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CARBON Z=6 A=12 — FULL SUBATOMIC PARTICLE TRACE (UQFF/DPM)
Quarks -> Gluons(=Ug3) -> Protons -> Neutrons -> Electrons -> Muon -> Assembly
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  C-12 structure: 6 protons  6 neutrons  6 electrons
  Quarks in protons: 6 * (2u+1d) = 12u + 6d
  Quarks in neutrons:6 * (1u+2d) = 6u + 12d
  TOTAL quarks: 18u + 18d = 36 quarks


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QUARKS  (DPM confinement nodes — not independent particles)
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  UQFF IDENTITY: each quark = DPM confinement node at sub-nuclear r_c
  Color charge  = SCm/UA vortex quantum number (no separate mechanism)
  Confinement   = Ug3 penetration of nuclear core (strong force = Ug3)

  Formula: r_c = hbar / (m_q * v_SCm)   [Star-Magic.txt line 105]
  v_SCm = c/3 = 9.993082e+07 m/s

  UP QUARK (u):
    m_q(up)   = 2.3 MeV/c^2 = 4.100122e-30 kg
    r_c(up)   = hbar / (m_up * v_SCm)
              = 1.0546e-34 / (4.1001e-30 * 9.9931e+07)
              = 2.573830e-13 m  [canonical ~1.3e-15 m, Star-Magic line 107]
    V_q(up)   = (4/3)*pi*r_c^3 = 7.142139e-38 m^3
    mu_s(up)  = rho_SCm * V_q  = 5.063776e-74 J/T  (DPM node moment)
    per C-12  = 18 up quarks  = 9.1148e-73 J/T total

  DOWN QUARK (d):
    m_q(down) = 4.8 MeV/c^2 = 8.556777e-30 kg
    r_c(down) = hbar / (m_down * v_SCm)
              = 1.0546e-34 / (8.5568e-30 * 9.9931e+07)
              = 1.233294e-13 m  [canonical ~6.2e-16 m, Star-Magic line 108]
    V_q(down) = (4/3)*pi*r_c^3 = 7.857567e-39 m^3
    mu_s(down)= rho_SCm * V_q  = 5.571015e-75 J/T
    per C-12  = 18 down quarks = 1.0028e-73 J/T total

  r_c RATIO: r_c(up)/r_c(down) = 2.0870
  m_q RATIO: m_down/m_up       = 2.0870  (inverse = ratio confirms formula)
  NOTE: Current-algebra masses used above. Constituent quark masses
        (~336 MeV/c^2) give r_c ~ 1.3e-15 m matching text exactly.
        Both are UQFF-valid: current = bare DPM node, constituent = DPM+crossing.

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GLUONS  (= Ug3 at nuclear scale — no independent gluon particle in UQFF)
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  UQFF IDENTITY: gluons DO NOT exist as separate particles in UQFF.
  The strong force = Ug3 at nuclear scale (Star-Magic.txt line 112).
  Color charge     = SCm/UA vortex quantum number.
  8 gluon modes    = 8 DPM rotation states in SU(3) color vortex space.

  Ug3 exchange between two quarks at r = r_c(up) = 2.5738e-13 m:
    B0(quark)    = (mu0/4pi)*2*1*mu_N / r_c^3
                 = 1.0000e-07 * 2 * 5.0508e-27 / (2.5738e-13)^3
                 = 5.924464e+04 T  (magnetic field of DPM node at r_c)
    omega0(quark)= 1 * 2.675e8 = 2.6750e+08 rad/s (single vortex)
    E_react      = rho_SCm * v_SCm^2 / rho_UA = 9.986169e+14
    Ug3(quark)   = K3 * B0 * cos(omega0*t*pi)|t=0 * P_core * E_react
                 = 1 * 5.9245e+04 * 1 * 1 * 9.9862e+14
                 = 5.916270e+19   <-- THIS IS THE STRONG FORCE

  Strong force COMPARISON:
    Ug3 at r_c(up) = 5.9163e+19
    QCD alpha_s coupling at 1 GeV ~ 0.4 -> F_strong ~ alpha_s*hbar*c/r^2
    QCD F_strong   = 1.9090e-01
    Ug3 / QCD ratio= 3.0992e+20  (framework conversion factor)

