{
  "boundary_inputs": {
    "curated_count": 15,
    "featured": [
      {
        "name": "Eq",
        "provider_module": "Init.Prelude",
        "role": "Compiled external provider used by selected Project declarations.",
        "used_by_selected_node_ids": [
          "26c4dc7e5f4912c1494c383fd3d50537f9cb6328e2450925e91201f48c5d8384",
          "2407611b2e8f0ff07b7d50cc8edfa17f744337c5a9ad013cf63d5ddb1eeb8840",
          "c6768fb635e387f90ed7c53fa90f5b4dfebcf526a42da7af360fbfdefc2284b6",
          "15b02dd39a6c9afbc2cc1f023c8e4b29cc806759b53b21c82065a410d00117ff",
          "caeef92045d974a18cb5eb41cd4c36b68c457337d1569671d296e8f3c437fec6",
          "ros-src-66d72b531c729bbbb88c",
          "ros-src-12cd2f1f5b7c20122525",
          "ros-src-e9192a6956be65f01319",
          "ros-src-90127c0d2347b370cebf",
          "ff5886cf6420336dbe578275731ad0361f521340e5e9760ec098cd284273b584",
          "ros-src-fd0d0f1b35e610326c61",
          "ros-src-5a50fb2b0e66cc98b48b",
          "ros-src-f4a0c4ce3fd3539df047",
          "ros-src-b6923a9d8a2600deada8",
          "ros-src-17077f9a98c052b8187b",
          "f13185dafb7e72e6ddc0775a43c0210faf488dbee88282e3fdd08359cc7d6ad9",
          "ros-src-0264d5c421660475138e",
          "c4c4491fa52a7fbdbfde28f3dd9f46756ece7e43d6d9f8b3afb346db83d351e4",
          "964e8b0b51be9a3fc80a3f61b3bcb1b8cf70461ce4137aed6128c4ced9074130",
          "ros-src-9bafbc8fb0b4e17a561f",
          "ros-src-de97a0d50513acd04c68",
          "ros-src-29cf209852c4aa58ce37",
          "0edd904a8f54cb2f656607289f4094b52459b64013e28ed399e00bc0acd454d8",
          "155676cd74606a102aa274be40c9fb294971cfef6df06897084c9fc89322f2cb",
          "ros-src-bb0af2c5f932153961a0",
          "7a1b136b8464e6029397491d4d05fa22de45ecb383b3384c4e0c2fcf7df3150a",
          "4448c461ec5cd20bf403d08c42baa0de790b14987f7d2ab766036cdccc4b7537",
          "66a6654fa9d1e8607b27f931148203017898635ae004e222a22fd8c88c82d2f2",
          "ros-src-31aabd9922e2649eed4e",
          "ros-src-11a8ca7b0e0585d03048",
          "ros-src-df1834dfd60f65282276",
          "94b7f2220243cb53c84a521c24f6eb1f35bc8222d4162b9ea134b4c10e9ea7b4",
          "ros-src-81fe97584de561879558",
          "ros-src-2520e88617ae5d993501",
          "637afab6889bdf11fe07e21325cab3df3d3f88baeb71dff1c973c7e2a3f1a794",
          "8b10daad485fe797ba4250420c41ce6ffba033b4085e1a302b3eed0c4dd5d141",
          "f34adabc1cac70dceb32acb212d5f7c0b85c259c2c330087932a6f3fe9f5e8a9",
          "956f7a6ee326f4d3fe0fff3198e6dde0fb0903ec6f51cfb6ad39f61c2663e298",
          "fd18e1a684c11c6d461ab0afb2c4c47e3636fb5b84f9a7cca39b472897e0f86d",
          "ros-src-c5203398c4e3f54aaba2",
          "106c2e5861a90efa2b3d1125a38099aaae4192ca2a311076da995a4ae3043e03",
          "f2686115c0a5647dbadc2b23862bf82db33c3680599f938b1b6342daaf7d4467",
          "ros-src-e3b1f13f7062428affde",
          "a6b19f4652225ea9cada7c02f05c27707d0bf713859210f56ebbbf0df233cd00",
          "1e09b496fe0e06eeb046e141957245bfb51a6b1b7b8c28cf44ffdefc9574de2f",
          "d4a5a6c0e99f5d6af2aa8ac954e42542f163c769257b313f68d69c5f1c0993e5",
          "f7ac96c3bcdff8225f7123d411c404580fab1d79b3975d601484f61837409226",
          "23a70d1e81d7c3d1ed7932a2de55be2e240d36d087130ed0dd8e21ce1e3d7013",
          "9739356612e228954ac5a7eda9eacad58edcc6c064c06a3df7680ce87004f11b",
          "9355a7df6defbdd54a898d97fa5d5ff61ac59614adb1ceee96df088d9c1a66b6",
          "ros-src-226735737ced2aab2395",
          "ros-src-41c50c1859ca16456aed",
          "ros-src-81911ae7885c6426216d",
          "ros-src-fc7b77ac48f451a51fc7",
          "ros-src-cb3bcdabc51450e2cc2c",
          "ros-src-724d3e7c71466fdf73d4",
          "9c5012403e7138fc2010b82937c3665b67957413b75f52e1a4527ad36e819be4",
          "ros-src-efc3d1d2d13099ffe9e1",
          "ros-src-478647f701abbfb9e2db"
        ]
      },
      {
        "name": "Membership.mem",
        "provider_module": "Init.Prelude",
        "role": "Compiled external provider used by selected Project declarations.",
        "used_by_selected_node_ids": [
          "005d767a3193a30c065ad807166f2e150c8ac3bbd28de67fd113b74463f676eb",
          "2407611b2e8f0ff07b7d50cc8edfa17f744337c5a9ad013cf63d5ddb1eeb8840",
          "c6768fb635e387f90ed7c53fa90f5b4dfebcf526a42da7af360fbfdefc2284b6",
          "15b02dd39a6c9afbc2cc1f023c8e4b29cc806759b53b21c82065a410d00117ff",
          "ros-src-66d72b531c729bbbb88c",
          "ros-src-12cd2f1f5b7c20122525",
          "ros-src-e9192a6956be65f01319",
          "ros-src-90127c0d2347b370cebf",
          "ff5886cf6420336dbe578275731ad0361f521340e5e9760ec098cd284273b584",
          "ros-src-fd0d0f1b35e610326c61",
          "ros-src-5a50fb2b0e66cc98b48b",
          "ros-src-f4a0c4ce3fd3539df047",
          "ros-src-b6923a9d8a2600deada8",
          "ros-src-17077f9a98c052b8187b",
          "f13185dafb7e72e6ddc0775a43c0210faf488dbee88282e3fdd08359cc7d6ad9",
          "ros-src-0264d5c421660475138e",
          "c4c4491fa52a7fbdbfde28f3dd9f46756ece7e43d6d9f8b3afb346db83d351e4",
          "964e8b0b51be9a3fc80a3f61b3bcb1b8cf70461ce4137aed6128c4ced9074130",
          "ros-src-9bafbc8fb0b4e17a561f",
          "ros-src-de97a0d50513acd04c68",
          "ros-src-29cf209852c4aa58ce37",
          "0edd904a8f54cb2f656607289f4094b52459b64013e28ed399e00bc0acd454d8",
          "155676cd74606a102aa274be40c9fb294971cfef6df06897084c9fc89322f2cb",
          "ros-src-bb0af2c5f932153961a0",
          "7a1b136b8464e6029397491d4d05fa22de45ecb383b3384c4e0c2fcf7df3150a",
          "4448c461ec5cd20bf403d08c42baa0de790b14987f7d2ab766036cdccc4b7537",
          "66a6654fa9d1e8607b27f931148203017898635ae004e222a22fd8c88c82d2f2",
          "ros-src-31aabd9922e2649eed4e",
          "ros-src-11a8ca7b0e0585d03048",
          "ros-src-df1834dfd60f65282276",
          "94b7f2220243cb53c84a521c24f6eb1f35bc8222d4162b9ea134b4c10e9ea7b4",
          "ros-src-81fe97584de561879558",
          "ros-src-2520e88617ae5d993501",
          "637afab6889bdf11fe07e21325cab3df3d3f88baeb71dff1c973c7e2a3f1a794",
          "8b10daad485fe797ba4250420c41ce6ffba033b4085e1a302b3eed0c4dd5d141",
          "f34adabc1cac70dceb32acb212d5f7c0b85c259c2c330087932a6f3fe9f5e8a9",
          "956f7a6ee326f4d3fe0fff3198e6dde0fb0903ec6f51cfb6ad39f61c2663e298",
          "fd18e1a684c11c6d461ab0afb2c4c47e3636fb5b84f9a7cca39b472897e0f86d",
          "ros-src-c5203398c4e3f54aaba2",
          "106c2e5861a90efa2b3d1125a38099aaae4192ca2a311076da995a4ae3043e03",
          "f2686115c0a5647dbadc2b23862bf82db33c3680599f938b1b6342daaf7d4467",
          "a6b19f4652225ea9cada7c02f05c27707d0bf713859210f56ebbbf0df233cd00",
          "1e09b496fe0e06eeb046e141957245bfb51a6b1b7b8c28cf44ffdefc9574de2f",
          "d4a5a6c0e99f5d6af2aa8ac954e42542f163c769257b313f68d69c5f1c0993e5",
          "f7ac96c3bcdff8225f7123d411c404580fab1d79b3975d601484f61837409226",
          "23a70d1e81d7c3d1ed7932a2de55be2e240d36d087130ed0dd8e21ce1e3d7013",
          "9739356612e228954ac5a7eda9eacad58edcc6c064c06a3df7680ce87004f11b",
          "9355a7df6defbdd54a898d97fa5d5ff61ac59614adb1ceee96df088d9c1a66b6",
          "ros-src-226735737ced2aab2395",
          "ros-src-41c50c1859ca16456aed",
          "ros-src-81911ae7885c6426216d",
          "ros-src-fc7b77ac48f451a51fc7",
          "ros-src-cb3bcdabc51450e2cc2c",
          "ros-src-724d3e7c71466fdf73d4",
          "9c5012403e7138fc2010b82937c3665b67957413b75f52e1a4527ad36e819be4",
          "ros-src-efc3d1d2d13099ffe9e1",
          "ros-src-478647f701abbfb9e2db"
        ]
      },
      {
        "name": "PseudoMetricSpace.toUniformSpace",
        "provider_module": "Mathlib.Topology.MetricSpace.Pseudo.Defs",
        "role": "Compiled external provider used by selected Project declarations.",
        "used_by_selected_node_ids": [
          "26c4dc7e5f4912c1494c383fd3d50537f9cb6328e2450925e91201f48c5d8384",
          "2407611b2e8f0ff07b7d50cc8edfa17f744337c5a9ad013cf63d5ddb1eeb8840",
          "fe5eb271ebd53bcf76dd017a38916fe9f0357061b245cae8d78921e5470ce824",
          "c6768fb635e387f90ed7c53fa90f5b4dfebcf526a42da7af360fbfdefc2284b6",
          "15b02dd39a6c9afbc2cc1f023c8e4b29cc806759b53b21c82065a410d00117ff",
          "caeef92045d974a18cb5eb41cd4c36b68c457337d1569671d296e8f3c437fec6",
          "ros-src-66d72b531c729bbbb88c",
          "ros-src-12cd2f1f5b7c20122525",
          "ros-src-e9192a6956be65f01319",
          "ros-src-90127c0d2347b370cebf",
          "ff5886cf6420336dbe578275731ad0361f521340e5e9760ec098cd284273b584",
