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TEST DESCRIPTION: √3 Confirmation — Fine Sweep + Resolution Check
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Author: Jonathan Shelton
Date: 2026-03-21
Status: PRE-REGISTERED (test description written BEFORE deployment)
Protocol: Outcome-agnostic. The data shows what it shows.
Engine: engine_4d.py (4D FDTD, audited v2)

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1. PURPOSE
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Phase 2 (48⁴) showed a STRUCTURAL TRANSITION at c_4D ≈ 1.700:
  - 25 peaks (vs 33 at ALL other c-values)
  - Dual/field ratio minimum at c ≈ 1.725
  - √3 ≈ 1.7321 falls in this transition zone

Two tests needed:
  A) FINE SWEEP: 11 values at 0.005 steps from 1.690 to 1.740
     Pins down the exact c-value where the structural transition occurs.
  B) RESOLUTION CHECK: Phase 3 (64⁴) at 3 key c-values
     Confirms the 25-peak anomaly isn't a Phase 2 resolution artifact.

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2. PRE-REGISTERED PREDICTIONS
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  P1: The 25-peak count at c=1.700 should PERSIST at Phase 3 resolution.
      If it disappears, it's a numerical artifact of N=48.

  P2: The fine sweep should show a NARROW transition zone where peak count
      drops below 33. The width and center of this zone are the measurement.

  P3: If the transition center falls at √3 = 1.7321 (within ±0.005),
      the √3 connection is confirmed. If it falls at 1.700 or elsewhere,
      √3 is an approximation and the true value needs interpretation.

  P4: The dual/field ratio minimum should also sharpen in the fine sweep.

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3. TEST A — FINE SWEEP (Phase 2, N=48)
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  c-values: [1.690, 1.695, 1.700, 1.705, 1.710, 1.715, 1.720, 1.725, 1.730, 1.735, 1.740]
  Phase: 2 (N=48)
  Periods: 50 (same as Phase 2 production sweep)

  Command:
    for c in 1.690 1.695 1.700 1.705 1.710 1.715 1.720 1.725 1.730 1.735 1.740; do
      python3 engine_4d.py --c $c --phase 2 --periods 50
    done

  Estimated time: ~14 min per c × 11 = ~2.5 hours

  Measurements: n_peaks, dual_to_field_ratio, autocorrelation, peak_to_noise

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4. TEST B — RESOLUTION CHECK (Phase 3, N=64)
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  c-values: [1.625, 1.700, 1.732]
    - 1.625: Fibonacci prediction (Phase 1 goldilocks)
    - 1.700: Structural transition point (Phase 2 anomaly)
    - 1.732: √3 (the geometric ratio)

  Phase: 3 (N=64)
  Periods: 50

  Command:
    for c in 1.625 1.700 1.732; do
      python3 engine_4d.py --c $c --phase 3 --periods 50
    done

  Estimated time: ~2-3 hours per c × 3 = ~6-9 hours

  GOTCHA: CFL with N=64 gives dt~5e-4, so each run is ~100,000 steps.
  Memory: 64⁴ = 16.8M grid points × 8 bytes × ~6 arrays ≈ 800 MB.
  Hetzner has 30GB RAM — fits comfortably.

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5. WHAT WOULD BE CONCLUSIVE
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  IF Test A shows the transition center at 1.730 ± 0.005 (within one step
  of √3) AND Test B shows 25 peaks persisting at N=64:
    → √3 as the structural transition point is CONFIRMED

  IF Test A shows the transition at 1.700 ± 0.005 (matching Steinberg but
  not √3) AND Test B shows 25 peaks at 1.700 but NOT at 1.732:
    → 1.700 is the true value, √3 is an approximation

  IF Test B shows the 25-peak anomaly DISAPPEARS at N=64:
    → Phase 2 artifact, not physical

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