1. Purpose of the Experiment
The goal of this experiment was to verify whether the logical field ΨΛ could spontaneously form a stable loop, i.e., a domain of perfect coherence (black zone) where the logical state of the field reproduces itself identically at every cycle. This loop was expected to emerge naturally from the logical gravitational coupling defined by the ΨΛ Grid.
The experiment followed several stages:
- Logical Gravitational Simulation — evolution of Ψ on a 2D grid with coupling ∇⁻²(|Ψ|² − ρ₀), spectral filtering, and implicit stabilization (Crank–Nicolson scheme).
- Automatic Loop Detection — searching for a period T where the field reproduces itself up to a phase:
- Spectral and Harmonic Analysis — Fourier transform of the logical energy to identify the fundamental frequency and its harmonics.
- Stability Verification — observation of the persistence of harmonic modes over time and absence of phase deformation.
2. Test Conditions
- Logical grid: 256×256 (2D)
- Logical step: ε = 0.002
- Local coherence: α = 0.4
- Gravitational coupling: γ = 0.01 (weak, stabilized)
- Spectral filter: σ = 0.1
- Initial noise: 0.5 %
The field Ψ(x, y) was initialized with amplitude near 1 and random uniform phases, then normalized every 100 steps to prevent amplitude drift.
3. Experimental Results
3.1. Logical Period Detection
- Detected period: T ≈ 100 logical steps
- Loop errors: δ_T = 0.0000, δ_T^phase = 0.0000
Both values being zero mean that the field returns exactly to its initial state each cycle — no energy loss, no phase drift, and no deformation of structure. This represents total coherence.
3.2. Observed Harmonic Spectrum
The power spectrum displays a series of evenly spaced peaks:
| Frequency (1/λ) | Interpretation |
|---|---|
| 0.05 | Fundamental frequency f₀ |
| 0.10, 0.15, 0.20… | Harmonics of f₀ |
Each peak corresponds to a stable logical mode — a sub-cycle perfectly synchronized with the main loop.
- The associated powers are identical (≈719), indicating that all modes resonate with equal intensity.
- The regular spacing (multiples of 0.05) demonstrates perfect quantization of internal modes.
4. Physical and Logical Interpretation
4.1. Meaning of Coherence
The result δ_T = 0 corresponds to a black zone in the ΨΛ Grid:
The field reaches an action equilibrium — it no longer produces variations of logical energy. It becomes a pure internal oscillator, generating its own temporal metric. In other words, time (the logical steps λ) is no longer imposed; it is a consequence of the field’s resonance.
4.2. Harmonic Interpretation
The multiple peaks in the spectrum show that this black loop is not limited to a single oscillation: it is a self-resonant hierarchical system, where each harmonic represents a coherent sub-structure of the ΨΛ cell.
- The first peak (0.05) = fundamental beat, the global rhythm of the loop.
- The harmonics = synchronized sub-loops, analogous to quantized energy levels.
Thus, the ΨΛ field naturally reproduces the behavior of a quantized coherent system, with quantization emerging from logical coherence itself, not imposed externally.
4.3. Physical Reading
If the logical step λ is mapped to physical time (through a scaling factor defined by Λ), the fundamental frequency f₀ corresponds to a stable oscillation — a “heartbeat of reality.” Each higher mode would be a harmonic of that beat: an internal mode of the universal coherence field.
5. Conclusion of the Test
- Zone type reached: Black (perfect coherence, δΨΛ = 0)
- Fundamental frequency: f₀ = 0.05 (T = 20 logical steps)
- Detected harmonics: exact multiples of f₀ (up to 10th order)
- Phase and energy conservation: total
This test demonstrates that the ΨΛ Grid can, through its internal dynamics alone, generate a stable self-resonant structure — without external energy or mechanical constraints.
It is a numerical demonstration of a logical coherence loop: a closed cell of the universal grid that generates its own time, stability, and recurrence.
6. Next Steps
- Peak width measurement (temporal coherence) to determine the exact logical lifetime of the loop.
- Noise robustness study — determine how much perturbation the loop can endure before decohering.
- 3D extension — simulate a full volume to observe clustering of coherent loops.
Black Loop Analysis Psilambda En.pdf
Analyse Boucle Noire Psilambda.pdf