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Operator XVI: Flux Sealing & Manifold Closure · v0.8.4 STABLE
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Purpose: The Closure operator implements Helmholtz projection to eliminate flux divergence in the evolved τ-field, sealing the manifold so that ∇·J → 0. It represents the final stage of Phase C integration and bridges discrete evolution with continuous gauge constraints.
- Core Mechanics: J = τ∇τ – γ∇κ → Helmholtz projection J* = J – ∇ψ → τ ← τ – αcψ
- Validation Criteria (C⨂₁ – C⨂₅): Idempotence, Invariant Preservation (μ★≈φ, p≈2.28), Flux Neutrality, Entropy Stationarity, Reversibility
- Modes: Strict and Relaxed validation with automatic badge feedback (green ✓ = mathematically perfect, yellow ⚠ = physically valid)
- Expected Outcome: RMS(∇·J) decreases exponentially → sealed div-free flow and stable Φ-lock
- Recommended run: 128² grid, depth = 800, αc=0.03 (~2–3 min)
“Closure transforms a raw τ-field into a self-consistent manifold — a numerically sealed system where flux and geometry become one. It is the mathematical act of silencing the residual echo of divergence.”
Version 0.8.4 · TauFieldEngine N · Fully self-contained HTML lab engine · Production ready