✅ Updated CIv6-ECA Hypothesis (Incorporating New Foundations)

CIv6-ECA: Structural Break via Algorithmic and Topological Dynamics in Symbolic Space

Hypothesis Structural breaks in univariate time series can be effectively detected by transforming numerical sequences into symbolic encodings (e.g., permutation, delta-sign) and evolving them using Elementary Cellular Automata (ECA). The resulting 2D symbolic dynamics expose regime shifts as discontinuities in algorithmic compressibility, topological structure, and circuit stability. These transitions manifest in:

  • Local and global anomalies in algorithmic information content (measured via BDM or CTM),
  • Disruption of spatial motifs or emergence of new generative rules,
  • Circuit rewiring within motif propagation paths (interpreted as rewired symbolic influence flows),
  • Collapse or emergence of torsional topological features when symbolic surfaces are encoded as point clouds for persistent homology.

A structural break, in this framing, is a failure of symbolic continuity—interpreted through compressibility collapse, rule transition, or torsion loss.

Rationale

  • ECA evolution acts as a computational microscope for symbolic causality, revealing structured transitions hidden from statistical models.
  • Algorithmic dynamics (BDM, CTM) quantify compression-phase shifts that align with semantic or causal boundaries.
  • Circuit Tracer analogy applies: breakpoints disrupt motif propagation graphs in the 2D symbolic space.
  • Torsion (Walch, Hodge) offers a sensitive topological signature of discrete, non-reconstructable change.
  • Sutskever’s theory frames joint compressibility breakdown as an irreducible regime boundary — which aligns with motif divergence in ECA-generated symbolic grids.

Supporting Literature

  • Zenil et al. – Algorithmic Information Dynamics and motif compressibility
  • Grosse et al. – Occam’s Razor and geometric modeling of latent generative structure
  • Sakabe et al. – Attribution drift from symbolic perturbations
  • BrightStar Labs (2025) – Emergent Models and symbolic substrate encoding
  • Maria Walch (2024) – Torsion as latent signal of topological fragility
  • Ilya Sutskever (2024) – Unsupervised learning as compression, joint vs. separate encoding signals
  • Anthropic (2025) – Circuit Tracer as latent graph indicator of regime shift