          "ros-src-fd0d0f1b35e610326c61",
          "ros-src-5a50fb2b0e66cc98b48b",
          "ros-src-f4a0c4ce3fd3539df047",
          "ros-src-b6923a9d8a2600deada8",
          "ros-src-17077f9a98c052b8187b",
          "f13185dafb7e72e6ddc0775a43c0210faf488dbee88282e3fdd08359cc7d6ad9",
          "ros-src-0264d5c421660475138e",
          "c4c4491fa52a7fbdbfde28f3dd9f46756ece7e43d6d9f8b3afb346db83d351e4",
          "964e8b0b51be9a3fc80a3f61b3bcb1b8cf70461ce4137aed6128c4ced9074130",
          "ros-src-9bafbc8fb0b4e17a561f",
          "ros-src-de97a0d50513acd04c68",
          "ros-src-29cf209852c4aa58ce37",
          "0edd904a8f54cb2f656607289f4094b52459b64013e28ed399e00bc0acd454d8",
          "155676cd74606a102aa274be40c9fb294971cfef6df06897084c9fc89322f2cb",
          "ros-src-bb0af2c5f932153961a0",
          "7a1b136b8464e6029397491d4d05fa22de45ecb383b3384c4e0c2fcf7df3150a",
          "4448c461ec5cd20bf403d08c42baa0de790b14987f7d2ab766036cdccc4b7537",
          "6cdd5b20c1ae2e69ab7bda0400ecc3876509dbfa7420f6561394f5c962b3509f",
          "66a6654fa9d1e8607b27f931148203017898635ae004e222a22fd8c88c82d2f2",
          "ros-src-31aabd9922e2649eed4e",
          "ros-src-11a8ca7b0e0585d03048",
          "ros-src-df1834dfd60f65282276",
          "94b7f2220243cb53c84a521c24f6eb1f35bc8222d4162b9ea134b4c10e9ea7b4",
          "ros-src-81fe97584de561879558",
          "ros-src-2520e88617ae5d993501",
          "637afab6889bdf11fe07e21325cab3df3d3f88baeb71dff1c973c7e2a3f1a794",
          "8b10daad485fe797ba4250420c41ce6ffba033b4085e1a302b3eed0c4dd5d141",
          "f34adabc1cac70dceb32acb212d5f7c0b85c259c2c330087932a6f3fe9f5e8a9",
          "956f7a6ee326f4d3fe0fff3198e6dde0fb0903ec6f51cfb6ad39f61c2663e298",
          "fd18e1a684c11c6d461ab0afb2c4c47e3636fb5b84f9a7cca39b472897e0f86d",
          "ros-src-c5203398c4e3f54aaba2",
          "106c2e5861a90efa2b3d1125a38099aaae4192ca2a311076da995a4ae3043e03",
          "f2686115c0a5647dbadc2b23862bf82db33c3680599f938b1b6342daaf7d4467",
          "ros-src-e3b1f13f7062428affde",
          "a6b19f4652225ea9cada7c02f05c27707d0bf713859210f56ebbbf0df233cd00",
          "1e09b496fe0e06eeb046e141957245bfb51a6b1b7b8c28cf44ffdefc9574de2f",
          "d4a5a6c0e99f5d6af2aa8ac954e42542f163c769257b313f68d69c5f1c0993e5",
          "f7ac96c3bcdff8225f7123d411c404580fab1d79b3975d601484f61837409226",
          "23a70d1e81d7c3d1ed7932a2de55be2e240d36d087130ed0dd8e21ce1e3d7013",
          "9739356612e228954ac5a7eda9eacad58edcc6c064c06a3df7680ce87004f11b",
          "9355a7df6defbdd54a898d97fa5d5ff61ac59614adb1ceee96df088d9c1a66b6",
          "ros-src-226735737ced2aab2395",
          "ros-src-41c50c1859ca16456aed",
          "ros-src-cb3bcdabc51450e2cc2c"
        ]
      },
      {
        "name": "OfNat.ofNat",
        "provider_module": "Init.Prelude",
        "role": "Compiled external provider used by selected Project declarations.",
        "used_by_selected_node_ids": [
          "ros-src-381b2fd00802311a7e69",
          "2407611b2e8f0ff07b7d50cc8edfa17f744337c5a9ad013cf63d5ddb1eeb8840",
          "c6768fb635e387f90ed7c53fa90f5b4dfebcf526a42da7af360fbfdefc2284b6",
          "15b02dd39a6c9afbc2cc1f023c8e4b29cc806759b53b21c82065a410d00117ff",
          "ros-src-66d72b531c729bbbb88c",
          "ros-src-12cd2f1f5b7c20122525",
          "ros-src-e9192a6956be65f01319",
          "ros-src-90127c0d2347b370cebf",
          "ff5886cf6420336dbe578275731ad0361f521340e5e9760ec098cd284273b584",
          "ros-src-fd0d0f1b35e610326c61",
          "ros-src-5a50fb2b0e66cc98b48b",
          "ros-src-f4a0c4ce3fd3539df047",
          "ros-src-b6923a9d8a2600deada8",
          "ros-src-17077f9a98c052b8187b",
          "f13185dafb7e72e6ddc0775a43c0210faf488dbee88282e3fdd08359cc7d6ad9",
          "ros-src-0264d5c421660475138e",
          "c4c4491fa52a7fbdbfde28f3dd9f46756ece7e43d6d9f8b3afb346db83d351e4",
          "964e8b0b51be9a3fc80a3f61b3bcb1b8cf70461ce4137aed6128c4ced9074130",
          "ros-src-9bafbc8fb0b4e17a561f",
          "ros-src-de97a0d50513acd04c68",
          "ros-src-29cf209852c4aa58ce37",
          "0edd904a8f54cb2f656607289f4094b52459b64013e28ed399e00bc0acd454d8",
          "155676cd74606a102aa274be40c9fb294971cfef6df06897084c9fc89322f2cb",
          "ros-src-bb0af2c5f932153961a0",
          "7a1b136b8464e6029397491d4d05fa22de45ecb383b3384c4e0c2fcf7df3150a",
          "4448c461ec5cd20bf403d08c42baa0de790b14987f7d2ab766036cdccc4b7537",
          "66a6654fa9d1e8607b27f931148203017898635ae004e222a22fd8c88c82d2f2",
          "ros-src-31aabd9922e2649eed4e",
          "ros-src-11a8ca7b0e0585d03048",
          "ros-src-df1834dfd60f65282276",
          "94b7f2220243cb53c84a521c24f6eb1f35bc8222d4162b9ea134b4c10e9ea7b4",
          "ros-src-81fe97584de561879558",
          "ros-src-2520e88617ae5d993501",
          "637afab6889bdf11fe07e21325cab3df3d3f88baeb71dff1c973c7e2a3f1a794",
          "8b10daad485fe797ba4250420c41ce6ffba033b4085e1a302b3eed0c4dd5d141",
          "f34adabc1cac70dceb32acb212d5f7c0b85c259c2c330087932a6f3fe9f5e8a9",
          "956f7a6ee326f4d3fe0fff3198e6dde0fb0903ec6f51cfb6ad39f61c2663e298",
          "fd18e1a684c11c6d461ab0afb2c4c47e3636fb5b84f9a7cca39b472897e0f86d",
          "ros-src-c5203398c4e3f54aaba2",
          "106c2e5861a90efa2b3d1125a38099aaae4192ca2a311076da995a4ae3043e03",
          "f2686115c0a5647dbadc2b23862bf82db33c3680599f938b1b6342daaf7d4467",
          "ros-src-e3b1f13f7062428affde",
          "a6b19f4652225ea9cada7c02f05c27707d0bf713859210f56ebbbf0df233cd00",
          "1e09b496fe0e06eeb046e141957245bfb51a6b1b7b8c28cf44ffdefc9574de2f",
          "f7ac96c3bcdff8225f7123d411c404580fab1d79b3975d601484f61837409226",
          "23a70d1e81d7c3d1ed7932a2de55be2e240d36d087130ed0dd8e21ce1e3d7013",
          "9739356612e228954ac5a7eda9eacad58edcc6c064c06a3df7680ce87004f11b",
          "9355a7df6defbdd54a898d97fa5d5ff61ac59614adb1ceee96df088d9c1a66b6",
          "ros-src-226735737ced2aab2395",
          "ros-src-41c50c1859ca16456aed",
          "ros-src-cb3bcdabc51450e2cc2c",
          "ros-src-724d3e7c71466fdf73d4",
          "ros-src-efc3d1d2d13099ffe9e1",
          "ros-src-478647f701abbfb9e2db"
        ]
      },
      {
        "name": "UniformSpace.toTopologicalSpace",
        "provider_module": "Mathlib.Topology.UniformSpace.Defs",
        "role": "Compiled external provider used by selected Project declarations.",
        "used_by_selected_node_ids": [
          "26c4dc7e5f4912c1494c383fd3d50537f9cb6328e2450925e91201f48c5d8384",
          "2407611b2e8f0ff07b7d50cc8edfa17f744337c5a9ad013cf63d5ddb1eeb8840",
          "fe5eb271ebd53bcf76dd017a38916fe9f0357061b245cae8d78921e5470ce824",
          "c6768fb635e387f90ed7c53fa90f5b4dfebcf526a42da7af360fbfdefc2284b6",
          "15b02dd39a6c9afbc2cc1f023c8e4b29cc806759b53b21c82065a410d00117ff",
          "caeef92045d974a18cb5eb41cd4c36b68c457337d1569671d296e8f3c437fec6",
          "ros-src-66d72b531c729bbbb88c",
          "ros-src-12cd2f1f5b7c20122525",
          "ros-src-e9192a6956be65f01319",
          "ros-src-90127c0d2347b370cebf",
          "ff5886cf6420336dbe578275731ad0361f521340e5e9760ec098cd284273b584",
          "ros-src-fd0d0f1b35e610326c61",
          "ros-src-5a50fb2b0e66cc98b48b",
          "ros-src-f4a0c4ce3fd3539df047",
          "ros-src-b6923a9d8a2600deada8",
          "ros-src-17077f9a98c052b8187b",
          "f13185dafb7e72e6ddc0775a43c0210faf488dbee88282e3fdd08359cc7d6ad9",
          "ros-src-0264d5c421660475138e",
          "c4c4491fa52a7fbdbfde28f3dd9f46756ece7e43d6d9f8b3afb346db83d351e4",
          "964e8b0b51be9a3fc80a3f61b3bcb1b8cf70461ce4137aed6128c4ced9074130",
          "ros-src-9bafbc8fb0b4e17a561f",
          "ros-src-de97a0d50513acd04c68",
          "ros-src-29cf209852c4aa58ce37",
          "0edd904a8f54cb2f656607289f4094b52459b64013e28ed399e00bc0acd454d8",
          "155676cd74606a102aa274be40c9fb294971cfef6df06897084c9fc89322f2cb",
          "ros-src-bb0af2c5f932153961a0",
          "7a1b136b8464e6029397491d4d05fa22de45ecb383b3384c4e0c2fcf7df3150a",
          "4448c461ec5cd20bf403d08c42baa0de790b14987f7d2ab766036cdccc4b7537",
          "6cdd5b20c1ae2e69ab7bda0400ecc3876509dbfa7420f6561394f5c962b3509f",
          "66a6654fa9d1e8607b27f931148203017898635ae004e222a22fd8c88c82d2f2",
          "ros-src-31aabd9922e2649eed4e",
          "ros-src-11a8ca7b0e0585d03048",
          "ros-src-df1834dfd60f65282276",
          "94b7f2220243cb53c84a521c24f6eb1f35bc8222d4162b9ea134b4c10e9ea7b4",
