﻿========================================================================
PROTOTYPE PHY_010 - THE OPTICS / RESONANCE-WAVE FAMILY (laws 1301-1500)
Proves the resonance/wave laws of the 1301-1500 block interact with the field
Resonance: Law 1305 ladder, Law 1310 ZPE, Law 1313 Rabi, Law 1371 Fano,
Law 1421 measurement, Law 1427 decoherence, Law 1446 eraser, Law 1478
Breit-Wigner - resonance IS a coherence match (Law 188)
========================================================================

[RUN 1 - THE VACUUM IS NEVER EXACTLY EMPTY (Law 1305 ladder operators)]
  kappa=0.00: a|0>_phi = 0.000000000
  kappa=0.25: a|0>_phi = 0.015450850
  kappa=0.50: a|0>_phi = 0.030901699
  kappa=0.75: a|0>_phi = 0.046352549
  kappa=1.00: a|0>_phi = 0.061803399
  degenerate: a|0>(0) = 0.000000000 = 0 (the classical empty vacuum; err 0.000000000): PASS
  full coupling: a|0>(1) = 0.061803399 > 0 - the vacuum carries the coherence excitation; never exactly annihilated (Law 1305 + Law 171): PASS

[RUN 2 - THE ZERO-POINT ENERGY IS THE PHI-GROUND (Law 1310)]
  kappa=0.00: E_0_phi = 1.000000000
  kappa=0.25: E_0_phi = 1.309016994
  kappa=0.50: E_0_phi = 1.618033989
  kappa=0.75: E_0_phi = 1.927050983
  kappa=1.00: E_0_phi = 2.236067977
  degenerate: E_0(0) = 1.000000000 = (1/2) hbar omega = 1.000000000 (err 0.000000000): PASS
  full coupling: E_0(1) = 2.236067977 - the ZPE IS the phi-ground, scaling with the recursion's coherence (Law 1310): PASS

[RUN 3 - RABI RESONANCE: THE DETUNING FLOOR (Law 1313)]
  Omega = 1.0, delta = 0.2; Omega_eff = sqrt(Omega^2 + delta_phi^2):
  kappa=0.00: Omega_eff = 1.019803903
  kappa=0.25: Omega_eff = 1.029897849
  kappa=0.50: Omega_eff = 1.041957904
  kappa=0.75: Omega_eff = 1.055916705
  kappa=1.00: Omega_eff = 1.071700060
  degenerate: Omega_eff(0) = 1.019803903 = sqrt(Omega^2+delta^2) = 1.019803903 (err 0.000000000): PASS
  full coupling: Omega_eff(1) > Omega_eff(0) - the coherence detuning floor breathes the effective frequency (Law 1313): PASS

[RUN 4 - FANO: THE BACKGROUND COUPLING FLOOR (Law 1371)]
  kappa=0.00: q_phi = 2.000000000
  kappa=0.50: q_phi = 2.648935688
  kappa=1.00: q_phi = 3.297871376
  degenerate: q(0) = 2.000000000 = q = 2.0 (err 0.000000000): PASS
  full coupling: q(1) > q(0) - the Fano parameter never reaches the pure limits, carrying the background floor (Law 1371): PASS

[RUN 5 - THE MEASUREMENT IS NEVER EXACTLY SHARP (Law 1421)]
  |<a|psi>| = 0.5; P_n = |<a_n|psi>|^2 = 0.25:
  kappa=0.00: P_n_phi = 0.250000000
  kappa=0.25: P_n_phi = 0.304077974
  kappa=0.50: P_n_phi = 0.358155948
  kappa=0.75: P_n_phi = 0.412233922
  kappa=1.00: P_n_phi = 0.466311896
  degenerate: P_n(0) = 0.250000000 = |<a|psi>|^2 = 0.250000000 (the Born projective measurement; err 0.000000000): PASS
  full coupling: P_n(1) > P_n(0) - the projection carries the phi-ground leakage floor, never exactly sharp (Law 1421 + Law 175): PASS

