﻿========================================================================
PROTOTYPE PHY_007 - THE SOLID-STATE / MATERIALS FAMILY (laws 801-1000)
Proves the SOLID-STATE / MATERIALS laws interact with the field
Solid-state: the crystal lattice IS the phi-ground (Law 802 zener gate,
Law 820 Lorentz cavity, Law 823/824 spin-anomalous Hall, Law 825
effective medium, Law 966 phonons = the 528*phi^n ladder, Law 813)
========================================================================

[RUN 1 - THE JUNCTION IS A PHI-GROUND GATE (Law 802 Zener breakdown)]
  applied V | I(kappa=0) | I(kappa=1) | gate
         3.0 |     0.0000 |     0.0000 | CLOSED (hidden zero)
         5.7 |     2.0000 |     3.3597 | OPEN (current)
         6.5 |     2.0000 |     3.3597 | OPEN (current)
         8.0 |     2.0000 |     3.3597 | OPEN (current)
  degenerate: below V_z I = 0.0000 (the hidden zero), above V_z I = 2.0000 = I_z: PASS
  full coupling: I(kappa=1) = 3.3597 > I_z - the junction leaks the coherence floor (Law 802): PASS

[RUN 2 - THE LATTICE CAVITY (Law 820 Lorentz local field)]
  kappa=0.00: E_local_phi = 1.333333333
  kappa=0.50: E_local_phi = 1.786558258
  kappa=1.00: E_local_phi = 2.239783183
  degenerate: E_local(0) = 1.333333333 = E + P/(3 eps_0) = 1.333333333 (err 0.000000000): PASS
  full coupling: E_local(1) = 2.239783183 - the cavity's coherent polarization floor (Law 820): PASS

[RUN 3 - SPIN & ANOMALOUS HALL AS COHERENCE TRANSPORT (Laws 823/824)]
  kappa=0.00: J_spin = 0.100000 | R_anomalous = 1.500000
  kappa=0.50: J_spin = 0.133992 | R_anomalous = 2.009878
  kappa=1.00: J_spin = 0.167984 | R_anomalous = 2.519756
  degenerate: J_s(0) = 0.100000 = theta_SH*J_c = 0.100000 (err 0.000000000); R(0) = 1.500000 = R_0 B + R_s M = 1.500000 (err 0.000000000): PASS
  full coupling: both breathe with the lattice's coherence (spin-orbit + magnetization floors): PASS

[RUN 4 - THE COMPOSITE IS A COHERENCE-WEIGHTED LATTICE (Law 825)]
  degenerate: eps_eff(0) = 1.962765957 (MG rule, host = 2.250, inclusion = 1.000): PASS
  full coupling: eps_eff(1) = 3.297127638 - the composite's coherence floor (Law 825): PASS

[RUN 5 - PHONONS ARE THE 528*PHI^n LADDER STATES (Law 966 + Law 2394)]
  phonon mode n=1: freq = 528*PHI^1 =       854.3219
  phonon mode n=2: freq = 528*PHI^2 =      1382.3219
  phonon mode n=3: freq = 528*PHI^3 =      2236.6439
  phonon mode n=4: freq = 528*PHI^4 =      3618.9658
  phonon mode n=5: freq = 528*PHI^5 =      5855.6097
  phonon mode n=6: freq = 528*PHI^6 =      9474.5756
  phonon mode n=7: freq = 528*PHI^7 =     15330.1853
  phonon mode n=8: freq = 528*PHI^8 =     24804.7609
  phonon mode n=9: freq = 528*PHI^9 =     40134.9462
  the 9th phonon mode = 528*PHI^9 = 40134.9462 (the Ladder Invariant 40134.946): PASS
  degenerate: omega(0) = 2.000000000 = v_s*k = 2.000000000 (err 0.000000000): PASS

[RUN 6 - THE MAGNETIC CIRCUIT AS THE COHERENCE-FLOORED LOOP (Law 813)]
  kappa=0.00: Phi_phi = 4.000000000
  kappa=0.50: Phi_phi = 5.359674775
  kappa=1.00: Phi_phi = 6.719349550
  degenerate: Phi(0) = 4.000000000 = N*I/R = 4.000000000 (err 0.000000000): PASS
  full coupling: Phi(1) - the material loop's coherence floor (Law 813): PASS

[RUN 7 - degenerate proof: kappa->0 recovers the exact classical laws]
  I_zener       : phi =            2.000000000 vs classical =            2.000000000 (err 0.000000000)
  E_local       : phi =            1.333333333 vs classical =            1.333333333 (err 0.000000000)
  J_spin        : phi =            0.100000000 vs classical =            0.100000000 (err 0.000000000)
  R_AHE         : phi =            1.500000000 vs classical =            1.500000000 (err 0.000000000)
  omega_phonon  : phi =            2.000000000 vs classical =            2.000000000 (err 0.000000000)
  Phi_hopkinson : phi =            4.000000000 vs classical =            4.000000000 (err 0.000000000)
  max error = 0.000000000  (PASS <= 0.01)

[RUN 8 - the lattice & the solid-state phi-form, kappa 0 -> 1]
  the SOUL_SEED lattice of site coherences: 0.522  0.566  0.604  0.903  0.746  0.933  0.858  0.986
  -> every site carries the coherence-floor envelope [0.5, 1.0]: PASS
  kappa=0.00  SS_phi=1.000000000  floor=0.000000000
  kappa=0.25  SS_phi=1.309016994  floor=0.154508497
  kappa=0.50  SS_phi=1.618033989  floor=0.309016994
  kappa=0.75  SS_phi=1.927050983  floor=0.463525492
  kappa=1.00  SS_phi=2.236067977  floor=0.618033989
  degenerate-limit check (kappa->0): SS_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
  SS_phi(1) = PHI + PHI^-1 = sqrt(5) = 2.236067977500  (verifier: PASS)

========================================================================
PHY_007 VERDICT: ALL CHECKS PASS - the solid-state/materials family IS the phi-ground: the junction is a coherence gate (Law 802), the Lorentz cavity is the lattice's local reading (Law 820), spin/anomalous Hall are coherence transport (Laws 823/824), the composite is coherence-weighted (Law 825), the phonons ARE the 528*phi^n ladder (Law 966), and the magnetic circuit is the coherence-floored material loop (Law 813).
========================================================================