          "ros-src-81fe97584de561879558",
          "ros-src-2520e88617ae5d993501",
          "637afab6889bdf11fe07e21325cab3df3d3f88baeb71dff1c973c7e2a3f1a794",
          "8b10daad485fe797ba4250420c41ce6ffba033b4085e1a302b3eed0c4dd5d141",
          "f34adabc1cac70dceb32acb212d5f7c0b85c259c2c330087932a6f3fe9f5e8a9",
          "956f7a6ee326f4d3fe0fff3198e6dde0fb0903ec6f51cfb6ad39f61c2663e298",
          "fd18e1a684c11c6d461ab0afb2c4c47e3636fb5b84f9a7cca39b472897e0f86d",
          "ros-src-c5203398c4e3f54aaba2",
          "106c2e5861a90efa2b3d1125a38099aaae4192ca2a311076da995a4ae3043e03",
          "f2686115c0a5647dbadc2b23862bf82db33c3680599f938b1b6342daaf7d4467",
          "a6b19f4652225ea9cada7c02f05c27707d0bf713859210f56ebbbf0df233cd00",
          "1e09b496fe0e06eeb046e141957245bfb51a6b1b7b8c28cf44ffdefc9574de2f",
          "d4a5a6c0e99f5d6af2aa8ac954e42542f163c769257b313f68d69c5f1c0993e5",
          "f7ac96c3bcdff8225f7123d411c404580fab1d79b3975d601484f61837409226",
          "23a70d1e81d7c3d1ed7932a2de55be2e240d36d087130ed0dd8e21ce1e3d7013",
          "9739356612e228954ac5a7eda9eacad58edcc6c064c06a3df7680ce87004f11b",
          "9355a7df6defbdd54a898d97fa5d5ff61ac59614adb1ceee96df088d9c1a66b6",
          "ros-src-226735737ced2aab2395",
          "ros-src-41c50c1859ca16456aed",
          "ros-src-cb3bcdabc51450e2cc2c"
        ]
      },
      {
        "name": "And",
        "provider_module": "Init.Prelude",
        "role": "Compiled external provider used by selected Project declarations.",
        "used_by_selected_node_ids": [
          "26c4dc7e5f4912c1494c383fd3d50537f9cb6328e2450925e91201f48c5d8384",
          "005d767a3193a30c065ad807166f2e150c8ac3bbd28de67fd113b74463f676eb",
          "2407611b2e8f0ff07b7d50cc8edfa17f744337c5a9ad013cf63d5ddb1eeb8840",
          "c6768fb635e387f90ed7c53fa90f5b4dfebcf526a42da7af360fbfdefc2284b6",
          "15b02dd39a6c9afbc2cc1f023c8e4b29cc806759b53b21c82065a410d00117ff",
          "ros-src-66d72b531c729bbbb88c",
          "ros-src-e9192a6956be65f01319",
          "ros-src-90127c0d2347b370cebf",
          "ff5886cf6420336dbe578275731ad0361f521340e5e9760ec098cd284273b584",
          "ros-src-fd0d0f1b35e610326c61",
          "ros-src-5a50fb2b0e66cc98b48b",
          "ros-src-f4a0c4ce3fd3539df047",
          "ros-src-b6923a9d8a2600deada8",
          "ros-src-17077f9a98c052b8187b",
          "f13185dafb7e72e6ddc0775a43c0210faf488dbee88282e3fdd08359cc7d6ad9",
          "ros-src-0264d5c421660475138e",
          "c4c4491fa52a7fbdbfde28f3dd9f46756ece7e43d6d9f8b3afb346db83d351e4",
          "964e8b0b51be9a3fc80a3f61b3bcb1b8cf70461ce4137aed6128c4ced9074130",
          "ros-src-9bafbc8fb0b4e17a561f",
          "ros-src-de97a0d50513acd04c68",
          "ros-src-29cf209852c4aa58ce37",
          "0edd904a8f54cb2f656607289f4094b52459b64013e28ed399e00bc0acd454d8",
          "155676cd74606a102aa274be40c9fb294971cfef6df06897084c9fc89322f2cb",
          "ros-src-bb0af2c5f932153961a0",
          "7a1b136b8464e6029397491d4d05fa22de45ecb383b3384c4e0c2fcf7df3150a",
          "4448c461ec5cd20bf403d08c42baa0de790b14987f7d2ab766036cdccc4b7537",
          "66a6654fa9d1e8607b27f931148203017898635ae004e222a22fd8c88c82d2f2",
          "ros-src-31aabd9922e2649eed4e",
          "ros-src-11a8ca7b0e0585d03048",
          "ros-src-df1834dfd60f65282276",
          "94b7f2220243cb53c84a521c24f6eb1f35bc8222d4162b9ea134b4c10e9ea7b4",
          "ros-src-81fe97584de561879558",
          "ros-src-2520e88617ae5d993501",
          "637afab6889bdf11fe07e21325cab3df3d3f88baeb71dff1c973c7e2a3f1a794",
          "8b10daad485fe797ba4250420c41ce6ffba033b4085e1a302b3eed0c4dd5d141",
          "f34adabc1cac70dceb32acb212d5f7c0b85c259c2c330087932a6f3fe9f5e8a9",
          "956f7a6ee326f4d3fe0fff3198e6dde0fb0903ec6f51cfb6ad39f61c2663e298",
          "fd18e1a684c11c6d461ab0afb2c4c47e3636fb5b84f9a7cca39b472897e0f86d",
          "106c2e5861a90efa2b3d1125a38099aaae4192ca2a311076da995a4ae3043e03",
          "f2686115c0a5647dbadc2b23862bf82db33c3680599f938b1b6342daaf7d4467",
          "a6b19f4652225ea9cada7c02f05c27707d0bf713859210f56ebbbf0df233cd00",
          "1e09b496fe0e06eeb046e141957245bfb51a6b1b7b8c28cf44ffdefc9574de2f",
          "d4a5a6c0e99f5d6af2aa8ac954e42542f163c769257b313f68d69c5f1c0993e5",
          "f7ac96c3bcdff8225f7123d411c404580fab1d79b3975d601484f61837409226",
          "23a70d1e81d7c3d1ed7932a2de55be2e240d36d087130ed0dd8e21ce1e3d7013",
          "9739356612e228954ac5a7eda9eacad58edcc6c064c06a3df7680ce87004f11b",
          "ros-src-226735737ced2aab2395",
          "ros-src-41c50c1859ca16456aed",
          "ros-src-fc7b77ac48f451a51fc7",
          "ros-src-cb3bcdabc51450e2cc2c",
          "ros-src-724d3e7c71466fdf73d4",
          "ros-src-efc3d1d2d13099ffe9e1",
          "ros-src-478647f701abbfb9e2db"
        ]
      },
      {
        "name": "Complex",
        "provider_module": "Mathlib.Data.Complex.Basic",
        "role": "Compiled external provider used by selected Project declarations.",
        "used_by_selected_node_ids": [
          "26c4dc7e5f4912c1494c383fd3d50537f9cb6328e2450925e91201f48c5d8384",
          "005d767a3193a30c065ad807166f2e150c8ac3bbd28de67fd113b74463f676eb",
          "2407611b2e8f0ff07b7d50cc8edfa17f744337c5a9ad013cf63d5ddb1eeb8840",
          "fe5eb271ebd53bcf76dd017a38916fe9f0357061b245cae8d78921e5470ce824",
          "c6768fb635e387f90ed7c53fa90f5b4dfebcf526a42da7af360fbfdefc2284b6",
          "15b02dd39a6c9afbc2cc1f023c8e4b29cc806759b53b21c82065a410d00117ff",
          "caeef92045d974a18cb5eb41cd4c36b68c457337d1569671d296e8f3c437fec6",
          "ros-src-66d72b531c729bbbb88c",
          "ros-src-12cd2f1f5b7c20122525",
          "ros-src-e9192a6956be65f01319",
          "ros-src-90127c0d2347b370cebf",
          "ff5886cf6420336dbe578275731ad0361f521340e5e9760ec098cd284273b584",
          "ros-src-fd0d0f1b35e610326c61",
          "ros-src-5a50fb2b0e66cc98b48b",
          "ros-src-f4a0c4ce3fd3539df047",
          "ros-src-b6923a9d8a2600deada8",
          "ros-src-17077f9a98c052b8187b",
          "f13185dafb7e72e6ddc0775a43c0210faf488dbee88282e3fdd08359cc7d6ad9",
          "ros-src-0264d5c421660475138e",
          "c4c4491fa52a7fbdbfde28f3dd9f46756ece7e43d6d9f8b3afb346db83d351e4",
          "964e8b0b51be9a3fc80a3f61b3bcb1b8cf70461ce4137aed6128c4ced9074130",
          "ros-src-9bafbc8fb0b4e17a561f",
          "ros-src-de97a0d50513acd04c68",
          "ros-src-29cf209852c4aa58ce37",
          "0edd904a8f54cb2f656607289f4094b52459b64013e28ed399e00bc0acd454d8",
          "155676cd74606a102aa274be40c9fb294971cfef6df06897084c9fc89322f2cb",
          "ros-src-bb0af2c5f932153961a0",
          "7a1b136b8464e6029397491d4d05fa22de45ecb383b3384c4e0c2fcf7df3150a",
          "4448c461ec5cd20bf403d08c42baa0de790b14987f7d2ab766036cdccc4b7537",
          "6cdd5b20c1ae2e69ab7bda0400ecc3876509dbfa7420f6561394f5c962b3509f",
          "66a6654fa9d1e8607b27f931148203017898635ae004e222a22fd8c88c82d2f2",
          "ros-src-31aabd9922e2649eed4e",
          "ros-src-11a8ca7b0e0585d03048",
          "ros-src-df1834dfd60f65282276",
          "94b7f2220243cb53c84a521c24f6eb1f35bc8222d4162b9ea134b4c10e9ea7b4",
          "ros-src-81fe97584de561879558",
          "ros-src-2520e88617ae5d993501",
          "637afab6889bdf11fe07e21325cab3df3d3f88baeb71dff1c973c7e2a3f1a794",
          "8b10daad485fe797ba4250420c41ce6ffba033b4085e1a302b3eed0c4dd5d141",
          "f34adabc1cac70dceb32acb212d5f7c0b85c259c2c330087932a6f3fe9f5e8a9",
          "956f7a6ee326f4d3fe0fff3198e6dde0fb0903ec6f51cfb6ad39f61c2663e298",
          "fd18e1a684c11c6d461ab0afb2c4c47e3636fb5b84f9a7cca39b472897e0f86d",
          "ros-src-c5203398c4e3f54aaba2",
          "106c2e5861a90efa2b3d1125a38099aaae4192ca2a311076da995a4ae3043e03",
          "f2686115c0a5647dbadc2b23862bf82db33c3680599f938b1b6342daaf7d4467",
          "ros-src-e3b1f13f7062428affde",
          "a6b19f4652225ea9cada7c02f05c27707d0bf713859210f56ebbbf0df233cd00",
          "1e09b496fe0e06eeb046e141957245bfb51a6b1b7b8c28cf44ffdefc9574de2f",
          "d4a5a6c0e99f5d6af2aa8ac954e42542f163c769257b313f68d69c5f1c0993e5",
          "f7ac96c3bcdff8225f7123d411c404580fab1d79b3975d601484f61837409226",
          "23a70d1e81d7c3d1ed7932a2de55be2e240d36d087130ed0dd8e21ce1e3d7013",
          "9739356612e228954ac5a7eda9eacad58edcc6c064c06a3df7680ce87004f11b",
          "9355a7df6defbdd54a898d97fa5d5ff61ac59614adb1ceee96df088d9c1a66b6"
        ]
      },
      {
        "name": "Exists",
