{
  "verdicts": {
    "C1": "PASS",
    "C2": "PASS",
    "C3": "PASS",
    "C4": "PASS",
    "C5": "UNMEASURED",
    "C6": "UNMEASURED",
    "C7": "UNMEASURED",
    "C8": "UNMEASURED",
    "C9": "UNMEASURED",
    "C10": "UNMEASURED"
  },
  "rows": {
    "C1": {
      "verdict": "PASS",
      "why": "LR Thm C1.9 + section A8.3 + Thm C1.10 + Remark C1.11 + Thm C1.13, hypotheses instantiated here",
      "trace": [
        "discharged by LR Thm C1.9 + section A8.3 + Thm C1.10 + Remark C1.11 + Thm C1.13, hypotheses instantiated here [CITED_THEOREM]"
      ]
    },
    "C2": {
      "verdict": "PASS",
      "why": "LR Thm C1.13's explicit factorisation + the C_d commonality computed here",
      "trace": [
        "discharged by LR Thm C1.13's explicit factorisation + the C_d commonality computed here [DERIVED_FROM_VERIFIED_INPUTS]"
      ]
    },
    "C3": {
      "verdict": "PASS",
      "why": "RUN-090's coordinate audit on the actual series in one cyclotomic coordinate",
      "trace": [
        "discharged by RUN-090's coordinate audit on the actual series in one cyclotomic coordinate [COMPUTED_HERE]"
      ]
    },
    "C4": {
      "verdict": "PASS",
      "why": "RUN-094's chain: Thm A6.1 -> section A6.2 -> Cor A6.3(i) -> Thm A2.1 case (3), with RUN-092's dim H^1_f = 1 and RUN-093's vacuous local conditions",
      "trace": [
        "discharged by RUN-094's chain: Thm A6.1 -> section A6.2 -> Cor A6.3(i) -> Thm A2.1 case (3), with RUN-092's dim H^1_f = 1 and RUN-093's vacuous local conditions [CITED_THEOREM]"
      ]
    },
    "C5": {
      "verdict": "UNMEASURED",
      "why": "no decomposition of D = C_arith (x) C_aux^{-1} into factors exists, so 'every defect factor' has no referent; and the criterion's mood is ENUMERATION, which no theorem label may discharge",
      "trace": [
        "mood demands an exhibited object; none exhibited"
      ]
    },
    "C6": {
      "verdict": "UNMEASURED",
      "why": "neither alternative is in hand: no theorem here supplies canonical period-de Rham cancellation, and no explicit residual pairing scalar eta_pdR has been exhibited",
      "trace": [
        "no discharge named"
      ]
    },
    "C7": {
      "verdict": "UNMEASURED",
      "why": "neither alternative is in hand: no auxiliary-to-arithmetic determinant comparison map exists, and no explicit kappa_det has been exhibited",
      "trace": [
        "no discharge named"
      ]
    },
    "C8": {
      "verdict": "UNMEASURED",
      "why": "the absence claim cannot be made for the target: 389.a1's prime-to-11 saturation of its rational modular-symbol line is unmeasured (RUN-090), so it is not known that no unit ambiguity is being attributed to a length there",
      "trace": [
        "no discharge named"
      ]
    },
    "C9": {
      "verdict": "UNMEASURED",
      "why": "the subject does not exist: there are no actual comparison objects, hence no transport graph and no edges, so 'no residual holonomy' would be vacuous rather than true",
      "trace": [
        "subject does not exist"
      ]
    },
    "C10": {
      "verdict": "UNMEASURED",
      "why": "neither alternative is in hand: no canonical section, and q_fin = 1 is a number, not an anchor (RUN-090's ACCEPT_NUMERICAL_ANCHOR = False)",
      "trace": [
        "no discharge named"
      ]
    }
  },
  "v1_verdicts": {
    "C1": "UNMEASURED",
    "C2": "UNMEASURED",
    "C3": "PASS",
    "C4": "UNMEASURED",
    "C5": "UNMEASURED",
    "C6": "UNMEASURED",
    "C7": "UNMEASURED",
    "C8": "UNMEASURED",
    "C9": "UNMEASURED",
    "C10": "UNMEASURED"
  },
  "upgrades": [
    "C1",
    "C2",
    "C4"
  ],
  "downgrades": [],
  "first_blocker_certificate_order": "C5",
  "first_blocker_attack_order": "C6",
  "first_blocker_dependency_order": "C8",
  "dependency_order": {
    "recorded_by": "src92 (RUN-090), item['dependencies']",
    "upstream_within_the_certificate": {
      "C1": [],
      "C2": [
        "C1"
      ],
      "C3": [],
      "C4": [
        "C1",
        "C3"
      ],
      "C5": [
        "C4"
      ],
      "C6": [
        "C4",
        "C5"
      ],
      "C7": [
        "C4",
        "C6"
      ],
      "C8": [],
      "C9": [
        "C4",
        "C5",
        "C6",
        "C7"
      ],
      "C10": [
        "C9"
      ]
    },
    "layer": {
      "C1": 0,
      "C3": 0,
      "C8": 0,
      "C2": 1,
      "C4": 1,
      "C5": 2,
      "C6": 3,
      "C7": 4,
      "C9": 5,
      "C10": 6
    },
    "topological_order": [
      "C1",
      "C3",
      "C8",
      "C2",
      "C4",
      "C5",
      "C6",
      "C7",
      "C9",
      "C10"
    ],
    "unordered_because_of_a_cycle": []
  },
  "frontier": {
    "attackable_now": [
      "C5",
      "C8"
    ],
    "blocked_by": {
      "C6": [
        "C5"
      ],
      "C7": [
        "C6"
      ],
      "C9": [
        "C5",
        "C6",
        "C7"
      ],
      "C10": [
        "C9"
      ]
    },
    "note": "C5's only in-certificate upstream is C4, which now passes, so the chain C4 opened has C5 next. C6 lists C5 as its upstream, C7 lists C6, C9 lists C5/C6/C7 and C10 lists C9 - so every other open item sits behind C5, directly or transitively, which is why the handoff's section 11 attack order (C6, C7, then C5) runs against the recorded dependencies. C8 has NO in-certificate upstream at all: it was never blocked by anything in the certificate and is open simply because nobody has attacked it, so it can be taken in parallel."
