CIv14 – Compression‑Driven Dynamic Viability

Hypothesis Statement

CIv14 extends CIv13’s symbolic-latent divergence detection into a self-monitoring cybernetic loop, where regime transitions are modeled as shifts in minimal generative programs. These shifts are detected via ΔBDM and ΔMDL signals, forecasted via decompression of symbolic sketches, and communicated to external agents via φ-scored program outputs. CIv14 thus operationalizes dynamic viability: the system maintains internal consistency while adapting to structural changes in real time.

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Principles

1. Dynamic Regime Modeling:

   • Regime change is defined as a statistically significant change in ΔBDM (≥ threshold θ_BDM) and ΔMDL (≥ θ_MDL) over a time window τ.
   • Temporal structure is captured via recursive compression → decompression cycles.

2. Compression–Prediction Equivalence:

   • Forecasting quality is strictly proportional to compressibility: $\text{Prediction Accuracy} \propto \text{ΔCompression Gain (ΔBDM)}$

3. Interpretability via Symbolic Regression:

   • Sketch outputs are scored with φ-metric (Non-Print & Non-Ordinal > Ordinal > Print).
   • Only φ ≥ φ_min outputs are communicated to stakeholders.

4. Neurosymbolic Integration:

   • Latent encoder (Transformer/TSEncoder) captures statistical dynamics.
   • Symbolic encoder captures discrete rules for minimal generative programs.
   • Divergence between streams signals regime shifts.

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Mechanism

• Symbolic Encoder:

  • Inputs: permutation/binary sequences of dimension d, delay τ.
  • Outputs: symbolic embeddings for minimal generative pattern detection.

• Latent Encoder:

  • Inputs: raw sequence segments.
  • Outputs: compressed latent vectors; used for divergence calculation.

• Complexity Monitor:

  • Compute ΔBDM per segment: $\Delta \text{BDM} = |\text{BDM}_{t+1} - \text{BDM}_t|$

  • Compute ΔMDL =

    MDL_{model+error,t+1} - MDL_{model+error,t}

  • If ΔBDM ≥ θ_BDM or ΔMDL ≥ θ_MDL → regime alert.

• Program Synthesis Head:

  • Generates candidate symbolic sketches.
  • φ scoring ensures quality and interpretability.

• Decompressor Forecaster:

  • Runs symbolic sketch forward to simulate next window.
  • Forecast compared to actual sequence → updates ΔMDL/ΔBDM.

• Divergence Integration:

  • Combine latent-symbolic divergence and ΔBDM for regime probability.

• External Interface:

  • Outputs φ-scored sketches and predicted sequence segments to analysts or agents.

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Success Metrics

• Forecast Accuracy: MSE between predicted and observed sequences.
• Compression Efficiency: Increase in ΔBDM per detected regime.
• Interpretability: Ratio of non-print φ outputs ≥ φ_min.
• Regime Detection Recall: True positive rate for known regime shifts.
• Internal Consistency: Stabilization of ΔMDL after regime adaptation.

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References

1. Hernández-Espinosa et al., 2024 – SuperARC
2. Zenil et al., 2018 – BDM/CTM complexity methods
3. Riedel & Zenil, 2025 – ECA rule minimality and causal decomposition
4. Maturana & Varela, 1980 – Autopoiesis

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Substrate Variants

Symbolic Substrate

• Mechanistic Role:

  • Encodes discrete causal structures through compressive motifs, capturing minimal generative programs.
  • Functions as a model-agnostic detection layer for algorithmic, topological, and semantic regime shifts.

• Key Signals:

  • φ (Program Length): Measures the length of the minimal program required to generate a sequence. Shorter programs indicate higher compressibility and potential for generalization.
  • Δφ (Program Length Change): Tracks changes in program length over time, signaling shifts in the underlying generative process.
  • Divergence Metrics: Quantifies the divergence between symbolic representations and latent encodings, indicating structural breaks or regime changes.

• Integration with Other Substrates:

  • Provides interpretable outputs (e.g., φ-scored sketches) that inform and guide the adaptation of latent models.
  • Works in tandem with the latent substrate to detect and explain regime shifts, facilitating a comprehensive understanding of system dynamics.

Latent Substrate

• Mechanistic Role:

  • Captures compressed dynamics of sequences, encoding fluid semantic continuity via distributed representations.
  • Monitors structural complexity and stability, identifying anomalies or shifts in the data stream.

• Key Signals:

  • ΔBDM (Bayesian Description Length Change): Measures changes in the description length of the model’s posterior distribution, indicating shifts in data structure.
  • ΔMDL (Minimum Description Length Change): Assesses changes in the model’s ability to compress data, reflecting the emergence of new patterns or regimes.
  • Forecast Error (MSE): Evaluates the accuracy of predictions, with increased error signaling potential regime changes.

• Integration with Other Substrates:

  • Provides statistical insights that complement symbolic representations, enhancing the system’s ability to detect and adapt to structural changes.
  • Collaborates with the symbolic substrate to generate and evaluate potential explanations for observed shifts.

Unified Substrate

• Mechanistic Role:

  • Integrates symbolic and latent representations to form a cohesive understanding of system dynamics.
  • Facilitates the forecasting of future states and the generation of interpretable outputs for external agents.

• Key Signals:

  • Regime Probability: Combines ΔBDM, ΔMDL, and divergence metrics to assess the likelihood of a regime shift.
  • Forecasted Sequences: Generated through decompression of symbolic sketches, providing potential future trajectories.
  • φ-Scored Outputs: Represents the interpretability and quality of generated outputs, guiding stakeholder interactions.

• Integration with Other Substrates:

  • Serves as the interface between internal processing and external communication, ensuring that the system’s outputs are both accurate and understandable.
  • Enables a feedback loop where external inputs can influence internal representations, promoting adaptive behavior.

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