        "provider_module": "Init.Core",
        "role": "Compiled external provider used by selected Project declarations.",
        "used_by_selected_node_ids": [
          "26c4dc7e5f4912c1494c383fd3d50537f9cb6328e2450925e91201f48c5d8384",
          "c6768fb635e387f90ed7c53fa90f5b4dfebcf526a42da7af360fbfdefc2284b6",
          "15b02dd39a6c9afbc2cc1f023c8e4b29cc806759b53b21c82065a410d00117ff",
          "caeef92045d974a18cb5eb41cd4c36b68c457337d1569671d296e8f3c437fec6",
          "ros-src-66d72b531c729bbbb88c",
          "ros-src-e9192a6956be65f01319",
          "ros-src-90127c0d2347b370cebf",
          "ff5886cf6420336dbe578275731ad0361f521340e5e9760ec098cd284273b584",
          "ros-src-fd0d0f1b35e610326c61",
          "ros-src-5a50fb2b0e66cc98b48b",
          "ros-src-f4a0c4ce3fd3539df047",
          "ros-src-b6923a9d8a2600deada8",
          "ros-src-17077f9a98c052b8187b",
          "f13185dafb7e72e6ddc0775a43c0210faf488dbee88282e3fdd08359cc7d6ad9",
          "ros-src-0264d5c421660475138e",
          "c4c4491fa52a7fbdbfde28f3dd9f46756ece7e43d6d9f8b3afb346db83d351e4",
          "964e8b0b51be9a3fc80a3f61b3bcb1b8cf70461ce4137aed6128c4ced9074130",
          "ros-src-9bafbc8fb0b4e17a561f",
          "ros-src-de97a0d50513acd04c68",
          "ros-src-29cf209852c4aa58ce37",
          "0edd904a8f54cb2f656607289f4094b52459b64013e28ed399e00bc0acd454d8",
          "155676cd74606a102aa274be40c9fb294971cfef6df06897084c9fc89322f2cb",
          "ros-src-bb0af2c5f932153961a0",
          "7a1b136b8464e6029397491d4d05fa22de45ecb383b3384c4e0c2fcf7df3150a",
          "4448c461ec5cd20bf403d08c42baa0de790b14987f7d2ab766036cdccc4b7537",
          "66a6654fa9d1e8607b27f931148203017898635ae004e222a22fd8c88c82d2f2",
          "ros-src-31aabd9922e2649eed4e",
          "ros-src-11a8ca7b0e0585d03048",
          "ros-src-df1834dfd60f65282276",
          "94b7f2220243cb53c84a521c24f6eb1f35bc8222d4162b9ea134b4c10e9ea7b4",
          "ros-src-81fe97584de561879558",
          "637afab6889bdf11fe07e21325cab3df3d3f88baeb71dff1c973c7e2a3f1a794",
          "8b10daad485fe797ba4250420c41ce6ffba033b4085e1a302b3eed0c4dd5d141",
          "f34adabc1cac70dceb32acb212d5f7c0b85c259c2c330087932a6f3fe9f5e8a9",
          "956f7a6ee326f4d3fe0fff3198e6dde0fb0903ec6f51cfb6ad39f61c2663e298",
          "fd18e1a684c11c6d461ab0afb2c4c47e3636fb5b84f9a7cca39b472897e0f86d",
          "ros-src-c5203398c4e3f54aaba2",
          "106c2e5861a90efa2b3d1125a38099aaae4192ca2a311076da995a4ae3043e03",
          "f2686115c0a5647dbadc2b23862bf82db33c3680599f938b1b6342daaf7d4467",
          "a6b19f4652225ea9cada7c02f05c27707d0bf713859210f56ebbbf0df233cd00",
          "1e09b496fe0e06eeb046e141957245bfb51a6b1b7b8c28cf44ffdefc9574de2f",
          "d4a5a6c0e99f5d6af2aa8ac954e42542f163c769257b313f68d69c5f1c0993e5",
          "f7ac96c3bcdff8225f7123d411c404580fab1d79b3975d601484f61837409226",
          "23a70d1e81d7c3d1ed7932a2de55be2e240d36d087130ed0dd8e21ce1e3d7013",
          "9739356612e228954ac5a7eda9eacad58edcc6c064c06a3df7680ce87004f11b",
          "ros-src-226735737ced2aab2395",
          "ros-src-41c50c1859ca16456aed",
          "ros-src-fc7b77ac48f451a51fc7",
          "ros-src-cb3bcdabc51450e2cc2c",
          "ros-src-724d3e7c71466fdf73d4",
          "9c5012403e7138fc2010b82937c3665b67957413b75f52e1a4527ad36e819be4",
          "ros-src-efc3d1d2d13099ffe9e1",
          "ros-src-478647f701abbfb9e2db"
        ]
      },
      {
        "name": "Semiring.toNonAssocSemiring",
        "provider_module": "Mathlib.Algebra.Ring.Defs",
        "role": "Compiled external provider used by selected Project declarations.",
        "used_by_selected_node_ids": [
          "26c4dc7e5f4912c1494c383fd3d50537f9cb6328e2450925e91201f48c5d8384",
          "2407611b2e8f0ff07b7d50cc8edfa17f744337c5a9ad013cf63d5ddb1eeb8840",
          "fe5eb271ebd53bcf76dd017a38916fe9f0357061b245cae8d78921e5470ce824",
          "c6768fb635e387f90ed7c53fa90f5b4dfebcf526a42da7af360fbfdefc2284b6",
          "15b02dd39a6c9afbc2cc1f023c8e4b29cc806759b53b21c82065a410d00117ff",
          "caeef92045d974a18cb5eb41cd4c36b68c457337d1569671d296e8f3c437fec6",
          "ros-src-66d72b531c729bbbb88c",
          "ros-src-12cd2f1f5b7c20122525",
          "ros-src-e9192a6956be65f01319",
          "ros-src-90127c0d2347b370cebf",
          "ff5886cf6420336dbe578275731ad0361f521340e5e9760ec098cd284273b584",
          "ros-src-fd0d0f1b35e610326c61",
          "ros-src-5a50fb2b0e66cc98b48b",
          "ros-src-f4a0c4ce3fd3539df047",
          "ros-src-b6923a9d8a2600deada8",
          "ros-src-17077f9a98c052b8187b",
          "f13185dafb7e72e6ddc0775a43c0210faf488dbee88282e3fdd08359cc7d6ad9",
          "ros-src-0264d5c421660475138e",
          "c4c4491fa52a7fbdbfde28f3dd9f46756ece7e43d6d9f8b3afb346db83d351e4",
          "964e8b0b51be9a3fc80a3f61b3bcb1b8cf70461ce4137aed6128c4ced9074130",
          "ros-src-9bafbc8fb0b4e17a561f",
          "ros-src-de97a0d50513acd04c68",
          "ros-src-29cf209852c4aa58ce37",
          "0edd904a8f54cb2f656607289f4094b52459b64013e28ed399e00bc0acd454d8",
          "155676cd74606a102aa274be40c9fb294971cfef6df06897084c9fc89322f2cb",
          "ros-src-bb0af2c5f932153961a0",
          "7a1b136b8464e6029397491d4d05fa22de45ecb383b3384c4e0c2fcf7df3150a",
          "4448c461ec5cd20bf403d08c42baa0de790b14987f7d2ab766036cdccc4b7537",
          "66a6654fa9d1e8607b27f931148203017898635ae004e222a22fd8c88c82d2f2",
          "ros-src-31aabd9922e2649eed4e",
          "ros-src-11a8ca7b0e0585d03048",
          "ros-src-df1834dfd60f65282276",
          "94b7f2220243cb53c84a521c24f6eb1f35bc8222d4162b9ea134b4c10e9ea7b4",
          "ros-src-81fe97584de561879558",
          "ros-src-2520e88617ae5d993501",
          "637afab6889bdf11fe07e21325cab3df3d3f88baeb71dff1c973c7e2a3f1a794",
          "8b10daad485fe797ba4250420c41ce6ffba033b4085e1a302b3eed0c4dd5d141",
          "f34adabc1cac70dceb32acb212d5f7c0b85c259c2c330087932a6f3fe9f5e8a9",
          "956f7a6ee326f4d3fe0fff3198e6dde0fb0903ec6f51cfb6ad39f61c2663e298",
          "fd18e1a684c11c6d461ab0afb2c4c47e3636fb5b84f9a7cca39b472897e0f86d",
          "ros-src-c5203398c4e3f54aaba2",
          "106c2e5861a90efa2b3d1125a38099aaae4192ca2a311076da995a4ae3043e03",
          "f2686115c0a5647dbadc2b23862bf82db33c3680599f938b1b6342daaf7d4467",
          "ros-src-e3b1f13f7062428affde",
          "a6b19f4652225ea9cada7c02f05c27707d0bf713859210f56ebbbf0df233cd00",
          "1e09b496fe0e06eeb046e141957245bfb51a6b1b7b8c28cf44ffdefc9574de2f",
          "f7ac96c3bcdff8225f7123d411c404580fab1d79b3975d601484f61837409226",
          "23a70d1e81d7c3d1ed7932a2de55be2e240d36d087130ed0dd8e21ce1e3d7013",
          "9739356612e228954ac5a7eda9eacad58edcc6c064c06a3df7680ce87004f11b",
          "9355a7df6defbdd54a898d97fa5d5ff61ac59614adb1ceee96df088d9c1a66b6",
          "ros-src-226735737ced2aab2395",
          "ros-src-41c50c1859ca16456aed",
          "ros-src-cb3bcdabc51450e2cc2c"
        ]
      },
      {
        "name": "Complex.instNormedField",
        "provider_module": "Mathlib.Analysis.Complex.Basic",
        "role": "Compiled external provider used by selected Project declarations.",
        "used_by_selected_node_ids": [
          "26c4dc7e5f4912c1494c383fd3d50537f9cb6328e2450925e91201f48c5d8384",
          "005d767a3193a30c065ad807166f2e150c8ac3bbd28de67fd113b74463f676eb",
          "2407611b2e8f0ff07b7d50cc8edfa17f744337c5a9ad013cf63d5ddb1eeb8840",
          "fe5eb271ebd53bcf76dd017a38916fe9f0357061b245cae8d78921e5470ce824",
          "c6768fb635e387f90ed7c53fa90f5b4dfebcf526a42da7af360fbfdefc2284b6",
          "15b02dd39a6c9afbc2cc1f023c8e4b29cc806759b53b21c82065a410d00117ff",
          "caeef92045d974a18cb5eb41cd4c36b68c457337d1569671d296e8f3c437fec6",
          "ros-src-66d72b531c729bbbb88c",
          "ros-src-12cd2f1f5b7c20122525",
          "ros-src-e9192a6956be65f01319",
          "ros-src-90127c0d2347b370cebf",
          "ff5886cf6420336dbe578275731ad0361f521340e5e9760ec098cd284273b584",
          "ros-src-fd0d0f1b35e610326c61",
          "ros-src-5a50fb2b0e66cc98b48b",
          "ros-src-f4a0c4ce3fd3539df047",
          "ros-src-b6923a9d8a2600deada8",
          "ros-src-17077f9a98c052b8187b",
          "f13185dafb7e72e6ddc0775a43c0210faf488dbee88282e3fdd08359cc7d6ad9",
          "ros-src-0264d5c421660475138e",
          "c4c4491fa52a7fbdbfde28f3dd9f46756ece7e43d6d9f8b3afb346db83d351e4",
          "964e8b0b51be9a3fc80a3f61b3bcb1b8cf70461ce4137aed6128c4ced9074130",
