🔬 REGIME LENS (κ–Λ)

Purpose

The Regime Lens is a deterministic analytical visualizer that exposes the relationship between discrete curvature κₙ and admissibility threshold Λ in UNNS recursive dynamics.

Autonomy Guarantees

• Does not depend on any Chamber
• Does not compute κₙ (only visualizes existing data)
• Does not modify input data
• Does not persist state
• May be run as standalone local file

Input Format

Accepts UNNS run JSON files with schema UNNS_FOUNDATIONS_RUN/v1:

{
  "schema": "UNNS_FOUNDATIONS_RUN/v1",
  "config": { ... },
  "steps": [
    {
      "n": 0,
      "kappa": 0.0000,
      "admissible": true,
      ...
    },
    ...
  ]
}

Only steps[].n and steps[].kappa are operationally required.

Controls

• Λ Slider: Adjust admissibility threshold (live updates)
• Reset View: Return to initial threshold
• Clear Data: Remove loaded run and start over

Behavioral Rules

• κₙ is immutable (no smoothing, no normalization, no recomputation)
• Λ is a pure comparator (the only boundary)
• Classification = κₙ > Λ (no hidden thresholds)
• Idempotent: Same JSON + same Λ → identical output

Performance

• ≤ 1,000 steps: instant
• ≤ 10,000 steps: ≤ 20 ms
• Λ updates do not trigger re-render of κₙ path

Conceptual Alignment

In UNNS terms, this module exposes:

• τ-filtered sub-structures (observable regimes)
• Collapse as derived boundary (Λ demarcation)
• Observability as parametric lens (Λ controls what survives)

This is structural analysis, not interpretive modeling.

Non-Goals (Explicit)

The Regime Lens:

• Does not validate UNNS theory
• Does not judge correctness
• Does not predict behavior
• Does not claim physical meaning
• Does not reinterpret ZFC, logic, or collapse