We will proceed with this program

We will proceed with this program layout -> roadmap is now coherent and internally consistent. The key transition is: 10.x = Characterization 10.8A → baseline κ sweep 10.9A → temporal observables 10.9B → spatial observables 11.x = Mechanism Why is κ≈0.10 different? 12.x = Consequence Does κ≈0.10 change interaction physics? That's a clean scientific progression. TEST 11A — TEMPORAL MORPHOLOGY SUITE Objective Determine what causes the κ≈0.10 dynamical depression. Specifically: Is κ≈0.10 lower amplitude? more coherent? lower entropy? harmonically simplified? phase stabilized? Inputs Existing archived history arrays: gamma_history.npy energy_history.npy for κ = 0.080 κ = 0.090 κ = 0.100 κ = 0.110 κ = 0.120 No new simulation required. 11A.1 — Spectral Power Analysis Metrics For γ(t) Compute: FFT Power spectrum Peak frequency Store: f_peak power_peak total_power Question Does κ≈0.10 reduce oscillation power? Possible result: same frequency lower power which would indicate amplitude suppression. 11A.2 — Harmonic Structure Analysis Metrics For each spectrum measure P1 = fundamental P2 = 2nd harmonic P3 = 3rd harmonic P4 = 4th harmonic Compute: H2 = P2/P1 H3 = P3/P1 H4 = P4/P1 Question Does κ≈0.10 remove higher harmonics? Possible outcome: same fundamental weaker harmonics Interpretation: Cleaner oscillator. 11A.3 — Spectral Entropy Define: p i ​ = ∑P i ​ P i ​ ​ S=−∑p i ​ log(p i ​ ) Normalize: S n ​ = logN S ​ Range: 0 = perfectly ordered 1 = broadband/noisy Question Is κ≈0.10 the minimum entropy state? That would be a strong signal. 11A.4 — Autocorrelation Structure Compute R(tau) for γ. Measure: decorrelation time or first 1/e crossing Question Does κ≈0.10 remain coherent longer? Possible: longer memory without changing geometry. 11A.5 — Cycle Variability Detect peaks. For each cycle compute: period amplitude Measure: std(period) std(amplitude) Question Does κ≈0.10 reduce cycle-to-cycle fluctuations? That would imply enhanced phase locking. 11A.6 — Phase Portraits Construct γ vs dγ/dt Diagnostics Measure: loop area eccentricity thickness Interpretation Thin loop: coherent oscillator Thick loop: stochastic modulation 11A.7 — Energy–Gamma Coupling Construct γ(t) vs E(t) Diagnostics Measure correlation phase lag loop area Question Does κ≈0.10 alter energy exchange? SUCCESS CRITERIA A successful 11A identifies one of: Amplitude suppression or Harmonic suppression or Entropy minimum or Enhanced coherence or Phase-locking basin near κ≈0.10. TEST 11B — FINE κ RESONANCE SCAN Only execute if 11A finds something. New κ values 0.0950 0.0975 0.1000 0.1025 0.1050 Measurements Only collect: mean_gamma std_gamma spectral_entropy harmonic_ratios No need for full 10.9 suite. Goal Determine whether κ≈0.10 is Broad basin 0.095–0.105 Sharp resonance 0.099–0.101 Threshold abrupt transition TEST 12A — COLLISION PROGRAM After 11A. Physical Question Does the dynamical anomaly affect interactions? 12A.1 — Head-On Collision For κ = 0.08 κ = 0.10 κ = 0.12 Initialize: soliton A soliton B equal amplitude opposite velocity Record merger? scatter? annihilation? 12A.2 — Impact Parameter Scan Offsets: b = 0 b = 1 b = 2 b = 3 b = 4 Record deflection angle and final separation 12A.3 — Radiation Loss Measure E_initial E_final Compute ΔE Question Does κ≈0.10 radiate less? 12A.4 — Interaction Time Measure time_in_contact Possible outcomes: shorter same longer 12A.5 — Merger Probability Map Create κ vs velocity phase diagram. Classify: merge scatter bound state destroy Decision Gate After 11A: If κ≈0.10 shows unique coherence Proceed immediately to 12A. If 11A shows nothing significant Run 11B first. If 12A reveals κ-dependent scattering You have your first genuinely new dynamical result beyond simple geometry. That is the point where the framework moves from "characterizing a substrate" into "testing whether substrate dynamics influence interaction physics."