          "ros-src-9bafbc8fb0b4e17a561f",
          "ros-src-de97a0d50513acd04c68",
          "ros-src-29cf209852c4aa58ce37",
          "0edd904a8f54cb2f656607289f4094b52459b64013e28ed399e00bc0acd454d8",
          "155676cd74606a102aa274be40c9fb294971cfef6df06897084c9fc89322f2cb",
          "ros-src-bb0af2c5f932153961a0",
          "7a1b136b8464e6029397491d4d05fa22de45ecb383b3384c4e0c2fcf7df3150a",
          "4448c461ec5cd20bf403d08c42baa0de790b14987f7d2ab766036cdccc4b7537",
          "6cdd5b20c1ae2e69ab7bda0400ecc3876509dbfa7420f6561394f5c962b3509f",
          "66a6654fa9d1e8607b27f931148203017898635ae004e222a22fd8c88c82d2f2",
          "ros-src-31aabd9922e2649eed4e",
          "ros-src-11a8ca7b0e0585d03048",
          "ros-src-df1834dfd60f65282276",
          "94b7f2220243cb53c84a521c24f6eb1f35bc8222d4162b9ea134b4c10e9ea7b4",
          "ros-src-81fe97584de561879558",
          "ros-src-2520e88617ae5d993501",
          "637afab6889bdf11fe07e21325cab3df3d3f88baeb71dff1c973c7e2a3f1a794",
          "8b10daad485fe797ba4250420c41ce6ffba033b4085e1a302b3eed0c4dd5d141",
          "f34adabc1cac70dceb32acb212d5f7c0b85c259c2c330087932a6f3fe9f5e8a9",
          "956f7a6ee326f4d3fe0fff3198e6dde0fb0903ec6f51cfb6ad39f61c2663e298",
          "fd18e1a684c11c6d461ab0afb2c4c47e3636fb5b84f9a7cca39b472897e0f86d",
          "ros-src-c5203398c4e3f54aaba2",
          "106c2e5861a90efa2b3d1125a38099aaae4192ca2a311076da995a4ae3043e03",
          "f2686115c0a5647dbadc2b23862bf82db33c3680599f938b1b6342daaf7d4467",
          "a6b19f4652225ea9cada7c02f05c27707d0bf713859210f56ebbbf0df233cd00",
          "1e09b496fe0e06eeb046e141957245bfb51a6b1b7b8c28cf44ffdefc9574de2f",
          "d4a5a6c0e99f5d6af2aa8ac954e42542f163c769257b313f68d69c5f1c0993e5",
          "f7ac96c3bcdff8225f7123d411c404580fab1d79b3975d601484f61837409226",
          "23a70d1e81d7c3d1ed7932a2de55be2e240d36d087130ed0dd8e21ce1e3d7013",
          "9739356612e228954ac5a7eda9eacad58edcc6c064c06a3df7680ce87004f11b",
          "9355a7df6defbdd54a898d97fa5d5ff61ac59614adb1ceee96df088d9c1a66b6"
        ]
      },
      {
        "name": "Ring.toSemiring",
        "provider_module": "Mathlib.Algebra.Ring.Defs",
        "role": "Compiled external provider used by selected Project declarations.",
        "used_by_selected_node_ids": [
          "005d767a3193a30c065ad807166f2e150c8ac3bbd28de67fd113b74463f676eb",
          "2407611b2e8f0ff07b7d50cc8edfa17f744337c5a9ad013cf63d5ddb1eeb8840",
          "c6768fb635e387f90ed7c53fa90f5b4dfebcf526a42da7af360fbfdefc2284b6",
          "15b02dd39a6c9afbc2cc1f023c8e4b29cc806759b53b21c82065a410d00117ff",
          "ros-src-66d72b531c729bbbb88c",
          "ros-src-12cd2f1f5b7c20122525",
          "ros-src-e9192a6956be65f01319",
          "ros-src-90127c0d2347b370cebf",
          "ff5886cf6420336dbe578275731ad0361f521340e5e9760ec098cd284273b584",
          "ros-src-fd0d0f1b35e610326c61",
          "ros-src-5a50fb2b0e66cc98b48b",
          "ros-src-f4a0c4ce3fd3539df047",
          "ros-src-b6923a9d8a2600deada8",
          "ros-src-17077f9a98c052b8187b",
          "f13185dafb7e72e6ddc0775a43c0210faf488dbee88282e3fdd08359cc7d6ad9",
          "ros-src-0264d5c421660475138e",
          "c4c4491fa52a7fbdbfde28f3dd9f46756ece7e43d6d9f8b3afb346db83d351e4",
          "964e8b0b51be9a3fc80a3f61b3bcb1b8cf70461ce4137aed6128c4ced9074130",
          "ros-src-9bafbc8fb0b4e17a561f",
          "ros-src-de97a0d50513acd04c68",
          "ros-src-29cf209852c4aa58ce37",
          "0edd904a8f54cb2f656607289f4094b52459b64013e28ed399e00bc0acd454d8",
          "155676cd74606a102aa274be40c9fb294971cfef6df06897084c9fc89322f2cb",
          "ros-src-bb0af2c5f932153961a0",
          "7a1b136b8464e6029397491d4d05fa22de45ecb383b3384c4e0c2fcf7df3150a",
          "4448c461ec5cd20bf403d08c42baa0de790b14987f7d2ab766036cdccc4b7537",
          "6cdd5b20c1ae2e69ab7bda0400ecc3876509dbfa7420f6561394f5c962b3509f",
          "66a6654fa9d1e8607b27f931148203017898635ae004e222a22fd8c88c82d2f2",
          "ros-src-31aabd9922e2649eed4e",
          "ros-src-11a8ca7b0e0585d03048",
          "ros-src-df1834dfd60f65282276",
          "94b7f2220243cb53c84a521c24f6eb1f35bc8222d4162b9ea134b4c10e9ea7b4",
          "ros-src-81fe97584de561879558",
          "ros-src-2520e88617ae5d993501",
          "637afab6889bdf11fe07e21325cab3df3d3f88baeb71dff1c973c7e2a3f1a794",
          "8b10daad485fe797ba4250420c41ce6ffba033b4085e1a302b3eed0c4dd5d141",
          "f34adabc1cac70dceb32acb212d5f7c0b85c259c2c330087932a6f3fe9f5e8a9",
          "956f7a6ee326f4d3fe0fff3198e6dde0fb0903ec6f51cfb6ad39f61c2663e298",
          "fd18e1a684c11c6d461ab0afb2c4c47e3636fb5b84f9a7cca39b472897e0f86d",
          "ros-src-c5203398c4e3f54aaba2",
          "106c2e5861a90efa2b3d1125a38099aaae4192ca2a311076da995a4ae3043e03",
          "f2686115c0a5647dbadc2b23862bf82db33c3680599f938b1b6342daaf7d4467",
          "ros-src-e3b1f13f7062428affde",
          "a6b19f4652225ea9cada7c02f05c27707d0bf713859210f56ebbbf0df233cd00",
          "1e09b496fe0e06eeb046e141957245bfb51a6b1b7b8c28cf44ffdefc9574de2f",
          "d4a5a6c0e99f5d6af2aa8ac954e42542f163c769257b313f68d69c5f1c0993e5",
          "f7ac96c3bcdff8225f7123d411c404580fab1d79b3975d601484f61837409226",
          "23a70d1e81d7c3d1ed7932a2de55be2e240d36d087130ed0dd8e21ce1e3d7013",
          "9739356612e228954ac5a7eda9eacad58edcc6c064c06a3df7680ce87004f11b",
          "ros-src-226735737ced2aab2395",
          "ros-src-41c50c1859ca16456aed",
          "ros-src-cb3bcdabc51450e2cc2c"
        ]
      },
      {
        "name": "Semiring.toMonoid",
        "provider_module": "Mathlib.Algebra.Ring.Defs",
        "role": "Compiled external provider used by selected Project declarations.",
        "used_by_selected_node_ids": [
          "26c4dc7e5f4912c1494c383fd3d50537f9cb6328e2450925e91201f48c5d8384",
          "2407611b2e8f0ff07b7d50cc8edfa17f744337c5a9ad013cf63d5ddb1eeb8840",
          "fe5eb271ebd53bcf76dd017a38916fe9f0357061b245cae8d78921e5470ce824",
          "c6768fb635e387f90ed7c53fa90f5b4dfebcf526a42da7af360fbfdefc2284b6",
          "15b02dd39a6c9afbc2cc1f023c8e4b29cc806759b53b21c82065a410d00117ff",
          "caeef92045d974a18cb5eb41cd4c36b68c457337d1569671d296e8f3c437fec6",
          "ros-src-66d72b531c729bbbb88c",
          "ros-src-12cd2f1f5b7c20122525",
          "ros-src-e9192a6956be65f01319",
          "ros-src-90127c0d2347b370cebf",
          "ff5886cf6420336dbe578275731ad0361f521340e5e9760ec098cd284273b584",
          "ros-src-fd0d0f1b35e610326c61",
          "ros-src-5a50fb2b0e66cc98b48b",
          "ros-src-f4a0c4ce3fd3539df047",
          "ros-src-b6923a9d8a2600deada8",
          "ros-src-17077f9a98c052b8187b",
          "f13185dafb7e72e6ddc0775a43c0210faf488dbee88282e3fdd08359cc7d6ad9",
          "ros-src-0264d5c421660475138e",
          "c4c4491fa52a7fbdbfde28f3dd9f46756ece7e43d6d9f8b3afb346db83d351e4",
          "964e8b0b51be9a3fc80a3f61b3bcb1b8cf70461ce4137aed6128c4ced9074130",
          "ros-src-9bafbc8fb0b4e17a561f",
          "ros-src-de97a0d50513acd04c68",
          "ros-src-29cf209852c4aa58ce37",
          "0edd904a8f54cb2f656607289f4094b52459b64013e28ed399e00bc0acd454d8",
          "155676cd74606a102aa274be40c9fb294971cfef6df06897084c9fc89322f2cb",
          "ros-src-bb0af2c5f932153961a0",
          "7a1b136b8464e6029397491d4d05fa22de45ecb383b3384c4e0c2fcf7df3150a",
          "4448c461ec5cd20bf403d08c42baa0de790b14987f7d2ab766036cdccc4b7537",
          "66a6654fa9d1e8607b27f931148203017898635ae004e222a22fd8c88c82d2f2",
          "ros-src-31aabd9922e2649eed4e",
          "ros-src-11a8ca7b0e0585d03048",
          "ros-src-df1834dfd60f65282276",
          "94b7f2220243cb53c84a521c24f6eb1f35bc8222d4162b9ea134b4c10e9ea7b4",
          "ros-src-81fe97584de561879558",
          "ros-src-2520e88617ae5d993501",
          "637afab6889bdf11fe07e21325cab3df3d3f88baeb71dff1c973c7e2a3f1a794",
          "8b10daad485fe797ba4250420c41ce6ffba033b4085e1a302b3eed0c4dd5d141",
          "f34adabc1cac70dceb32acb212d5f7c0b85c259c2c330087932a6f3fe9f5e8a9",
          "956f7a6ee326f4d3fe0fff3198e6dde0fb0903ec6f51cfb6ad39f61c2663e298",
          "fd18e1a684c11c6d461ab0afb2c4c47e3636fb5b84f9a7cca39b472897e0f86d",
          "ros-src-c5203398c4e3f54aaba2",
          "106c2e5861a90efa2b3d1125a38099aaae4192ca2a311076da995a4ae3043e03",
          "f2686115c0a5647dbadc2b23862bf82db33c3680599f938b1b6342daaf7d4467",
          "ros-src-e3b1f13f7062428affde",
          "a6b19f4652225ea9cada7c02f05c27707d0bf713859210f56ebbbf0df233cd00",
