{
  "vertices": [
    "L0",
    "L1",
    "L2",
    "L2'",
    "L3",
    "L4"
  ],
  "edges": {
    "Psi_1": {
      "from": "L1",
      "to": "L0",
      "theorem": "LR C1.9 (LZ16 regulator)",
      "labels": {
        "actual map": true,
        "same map under theorem": null,
        "frame change": false,
        "lattice change": false,
        "partner factor": true,
        "exact comparison": true
      },
      "divisors_attached": [
        "X^n",
        "L_E",
        "L_p(Ad g)"
      ],
      "note": "partner enters through eta_g and L_p^g; all partner factors are P-slots"
    },
    "Psi_2": {
      "from": "L1",
      "to": "L2",
      "theorem": "LR C1.6-C1.8",
      "labels": {
        "actual map": true,
        "same map under theorem": null,
        "frame change": false,
        "lattice change": false,
        "partner factor": false,
        "exact comparison": true
      },
      "divisors_attached": [
        "X^n"
      ]
    },
    "Psi_3": {
      "from": "L2",
      "to": "L3",
      "theorem": "LR C1.13 (Prop C1.1 lift)",
      "labels": {
        "actual map": true,
        "same map under theorem": null,
        "frame change": false,
        "lattice change": false,
        "partner factor": true,
        "exact comparison": true
      },
      "divisors_attached": [
        "log^{[r+1]}",
        "L_p(Ad g)"
      ]
    },
    "Psi_4": {
      "from": "L3",
      "to": "L4",
      "theorem": "Kato's reciprocity (through LR)",
      "labels": {
        "actual map": true,
        "same map under theorem": null,
        "frame change": true,
        "lattice change": false,
        "partner factor": false,
        "exact comparison": true
      },
      "note": "the period frame gamma^+- enters and cancels (RUN-099); eta_pdR = 1"
    },
    "A'": {
      "from": "L2",
      "to": "L4",
      "theorem": "the regulator on the leading term (C1.9 with C1.7/C1.8)",
      "labels": {
        "actual map": true,
        "same map under theorem": true,
        "frame change": false,
        "lattice change": false,
        "partner factor": true,
        "exact comparison": true
      },
      "same_as": "Psi_4 o Psi_3",
      "witness": "C1.13's proof + Eq. 11 (RUN-100)"
    },
    "id": {
      "from": "L2",
      "to": "L2'",
      "theorem": "PC-001 section 1 (a definition naming LR's object)",
      "labels": {
        "actual map": false,
        "same map under theorem": true,
        "frame change": false,
        "lattice change": false,
        "partner factor": false,
        "exact comparison": true
      },
      "same_as": "identity of L2",
      "witness": "dictionary identification: PC-001 section 1 names LR's object; slots matched RUN-094/095"
    },
    "Psi_3^PC": {
      "from": "L2'",
      "to": "L3",
      "theorem": "PC-001 (1) = C1.13 in six slots",
      "labels": {
        "actual map": true,
        "same map under theorem": true,
        "frame change": false,
        "lattice change": false,
        "partner factor": true,
        "exact comparison": true
      },
      "same_as": "Psi_3 o id^{-1}",
      "witness": "the six-slot dictionary (C/q_f -> C_pi; C_d = S_5(0) = 26 numerically; log <-> j; L_p(g x tau)/L_p(Ad g) <-> lambda_i/D_i; kappa <-> z_i), RUN-094/095"
    }
  },
  "loops": {
    "b_f+ <-> omega_f": {
      "at": "L0",
      "tag": "G",
      "value": "u (RUN-096 gauge law)"
    },
    "X uniformiser": {
      "at": "L0",
      "tag": "G",
      "value": "inside c_lead / q_f (RUN-096/097)"
    },
    "Kummer <-> ES realisation of Theta_aux": {
      "at": "L0",
      "tag": "G",
      "value": "C4 PASS by theorem (A2.1(3), A6.3(i)); a realisation of the same element, not a second vertex"
    },
    "period frame Omega^+- / lambda^+-": {
      "at": "L4",
      "tag": "G",
      "value": "cancels along the route (RUN-099); lambda measured 1, 6"
    },
    "Gauss(chi_8)": {
      "at": "L4",
      "tag": "G",
      "value": "G(chi_8)^2 = 8"
    },
    "gamma_Kato <-> gamma_tree": {
      "at": "L3/L4",
      "tag": "L",
      "value": "q (RUN-099, bucket q_D, v_11 UNMEASURED)"
    },
    "lattice indices": {
      "at": "L4",
      "tag": "L",
      "value": "2, 2 / 2, 1 (RUN-080/096)"
    },
    "partner factors": {
      "at": "L3/L4",
      "tag": "P",
      "value": "E_adj_i, Pi_i, lambda_i(0), kappa_E, ell_0 (net 0 in delta)"
    }
  },
  "E_labels": {
    "eta_pdR": {
      "on": "Psi_4",
      "status": "resolved",
      "value": 1,
      "by": "RUN-099"
    },
    "kappa_det": {
      "on": "the composite",
      "status": "resolved",
      "value": 1,
      "by": "RUN-100"
    },
    "id(LR class, PC-001 projected class)": {
      "on": "id",
      "status": "resolved",
      "value": 1,
      "by": "this round: dictionary identification: PC-001 section 1 names LR's object; slots matched RUN-094/095"
    },
    "C_pi": {
      "on": "Psi_1 / Psi_2 (an edge label, invariant under both frames)",
      "status": "a label, not a cycle",
      "value": "C = c*_f(r), unmeasured numerically",
      "by": "RUN-096"
    }
  },
  "merges": {
    "A' = Psi_4 o Psi_3": "C1.13's proof + Eq. 11 (RUN-100)",
    "Psi_3^PC o id = Psi_3": "the six-slot dictionary (RUN-094/095)"
  },
  "divisors": {
    "L_E": "Psi_1 (RUN-098)",
    "X^n": "Psi_2 (the named extraction)",
    "log^{[r+1]}": "Psi_3 (C1.8)"
  },
  "every_edge_answers_the_six_questions": true,
  "every_merge_has_a_witness": true,
  "agrees": true
}