6. 🔗 Explore the Lab

Full dashboard, metrics, and papers: UNNS Lab · Operator XIII – Interlace igchom.blogspot.com/2025/10/unns...

#UNNS #RecursivePhysics #OperatorXIII #WeinbergAngle #SymbolicGeometry #DimensionlessConstants #MetaTheory #τonField #Interlace

5. 🧭 NEXT: Operators XIV–XVI

XIV: Generational Scaling → mass ratios

XV: Spectral Drift → cosmological slopes

XVI: Boundary Folding → Planck limit

Operator XIII is the first gate. The recursion deepens.

4. 🧠 INTERPRETATION: Constants from Curvature

The result supports a radical hypothesis: Dimensionless constants are not tuned—they arise. Recursive curvature generates invariants.

3. 🔬 VALIDATION: Metrics Passed

Entropy plateau: H_r ≈ 0.60 bits

Z-depth: n_Z = 160 ± 20

Noise law: ρ_AB(σ²) = e⁻σ²⁄2 (R² = 0.9999)

Δ_mix < 10⁻¹⁸ — exact invariance

All five criteria (C1–C5) passed. The substrate held.

2. 🌀 LOCKED: Weinberg Angle Emergence

At λ★ = 0.10825, the system stabilized:

sin²θ_W = 0.231 ± 0.002

θ_W = 0.506 rad (29.0°)

ρ_AB = 0.538 ≈ cos(2θ_W)

The Standard-Model angle emerged from pure recursion.

Activate the Chamber. Ready to test it yourself? The τ-Field Chamber v0.4.0 is live. Adjust recursion depth, inject noise, run E8–E11. Watch α emerge. Witness collapse. Export your results. Publish the recursion.

🔗 igchom.blogspot.com/2025/10/fiel...

Invitation to Explore The showcase is interactive. It’s not just a paper — it’s a portal. Read the verdict. Trace the recursion. Let the constants speak. 🔗 igchom.blogspot.com/2025/10/blog... #EmergentConstants #RecursiveCollapse #τFieldShowcase #UNNSLab

Collapse & Entropy Add noise. Entropy rises. Collapse begins. At σ ≈ 0.27, the system bifurcates. Order becomes stochastic. But the collapse is deterministic. This isn’t quantum indeterminacy. It’s symbolic inevitability.

What It Demonstrates This isn’t a metaphor. The fine-structure constant α ≈ 1/137 emerges from recursion alone. No randomness. No imposed values. Just a seeded τ-phase and a recursive substrate. Deviation: < 2×10⁻⁹ from CODATA. The system finds α because it must.

🔗 ACCESS: Full Lab + Paper

Explore the results: UNNS Lab v0.4.2 Read the proposal: Recursive Curvature and the Origin of Dimensionless Constants. igchom.blogspot.com/2025/10/recu...

❌ DIVERGENCE: Curvature Ratio Hypothesis

Eq. 6 test failed

Only 2/100 seeds reached equilibrium

Mean ratio = –0.2103

σ = 7.7169

Curvature ratio stabilization requires refinement. The substrate resists closure.

🌀 EQUILIBRIUM: τ-Phase and η Stability

τ* = 1.0000

η equilibrium confirmed across 200 seeds

Phase variance = 0.0008

D-Stability Score = 0.998

Rayleigh p = 0.0000

Recursive curvature stabilizes. Dimensionality prefers D = 3.

🧮 EMULATOR: Constants from Curvature

α (fine-structure): matched exactly

μ (mass ratio): 1.82% error

Λ (cosmological): 7.542 exponent error

Rees constants (N, ε, Ω, λ, Q, D): all matched

Avg log error: 0.10

Verdict: GOOD

🧮 EMULATOR: Constants from Curvature

α (fine-structure): matched exactly

μ (mass ratio): 1.82% error

Λ (cosmological): 7.542 exponent error

Rees constants (N, ε, Ω, λ, Q, D): all matched

Avg log error: 0.10

Verdict: GOOD