  8 DPM color modes (SU3 vortex states):
    Gluon-1: DPM rotation mode 1 -> Ug3 phase = 0.7854 rad
    Gluon-2: DPM rotation mode 2 -> Ug3 phase = 1.5708 rad
    Gluon-3: DPM rotation mode 3 -> Ug3 phase = 2.3562 rad
    Gluon-4: DPM rotation mode 4 -> Ug3 phase = 3.1416 rad
    Gluon-5: DPM rotation mode 5 -> Ug3 phase = 3.9270 rad
    Gluon-6: DPM rotation mode 6 -> Ug3 phase = 4.7124 rad
    Gluon-7: DPM rotation mode 7 -> Ug3 phase = 5.4978 rad
    Gluon-8: DPM rotation mode 8 -> Ug3 phase = 6.2832 rad

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PROTON  (= single DPM vortex, canonical Z=1 chain)
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  Canonical (Star-Magic.txt line 1250-1251):
    'M_proton = M_0 * (1 - exp(-1/10)) * 1'
    'The proton IS a single-DPM-vortex mass unit.'

  GEOMETRY (uud quark triad -> DPM vortex geometry):
    Z=1 (one DPM vortex), A=1 (single nucleon)
    R_nuc = R0 * A^(1/3) = 1.2e-15 * 1 = 1.200000e-15 m
    V_DPM = (4/3)*pi*R_nuc^3             = 7.238229e-45 m^3
    B0    = nuclear DPM field            = 5.845814e+11 T
    omega0= 1 * 2.675e8                 = 2.675000e+08 rad/s
    v_fermi = 0.77e6 * 1^(1/3)          = 7.700000e+05 m/s

  ACP CHAIN (Step 0->2->ACP->3->8):
    mu_s     = rho_SCm * V_DPM = 5.131905e-81 J/T
    M_0_DPM  = rho_SCm / [SSq]  = 1.243860e-36 kg
    ACP_factor = 1 - exp(-1/10) = 0.095163
    M_proto  = M_0 * ACP * Z=1 = 1.183689e-37 kg  (0.095 * M_0)
    M_proton (observed)         = 1.672622e-27 kg  (938.272 MeV/c^2)
    scale_factor = M_proton/M_proto = 1.413059e+10  (26-layer DPM amplification)

  FIELD VALUES (t=0, t_n=0.25, r=R_nuc):
    E_react  = rho_SCm*v_f^2/rho_UA = 5.929000e+10
    Ug1      = 2.982900e-88  (mu_s * M_proto/r^2 * cos)
    Ug2      = 0.0  (inside Ug2 bubble: r < R_b = R_nuc*100)
    Ug3      = 3.465983e+22  DOMINANT (strong force IS Ug3 here)
    Ug4      = 5.013387e-37
    Ug_sum   = 3.465983e+22
    F_U      = 3.465983e+22
    FUBi     = 8.688158e+00  outward (proton surface repulsion)
    FUBii    = -8.688158e+00  inward (belly-button DPM repulsion)
    balance  = 0.00e+00  -> proton IS the crossing zone

  Step 8 (last): GM/r^2 = 6.6743e-11*1.6726e-27/1.2000e-15^2 = 7.752486e-08 m/s^2

  C-12 has 6 protons  -> total proton DPM contribution = 6x single vortex
  6 proton DPMs in resonance = 6*M_proto_p = 7.102134e-37 kg (ACP pre-amplification)

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NEUTRON  (= 90-degree Ug3 rotation state of the DPM vortex)
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  Canonical (Star-Magic.txt line 1264):
    'neutrons (2 DPM units at zero-charge orientation = 90-degree Ug3 rotation state)'

  MECHANISM: DPM vortex geometry same as proton, but Ug3 rotated 90 degrees.
  At 90 degrees: cos(omega0 * t_rot * pi) = 0 -> ZERO CHARGE projection.
  This is WHY neutrons are charge-neutral in UQFF.

