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🔍 Current Formulations and Their Application Leakage

CIv7-ECA

Structural break detection using Elementary Cellular Automata on symbolic representations of univariate time series.

• Substrate: Symbolic / discrete
• Mechanism: ECA evolution + compressibility as indicator of symbolic regime change
• Leakage: “Structural break” + “time series” ties it tightly to financial/temporal data

CIv7-LLM

Latent Fault Geometry via Compression-Aligned Failure Surfaces in Language Models.

• Substrate: Latent / continuous
• Mechanism: LLM residual streams, attention trajectories, geometric fault surfaces
• Leakage: Focus on LLMs and “language models” as application-specific rather than archetypal

CIv7-Unified

Dual-substrate compression failure reveals causal and conceptual breakdowns in intelligent systems.

• Substrate: Symbolic ↔ Latent
• Mechanism: Failure of mutual compression or alignment = signal of intelligence boundary condition
• Leakage: Minor — most abstract already, but still drags examples from text segmentation or token failure

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🧠 General Essence: What Are You Really Claiming?

Here’s a distilled meta-hypothesis that sits above all three:

Intelligence is the capacity of a system to maintain compressible coherence between symbolic and latent representations of its environment and self.

When these representations diverge—that is, when symbolic and latent substrates fail to compress each other—the system encounters a boundary of understanding, manifesting as structural, causal, or conceptual discontinuity.

This captures:

• Compression as a universal diagnostic of order, structure, and meaning.
• Symbolic and latent representations as dual modes of encoding reality (topological vs. semantic).
• Intelligence as a balancing act between them—cybernetics as the dynamic coupling.

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🧱 Proposed Abstract Formulations

We now rewrite your three hypotheses without any application-domain anchors:

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CIv7-ECA → Symbolic Substrate Hypothesis

Symbolic Compression Faults as Discontinuities in Causal Representation

A symbolic substrate (e.g., discrete automata) evolves over time through rule-based transformations. When its compressibility changes sharply, it signals a transition in the underlying causal model encoded in the symbol dynamics. These “faults” reflect boundaries between internally coherent regimes.

• Key Mechanism: Compression change (via BDM or MDL) of symbolic patterns under rule-based evolution
• Essence: Algorithmic representation drift or fracture
• Cybernetic Interpretation: Symbolic causal inference loop destabilized

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CIv7-LLM → Latent Substrate Hypothesis

Latent Fault Geometry as a Signature of Representational Collapse

In latent systems (e.g., high-dimensional embeddings), coherence is maintained when attention or residual flows evolve smoothly. When compression fails—i.e., gradients, flows, or predictions become disordered—this exposes a representational fracture, indicating the system can no longer maintain a compressive model of its state space.

• Key Mechanism: Compression-aligned manifold smoothness; failure surfaces
• Essence: Latent instability as failure of semantic compactness
• Cybernetic Interpretation: Internal model collapse in high-dimensional control loop

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CIv7-Unified → Dual Substrate Hypothesis

Intelligence Emerges from the Coherence of Symbolic and Latent Compression

A cybernetic system maintains intelligence when its symbolic and latent representations remain jointly compressible. Disagreement—when one substrate can no longer predict or compress the other—marks a boundary of semantic coherence, revealing a structural or conceptual fault line.

• Key Mechanism: Compression failure between modalities
• Essence: Faults as signals of conceptual divergence or model mismatch
• Cybernetic Interpretation: Breakdown in bidirectional encoding-decoding between world models

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🌐 Why This Matters

This abstraction allows:

• Generalization beyond LLMs or ECAs — applicable to any system with dual representational layers.
• Application to multi-agent systems, AI safety, curriculum learning, neuromorphic modeling, etc.
• Clearer framing for epistemological boundaries in intelligent systems: where the map stops matching the territory.

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