CIv7 Unified Framework: Compression-Aligned Causal Geometry Across Symbolic and Latent Substrates

Hypothesis

Causal intelligence emerges from the ability to jointly compress structured input (X) and task-aligned signal (Y) into a shared, minimally distorted representation. Whether the substrate is symbolic (e.g., sequences evolved under Cellular Automata) or latent (e.g., attention and activation paths in Transformers), failure to align these compressive surfaces manifests as structural discontinuities—points where the model’s internal geometry breaks down.

CIv7 posits that both symbolic systems (like ECAs) and latent systems (like LLMs) share a universal compressive logic, wherein:

  • The compressive substrate builds a coherent internal geometry (e.g., motif lattice or residual manifold).
  • Prediction corresponds to smooth extrapolation over this geometry.
  • Failures—hallucinations, phase transitions, symbolic rewirings—reflect loss of this compressive coherence.

This yields a unified theory of symbolic and latent AI systems, where intelligence arises not from surface performance but from preservation of internal causal geometry across representational layers.

Core Components

1. Compressive Substrate as Causal Geometry

  • In CIv7-ECA, ECA-evolved 2D symbolic substrates encode algorithmic motifs, with structural breaks revealing phase shifts, entropy collapses, or symmetry fractures.
  • In CIv7-LLM, the LLM’s residual stream forms a latent topological manifold, with behavioral failures (e.g., hallucinations, steering unreliability) arising from compression-phase discontinuities.

2. Discontinuity as a Hallmark of Failure

Both systems reveal analogous discontinuity phenomena, including:

  • Joint compression failure: X and Y become decorrelated across layers (Sutskever).
  • Steering unreliability: Latent or symbolic vector shifts yield non-linear, unpredictable responses (Braun et al.).
  • Torsional collapse: Loss of coherent cohomology in attention/activation space or symbolic fault lines (Walch, Hodge).
  • Conceptual distortion: Compression-meaning divergence in clustering and motif aggregation (Shani et al.).
  • Phase bifurcation: Substrate topology splits into incoherent attractors under pressure from SFT-RL regime shifts or motif degeneracy (SASR, AlphaEvolve).

3. Causal Symmetry and Langlands Duality

  • Attention layers (geometry) and MLPs (algebra) form a dual symbolic system in LLMs (Hodge et al.).
  • ECAs encode similar algebraic-topological invariants through motif reconfiguration and circuit attention.
  • The Langlands analogy connects symbolic and latent failures as dual expressions of broken correspondence.

Distinguished Applications

  • Thematic Intelligence in Text (CIv7-LLM): LLM latent space is used to extract, compress, and align semantic motifs across documents. Discontinuities manifest as collapse of latent thematic manifolds, misclustering, and failure of steering vectors to enforce coherent perspectives.
  • Structural Break Detection in Time Series (CIv7-ECA): Symbolic encodings of numeric series are evolved through ECAs, with motif entropy collapse, torsion, and predictive breakdown revealing causal regime shifts invisible to traditional statistics.

Key Insight: Joint Compression as Shared Structure Discovery

As Ilya Sutskever observed, “Compression is prediction. Joint compression reveals shared structure.” This becomes the keystone of CIv7: when symbolic and latent substrates can be jointly compressed, they reinforce each other’s causal alignments.

  • Structural breaks in ECA and meaning breaks in LLMs are two sides of the same phenomenon.
  • Cross-substrate diagnosis is possible: failures in one system predict and explain failures in the other.
  • This paves the way for hybrid symbolic-latent architectures that self-monitor discontinuities as compression-aligned causal faults.