The model's primary falsifiable claim is that dark matter density is history-integrated:

The Prediction: Post-starburst (E+A) galaxies must exhibit a $1.8 \pm 0.2 \times$ higher dynamical-to-baryonic mass ratio compared to quiescent galaxies of identical current stellar mass.

Testability: This signature is uniquely distinguishable from $\Lambda$CDM and can be verified using deep IFU spectroscopy from surveys like MaNGA, SAMI, and upcoming MSE/4MOST projects.

🛠 Strategic Research Terminal (v3.9)

The repository includes research.html, a high-fidelity WebGL interactive visualizer implementing the v7.9 tensor logic.

Features:

Integrated History Simulation: Observe how past star formation events create a permanent "Archival Ghost" in the gravitational potential.

Gaia DR3 Calibration: Validates local dark matter density against the $0.47 \pm 0.1 \text{ GeV/cm}^3$ benchmark (Lim et al. 2025).

Sensitivity Analysis: Real-time manipulation of the substrate hierarchy ($\alpha$) and string-inspired coupling ($\eta$).

📂 Repository Structure

File

Description

formalism.md

Comprehensive Tensor EFT derivation, $T_{\mu\nu}$ variation, and conservation laws.

theorem.md

Formal proof of the Mass-Complexity Equivalence (MCE) and numerical consistency.

research.html

Interactive Strategic Terminal (v3.9). Open in any modern browser for empirical testing.

PAPER_OUTLINE.md

Strategic roadmap for JCAP/PRD submission and comparative analysis.

Technical Keywords: Dark Matter Phenomenology / Effective Field Theory / Information Archival / Memory Burden / Emergent Gravity