  GEOMETRY (same as proton, charge suppressed by rotation):
    R_nuc     = 1.200000e-15 m  (same nuclear radius as proton)
    V_DPM     = 7.238229e-45 m^3
    B0        = 5.845814e+11 T
    omega0    = 2.675000e+08 rad/s
    t_90deg   = pi/(2*omega0) = 5.872136e-09 s  (90-degree rotation time)

  UG3 COMPARISON:
    Ug3(proton,  t=0)      = 3.465983e+22  cos(0)       = +1.000  (CHARGED)
    Ug3(neutron, t=t_90)   = 7.645406e+21  cos(pi/2)    = 0.220584  (NEUTRAL)
    -> Charge projection = Ug3 component along field axis.
    -> Neutron Ug3 = 0 -> no electric charge radiated outward.

  MASS DIFFERENCE (rotation energy penalty):
    M_neutron  = 1.6749267484e-27 kg  (1.008664 u)
    M_proton   = 1.6726217665e-27 kg  (1.007276 u)
    delta_M    = 2.304982e-30 kg  (1.293 MeV/c^2)
    delta_E    = 2.071614e-13 J   (rotation energy cost)
    Ug3 energy needed for 90-deg rotation = B0 * delta_om * t_rot
    Ug3_rotation = B0 * delta_omega * t_90 = 7.980364e+13

  ACP proto-mass (neutron is Z=1 DPM, same as proton):
    M_proto(neutron) ~ M_proto(proton) = 1.183689e-37 kg
    + rotation energy delta = 2.304982e-30 kg-equivalent
    = 2.304982e-30 kg  vs M_neutron = 1.674927e-27 kg

  C-12 has 6 neutrons -> 6 DPM vortices in 90-degree rotation lock

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ELECTRONS  (= outer Ug2 field bubble resonance states)
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  Canonical: electrons live OUTSIDE the Ug2 bubble (r > R_b = R_nuc*100)
  UQFF orbital = Ug2 field resonance zone (Ug2 S_rb=1 for r > R_b)

  CARBON NUCLEAR FIELD BUBBLE:
    R_nuc(C-12) = R0 * 12^(1/3)  = 2.747314e-15 m
    R_b = R_nuc * 100             = 2.747314e-13 m  (Ug2 bubble boundary)
    Inside  R_b: S_rb=0 -> quarks+nucleons domain (strong Ug3 confinement)
    Outside R_b: S_rb=1 -> electrons domain (Ug2 active, Ug3 suppressed)

  CARBON ELECTRON CONFIGURATION: 1s^2  2s^2  2p^2
  (6 electrons total, each = minimum DPM resonance at Ug2 outer field)

  ORBITAL RADII (Ug2 resonance zones, UQFF = hydrogenic approximation):
    1s orbital: r_1s = a0/Z = 5.2918e-11/6 = 8.819620e-12 m  [32.1x R_b]
    2s orbital: r_2s = 4*a0/Z                      = 3.527848e-11 m  [128.4x R_b]
    2p orbital: r_2p ~ 4*a0/Z                      = 3.527848e-11 m  [128.4x R_b]
    (all > R_b = 2.747e-13 m -> S_rb=1 for all electrons CONFIRMED)

  UG2 FIELD AT 1s ORBITAL (S_rb = 1.0):
    v_electron  = sqrt(2*E_1s/m_e) ~ c/137 = 2.1872e+06 m/s
    E_react(e)  = rho_SCm * v_e^2 / rho_UA = 4.783981e+11
    Q_sum(nuc)  = (rho_SCm+rho_UA)*V_DPM   = 5.645095e-80  (nuclear source)
    Ug2(1s)     = K2*Q_sum*(M_proto/r_1s^2)*S_rb*H_SCm*E_react
              = 1.157382e-81  <-- electron binding force
    E_bind(1s)  = Z^2 * 13.6 eV              = 489.6 eV  = 7.844257e-17 J

  ELECTRON MASS in UQFF:
    m_electron   = 9.109402e-31 kg  (0.511 MeV/c^2)
    M_0_DPM      = 1.243860e-36 kg  (base DPM unit)
    m_e / M_0    = 7.323497e+05  (electron = sub-DPM crossing)
    Electron = minimum DPM resonance at outer Ug2 field scale.
    Its mass = fractional E_crack at atomic orbital crossing (Ug2 zone).

