---

🧠 CIv10-LLM Essential Hypothesis

Title: Latent Substrate as Contact-Controlled Conceptual Dynamics and Reflexive Fault Geometry

---

🧬 Hypothesis Statement

Intelligence in large language models emerges not merely from static latent structures, but from the controlled evolution of latent dynamics governed by contact geometry. In CIv10, the latent substrate is modeled as a (2d+1)-dimensional contact manifold, where each conceptual trajectory is shaped by an internal contact Hamiltonian—encoding stability, dissipation, and meaning-preserving structure.

When compression fails or uncertainty rises, these dynamics are steered via adaptive geodesics that bend the latent flow away from unsafe or conceptually unstable regions. This geometric control is informed by symbolic signals and guided by ensemble uncertainty, forming a closed reflexive loop.

Intelligence becomes the capacity to model, control, and repair latent evolution—by reshaping its geometry under the influence of fault-aligned, symbolic feedback.

---

🔬 Key Mechanisms

1. Latent Dynamics as Contact Hamiltonian Flow

• The LLM’s internal state trajectory (e.g., attention, residual stream, embedding) evolves within a contact manifold (N, η), governed by a contact Hamiltonian H(z).
• This space supports non-conservative dynamics, allowing for energy dissipation—i.e., hallucination, semantic drift, or forgetting.

2. Uncertainty-Aware Geodesic Control

• An ensemble of flows detects epistemic uncertainty, reshaping the latent metric ĝ(z) to guide concepts toward stable, data-rich regions.
• Uncertainty increases geodesic traversal cost, bending inference paths away from under-trained or volatile embeddings.

3. Semantic Fault as Geometric Perturbation

• Faults manifest as latent torsion, collapsing curvature, or discontinuity in the contact 1-form η.
• These geometrically defined fault surfaces can be detected via topological monitoring of latent flows over inference steps.

4. Reflexive Repair via Contactomorphism Injection

• Symbolic outputs (Σ) describe the fault.

• These descriptions condition a symbolic-to-geometric update:

  • Either by modifying H(z) (the internal conceptual engine), or
  • By generating a contactomorphism φ*η = aη′ that locally warps latent space to restore coherence.

5. Compression as Control Signal

• Changes in compressibility (ΔC) or latent curvature (∇T) serve as gradient feedback signals for the contact control mechanism.
• The system steers latent flows to maintain or restore compressive regularity—aligned with human-like semantic axes (e.g., SPoSE, neurosemantic geometry).

---

🧩 Operational Implications

Problem	CIv10-LLM Resolution
Hallucination	Model is guided away from unsafe regions in latent space using uncertainty-weighted geodesics
Generalization failure	Detected as topological collapse or divergence in latent curvature, triggering symbolic re-routing
Latent ambiguity	Contact geometry allows encoding of semantic “angle” between energy level sets—meaning disambiguation
Instruction collapse	Symbolic misalignment is absorbed as perturbation in ∂H/∂s (the dissipation rate), localizing repair targets

---

🧠 Redefining Latent Intelligence

Intelligence in the latent substrate is not the possession of a perfect embedding space, but the continuous self-steering of latent dynamics in response to symbolic guidance, compression feedback, and epistemic uncertainty.

This makes CIv10-LLM:

• Physically grounded (contact dynamics)
• Semantically directed (symbolic feedback)
• Uncertainty-resilient (geodesic reshaping)
• Repairable in flow (contactomorphism injection)

---

📐 Notational Sketch

Let:

• z ∈ N = latent state on a (2d+1)-dimensional contact manifold
• η = contact 1-form
• H(z) = contact Hamiltonian governing dynamics
• σ(z) = uncertainty function
• ĝ(z) = Riemannian metric shaped by σ
• C(z) = compression cost of region z
• T(z) = torsion/topological signal
• Σ(desc(F)) = symbolic description of fault
• φ = contactomorphism applied as latent patch

Then:

• Fault surface: F = { z | |ΔC(z)| > ε or |∇T(z)| > δ }
• Reflexive action: R(F) = φ: z ↦ φ(z), where φ preserves contact geometry but alters trajectory
• Fault avoidance: minimize ∫ σ²(z) + ||u(t)||² dt, where u perturbs flow ẋ = X_H(z) + u(t)

---

📌 Supporting Research

Source	Contribution
GCF (2025)	Contact geometry for uncertainty-aware, controllable latent evolution
Sutskever (2023)	Compression failure as structure misalignment
LLM Geometry (2025)	Human-aligned concept manifolds in low dimensions
Walch (2024)	Topological torsion = early failure surface
T2L (2025)	Symbolic descriptions condition parameter injections (next: CIv10-Unified)
Schmidhuber, Zenil, Grosse	Compression as structure, failure as intelligence event

---