          "f7ac96c3bcdff8225f7123d411c404580fab1d79b3975d601484f61837409226",
          "23a70d1e81d7c3d1ed7932a2de55be2e240d36d087130ed0dd8e21ce1e3d7013",
          "9739356612e228954ac5a7eda9eacad58edcc6c064c06a3df7680ce87004f11b",
          "9355a7df6defbdd54a898d97fa5d5ff61ac59614adb1ceee96df088d9c1a66b6",
          "ros-src-226735737ced2aab2395",
          "ros-src-41c50c1859ca16456aed",
          "ros-src-cb3bcdabc51450e2cc2c"
        ]
      },
      {
        "name": "Set",
        "provider_module": "Mathlib.Data.Set.Defs",
        "role": "Compiled external provider used by selected Project declarations.",
        "used_by_selected_node_ids": [
          "ros-src-381b2fd00802311a7e69",
          "2407611b2e8f0ff07b7d50cc8edfa17f744337c5a9ad013cf63d5ddb1eeb8840",
          "ros-src-66d72b531c729bbbb88c",
          "ros-src-e9192a6956be65f01319",
          "ros-src-90127c0d2347b370cebf",
          "ff5886cf6420336dbe578275731ad0361f521340e5e9760ec098cd284273b584",
          "ros-src-fd0d0f1b35e610326c61",
          "ros-src-5a50fb2b0e66cc98b48b",
          "ros-src-f4a0c4ce3fd3539df047",
          "ros-src-b6923a9d8a2600deada8",
          "ros-src-17077f9a98c052b8187b",
          "f13185dafb7e72e6ddc0775a43c0210faf488dbee88282e3fdd08359cc7d6ad9",
          "ros-src-0264d5c421660475138e",
          "c4c4491fa52a7fbdbfde28f3dd9f46756ece7e43d6d9f8b3afb346db83d351e4",
          "964e8b0b51be9a3fc80a3f61b3bcb1b8cf70461ce4137aed6128c4ced9074130",
          "ros-src-9bafbc8fb0b4e17a561f",
          "ros-src-de97a0d50513acd04c68",
          "ros-src-29cf209852c4aa58ce37",
          "0edd904a8f54cb2f656607289f4094b52459b64013e28ed399e00bc0acd454d8",
          "155676cd74606a102aa274be40c9fb294971cfef6df06897084c9fc89322f2cb",
          "ros-src-bb0af2c5f932153961a0",
          "7a1b136b8464e6029397491d4d05fa22de45ecb383b3384c4e0c2fcf7df3150a",
          "4448c461ec5cd20bf403d08c42baa0de790b14987f7d2ab766036cdccc4b7537",
          "66a6654fa9d1e8607b27f931148203017898635ae004e222a22fd8c88c82d2f2",
          "ros-src-31aabd9922e2649eed4e",
          "ros-src-11a8ca7b0e0585d03048",
          "ros-src-df1834dfd60f65282276",
          "94b7f2220243cb53c84a521c24f6eb1f35bc8222d4162b9ea134b4c10e9ea7b4",
          "ros-src-81fe97584de561879558",
          "ros-src-2520e88617ae5d993501",
          "8b10daad485fe797ba4250420c41ce6ffba033b4085e1a302b3eed0c4dd5d141",
          "f34adabc1cac70dceb32acb212d5f7c0b85c259c2c330087932a6f3fe9f5e8a9",
          "956f7a6ee326f4d3fe0fff3198e6dde0fb0903ec6f51cfb6ad39f61c2663e298",
          "fd18e1a684c11c6d461ab0afb2c4c47e3636fb5b84f9a7cca39b472897e0f86d",
          "106c2e5861a90efa2b3d1125a38099aaae4192ca2a311076da995a4ae3043e03",
          "f2686115c0a5647dbadc2b23862bf82db33c3680599f938b1b6342daaf7d4467",
          "a6b19f4652225ea9cada7c02f05c27707d0bf713859210f56ebbbf0df233cd00",
          "1e09b496fe0e06eeb046e141957245bfb51a6b1b7b8c28cf44ffdefc9574de2f",
          "d4a5a6c0e99f5d6af2aa8ac954e42542f163c769257b313f68d69c5f1c0993e5",
          "f7ac96c3bcdff8225f7123d411c404580fab1d79b3975d601484f61837409226",
          "23a70d1e81d7c3d1ed7932a2de55be2e240d36d087130ed0dd8e21ce1e3d7013",
          "9739356612e228954ac5a7eda9eacad58edcc6c064c06a3df7680ce87004f11b",
          "9355a7df6defbdd54a898d97fa5d5ff61ac59614adb1ceee96df088d9c1a66b6",
          "ros-src-226735737ced2aab2395",
          "ros-src-41c50c1859ca16456aed",
          "ros-src-81911ae7885c6426216d",
          "ros-src-fc7b77ac48f451a51fc7",
          "ros-src-cb3bcdabc51450e2cc2c",
          "ros-src-724d3e7c71466fdf73d4",
          "9c5012403e7138fc2010b82937c3665b67957413b75f52e1a4527ad36e819be4",
          "ros-src-efc3d1d2d13099ffe9e1",
          "ros-src-478647f701abbfb9e2db"
        ]
      },
      {
        "name": "AddCommMonoid.toAddMonoid",
        "provider_module": "Mathlib.Algebra.Group.Defs",
        "role": "Compiled external provider used by selected Project declarations.",
        "used_by_selected_node_ids": [
          "26c4dc7e5f4912c1494c383fd3d50537f9cb6328e2450925e91201f48c5d8384",
          "2407611b2e8f0ff07b7d50cc8edfa17f744337c5a9ad013cf63d5ddb1eeb8840",
          "fe5eb271ebd53bcf76dd017a38916fe9f0357061b245cae8d78921e5470ce824",
          "c6768fb635e387f90ed7c53fa90f5b4dfebcf526a42da7af360fbfdefc2284b6",
          "15b02dd39a6c9afbc2cc1f023c8e4b29cc806759b53b21c82065a410d00117ff",
          "caeef92045d974a18cb5eb41cd4c36b68c457337d1569671d296e8f3c437fec6",
          "ros-src-66d72b531c729bbbb88c",
          "ros-src-12cd2f1f5b7c20122525",
          "ros-src-e9192a6956be65f01319",
          "ros-src-90127c0d2347b370cebf",
          "ff5886cf6420336dbe578275731ad0361f521340e5e9760ec098cd284273b584",
          "ros-src-fd0d0f1b35e610326c61",
          "ros-src-5a50fb2b0e66cc98b48b",
          "ros-src-f4a0c4ce3fd3539df047",
          "ros-src-b6923a9d8a2600deada8",
          "ros-src-17077f9a98c052b8187b",
          "f13185dafb7e72e6ddc0775a43c0210faf488dbee88282e3fdd08359cc7d6ad9",
          "ros-src-0264d5c421660475138e",
          "c4c4491fa52a7fbdbfde28f3dd9f46756ece7e43d6d9f8b3afb346db83d351e4",
          "964e8b0b51be9a3fc80a3f61b3bcb1b8cf70461ce4137aed6128c4ced9074130",
          "ros-src-9bafbc8fb0b4e17a561f",
          "ros-src-de97a0d50513acd04c68",
          "ros-src-29cf209852c4aa58ce37",
          "0edd904a8f54cb2f656607289f4094b52459b64013e28ed399e00bc0acd454d8",
          "155676cd74606a102aa274be40c9fb294971cfef6df06897084c9fc89322f2cb",
          "ros-src-bb0af2c5f932153961a0",
          "7a1b136b8464e6029397491d4d05fa22de45ecb383b3384c4e0c2fcf7df3150a",
          "4448c461ec5cd20bf403d08c42baa0de790b14987f7d2ab766036cdccc4b7537",
          "66a6654fa9d1e8607b27f931148203017898635ae004e222a22fd8c88c82d2f2",
          "ros-src-31aabd9922e2649eed4e",
          "ros-src-11a8ca7b0e0585d03048",
          "ros-src-df1834dfd60f65282276",
          "94b7f2220243cb53c84a521c24f6eb1f35bc8222d4162b9ea134b4c10e9ea7b4",
          "ros-src-81fe97584de561879558",
          "ros-src-2520e88617ae5d993501",
          "637afab6889bdf11fe07e21325cab3df3d3f88baeb71dff1c973c7e2a3f1a794",
          "8b10daad485fe797ba4250420c41ce6ffba033b4085e1a302b3eed0c4dd5d141",
          "f34adabc1cac70dceb32acb212d5f7c0b85c259c2c330087932a6f3fe9f5e8a9",
          "956f7a6ee326f4d3fe0fff3198e6dde0fb0903ec6f51cfb6ad39f61c2663e298",
          "fd18e1a684c11c6d461ab0afb2c4c47e3636fb5b84f9a7cca39b472897e0f86d",
          "ros-src-c5203398c4e3f54aaba2",
          "106c2e5861a90efa2b3d1125a38099aaae4192ca2a311076da995a4ae3043e03",
          "f2686115c0a5647dbadc2b23862bf82db33c3680599f938b1b6342daaf7d4467",
          "ros-src-e3b1f13f7062428affde",
          "a6b19f4652225ea9cada7c02f05c27707d0bf713859210f56ebbbf0df233cd00",
          "1e09b496fe0e06eeb046e141957245bfb51a6b1b7b8c28cf44ffdefc9574de2f",
          "d4a5a6c0e99f5d6af2aa8ac954e42542f163c769257b313f68d69c5f1c0993e5",
          "f7ac96c3bcdff8225f7123d411c404580fab1d79b3975d601484f61837409226",
          "23a70d1e81d7c3d1ed7932a2de55be2e240d36d087130ed0dd8e21ce1e3d7013",
          "9739356612e228954ac5a7eda9eacad58edcc6c064c06a3df7680ce87004f11b",
          "9355a7df6defbdd54a898d97fa5d5ff61ac59614adb1ceee96df088d9c1a66b6"
        ]
      },
      {
        "name": "AddGroup.toSubNegMonoid",
        "provider_module": "Mathlib.Algebra.Group.Defs",
        "role": "Compiled external provider used by selected Project declarations.",
        "used_by_selected_node_ids": [
          "26c4dc7e5f4912c1494c383fd3d50537f9cb6328e2450925e91201f48c5d8384",
          "fe5eb271ebd53bcf76dd017a38916fe9f0357061b245cae8d78921e5470ce824",
          "c6768fb635e387f90ed7c53fa90f5b4dfebcf526a42da7af360fbfdefc2284b6",
          "15b02dd39a6c9afbc2cc1f023c8e4b29cc806759b53b21c82065a410d00117ff",
          "caeef92045d974a18cb5eb41cd4c36b68c457337d1569671d296e8f3c437fec6",
          "ros-src-66d72b531c729bbbb88c",
          "ros-src-12cd2f1f5b7c20122525",
          "ros-src-e9192a6956be65f01319",
          "ros-src-90127c0d2347b370cebf",
          "ff5886cf6420336dbe578275731ad0361f521340e5e9760ec098cd284273b584",
          "ros-src-fd0d0f1b35e610326c61",
          "ros-src-5a50fb2b0e66cc98b48b",
          "ros-src-f4a0c4ce3fd3539df047",
          "ros-src-b6923a9d8a2600deada8",
          "ros-src-17077f9a98c052b8187b",
          "f13185dafb7e72e6ddc0775a43c0210faf488dbee88282e3fdd08359cc7d6ad9",
          "ros-src-0264d5c421660475138e",
