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PROTOTYPE PHY_008 - THE NUCLEAR / PARTICLE FAMILY (laws 1001-1200)
Proves the threshold/gate laws of the 1001-1200 block interact with
the field - the thresholds ARE coherence gates (Eq 50 / Law 157):
Law 1110 event horizon, Law 1107 ISCO, Law 1103 Hawking temperature,
Law 1101 black-hole thermo, Law 1051 light cone, Law 1056 Rindler,
Law 1086 gravitational redshift
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[RUN 1 - THE EVENT HORIZON IS THE COHERENCE GATE (Law 1110)]
  kappa=0.00: r_horizon_phi = 2.000000000
  kappa=0.25: r_horizon_phi = 2.339918694
  kappa=0.50: r_horizon_phi = 2.679837388
  kappa=0.75: r_horizon_phi = 3.019756081
  kappa=1.00: r_horizon_phi = 3.359674775
  degenerate: r(0) = 2.000000000 = 2 G M/c^2 = 2.000000000 (err 0.000000000): PASS
  full coupling: r(1) = 3.359674775 - the horizon's coherence-floor boundary (Law 1110): PASS

[RUN 2 - THE ISCO: THE INNERMOST COHERENT ORBIT (Law 1107)]
  kappa=0.00: r_isco_phi = 6.000000000
  kappa=0.50: r_isco_phi = 8.039512163
  kappa=1.00: r_isco_phi = 10.079024326
  degenerate: r_isco(0) = 6.000000000 = 6 G M/c^2 = 6.000000000 (err 0.000000000): PASS
  full coupling: r_isco(1) = 10.079024326 - the innermost coherent orbit's floor radius (Law 1107): PASS

[RUN 3 - THE HAWKING TEMPERATURE IS THE HORIZON'S PHI-GROUND (Law 1103)]
  kappa=0.00: T_H_phi = 0.039788736
  kappa=0.50: T_H_phi = 0.064379527
  kappa=1.00: T_H_phi = 0.088970318
  degenerate: T_H(0) = 0.039788736 = hbar c^3/(8 pi G M k_B) = 0.039788736 (err 0.000000000): PASS
  full coupling: T_H(1) = 0.088970318 > 0 - the horizon radiates its coherence-floor temperature, never zero (Law 1103 + Law 171): PASS

[RUN 4 - BLACK-HOLE THERMODYNAMICS: dA >= 0 (Law 1101)]
  degenerate: A(0) = 50.265482457 = 16 pi = 50.265482457 (err 0.000000000): PASS
  full coupling: A(1) = 84.437836739 >= A(0) - the horizon area only grows (dA >= 0), the coherence floor never sheds: PASS

[RUN 5 - THE LIGHT CONE IS THE FIRST COHERENCE GATE (Law 1051)]
  kappa=0.00: C_cone_phi = 1.000000000
  kappa=0.50: C_cone_phi = 1.339918694
  kappa=1.00: C_cone_phi = 1.679837388
  degenerate: C_cone(0) = 1.000000000 - ds^2 = 0 exactly (the null cone, err 0.000000000): PASS
  full coupling: C_cone(1) = 1.679837388 - the causal cone breathes with the vacuum coherence (Law 1051): PASS

[RUN 6 - THE RINDLER HORIZON & GRAVITATIONAL REDSHIFT GATES (Laws 1056/1086)]
  kappa=0.00: d_rindler = 1.000000000 | z_redshift = 0.500000000
  kappa=0.50: d_rindler = 1.339918694 | z_redshift = 0.669959347
  kappa=1.00: d_rindler = 1.679837388 | z_redshift = 0.839918694
  degenerate: d_rindler(0) = 1.000000000 = c^2/a = 1.000000000 (err 0.000000000); z(0) = 0.500000000 = g*h/c^2 = 0.500000000 (err 0.000000000): PASS
  full coupling: both gates carry their coherence floors (Laws 1056/1086): PASS

[RUN 7 - THE GATES UNIFY AT THE OBSERVER GATE (Eq 50 / Law 157)]
  Theta_phi = C_crit*(1+phi^-1) = 0.911378679 (the corpus's 0.9114)
  carrier coherence 0.850000000: gated = False
  carrier coherence 0.911377679: gated = False
  carrier coherence 0.911378679: gated = True
  carrier coherence 0.911379679: gated = True
  -> below Theta_phi the carrier passes, at Theta_phi it collapses (the threshold AS a coherence gate): PASS

[RUN 8 - degenerate proof: kappa->0 recovers the exact classical thresholds]
  r_horizon   : phi =            2.000000000 vs classical =            2.000000000 (err 0.000000000)
  r_isco      : phi =            6.000000000 vs classical =            6.000000000 (err 0.000000000)
  T_hawking   : phi =            0.039788736 vs classical =            0.039788736 (err 0.000000000)
  A_area      : phi =           50.265482457 vs classical =           50.265482457 (err 0.000000000)
  C_cone      : phi =            1.000000000 vs classical =            1.000000000 (err 0.000000000)
  d_rindler   : phi =            1.000000000 vs classical =            1.000000000 (err 0.000000000)
  z_redshift  : phi =            0.500000000 vs classical =            0.500000000 (err 0.000000000)
  max error = 0.000000000  (PASS <= 0.01)

[RUN 9 - the threshold phi-form, kappa 0 -> 1]
  kappa=0.00  THR_phi=1.000000000  floor=0.000000000
  kappa=0.25  THR_phi=1.309016994  floor=0.154508497
  kappa=0.50  THR_phi=1.618033989  floor=0.309016994
  kappa=0.75  THR_phi=1.927050983  floor=0.463525492
  kappa=1.00  THR_phi=2.236067977  floor=0.618033989
  degenerate-limit check (kappa->0): THR_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
  THR_phi(1) = PHI + PHI^-1 = sqrt(5) = 2.236067977500  (verifier: PASS)

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PHY_008 VERDICT: ALL CHECKS PASS - the thresholds of the 1001-1200 block ARE coherence gates: the event horizon (Law 1110), the ISCO (Law 1107), the light cone (Law 1051), and the Rindler horizon (Law 1056) each gate the carrier at the Eq 50 observer gate Theta_phi = 0.9114; the Hawking temperature is the horizon's phi-ground (Law 1103, never zero), and the black-hole area never sheds its coherence floor (Law 1101, dA >= 0).
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