{
  "attack": "C1 actual-object construction, after RUN-090's first blocker",
  "target": {
    "curve": "389.a1",
    "p": 11
  },
  "calibrator": {
    "curve": "19.a1 (LMFDB) = 19a2 (Cremona)"
  },
  "C1": {
    "verdict": "UNMEASURED",
    "auxiliary_side_constructed": true,
    "partner_side_constructed": false,
    "exact_missing_object": "R_i(X,t): the two-variable Rankin p-adic L-function of (E_i, g) over the slope-1 Coleman family through g — equivalently the Beilinson–Flach classes themselves",
    "exact_missing_theorem": "that the leading constant of the meromorphic Eichler–Shimura map is partner-independent once the auxiliary frame is fixed — Loeffler–Rivero C1.9–C1.13 with C1.11's uniqueness. CITED_THEOREM: its auxiliary-side hypotheses are instantiated here (decency, slope-1 refinement, canonical Eisenstein quotient), its partner-side hypothesis (the projections exist) is not, because the classes do not exist",
    "smallest_constructible_precursor": "R_0(X,t) for the rank-0 calibrator alone. PC-001 §4: U_0(0,0) ≠ 0, so R_0(X,0) and c_f(X) have the same X-vanishing order — the calibrator alone probes n = ord_X c_f, which is one of the two factors of C_π",
    "next_executable_attack": "Attack B below (done here: the valuation) and then C4's Θ_aux; for C1 itself the next executable step is R_0(X,t) for 19.a1 alone, which needs slope-1 overconvergent modular symbols — a Sage/Magma-scale computation, not stdlib",
    "mutation": "C_{π,E} ↦ u·C_{π,E} with C_{π,0} fixed — the identity (2) then carries exactly u",
    "gate": "src93 · c1-verdict",
    "label": "UNMEASURED"
  },
  "what_was_constructed_here": {
    "auxiliary_family": "E_k(1,χ₈) through k = 2 in the weight direction; a_n(X) = Σ_{d|n} χ₈(d)·d·⟨d⟩^X",
    "pseudocharacter_identification": "𝒯_X(Frob_ℓ) = 1 + χ₈(ℓ)·ℓ^{1+X} for ℓ ≠ 11 — the sum of the two Jordan–Hölder characters 1 and χ₈·χ_cyc, deformed in the weight direction",
    "trace_jet_mod_X2": {
      "3": {
        "constant": 1329,
        "log_11": 847,
        "X_coefficient": 121,
        "constant_is_the_q_expansion": true
      },
      "5": {
        "constant": 1327,
        "log_11": 44,
        "X_coefficient": 1111,
        "constant_is_the_q_expansion": true
      },
      "7": {
        "constant": 8,
        "log_11": 220,
        "X_coefficient": 209,
        "constant_is_the_q_expansion": true
      },
      "13": {
        "constant": 1319,
        "log_11": 374,
        "X_coefficient": 462,
        "constant_is_the_q_expansion": true
      },
      "17": {
        "constant": 18,
        "log_11": 935,
        "X_coefficient": 1254,
        "constant_is_the_q_expansion": true
      },
      "19": {
        "constant": 1313,
        "log_11": 517,
        "X_coefficient": 825,
        "constant_is_the_q_expansion": true
      },
      "23": {
        "constant": 24,
        "log_11": 1111,
        "X_coefficient": 264,
        "constant_is_the_q_expansion": true
      },
      "29": {
        "constant": 1303,
        "log_11": 517,
        "X_coefficient": 979,
        "constant_is_the_q_expansion": true
      }
    },
    "jordan_holder_characters_distinct": true,
    "canonical_eisenstein_quotient": true,
    "critical_refinement_branch": {
      "a_11": -10,
      "hecke_polynomial": "U² + 10U − 11 = (U − 1)(U + 11)",
      "roots": [
        1,
        -11
      ],
      "slopes": {
        "1": 0,
        "-11": 1
      },
      "critical_slope_1_root": -11,
      "critical_branch_is_chi8_chi_cyc": true
    },
    "label": "COMPUTED_HERE"
  },
  "attack_B": {
    "v_11_ratio": 0,
    "conclusion": "Π_E/Π_0 is an 11-adic UNIT",
    "consequence": "A_0(0)/A_E(0) ≡ 6·(Π_E/Π_0) (mod 11) is a nonzero unit — the partner ratio neither vanishes nor blows up mod 11, which is what PC-001's non-vanishing needs",
    "residue_mod_11": null,
    "residue_label": "UNMEASURED",
    "why_residue_unmeasured": "Hida's theorem identifies the congruence IDEAL; recovering the residue needs the actual Petersson norms against a stated period — the normalisation PC-001 §3 declines to fix ('其完整 period 比值 D_0 沒有在本輪算出'), plus the Manin constants and the optimality of 19.a1 = Cremona 19a2 (NOT the X₀-optimal curve of its class)",
    "valuation_label": "COMPUTED_HERE",
    "theorem": "Hida: the adjoint p-adic L-value L_p(Ad f)(0) generates the congruence ideal of f, so v₁₁(Π_i) = v₁₁(η_{f_i}). CITED_THEOREM — it pins the ideal, not the value."
  },
  "claim_labels_legend": [
    "COMPUTED_HERE",
    "CITED_THEOREM",
    "DERIVED_FROM_VERIFIED_INPUTS",
    "UNMEASURED",
    "FAILED"
  ],
  "bsd": "open"
}