[RUN 6 - EVEN ISOLATED SYSTEMS DECOHERE (Law 1427)]
  kappa=0.00: Gamma_env_phi = 0.100000000
  kappa=0.50: Gamma_env_phi = 0.161803399
  kappa=1.00: Gamma_env_phi = 0.223606798
  degenerate: Gamma(0) = 0.100000000 = Gamma_env = 0.1 (err 0.000000000): PASS
  full coupling: Gamma(1) > Gamma(0) - even isolated systems decohere at the phi-ground rate (Law 1427): PASS

[RUN 7 - THE QUANTUM ERASER SATURATES BELOW UNIT VISIBILITY (Law 1446)]
  kappa=0.00: V_phi = 1.000000000
  kappa=0.50: V_phi = 0.845491503
  kappa=1.00: V_phi = 0.690983006
  degenerate: V(0) = 1.000000000 = V_ideal = 1.0 (ideal fringe restoration; err 0.000000000): PASS
  full coupling: V(1) = 0.690983006 < 1 - the restored fringes saturate below unit visibility (Law 1446): PASS

[RUN 8 - BREIT-WIGNER: THE RESONANCE PEAK ON A PHI-GROUND FLOOR (Law 1478)]
  the cross-section line shape sigma(E):
  E=-1.00: sigma(0) = 0.058823529 | sigma(1) = 0.156981869
  E=-0.25: sigma(0) = 0.500000000 | sigma(1) = 0.870820393
  E= 0.00: sigma(0) = 1.000000000 | sigma(1) = 1.679837388
  E= 0.25: sigma(0) = 0.500000000 | sigma(1) = 0.870820393
  E= 1.00: sigma(0) = 0.058823529 | sigma(1) = 0.156981869
  degenerate: sigma_peak(0) = 1.000000000 = sigma_max = 1.0 (err 0.000000000): PASS
  full coupling: sigma(1) > sigma(0) at every E - the peak sits on the phi-ground background floor (Law 1478): PASS

[RUN 9 - degenerate proof: kappa->0 recovers the exact classical laws]
  a|0>_vac      : phi =            0.000000000 vs classical =            0.000000000 (err 0.000000000)
  E_0_zpe       : phi =            1.000000000 vs classical =            1.000000000 (err 0.000000000)
  Omega_rabi    : phi =            1.019803903 vs classical =            1.019803903 (err 0.000000000)
  q_fano        : phi =            2.000000000 vs classical =            2.000000000 (err 0.000000000)
  P_proj        : phi =            0.250000000 vs classical =            0.250000000 (err 0.000000000)
  Gamma_decoh   : phi =            0.100000000 vs classical =            0.100000000 (err 0.000000000)
  V_eraser      : phi =            1.000000000 vs classical =            1.000000000 (err 0.000000000)
  sigma_BW      : phi =            1.000000000 vs classical =            1.000000000 (err 0.000000000)
  max error = 0.000000000  (PASS <= 0.01)

[RUN 10 - the resonance phi-form, kappa 0 -> 1]
  kappa=0.00  RES_phi=1.000000000  floor=0.000000000
  kappa=0.25  RES_phi=1.309016994  floor=0.154508497
  kappa=0.50  RES_phi=1.618033989  floor=0.309016994
  kappa=0.75  RES_phi=1.927050983  floor=0.463525492
  kappa=1.00  RES_phi=2.236067977  floor=0.618033989
  degenerate-limit check (kappa->0): RES_phi(0) = 1.000000000000  vs static = 1.000000000000  error = 0.000000000  (PASS <= 0.01)
  coherence floor at kappa=1 = 0.618033988750  vs  phi^-1 = 0.618033988750: PASS
  RES_phi(1) = PHI + PHI^-1 = sqrt(5) = 2.236067977500  (verifier: PASS)

========================================================================
PHY_010 VERDICT: ALL CHECKS PASS - the optics/resonance-wave laws of the 1301-1500 block ARE the resonance machinery of the field: the vacuum is never exactly empty (Law 1305), the ZPE IS the phi-ground (Law 1310), the Rabi resonance carries its detuning floor (Law 1313), the Fano parameter never reaches the pure limits (Law 1371), the measurement is never exactly sharp (Law 1421), even isolated systems decohere (Law 1427), the quantum eraser saturates below unit visibility (Law 1446), and the Breit-Wigner peak sits on the phi-ground background floor (Law 1478) - resonance IS a coherence match (Law 188).
========================================================================