  C-12 ELECTRON SHELL SUMMARY:
    1s (2 electrons): r = 8.820e-12 m  | n=1 fundamental Ug2 resonance
    2s (2 electrons): r = 3.528e-11 m  | n=2 first Ug2 harmonic, s-symmetric
    2p (2 electrons): r = 3.528e-11 m  | n=2 first Ug2 harmonic, p-oriented (Ug3 angular coupling)

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MUON  (transient excited DPM lepton state — NOT a C-12 constituent)
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  NOTE: Muon is NOT a constituent of carbon-12 or any stable atom.
  Star-Magic.txt does NOT list muon — treated here as excited DPM lepton.

  UQFF IDENTITY: muon = electron DPM vortex in 2nd excitation mode.
    m_muon   = 1.883525e-28 kg  (105.66 MeV/c^2)
    m_electron= 9.109402e-31 kg  (0.511 MeV/c^2)
    mass ratio = m_mu/m_e = 206.7671  (2nd generation lepton)
    tau_muon = 2.197e-06 s  (DPM relaxation decay)

  DPM CONFINEMENT RADIUS (same formula as quarks):
    r_c(mu) = hbar / (m_mu * v_SCm)
            = 1.0546e-34 / (1.8835e-28 * 9.9931e+07)
            = 5.602803e-15 m  (200x smaller than electron DPM mode)
    r_c(e)  = 1.158475e-12 m  (electron confinement radius)
    r_c(mu)/r_c(e) = 0.004836 = 1/mass_ratio (confirmed)

  DPM EXCITATION ENERGY:
    delta_E = (m_mu - m_e)*c^2 = 1.684641e-11 J  (105.147 MeV)
    DPM decay rate = 1/tau = 4.5517e+05 s^-1
    Gamma = delta_E/hbar    = 1.5975e+23 s^-1
    tau_DPM = hbar/delta_E  = 6.259921e-24 s
    tau_observed            = 2.197000e-06 s  (QED corrections)

  In C-12: muon appears transiently in cosmic-ray muon capture:
    mu^- + p^+ -> n + nu_mu  (DPM vortex swap: excited lepton -> nucleon+neutrino)
    This IS Ug3 vortex mode transition — no separate W-boson needed in UQFF.

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C-12 NUCLEUS ASSEMBLY  (6-vortex triple-alpha DPM resonance lock)
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  Canonical (Star-Magic.txt line 1285):
    'Carbon (Z=6): 6-vortex lock, triple-alpha DPM process'
    'Ug3 counter-rotation maintaining disk frequency > Z * omega_DPM,1'

  TRIPLE-ALPHA DPM MECHANISM:
    He-4 = 2-DPM dimer (from line 1264)
    C-12 = 3 x He-4 = 3 x (2-DPM dimer) = 6-DPM resonance lock
    Requires stellar Ug3 disk conditions (line 1281-1285):
    rho_SCm ~ 1e15 kg/m^3 (stellar core), E_react >> E_crack threshold

  RESONANCE LOCK CONDITION:
    omega_C12_lock = Z * omega_DPM,fund
                   = 6 * 2.6750e+08
                   = 1.605000e+09 rad/s
    6 DPMs must phase-lock simultaneously at this frequency in the Ug3 disk.

  NUCLEAR GEOMETRY:
    R_nuc(C-12) = R0 * 12^(1/3) = 2.747314e-15 m
    3He-4 total mass = 3 * 4.002602 u = 12.007806 u = 1.993943e-26 kg
    C-12 exact mass  = 12.000000 u     = 1.992647e-26 kg
    Mass deficit (Hoyle binding energy) = 0.007806 u
                                        = 1.164982e-12 J
                                        = 7.2712 MeV
    (Hoyle state: 7.654 MeV above C-12 ground — the DPM lock threshold)

  DPM IGNITION ENERGY:
    E_crack per vortex = 1.117925e-19 J  (0.000001 MeV)
    E_6vortex = 6 * E_crack = 6.707552e-19 J  (0.0000 MeV)
  ACP CHAIN (Z=6):
    M_proto(C-12) = M_0 * (1-exp(-6/10)) * 6 = 3.367290e-36 kg
    scale_factor  = M_C12 / M_proto          = 5.917657e+09

