⚙️ CHAMBER κ₃: NESTED OBSERVABILITY v0.1.1

Operator κ₃ – Gate Configuration Selector with Ω-Calibration
🔬 Step 1: Ω-Calibration Pre-Pass (Required)
📊 Step 2: Gate Sweep Configuration
Visualization
Σ₂⁰(t) Time Series
Persistence Map P(Ω₁,Ω₂)
Re-entry Count R(Ω₁,Ω₂)
τ-Field (current)
Metrics
Current (Ω₁,Ω₂)
—
Persistence P
—
Re-entry R
—
Lock Regions
—
CV(P)
—
Status
Ready
CK3 Validation (v0.1.1)
Criterion Target Result Status
CK3.0: Calibration Present Required — —
CK3.1: Ω-Grid Coverage ≥ 64 pairs — —
CK3.2: Persistence Diversity CV(P) ≥ 0.3 — —
CK3.3: Re-entry Detection Total R ≥ 1 — —
CK3.4: Gate-Lock Contrast P_max / P_min ≥ 3.0 — —
📚 Laboratory Guide

Chamber κ₃ v0.1.1: What Changed

Delta from v0.1:

Added mandatory Ω-calibration pre-pass that measures Σ₂⁰ support before any gate sweep. This prevents the "flat P(g)=1" failure mode where Ω₂ range is completely below the actual signal.

v0.1.1 adds:

  • CK3.0: Blocking prerequisite - calibration must be run first
  • Ω-calibration statistics: Σ_min, Σ_max, Σ_mean, Σ_std
  • Recommended Ω₂ range: Auto-computed from signal support
  • Calibration export: omega_calibration block in JSON

Workflow (v0.1.1)

  1. Run Calibration: Measures Σ₂⁰ statistics over τ-relaxation
  2. Review Recommendations: Check suggested Ω₂ range
  3. Apply or Adjust: Use recommended range or customize
  4. Run Gate Sweep: Scan (Ω₁,Ω₂) space with calibrated thresholds
  5. Validate: Check CK3.0-CK3.4 acceptance criteria
  6. Export: Save JSON with calibration + results
🎯 Re-Entry Targeting Protocol (Click to expand)

File: kappa3_reentry_targeting_protocol.md

If CK3.3 fails (R=0), use this escalating intervention strategy to force re-entry opportunity:

🎯 Run 1: Minimal (stride=2)

Grid: 64×64
λ: 0.108
Stride: 2 (was 20)
Observable: Global Variance
Expected: 10× temporal resolution unmasks sub-relaxation fluctuations
Runtime: ~10 min

🎯 Run 2: Observable (if Run 1 fails)

[Same as Run 1]
Observable: Windowed Contrast (w=5)
Expected: Local contrast fluctuations visible
Runtime: ~10 min

🎯 Run 3: Coupling (if Run 2 fails)

[Same as Run 2]
λ: 0.15 (was 0.108)
Expected: Stronger spatial competition induces micro-rebounds
Runtime: ~10 min
✅ Stop immediately when: Total R ≥ 1 (CK3.3 passes)

Note: All three interventions are measurement-only adjustments (no dynamics changes, no validator weakening). Both VALIDATED (with re-entry) and REJECTED (monotone) are valid κ₃ results.

Interpretation Rule (Formal)

If CK3.0 passes but CK3.2-CK3.4 fail, the correct conclusion is:

"Under the measured Σ₂⁰ support, the tested Ω₂ range does not discriminate observability."

NOT: κ₃ failed. NOT: observability is trivial. NOT: dynamics are absent.

This is purely a statement about measurement calibration.

What κ₃ Actually Measures

Persistence Score:

P(g) = (1/T) · Σₖ 𝟙[Σ₂⁰(tₖ) > Ω₂]

Fraction of measurement times where observability signal is above gate threshold.

Re-entry Count:

R(g) = #{k>0 | bₖ₋₁=0 ∧ bₖ=1}

Number of times observability returns after being below threshold (upcrossing events).

Gate-Lock:

Lock(g) ⇔ P(g) ≥ 0.8

Operational label for high-persistence regimes (not a mechanism claim).

JSON Schema Compliance (v0.1.1)

Exported data conforms to the formal κ₃ JSON schema (validator-ready):

  • schema: "unns.kappa3.v0.1.1"
  • Mandatory blocks: config, omega_calibration, omega_grid, results, validation
  • CK3.0 enforcement: Calibration block required for export
  • Verdict rules: VALIDATED iff all CK3.x pass, REJECTED otherwise

Schema guarantees:

  • Array length consistency (all result arrays = total_pairs)
  • Statistical integrity (p_min ≤ p_max, sigma_min ≤ sigma_max)
  • Deterministic pairing order (omega_grid defines traversal)
  • Machine-checkable validation (no dynamics interpretation needed)