          "c4c4491fa52a7fbdbfde28f3dd9f46756ece7e43d6d9f8b3afb346db83d351e4",
          "964e8b0b51be9a3fc80a3f61b3bcb1b8cf70461ce4137aed6128c4ced9074130",
          "ros-src-9bafbc8fb0b4e17a561f",
          "ros-src-de97a0d50513acd04c68",
          "ros-src-29cf209852c4aa58ce37",
          "0edd904a8f54cb2f656607289f4094b52459b64013e28ed399e00bc0acd454d8",
          "155676cd74606a102aa274be40c9fb294971cfef6df06897084c9fc89322f2cb",
          "ros-src-bb0af2c5f932153961a0",
          "7a1b136b8464e6029397491d4d05fa22de45ecb383b3384c4e0c2fcf7df3150a",
          "4448c461ec5cd20bf403d08c42baa0de790b14987f7d2ab766036cdccc4b7537",
          "66a6654fa9d1e8607b27f931148203017898635ae004e222a22fd8c88c82d2f2",
          "ros-src-31aabd9922e2649eed4e",
          "ros-src-11a8ca7b0e0585d03048",
          "ros-src-df1834dfd60f65282276",
          "94b7f2220243cb53c84a521c24f6eb1f35bc8222d4162b9ea134b4c10e9ea7b4",
          "ros-src-81fe97584de561879558",
          "ros-src-2520e88617ae5d993501",
          "637afab6889bdf11fe07e21325cab3df3d3f88baeb71dff1c973c7e2a3f1a794",
          "8b10daad485fe797ba4250420c41ce6ffba033b4085e1a302b3eed0c4dd5d141",
          "f34adabc1cac70dceb32acb212d5f7c0b85c259c2c330087932a6f3fe9f5e8a9",
          "956f7a6ee326f4d3fe0fff3198e6dde0fb0903ec6f51cfb6ad39f61c2663e298",
          "fd18e1a684c11c6d461ab0afb2c4c47e3636fb5b84f9a7cca39b472897e0f86d",
          "ros-src-c5203398c4e3f54aaba2",
          "106c2e5861a90efa2b3d1125a38099aaae4192ca2a311076da995a4ae3043e03",
          "f2686115c0a5647dbadc2b23862bf82db33c3680599f938b1b6342daaf7d4467",
          "ros-src-e3b1f13f7062428affde",
          "a6b19f4652225ea9cada7c02f05c27707d0bf713859210f56ebbbf0df233cd00",
          "f7ac96c3bcdff8225f7123d411c404580fab1d79b3975d601484f61837409226",
          "23a70d1e81d7c3d1ed7932a2de55be2e240d36d087130ed0dd8e21ce1e3d7013",
          "9739356612e228954ac5a7eda9eacad58edcc6c064c06a3df7680ce87004f11b",
          "9355a7df6defbdd54a898d97fa5d5ff61ac59614adb1ceee96df088d9c1a66b6",
          "ros-src-226735737ced2aab2395",
          "ros-src-41c50c1859ca16456aed",
          "ros-src-cb3bcdabc51450e2cc2c"
        ]
      }
    ],
    "raw_count": 2690,
    "summary": "2690 exact Boundary Inputs: EXTERNAL_COMPILED_DECLARATION 2233, OMITTED_INTERNAL_NATIVE_DECLARATION 457. Selected reachability is retained through every omitted internal declaration."
  },
  "graph": {
    "display_edge_count": 88,
    "full_formal_graph_sha256": "e0c69751546f310fb7e15d2915c7e7b0f6a710eb0bc33269b24c2b228bcb5425",
    "full_project_level_map_sha256": "92f8677874684b6e10ed2f1f4921711facee0926086f7fc073989e6a34a04e6e",
    "maximum_level": 10,
    "naive_induced_lost_pairs": 355,
    "node_count": 63,
    "orientation": "dependent_to_prerequisite",
    "reachability_count": 509
  },
  "identity": {
    "slug": "rosenberg",
    "title": "Rosenberg Compact-Operator Model"
  },
  "overview": {
    "bridges": [
      {
        "preset_id": "faithfulness",
        "terminal_node_ids": [
          "66a6654fa9d1e8607b27f931148203017898635ae004e222a22fd8c88c82d2f2"
        ],
        "text": "A pure state detecting a nonzero kernel element yields a nonzero irreducible GNS representation. Because every nonzero irreducible representation lies in the unique unitary-equivalence class represented by π, unitary equivalence forces the kernel element to act nontrivially, a contradiction.",
        "title": "Faithfulness"
      },
      {
        "preset_id": "characters-eigenvectors",
        "terminal_node_ids": [
          "7a1b136b8464e6029397491d4d05fa22de45ecb383b3384c4e0c2fcf7df3150a"
        ],
        "text": "A character on a closed star subalgebra of the minimal unitization extends to a pure state. For a character distinct from the scalar character, the restricted GNS representation produces a unit joint eigenvector with that prescribed character.",
        "title": "Characters and eigenvectors"
      },
      {
        "preset_id": "countability-scalar-corner",
        "terminal_node_ids": [
          "ff5886cf6420336dbe578275731ad0361f521340e5e9760ec098cd284273b584",
          "964e8b0b51be9a3fc80a3f61b3bcb1b8cf70461ce4137aed6128c4ced9074130"
        ],
        "text": "Distinct character eigenvectors are orthogonal. Separability of H makes the nonscalar character space countable; an isolated character then yields a nonzero projection whose corner is scalar.",
        "title": "Countability and a scalar corner"
      },
      {
        "preset_id": "every-compact",
        "terminal_node_ids": [
          "0edd904a8f54cb2f656607289f4094b52459b64013e28ed399e00bc0acd454d8"
        ],
        "text": "A rank-one image and irreducible interpolation give exact preimages for operators of the form rankOne. Closed range and finite-rank approximation then give an exact preimage for every compact operator.",
        "title": "Every compact operator has a preimage"
      },
      {
        "preset_id": "only-compact",
        "terminal_node_ids": [
          "94b7f2220243cb53c84a521c24f6eb1f35bc8222d4162b9ea134b4c10e9ea7b4"
        ],
        "text": "If some represented operator were noncompact, a character would separate a maximal abelian witness from the compact-preimage ideal. The resulting eigenvector conflicts with a rank-one preimage, so every image operator is compact.",
        "title": "Every represented operator is compact"
      },
      {
        "preset_id": "unital-consequences",
        "terminal_node_ids": [
          "f34adabc1cac70dceb32acb212d5f7c0b85c259c2c330087932a6f3fe9f5e8a9"
        ],
        "text": "For a unital algebra, the version quantifying competitors through the nonunital representation interface yields the same unique-class condition. Compactness of the identity image forces H to be finite-dimensional, then injectivity forces A to be finite-dimensional, giving the stated nonexistence consequence.",
        "title": "Unital finite-dimensional consequences"
      },
      {
        "preset_id": "density",
        "route_id": "density",
        "selected_count": 45,
        "terminal_node_ids": [
          "ros-src-31aabd9922e2649eed4e",
          "ros-src-11a8ca7b0e0585d03048",
          "ros-src-90127c0d2347b370cebf",
          "ros-src-e9192a6956be65f01319"
        ],
        "text": "The compact-operator model route extends from separable representation spaces to an irreducible representation space with a norm-dense subset of cardinality strictly below the continuum. The nonunital statements retain the ordinary singleton-model hypotheses. Contrapositively, a singleton model that is not a compact-operator model forces every norm-dense subset of its representation space, and every norm-dense subset of the algebra, to have cardinality at least the continuum. This is a source-only extension of the reviewed 33-Card route; it creates no additional Cards. These statements are about the singleton irreducible model; the lower bound on its Hilbert space does not apply to arbitrary faithful reducible representations.",
        "title": "Density below the continuum and the compact-operator model"
      }
    ],
    "hypotheses": "A is nonzero and may be genuinely nonunital. H is separable. The representation π is nonzero and irreducible, and every nonzero irreducible representation of A is unitarily equivalent to π. No separability of A, prior faithfulness or simplicity is assumed. The unital finite-dimensional consequences have their own exact hypotheses.",
    "principal_result": "Let A be a nonzero complex C*-algebra, not assumed unital, and let π act on a separable complex Hilbert space H as a representative of the unique unitary-equivalence class of nonzero irreducible representations of A. Then π is injective, every represented operator is compact, and every compact operator on H has an exact preimage in A.",
    "scope_limits": "The 33 Card explanations have completed source-exposition correspondence review against exact MathlibAnnex v0.4.0 source. The compact-operator characterization is unbundled; no bundled StarAlgEquiv is supplied. The original 1953 paper and the Farah book remain unacquired and unreviewed in this record.",
    "why_it_matters": "The result identifies A, through π, with the compact-operator model in an exact unbundled sense. The Project exposes the reusable proof route through faithfulness, character eigenvectors, countability, scalar corners, rank-one preimages and compact approximation."