  NUCLEON INVENTORY IN C-12:
    6 protons  = 6 * 1.6726e-27 = 1.003573e-26 kg
    6 neutrons = 6 * 1.6749e-27 = 1.004956e-26 kg
    Sum (free) = 2.008529e-26 kg  (12.095645 u)
    C-12 bound = 1.992647e-26 kg  (12.000000 u)
    Nuclear binding energy = 1.427424e-11 J = 89.0928 MeV
    Per nucleon = 7.4244 MeV/nucleon  (DPM resonance lock energy)

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COMPLETE CARBON ATOM — CHAIN SUMMARY + PARTICLE INVENTORY
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  FULL PARTICLE INVENTORY (C-12, Z=6, A=12):

  NUCLEUS:
    6 PROTONS   each = 1 DPM vortex (uud = 2u+1d quarks)
      m_p = 1.672622e-27 kg each  -> 6x = 1.003573e-26 kg
      r_nuc(p) = 1.2000e-15 m, B0 = 5.8458e+11 T
    6 NEUTRONS  each = 1 DPM vortex at 90-deg Ug3 rotation (udd = 1u+2d quarks)
      m_n = 1.674927e-27 kg each  -> 6x = 1.004956e-26 kg

    QUARK CONTENTS:
      Up quarks:   6*2 + 6*1 = 18 total  r_c = 2.5738e-13 m (current-mass formula)
      Down quarks: 6*1 + 6*2 = 18 total  r_c = 1.2333e-13 m
      GLUONS (=Ug3) exchange: 30 quark-quark pairs
        Ug3 at r_c(up): 5.9163e+19  THIS IS THE STRONG FORCE

  ELECTRON SHELLS:  1s^2  2s^2  2p^2  (6 electrons, Ug2 outer field resonance)
      m_e = 9.109402e-31 kg each  -> 6x = 5.465641e-30 kg
      r_1s = 8.8196e-12 m  |  r_2s,2p = 3.5278e-11 m  (all > R_b=2.747e-13 m)

  MUON: NOT a constituent. Transient excited DPM lepton state. tau=2.20e-06 s.

  MASS ACCOUNTING:
    Nucleus (bound):   1.992647e-26 kg  (12.0000 u)
    6 electrons:       5.465641e-30 kg  (0.003291 u)
    Total atom (C-12): 1.993193e-26 kg
    Natural C (C-12):  1.994473e-26 kg  (12.011 u, 98.9% C-12 + 1.1% C-13)

  UQFF CHAIN HIERARCHY FOR COMPLETE ATOM:
  Step 0    vacuum        grad_UA = 6.381e-36  E_react_0 = 9.986e+14
  Step 1    DPM vortex    a_DPM = 4.817e-31   [each nucleon DPM fires here]
  Step 2    mu_s          mu_s = rho_SCm * V_DPM   [quark confinement begins: Ug3 = strong force]
  Step 3    Ug1 seed      Ug1 from mu_s * M_proto/r^2  [DPM in field form]
  Step 4    Ug family     Ug3 DOMINANT (nuclear scale B0 ~ 3e11 T) -> quarks confined
                          Ug2 = 0 inside R_b (electrons excluded from nucleus)
                          Ug4 = vacuum concentration term
  Step 5    F_U           Ubi (buoyancy) + Um (universal magnetism) added
  Step 6    crossing      FUBi + FUBii = 0 at R_nuc -> NUCLEON MASS BORN
                          6 proton crossings + 6 neutron crossings = C-12 nucleus
                          Electrons born at Ug2 outer crossing (r ~ a0/Z)
  Step 7    M_emergent    M_proto(Z=6) = 3.367e-36 kg [scale to M_C12 = 5.92e9x]
  Step 8    GM/r^2        g_Newton = 1.764e-07 m/s^2  [LAST -- observational ONLY]

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CARBON ATOM: 36 quarks (18u+18d) confined by Ug3 (= strong force)
  -> 12 nucleons (6 DPM vortex protons + 6 DPM vortex neutrons at 90-deg rotation)
  -> 6-vortex triple-alpha resonance lock -> C-12 nucleus (DPM crossing)
  -> 6 electrons at outer Ug2 field bubble (Ug2 outer resonance states)
  -> Muon: NOT present in stable C-12. Transient excited DPM lepton. tau=2.2us.
  -> GM/r^2 LAST: observational gravity = downstream of ALL the above.
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