Siglet-Qubits — Part 3: Emergent Clustering & Symbolic Behavior

Welcome to Part 3 of the Siglet-Qubits series. Here we bring the theory to life—tracking how simulated siglet populations behave under pressure, entropy, and symbolic variance. What begins as noise begins to reveal pattern. And in that pattern, meaning.

Experimental Setup

To study symbolic emergence, we ran multi-wave simulations with varying parameters:

• Siglet population sizes: 10, 25, 50, 100
• Embedding dimensions: 128 and 512
• Noise perturbations: ±2% Gaussian jitter on τ, μ, and r
• Clustering methods: Spectral Clustering, DBSCAN, and UMAP + KMeans

Each run generated thousands of siglet trajectory vectors using the truth_potential() function defined in Part 2.

Evaluation Criteria

Clustering validity was assessed using:

| Metric | Meaning | |---------------------|----------------------------------------------| | Silhouette Score | Internal cluster cohesion vs. separation | | Modality Consistency | Cross-modal similarity (μ coherence) | | Drift Robustness | Cluster label consistency under ± noise | | Ethical Separation | Vector field divergence in ε space |

Additional metrics like entropy delta and stability over time were used to prune unstable clusters.

Sample Results

One representative run (25 siglets, 512-dim) produced:

• 3 stable clusters with avg Silhouette = 0.72
• Mean modality coherence μ = 0.83
• Drift robustness under noise = 94.1%
• High ethical gradient separation (>0.65) between clusters

These results suggest real, not random, divergence in symbolic behavior.

Cluster Signatures

We found symbolic traits consistently emerging:

• Cluster A: high τ and μ, moderate r, strong ε alignment — “steadfast” agents
• Cluster B: low τ, high r, chaotic ε — “shifting mirrors”
• Cluster C: medium everything, but max compression c — “symbolic bridges”

These signatures emerged without supervision. They reflect stable behavioral modalities under symbolic computation pressure.

Reverse-Mapping Ethical Anchors

By tracing the ε vectors from high-fidelity siglets and comparing them to known ethical anchors (idealized ε̂), we could measure alignment delta:

Δε = ||ε_siglet - ε̂||

Siglets with low Δε were mapped back into source embeddings, forming a basis for reverse-mapped ethical observables.

These are not hard-coded ethics—they are discovered patterns of stability.

Visualizing the Field

Using UMAP + t-SNE projections, siglet dynamics form trajectories in latent space. When colored by cluster and noise tolerance, regions of symbolic order emerge—ethically stable zones where drift is low and resonance high.

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In Part 4, we extend this into alignment systems and comparative frameworks. What does it mean to say a cluster is ethical? And how do symbolic systems declare alignment without semantic content?

We'll answer these next.