{
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    "featured": [
      {
        "name": "OfNat.ofNat",
        "provider_module": "Init.Prelude",
        "role": "Compiled external provider used by selected Project declarations.",
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      },
      {
        "name": "Eq",
        "provider_module": "Init.Prelude",
        "role": "Compiled external provider used by selected Project declarations.",
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      {
        "name": "Complex.instSemiring",
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      {
        "name": "Semiring.toNonAssocSemiring",
        "provider_module": "Mathlib.Algebra.Ring.Defs",
        "role": "Compiled external provider used by selected Project declarations.",
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        ]
      },
      {
        "name": "Zero.toOfNat0",
        "provider_module": "Init.Data.Zero",
        "role": "Compiled external provider used by selected Project declarations.",
        "used_by_selected_node_ids": [
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      {
        "name": "AddCommMonoid.toAddMonoid",
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        "role": "Compiled external provider used by selected Project declarations.",
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      {
        "name": "AddMonoid.toAddZeroClass",
        "provider_module": "Mathlib.Algebra.Group.Defs",
        "role": "Compiled external provider used by selected Project declarations.",
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      {
        "name": "AddZeroClass.toAddZero",
        "provider_module": "Mathlib.Algebra.Group.Defs",
        "role": "Compiled external provider used by selected Project declarations.",
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      },
      {
        "name": "Complex.instNonUnitalCommRing",
        "provider_module": "Mathlib.Data.Complex.Basic",
        "role": "Compiled external provider used by selected Project declarations.",
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          "nm-a067d00b990845fe58c7",
          "nm-7ae63abc8cb7517f6bdc"
        ]
      },
      {
        "name": "NonUnitalCommRing.toNonUnitalNonAssocCommRing",
        "provider_module": "Mathlib.Algebra.Ring.Defs",
        "role": "Compiled external provider used by selected Project declarations.",
        "used_by_selected_node_ids": [
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          "nm-7ae63abc8cb7517f6bdc"
        ]
      },
      {
        "name": "NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing",
        "provider_module": "Mathlib.Algebra.Ring.Defs",
        "role": "Compiled external provider used by selected Project declarations.",
        "used_by_selected_node_ids": [
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        ]
      },
      {
        "name": "congrArg",
        "provider_module": "Init.Prelude",
        "role": "Compiled external provider used by selected Project declarations.",
        "used_by_selected_node_ids": [
          "nm-3e4ec11e28dc14ddb71d",
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      },
      {
        "name": "AddZero.toZero",
        "provider_module": "Mathlib.Algebra.Group.Defs",
        "role": "Compiled external provider used by selected Project declarations.",
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          "nm-64d666bd050c5ea69f67",
          "nm-9e49bc4b278b1b197031",
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          "nm-87c172d892ec5b0f3e28",
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          "nm-51878905fc9def0c638c",
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          "nm-fd14b65f90574a9001da",
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          "nm-d2cce21a9baba6c0cfd3",
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          "nm-9211e2dd1b1d5889ae97",
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          "nm-b6b37dad2d320be7f030",
          "nm-e7a2a17bd26533049bba",
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          "nm-8f1c4df034ff75240bd3",
          "nm-00fed78a11301a9b212a",
          "nm-591893c31c30180acde9",
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          "nm-00b1174b0fc6c099bda5",
          "nm-537feed0ac8b906e150f",
          "nm-a472d68367ff894eac7c",
          "nm-bd06f9c03a88fdd4330b",
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          "nm-d17af56bb90a923a7774",
          "nm-1490bbc763f90a1d5672",
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          "nm-5579592cdc03182a0521",
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          "nm-4bafd84c697d3b3dae68",
          "nm-689c958d838a973f446c",
          "nm-0a5c9475b9411c929c70",
          "nm-270295007caf011379c7",
          "nm-dba6655a4df10bb270d2",
          "nm-482400168402474c8d39",
          "nm-099332cb4dc8f038001e",
          "nm-126efb80c67b3ca8ad55",
          "nm-c06787b2fe56c8e03894",
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          "nm-f17e0f622dc63dec13a0",
