{
  "candidates": {
    "A": {
      "path": "C_aux <-Psi_1- BF family line -Psi_2-> leading line -Psi_3 (C1.13)-> Kato line -Psi_4 (Kato)-> C_arith",
      "theorems": [
        "C1.9 / LZ16 regulator",
        "C1.6-C1.8",
        "C1.13 (Prop C1.1 lift)",
        "Kato reciprocity (through LR)"
      ],
      "status": "the route"
    },
    "A'": {
      "path": "leading line -regulator (C1.9 with C1.7/C1.8)-> C_arith, skipping C1.13 and Kato",
      "status": "the same map as Psi_4 Psi_3: C1.13 is PROVED by equating the two regulator images (Eq. 11 + Kato) and lifting by Prop C1.1",
      "induces_same_H1_map_as_A": true
    },
    "B": {
      "path": "a direct Eichler-Shimura / de Rham comparison C_aux -> C_arith not through the BF class",
      "status": "not a route: no theorem in the source connects an f-side crystalline line to a g-side L_p line except through the one object that sees both, the Rankin-Selberg class"
    },
    "C": {
      "path": "Kato's class -> the tree's modular-symbol series (src83) as a second arrow into C_arith",
      "status": "not a route: a change of GENERATOR of the target line by q = [gamma_Kato : gamma_tree] (RUN-099: tag L, bucket q_D); stays out of C7"
    }
  },
  "actual_independent_routes": 1,
  "A_and_A_prime_induce_the_same_H1_map": true,
  "the_agreement_is": "LR Eq. 11: L_p^g = L_p(g x psi) L_p(g x tau) / L_p(Ad g) - a theorem, checked on exact instances",
  "a_declared_same_candidate_that_differs": false,
  "C113_counted_once": "C1.13 is the conclusion of Route A's own step, never a second route",
  "agrees": true
}