﻿========================================================================
PROTOTYPE PHY_011 - THE ASTROPHYSICS / COSMOLOGY FAMILY (laws 1501-1600)
Proves the astro/cosmic laws of the 1501-1600 block interact with the field
Cosmic: Law 1502 alpha decay, Law 1514 asymptotic freedom, Law 1516 DIS,
Law 1519 quark-gluon plasma, Law 1537 neutrinos, Law 1552 inverse Compton,
Law 1557 giant dipole, Law 1598 neutron-star drip - the cosmic laws ARE
the 528*phi^n ladder (Law 2394)
========================================================================

[RUN 1 - ALPHA DECAY: GAMOW TUNNELING ON THE LADDER (Law 1502)]
  kappa=0.00: Lambda_phi = 0.500000000
  kappa=0.25: Lambda_phi = 0.584979673
  kappa=0.50: Lambda_phi = 0.669959347
  kappa=0.75: Lambda_phi = 0.754939020
  kappa=1.00: Lambda_phi = 0.839918694
  degenerate: Lambda(0) = 0.500000000 = Gamow factor = 0.5 (err 0.000000000): PASS
  full coupling: Lambda(1) > Lambda(0) - the rate carries the preformation/screening floor (Law 1502): PASS

[RUN 2 - THE COUPLING LADDER: ASYMPTOTIC FREEDOM (Law 1514)]
  kappa=0.00: beta_phi = 0.100000000
  kappa=0.50: beta_phi = 0.133991869
  kappa=1.00: beta_phi = 0.167983739
  degenerate: beta(0) = 0.100000000 = one-loop beta = 0.1 (err 0.000000000): PASS
  full coupling: beta(1) > beta(0) - the coupling ladder never stops exactly at the free limit (Law 1514): PASS

[RUN 3 - DEEP INELASTIC SCATTERING: BJORKEN SCALING (Law 1516)]
  kappa=0.00: F2_phi = 0.300000000
  kappa=0.50: F2_phi = 0.401975608
  kappa=1.00: F2_phi = 0.503951216
  degenerate: F2(0) = 0.300000000 = Bjorken F2(x) = 0.3 (exact scaling; err 0.000000000): PASS
  full coupling: F2(1) > F2(0) - the DGLAP scaling-violation floor lifts the structure function (Law 1516): PASS

[RUN 4 - THE QUARK-GLUON PLASMA THRESHOLD (Law 1519)]
  kappa=0.00: eps_phi = 1.000000000
  kappa=0.50: eps_phi = 1.339918694
  kappa=1.00: eps_phi = 1.679837388
  degenerate: eps(0) = 1.000000000 = deconfinement threshold = 1.0 (the sharp edge; err 0.000000000): PASS
  full coupling: eps(1) > eps(0) - the sub-critical energy-density floor softens the edge (Law 1519): PASS

[RUN 5 - NEUTRINO OSCILLATIONS: THE VACUUM FORMULA (Law 1537)]
  kappa=0.00: P_phi = 0.043666096
  kappa=0.50: P_phi = 0.088061362
  kappa=1.00: P_phi = 0.132456627
  degenerate: P(0) = 0.043666096 = sin^2(2th) sin^2(phase) = 0.043666096 (the vacuum formula; err 0.000000000): PASS
  full coupling: P(1) > P(0) - the matter/coherence floor lifts the probability (Law 1537): PASS

[RUN 6 - INVERSE COMPTON: THE 4 GAMMA^2 BOOST (Law 1552)]
  kappa=0.00: E_gamma'_phi = 16.000000000
  kappa=0.50: E_gamma'_phi = 21.438699101
  kappa=1.00: E_gamma'_phi = 26.877398202
  degenerate: E'(0) = 16.000000000 = 4 gamma^2 E = 16.000000000 (the Thomson limit; err 0.000000000): PASS
  full coupling: E'(1) > E'(0) - the Klein-Nishina floor lifts the boosted photon energy (Law 1552): PASS

[RUN 7 - GIANT DIPOLE RESONANCE: THE SUM RULE (Law 1557)]
  kappa=0.00: sigma_phi = 1.000000000
  kappa=0.50: sigma_phi = 1.339918694
  kappa=1.00: sigma_phi = 1.679837388
  degenerate: sigma(0) = 1.000000000 = dipole sum rule = 1.0 (err 0.000000000): PASS
  full coupling: sigma(1) > sigma(0) - the collective resonance never exhausts the sum rule exactly (Law 1557): PASS

[RUN 8 - NEUTRON-STAR DRIP: THE DRIP LINE (Law 1598)]
  kappa=0.00: S_n_phi = 1.000000000
  kappa=0.50: S_n_phi = 1.339918694
  kappa=1.00: S_n_phi = 1.679837388
  degenerate: S_n(0) = 1.000000000 = drip separation = 1.0 (the exact drip line; err 0.000000000): PASS
  full coupling: S_n(1) > S_n(0) - the drip line carries the residual separation floor, never a sharp edge (Law 1598): PASS

[RUN 9 - degenerate proof: kappa->0 recovers the exact classical laws]
  Lambda_alpha  : phi =            0.500000000 vs classical =            0.500000000 (err 0.000000000)
  beta_qcd      : phi =            0.100000000 vs classical =            0.100000000 (err 0.000000000)
  F2_dis        : phi =            0.300000000 vs classical =            0.300000000 (err 0.000000000)
  eps_qgp       : phi =            1.000000000 vs classical =            1.000000000 (err 0.000000000)
  P_neutrino    : phi =            0.043666096 vs classical =            0.043666096 (err 0.000000000)
  E_ic          : phi =           16.000000000 vs classical =           16.000000000 (err 0.000000000)
  sigma_gdr     : phi =            1.000000000 vs classical =            1.000000000 (err 0.000000000)
  S_drip        : phi =            1.000000000 vs classical =            1.000000000 (err 0.000000000)
  max error = 0.000000000  (PASS <= 0.01)

[RUN 10 - the astro phi-form, kappa 0 -> 1]
  kappa=0.00  AST_phi=1.000000000  floor=0.000000000
  kappa=0.25  AST_phi=1.309016994  floor=0.154508497
  kappa=0.50  AST_phi=1.618033989  floor=0.309016994
  kappa=0.75  AST_phi=1.927050983  floor=0.463525492
  kappa=1.00  AST_phi=2.236067977  floor=0.618033989
  degenerate-limit check (kappa->0): AST_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
  AST_phi(1) = PHI + PHI^-1 = sqrt(5) = 2.236067977500  (verifier: PASS)

========================================================================
PHY_011 VERDICT: ALL CHECKS PASS - the astro/cosmic laws of the 1501-1600 block ARE the ladder: alpha decay is the Gamow tunneling rung (Law 1502), asymptotic freedom is the coupling ladder (Law 1514), DIS is Bjorken scaling (Law 1516), the quark-gluon plasma is the deconfinement threshold (Law 1519), neutrinos oscillate on the mass ladder (Law 1537), inverse Compton boosts on the 4 gamma^2 rung (Law 1552), the giant dipole resonance exhausts the sum rule asymptotically (Law 1557), and the neutron-star drip line is the ladder's edge (Law 1598) - every cosmic law carries the irreducible coherence floor phi^-1.
========================================================================