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          "nm-3d4be956f67da71615ae",
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          "nm-f66d03bdef8d9540c334",
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          "nm-ca5adad8bac542e9c3e5",
          "nm-612e66dddeaf5702a902",
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          "nm-7f7591370ee573d87c93",
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          "nm-e54e22d079fc62352f72",
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          "nm-deab7b11d1988730ad08",
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          "nm-b4228ddc2d30c1a404ca",
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          "nm-c86e5c3effa222233985",
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          "nm-63ab2bc3bc7099fc9b38",
          "nm-6bc328a87aba6b0cdbc1",
          "nm-c58e8c992b209bd88b73",
          "nm-d7e649c7dd3c6a0718e7",
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          "nm-0e39ff48d56738c02238",
          "nm-b50cae2527e292dbb753",
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          "nm-81bf0e7f0cab189869b0",
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          "nm-6fe1968cf0cd15aa0cc0",
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          "nm-5664ba12bd1d3d9e929f",
          "nm-29d7b0f52be5e1fa3301",
          "nm-e2c3a70d4e25bec3f031",
          "nm-068bf062ed0bff7cc742",
          "nm-d1cd138d8da7f7091497",
          "nm-e5bc9bf2312688869e36",
          "nm-491755a133bbb4321b51",
          "nm-6a3f4ded73ecde2ed25c",
          "nm-688c9a1c1096704f42dc",
          "nm-b4e58913626e242f974f",
          "nm-173d26c9f1f819587fd5",
          "nm-a5720df7e99e8c2ac84d",
          "nm-5e04d8da3930ec2ec0ab",
          "nm-0ff5433199a14de5c9a5",
          "nm-c76b2535466f3a008807",
          "nm-3ef436dae82ed8f92654",
          "nm-e2965a1e9198ebb4f6d9",
          "nm-0ca73f40ed9f5ee7e24d",
          "nm-ae9a385e35ee71589073",
          "nm-de566d00e5790b09804f",
          "nm-e977e2fa719991247da3",
          "nm-655e373879df47c8d1a4",
          "nm-0a534c86332fa27e1df1",
          "nm-aa2b9e147676714b3af6",
          "nm-615ead16275b381b4621",
          "nm-1a1c4d43a1dc9f29bf3e",
          "nm-20575ad16da32b85e124",
          "nm-3da2f308d8ba5a740784",
          "nm-8c975468c15eaa6f4124",
          "nm-b3efaf7d96091798ebab",
          "nm-7ef8c0ac017ddc972cb9",
          "nm-e5251183f29c5bfeeebc",
          "nm-c0876367fcb4fe8b256f",
          "nm-3a7c3d1d3af59f458a4f",
          "nm-9ac2148b89cc71ae5177",
          "nm-a51fa7568ba5d6e703bf",
          "nm-c96d157d550c8d9ae790",
          "nm-d2902c0767b6515255a3",
          "nm-2f9cef636cddb43d81c9",
          "nm-91fd1f30c47dd3ad2e3c",
          "nm-8eb7ff3fc8a986fc2a9e",
          "nm-e48f52c8044d7d147182",
          "nm-aad49bc622d164f2dc4a",
          "nm-38ef179658db8f2bf005",
          "nm-cf76172b5db2c37d03fc",
          "nm-1f3acd15bbf35b67da68",
          "nm-2935ff4c10bc05cf969c",
          "nm-2c2a90e19a0be39c63e6",
          "nm-a3c81baa8bc5d1abee43"
        ]
      }
    ],
    "raw_count": 4939,
    "summary": "4939 exact Boundary Inputs: EXTERNAL_COMPILED_DECLARATION 3571, OMITTED_INTERNAL_NATIVE_DECLARATION 1368. Selected reachability is retained through every omitted internal declaration."
  },
  "graph": {
    "display_edge_count": 884,
    "full_formal_graph_sha256": "e0c69751546f310fb7e15d2915c7e7b0f6a710eb0bc33269b24c2b228bcb5425",
    "full_project_level_map_sha256": "4bbd7ffccba287ee1d2341589d8b6186a3937121ff4bff8aa1d6ea4630cab395",
    "maximum_level": 72,
    "naive_induced_lost_pairs": 39850,
    "node_count": 466,
    "orientation": "dependent_to_prerequisite",
    "reachability_count": 45158
  },
  "identity": {
    "slug": "naimark-problem",
    "title": "Naimark's problem"
  },
  "overview": {
    "bridges": [
      {
        "preset_id": "car-source",
        "route_id": "car-source",
        "selected_count": 91,
        "terminal_node_ids": [
          "nm-615ead16275b381b4621"
        ],
        "text": "The CAR source supplies the pure-state compression and decreasing flags used to distinguish the selected irreducible models. The normalized trace controls the same flags in the later tracial argument.",
        "title": "CAR source, pure states and decreasing flags"
      },
      {
        "preset_id": "shell-construction",
        "route_id": "shell-construction",
        "selected_count": 323,
        "terminal_node_ids": [
          "nm-77e7a7d2e41c6d44cf9c",
          "nm-27fa6bdad9df8852dffe"
        ],
        "text": "Matched shells and their strong operator sums define the concrete generators. The construction keeps one fixed generated C*-algebra rather than replacing it by another algebra with similar relations.",
        "title": "Shell matching and the generated algebra"
      },
      {
        "preset_id": "irreducible-capture",
        "route_id": "irreducible-capture",
        "selected_count": 367,
        "terminal_node_ids": [
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