{
  "round": "RUN-102",
  "gate": "src104",
  "C10": "PASS / canonical",
  "state": "T0",
  "canonical_reduced_comparison": "Psi_red = Psi_4 Psi_3 Psi_2 Psi_1^{-1} in the reduced category",
  "preferred_flat_section": "s_can = the class of Psi_red",
  "rho": "1",
  "why": "all noncanonical choices live in G/L/P and were quotiented; eta_pdR = 1; kappa_det = 1; the residual graph is connected and flat (C9); the reduced comparison Psi_red is a theoremically natural transformation (C1.9 + C1.10, C1.6-C1.8, C1.13 + Prop C1.1, Kato), natural in the partner",
  "what_a_PASS_means": "PC-001 normalization certificate C1-C10 CLOSED as architecture; BSD OPEN; Round 030's post-normalization DAG A-G is next",
  "choice_table": {
    "b_f+": {
      "depends_on": "the auxiliary framing",
      "tag": "G",
      "quotiented_how": "replaced by C1.10's unique omega_f (RUN-096 gauge law; RUN-097 one free auxiliary frame)",
      "survives_in_Psi_red": false
    },
    "X uniformiser": {
      "depends_on": "the weight coordinate on V_1",
      "tag": "G",
      "quotiented_how": "inside c_lead / q_f; the leading coefficient at X = 0 is canonical whatever n (RUN-097/098)",
      "survives_in_Psi_red": false
    },
    "Gauss convention": {
      "depends_on": "Omega_F^- = Omega_E^-/G(chi_8), Attack 09",
      "tag": "G",
      "quotiented_how": "a convention slot, G(chi_8)^2 = 8 (RUN-090/097)",
      "survives_in_Psi_red": false
    },
    "Omega^+- / Betti basis gamma_g^+-": {
      "depends_on": "B2.1's chosen bases",
      "tag": "G",
      "quotiented_how": "cancels along Psi_4: kappa and L_p scale together (RUN-099)",
      "survives_in_Psi_red": false
    },
    "q = [gamma_Kato : gamma_tree]": {
      "depends_on": "two Z-structures on one Q-line",
      "tag": "L",
      "quotiented_how": "bucket q_D; a generator change, not a comparison scalar (RUN-099 + erratum)",
      "survives_in_Psi_red": false
    },
    "lattice indices": {
      "depends_on": "the tree's line inside the Manin lattice",
      "tag": "L",
      "quotiented_how": "lengths, C8 (RUN-096)",
      "survives_in_Psi_red": false
    },
    "partner arithmetic": {
      "depends_on": "E_adj_i, Pi_i, lambda_i(0), kappa_E, ell_0",
      "tag": "P",
      "quotiented_how": "removed first, Round 030 (16); net 0 in delta (RUN-097)",
      "survives_in_Psi_red": false
    },
    "C_d": {
      "depends_on": "the auxiliary d, (d, 6S) = 1",
      "tag": "cancels",
      "quotiented_how": "C_d^{-1} (x) kappa_d is d-independent; C_d = 26 cancels between Psi_1 and Psi_3 (RUN-098)",
      "survives_in_Psi_red": false
    },
    "L_p factors": {
      "depends_on": "L_p(g x psi), L_p(g x tau), L_p(Ad g)",
      "tag": "P / cancel",
      "quotiented_how": "Eq. 11 is the cancellation (RUN-098)",
      "survives_in_Psi_red": false
    },
    "eta_pdR": {
      "depends_on": "the period-de Rham pairing",
      "tag": "E",
      "quotiented_how": "= 1, one comparison pairing (RUN-099)",
      "survives_in_Psi_red": false
    },
    "kappa_det": {
      "depends_on": "the determinant functor",
      "tag": "E",
      "quotiented_how": "= 1, one route, functoriality (RUN-100)",
      "survives_in_Psi_red": false
    },
    "PC-001 / LR dictionary identity": {
      "depends_on": "PC-001 section 1",
      "tag": "E",
      "quotiented_how": "= 1, a definition (RUN-101)",
      "survives_in_Psi_red": false
    },
    "C_pi = c*_f(r)": {
      "depends_on": "f alone (C1.9, C1.11)",
      "tag": "E, exact, invariant",
      "quotiented_how": "net exponent 0: cancels against Psi_1's c_f once X^n is counted once (RUN-097/098)",
      "survives_in_Psi_red": false
    },
    "log^{[r+1]}, X^n": {
      "depends_on": "the two named extractions",
      "tag": "extraction",
      "quotiented_how": "canonical operations: C1.8's divisibility; the leading coefficient (RUN-098)",
      "survives_in_Psi_red": false
    },
    "n (the jet order)": {
      "depends_on": "C1.10",
      "tag": "jet order",
      "quotiented_how": "which coefficient is leading is decided by the class, not chosen (RUN-098: not a delta-factor)",
      "survives_in_Psi_red": false
    }
  },
  "surviving_arbitrary_choices": [],
  "arrows": {
    "Psi_1": {
      "map_canonical": "after choosing b_f+ (G), which C1.10's unique omega_f replaces",
      "up_to_unit_only": false,
      "choice_tagged": "G",
      "reduced": "canonical (C1.9 + C1.10)"
    },
    "Psi_2": {
      "map_canonical": "after choosing the uniformiser X (G); Theorem A6.1 forces the lattice exponent 1",