  },
  "presentation": {
    "kind_label": "Theorem Project",
    "notice": "Thirty-three Declaration Card expositions are available. The added density route is source-only and creates no Card.",
    "profile": "LFH_PUBLIC_PROFILE_SUCCESSOR_R1",
    "state": "PRIVATE_LOCAL_INTEGRATION"
  },
  "project_kind": "THEOREM_PROJECT",
  "record_type": "LFH_PROJECT_MANIFEST",
  "revision": "R1-CANDIDATE",
  "route_presets": [
    {
      "expected_visible_count": 9,
      "expected_visible_node_ids_sha256": "fb61f061911862a05270b7518765423cbcce46c2ee06e0f75a0ff620ba015bf3",
      "focus_semantics": "ANCESTOR_CLOSURE_IN_PROJECT",
      "full_project_level_map_sha256": "92f8677874684b6e10ed2f1f4921711facee0926086f7fc073989e6a34a04e6e",
      "id": "faithfulness",
      "label": "Faithfulness",
      "review_state": "EXISTING_33_CARD_ROUTE_RECHECKED_AGAINST_CURRENT_NATIVE_GRAPH",
      "status": "ACTIVE",
      "terminal_node_ids": [
        "66a6654fa9d1e8607b27f931148203017898635ae004e222a22fd8c88c82d2f2"
      ]
    },
    {
      "expected_visible_count": 8,
      "expected_visible_node_ids_sha256": "8c7ea2fd91f9c9b637f7b548cc59b88a8efbe556fa1f84478b4940e122e18208",
      "focus_semantics": "ANCESTOR_CLOSURE_IN_PROJECT",
      "full_project_level_map_sha256": "92f8677874684b6e10ed2f1f4921711facee0926086f7fc073989e6a34a04e6e",
      "id": "characters-eigenvectors",
      "label": "Characters and eigenvectors",
      "review_state": "EXISTING_33_CARD_ROUTE_RECHECKED_AGAINST_CURRENT_NATIVE_GRAPH",
      "status": "ACTIVE",
      "terminal_node_ids": [
        "7a1b136b8464e6029397491d4d05fa22de45ecb383b3384c4e0c2fcf7df3150a"
      ]
    },
    {
      "expected_visible_count": 14,
      "expected_visible_node_ids_sha256": "a282d6bc3ae93234f408b91dd037136f2b0c8a08afb96ae0345d785df0b882c9",
      "focus_semantics": "ANCESTOR_CLOSURE_IN_PROJECT",
      "full_project_level_map_sha256": "92f8677874684b6e10ed2f1f4921711facee0926086f7fc073989e6a34a04e6e",
      "id": "countability-scalar-corner",
      "label": "Countability and a scalar corner",
      "review_state": "EXISTING_33_CARD_ROUTE_RECHECKED_AGAINST_CURRENT_NATIVE_GRAPH",
      "status": "ACTIVE",
      "terminal_node_ids": [
        "964e8b0b51be9a3fc80a3f61b3bcb1b8cf70461ce4137aed6128c4ced9074130",
        "ff5886cf6420336dbe578275731ad0361f521340e5e9760ec098cd284273b584"
      ]
    },
    {
      "expected_visible_count": 19,
      "expected_visible_node_ids_sha256": "0b5595c5b70102c0a40abd2258fde787dc0f657acaff44b1003e31c04466a1b3",
      "focus_semantics": "ANCESTOR_CLOSURE_IN_PROJECT",
      "full_project_level_map_sha256": "92f8677874684b6e10ed2f1f4921711facee0926086f7fc073989e6a34a04e6e",
      "id": "every-compact",
      "label": "Every compact operator has a preimage",
      "review_state": "EXISTING_33_CARD_ROUTE_RECHECKED_AGAINST_CURRENT_NATIVE_GRAPH",
      "status": "ACTIVE",
      "terminal_node_ids": [
        "0edd904a8f54cb2f656607289f4094b52459b64013e28ed399e00bc0acd454d8"
      ]
    },
    {
      "expected_visible_count": 21,
      "expected_visible_node_ids_sha256": "755c60daefabc4d8fe1cfd5e5ba2d5a5a452d76db7cf27fcac1cf29ac944225f",
      "focus_semantics": "ANCESTOR_CLOSURE_IN_PROJECT",
      "full_project_level_map_sha256": "92f8677874684b6e10ed2f1f4921711facee0926086f7fc073989e6a34a04e6e",
      "id": "only-compact",
      "label": "Every represented operator is compact",
      "review_state": "EXISTING_33_CARD_ROUTE_RECHECKED_AGAINST_CURRENT_NATIVE_GRAPH",
      "status": "ACTIVE",
      "terminal_node_ids": [
        "94b7f2220243cb53c84a521c24f6eb1f35bc8222d4162b9ea134b4c10e9ea7b4"
      ]
    },
    {
      "expected_visible_count": 11,
      "expected_visible_node_ids_sha256": "242e4c4961e3aec24e997ebfbd1c2e98bf4751df3e00ddcde5a701bea961c559",
      "focus_semantics": "ANCESTOR_CLOSURE_IN_PROJECT",
      "full_project_level_map_sha256": "92f8677874684b6e10ed2f1f4921711facee0926086f7fc073989e6a34a04e6e",
      "id": "unital-consequences",
      "label": "Unital finite-dimensional consequences",
      "review_state": "EXISTING_33_CARD_ROUTE_RECHECKED_AGAINST_CURRENT_NATIVE_GRAPH",
      "status": "ACTIVE",
      "terminal_node_ids": [
        "f34adabc1cac70dceb32acb212d5f7c0b85c259c2c330087932a6f3fe9f5e8a9"
      ]
    },
    {
      "expected_visible_count": 45,
      "expected_visible_node_ids_sha256": "79d1ab6d41e9e71f3e089e73f73b42e4d312a0faeeb1982df5dea252b26ef7ae",
      "focus_semantics": "ANCESTOR_CLOSURE_IN_PROJECT",
      "full_project_level_map_sha256": "92f8677874684b6e10ed2f1f4921711facee0926086f7fc073989e6a34a04e6e",
      "id": "density",
      "label": "Density below the continuum",
      "review_state": "NEW_SOURCE_ONLY_BRIDGE_PENDING_OWNER_PROJECT_OVERVIEW_REVIEW",
      "status": "ACTIVE",
      "terminal_node_ids": [
        "ros-src-31aabd9922e2649eed4e",
        "ros-src-11a8ca7b0e0585d03048",
        "ros-src-90127c0d2347b370cebf",
        "ros-src-e9192a6956be65f01319"
      ]
    }
  ],
  "schema": "mathlibannex.lfh-theorem-project-successor.v1",
  "source_binding": {
    "commit": "437e6e46228bbb8e91211ebded349d7a30020e73",
    "entry_path": "MathlibAnnex/Projects/Rosenberg.lean",
    "entry_permalink": "https://github.com/r-tanaka-math/mathlib-annex/blob/437e6e46228bbb8e91211ebded349d7a30020e73/MathlibAnnex/Projects/Rosenberg.lean",
    "lfh_publication_state": "PRIVATE_CANDIDATE_NOT_AUTHORIZED",
    "manifest_permalink": "https://github.com/r-tanaka-math/mathlib-annex/blob/437e6e46228bbb8e91211ebded349d7a30020e73/docs/projects/rosenberg.json",
    "release_id": 392532070,
    "release_url": "https://github.com/r-tanaka-math/mathlib-annex/releases/tag/v0.4.0",
    "source_publication_state": "PUBLIC_RELEASE_READBACK_COMPLETE",
    "tag": "v0.4.0",
    "tree": "b752cf746a8660427937b3497f49c1797bf3ff3f"
  },
  "status": {
    "active_public_canonical_links": 33,
    "catalog_current": true,
    "lfh_publication_state": "PUBLIC",
    "owner_card_review": "APPROVED_REUSED_SOURCE_EXPOSITION_CORRESPONDENCE",
    "owner_project_overview_review": "NEW_DENSITY_BRIDGE_PENDING",
    "public_cards": 33,
    "source_release": "PUBLIC_V040",
    "state": "PUBLIC_BOUND_TO_V040_SOURCE",
    "website_effect": "PUBLIC_CURRENT"
  },
  "technical_identity": {
    "approved_exposition_records_sha256": "11b6ea11f79cb3f71258d81e2f5a53ad2f9967251e30c3e2704ace5f1dd46af2",
    "approved_review_items_sha256": "377f2d01ab7b6aee493a488ddad5cd6a80036e18ce10e72272096ab63f6782fa",
    "boundary_inputs_all": 2690,
    "boundary_inputs_curated": 15,
    "card_ref_set_sha256": "cd0a1f07158ec83c8d9350b7e9b63f41e3fe29ac6eb138e8630c30e6439ee4c3",
    "card_successor_map_sha256": "5fe53789e6616006309c72df76279cdd829004007a61651bdbfa297c6b9ff16a",
    "display_edges": 88,
    "full_native_graph_sha256": "e0c69751546f310fb7e15d2915c7e7b0f6a710eb0bc33269b24c2b228bcb5425",
    "graph_portable_sha256": "ef9c1507b18a89758ab43fe2be5efb02144590a80ea64825f97431c19ee9c1ae",
    "maximum_level": 10,
    "public_cards": 0,
    "reachability_pairs": 509,
    "selected_cards": 33,
    "source_tag": "v0.4.0"
  },
  "website_presentation": {
    "notice": "Thirty-three Declaration Card expositions are available. The added density route is source-only and creates no Card.",
    "card_action_label": "Open Declaration Card",
    "publication_authorized": true
  },
  "website_publication": {
    "publication_authorized": true,
    "publication_date": "2026-09-21",
    "canonical_url": "https://exactmathematics.org/mathlibannex/projects/rosenberg/",
    "batch": "EM_FULL_HP_PUBLICATION_R1",
    "owner_whole_site_publication_authorized": true,
    "new_mathematical_review": false
  }
}