  },
  "first_blocker_note": "'the first blocker' has no single-item answer any more, and the three orders show why. Round 030's numbering gives C5. A topological pass over RUN-090's recorded dependencies gives C8, because C8 has no in-certificate upstream at all. The handoff's section 11 attack order gives C6, and that one contradicts the recorded dependencies, since C6 lists C5 as its upstream. Round 030 states the certificate as a conjunction, so no order is part of the criterion; the useful answer is the FRONTIER - the open items whose upstreams have all passed - and that is exactly {C5, C8}.",
  "normalization_status": "NORMALIZATION-UNMEASURED",
  "subitems": {
    "C2": {
      "parent_sentence": "No partner arithmetic is hidden in the common line.",
      "parent_verdict": "PASS",
      "children": {
        "C2-STRUCTURE": {
          "asks": "is partner arithmetic kept out of the common line",
          "in_parent_sentence": true,
          "verdict": "PASS"
        },
        "C2-VALUE": {
          "asks": "is the numerical value of the partner factor Pi_E/Pi_0 known",
          "in_parent_sentence": false,
          "verdict": "OPEN"
        }
      },
      "mapping_back": "the parent takes the verdict of the child its own sentence asks about; a child outside the sentence is carried in the outside-certificate ledger and cannot change the parent either way",
      "consistent": true
    },
    "C4": {
      "parent_sentence": "The auxiliary leading tensor or equivalent q-blind source exists.",
      "parent_verdict": "PASS",
      "children": {
        "C4-LINE": {
          "asks": "does the auxiliary leading tensor / q-blind source exist",
          "in_parent_sentence": true,
          "verdict": "PASS"
        },
        "C4-EXACT-NORM": {
          "asks": "is the comparison scalar c_ES/Kum fixed",
          "in_parent_sentence": false,
          "verdict": "OPEN"
        }
      },
      "mapping_back": "the parent takes the verdict of the child its own sentence asks about; a child outside the sentence is carried in the outside-certificate ledger and cannot change the parent either way",
      "consistent": true
    }
  },
  "outside_certificate": {
    "BF-COORD": "no computed representative of kappa_d(f,g), hence none of B_{E,2} or r_{0,1}",
    "C2-VALUE": "Pi_E/Pi_0, the Petersson/period ratio, has no known value",
    "C4-EXACT-NORM": "c_ES/Kum, the scalar between [Theta_aux] and kappa(epsilon), is not fixed",
    "C_PI-TRIVIALISATION": "b_f^+ is non-canonical (LR section A8.3), so C_pi has no numerical value until one trivialisation is fixed; anything built from C_aux inherits that ambiguity"
  },
  "rules": {
    "unmeasured_to_pass": false,
    "closure_requires_all": true,
    "vacuous_absence_is_pass": false,
    "admissible_without_object": [
      "COMPUTED_HERE",
      "CITED_THEOREM",
      "DERIVED_FROM_VERIFIED_INPUTS"
    ],
    "admissible_with_object": [
      "COMPUTED_HERE"
    ]
  },
  "expected": {
    "C1": "PASS",
    "C2": "PASS",
    "C3": "PASS",
    "C4": "PASS",
    "C5": "UNMEASURED",
    "C6": "UNMEASURED",
    "C7": "UNMEASURED",
    "C8": "UNMEASURED",
    "C9": "UNMEASURED",
    "C10": "UNMEASURED"
  },
  "agrees": true
}