{
  "D_rational": {
    "verdict": "ISOMORPHISM",
    "map": "log_omega : H^1_f(Q_11, V) -> D_dR(V)/Fil^0 = Q_11, V = T (x) Q_11",
    "source_dimension": 1,
    "target_dimension": 1,
    "why_source_is_one_dimensional": "11 does not divide #E~(F_11) = 16, so E(Q_11) (x)^ Z_11 = E_1(Q_11) = Z_11 (RUN-106)",
    "nonzero": true,
    "argument": "a nonzero linear map between one-dimensional spaces over a field has zero kernel and is onto — Round 011 (3.1)-(3.2)",
    "label": "DERIVED_FROM_VERIFIED_INPUTS (RUN-106's v_11(log_omega(g)) = 1 < infinity)"
  },
  "D_integral": {
    "verdict": "INDEX_11",
    "map": "log_omega on the lattice: H^1_f(Q_11, T) -> Z_11",
    "image": "11^1 · Z_11",
    "index": 11,
    "declared": 11,
    "unit_isomorphism": false,
    "integrally_trivial": false,
    "label": "DERIVED_FROM_VERIFIED_INPUTS (RUN-106 computed v_11(log_omega(g)) = 1 from the formal group of the minimal model)"
  },
  "compatibility": {
    "statement": "rational reciprocity = ISOMORPHISM and integral reciprocity = index 11 are compatible",
    "why": "an isomorphism of Q_11-lines restricted to lattices is an injection with finite cokernel; the cokernel's order is the index",
    "D_can_pass_with_index_not_1": true
  },
  "C6": {
    "what_C6_settled": "η_pdR = 1 — the period/de Rham comparison pairing ⟨γ, ω⟩ of the normalisation route (Eichler–Shimura; Ω^± is its value on the chosen Betti basis), RUN-099",
    "eta_pdR": 1,
    "frozen": true,
    "does_it_overwrite_the_local_index": false,
    "forbidden_inference": "η_pdR = 1 ⇒ the local log normalisation is 1",
    "what_it_would_cost": "a factor 11: the integral image is 11^1 · Z_11, not Z_11",
    "index_after_the_forbidden_inference": 1
  },
  "ledger": {
    "rows": [
      {
        "factor": "local Bloch-Kato index at 11",
        "value": 11,
        "owner": "p-adic reciprocity / the leading-line integral realization",
        "entered_by": "D",
        "entered_times": 1,
        "E_may": "read it",
        "E_may_not": "enter it again"
      },
      {
        "factor": "global index [Lambda_E : ZP + ZQ]",
        "value": 1,
        "owner": "C_NT (RUN-106)",
        "entered_by": "C",
        "entered_times": 1,
        "E_may": "read it",
        "E_may_not": "enter it again"
      },
      {
        "factor": "11-adic index of loc_11(E(Q) (x) Z_11)",
        "value": 1,
        "owner": "RUN-104's H^2 torsion",
        "entered_by": "A",
        "entered_times": 1,
        "E_may": "read it",
        "E_may_not": "enter it again"
      }
    ],
    "double_entries": [],
    "rule": "an index enters exactly once, through the map it belongs to, with an owner named"
  },
  "index_matches_declared": true,
  "owner_named": true,
  "agrees": true
}