[
  {
    "id": "EQ01",
    "name": "Lattice local integration",
    "expression": "phi_local = tanh(energy)",
    "sources": [
      "S10",
      "S11"
    ],
    "status": "REPORTED_IMPLEMENTATION_DEFINITION"
  },
  {
    "id": "EQ02",
    "name": "Lattice global integration",
    "expression": "phi_global = tanh(sum(all strand states) / 256)",
    "sources": [
      "S10",
      "S11"
    ],
    "status": "REPORTED_IMPLEMENTATION_DEFINITION",
    "note": "Explicitly not IIT Phi;256=16 strands x16 dimensions."
  },
  {
    "id": "EQ03",
    "name": "Golden-ratio normalization",
    "expression": "b = 1 / (1 + ||Psi||^2 / phi), phi=(1+sqrt(5))/2",
    "sources": [
      "S10",
      "S11"
    ],
    "status": "REPORTED_IMPLEMENTATION_DEFINITION"
  },
  {
    "id": "EQ04",
    "name": "DNA memory learning",
    "expression": "theta_k_new = (1-alpha)*theta_k_old + alpha*w*psi_k(h(item))*Phi(importance)",
    "sources": [
      "S11"
    ],
    "status": "REPORTED_IMPLEMENTATION_DEFINITION"
  },
  {
    "id": "EQ05",
    "name": "DNA query",
    "expression": "K(query) = sum_k theta_k * psi_k(h(query))",
    "sources": [
      "S11"
    ],
    "status": "REPORTED_IMPLEMENTATION_DEFINITION"
  },
  {
    "id": "EQ06",
    "name": "Unity/importance weighting",
    "expression": "Phi(x) = 1/(1+abs(x-1))",
    "sources": [
      "S11"
    ],
    "status": "REPORTED_IMPLEMENTATION_DEFINITION"
  },
  {
    "id": "EQ07",
    "name": "Agent vector coherence",
    "expression": "C_ij = dot(theta_i,theta_j)/(norm(theta_i)*norm(theta_j))",
    "sources": [
      "S11"
    ],
    "status": "REPORTED_IMPLEMENTATION_DEFINITION",
    "note": "Zero-vector handling must come from original implementation."
  },
  {
    "id": "EQ08",
    "name": "Gate5000 transition",
    "expression": "state[i] = ((state[i] XOR input[i]) XOR flip) AND 1",
    "sources": [
      "S11"
    ],
    "status": "REPORTED_IMPLEMENTATION_DEFINITION"
  },
  {
    "id": "EQ09",
    "name": "Federation cross-talk",
    "expression": "dS_i/dt = -0.1*S_i + sum_{j != i} w_ij*Phi(C_ij)*tanh(S_j)",
    "sources": [
      "S11"
    ],
    "status": "REPORTED_IMPLEMENTATION_DEFINITION"
  },
  {
    "id": "EQ10",
    "name": "Federation discrete update",
    "expression": "S_i(t+1) = clamp01(S_i(t) + dt*dS_i/dt)",
    "sources": [
      "S11"
    ],
    "status": "REPORTED_IMPLEMENTATION_DEFINITION"
  },
  {
    "id": "EQ11",
    "name": "Average pairwise federation coherence",
    "expression": "C_fed = 2/[n*(n-1)] * sum_{i<j} C_ij",
    "sources": [
      "S11"
    ],
    "status": "REPORTED_IMPLEMENTATION_DEFINITION"
  },
  {
    "id": "EQ12",
    "name": "Unified binding-field score",
    "expression": "C = 1 - exp(-0.01*sum_{i=0}^{373} abs(binding_field[i]))",
    "sources": [
      "S11"
    ],
    "status": "REPORTED_IMPLEMENTATION_DEFINITION"
  },
  {
    "id": "EQ13",
    "name": "Historical Q expression",
    "expression": "Q = Psi * integral[C(t)*Phi(G(t))*||grad H(t)||/(1+||grad H(t)||)] dt",
    "sources": [
      "C01"
    ],
    "status": "RETAINED_CONTEXT_ONLY",
    "note": "Example from retained context, not verified final master equation."
  }
]