      "up_to_unit_only": false,
      "choice_tagged": "G",
      "reduced": "canonical: the leading coefficient at X = 0"
    },
    "Psi_3": {
      "map_canonical": "yes: a class equality (C1.13) lifted by Prop C1.1's injectivity; its scalar C = c*_f(r) is determined by f",
      "up_to_unit_only": false,
      "choice_tagged": "none (C_pi is E, exact, invariant; cancels)",
      "reduced": "canonical"
    },
    "Psi_4": {
      "map_canonical": "after fixing the Betti class gamma (frame): Kato's reciprocity is exact for z_gamma <-> L_p^(gamma); the frame cancels (RUN-099)",
      "up_to_unit_only": false,
      "choice_tagged": "G (frame), L (q)",
      "reduced": "canonical"
    }
  },
  "naturality": {
    "construction": {
      "389.a1": "LR C1.9-C1.13 + Kato with f = E_2(1, chi_8)'s critical refinement",
      "19.a1": "the same theorems (LR C1.9-C1.13, Kato) with the same auxiliary family"
    },
    "hypotheses_instantiated": {
      "389.a1": {
        "noble (B1.1)": true,
        "ordinary at 11": true,
        "residually irreducible at 11": true,
        "newform, weight 2, trivial nebentypus": true,
        "unit root mod 11": 7
      },
      "19.a1": {
        "noble (B1.1)": true,
        "ordinary at 11": true,
        "residually irreducible at 11": true,
        "newform, weight 2, trivial nebentypus": true,
        "unit root mod 11": 3
      }
    },
    "same_natural_construction": true,
    "functoriality": "the theorems are stated for any partner g under B1.1 / section B2 with the one auxiliary family: naturality in g",
    "agrees": true
  },
  "transport": {
    "paths": [
      "Psi_4 Psi_3 Psi_2 Psi_1^{-1}",
      "A' Psi_2 Psi_1^{-1}",
      "Psi_4 Psi_3^PC id Psi_2 Psi_1^{-1}"
    ],
    "path_independent": true,
    "C9_used": {
      "components": 1,
      "rep_I_trivial": true,
      "rep_II_trivial": true
    }
  },
  "anchor_rules": {
    "track_B_taken": false,
    "why_not": "Track A succeeded: no surviving choice, Psi_red canonical",
    "admissible_sources": [
      "19.a1 LR/Kato exact class equality, residual after G/L/P and eta_pdR = kappa_det = 1",
      "an exact rank-zero reciprocity theorem equating the two sources on the calibrator"
    ],
    "inadmissible_sources": [
      "an arbitrary nonzero vector",
      "q_fin = 1",
      "a numerical BSD-shaped identity",
      "the target's result read back onto the calibrator"
    ],
    "anchor_need_not_be_1": true,
    "agrees": true
  },
  "controls": {
    "A_canonical": {
      "input": "a natural isomorphism F => G with no residual choice",
      "state": "T0",
      "rho": "1",
      "accepted": true
    },
    "B_anchored": {
      "input": "a connected flat line system, Mon = 1, no preferred section, an exact base vector s_0 = 3 e",
      "state": "T1",
      "rho": "3",
      "accepted": true
    },
    "C_flat_unanchored": {
      "input": "the same flat system with no anchor",
      "state": "T1",
      "verdict": "UNMEASURED",
      "pass_refused": true
    },
    "agrees": true
  },
  "external_obligations_left_open": [
    "BF-COORD",
    "Pi_E / Pi_0",
    "c_ES / Kum",
    "v_11(q)",
    "n"
  ],
  "not_claimed": [
    "BSD",
    "any of DAG A-G (actual BF/Kato classes, fundamental-line identification, regulator bridge, reciprocity + nonannihilation, p-adic and complex leading lines, finite certificates)",
    "the numerical value of C_pi",
    "v_11(q)",
    "n",
    "Pi_i"
  ],
  "claim_labels": {
    "COMPUTED_HERE": [
      "path independence of the transported section on exact instances",
      "the three controls",
      "the choice table's consistency with the ledger"
    ],
    "CITED_THEOREM": [
      "LR C1.9, C1.10, C1.11, C1.6-C1.8, A6.1, C1.13 + Prop C1.1, Kato's reciprocity",
      "Round 030 C10, (20.1)-(20.2); Round 029 T0/T1/T2"
    ],
    "DERIVED_FROM_VERIFIED_INPUTS": [
      "RUN-095's hypotheses per partner",
      "RUN-096/097's ledger",
      "RUN-098's extractions",
      "RUN-099/100/101's resolved E-factors and graph"
    ],
    "UNMEASURED": [
      "BSD",
      "any of DAG A-G (actual BF/Kato classes, fundamental-line identification, regulator bridge, reciprocity + nonannihilation, p-adic and complex leading lines, finite certificates)",
      "the numerical value of C_pi",
      "v_11(q)",
      "n",
      "Pi_i"
    ],
    "FAILED": []
  },
  "status": {
    "C1-C9": "PASS",
    "C10": "PASS / canonical",
    "normalization_certificate": "CLOSED as architecture",
    "R0": "PASS (category C)",
    "BSD": "OPEN"
  }
}