Record 19 verified HPC batch manifests

manifests/batches/deepseek/000499.json

@@ -0,0 +1,148 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "deepseek/000499",
+  "batch_fingerprint": "5669818e55aa202831281c7f769bccb5b565ec214b3f7bb8fc48728181a3ed7b",
+  "evidence": {
+    "batch_fingerprint": "5669818e55aa202831281c7f769bccb5b565ec214b3f7bb8fc48728181a3ed7b",
+    "contamination_matches": [],
+    "failures": [],
+    "input_proofs": 50,
+    "input_units": 50,
+    "proofs": 50,
+    "published_proofs": 50,
+    "published_transitions": 116,
+    "replay_failures": [],
+    "trace_mode": "individual",
+    "transitions": 116,
+    "validation_failures": [],
+    "validation_rejected_proofs": 0,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/deepseek-000499-0000-aa88078346bfd64e.parquet",
+      "sha256": "aa88078346bfd64e1ab606c4cf6f0d3559f25c63a222eab0a9b96a85de5812dc",
+      "bytes": 268650,
+      "rows": 88,
+      "revision": "3ccd431b411f5443a88469e9af85fa5eacacb34d"
+    },
+    {
+      "path": "data/dev/deepseek-000499-0000-089aa6f7e309cb57.parquet",
+      "sha256": "089aa6f7e309cb57bec314cea7f9f5f96041040eb7120f842aa562b7c5eaf29c",
+      "bytes": 46038,
+      "rows": 8,
+      "revision": "3ccd431b411f5443a88469e9af85fa5eacacb34d"
+    },
+    {
+      "path": "data/internal_test/deepseek-000499-0000-4cc28db24d3a179a.parquet",
+      "sha256": "4cc28db24d3a179aaf6616c720759ac9e415396e8ad34faf8aff639d0efebc4f",
+      "bytes": 65706,
+      "rows": 20,
+      "revision": "3ccd431b411f5443a88469e9af85fa5eacacb34d"
+    }
+  ],
+  "proof_ids": [
+    "deepseek:thm_24998",
+    "deepseek:thm_24999",
+    "deepseek:thm_25000",
+    "deepseek:thm_25001",
+    "deepseek:thm_25002",
+    "deepseek:thm_25003",
+    "deepseek:thm_25004",
+    "deepseek:thm_25005",
+    "deepseek:thm_25006",
+    "deepseek:thm_25007",
+    "deepseek:thm_25008",
+    "deepseek:thm_25009",
+    "deepseek:thm_25010",
+    "deepseek:thm_25011",
+    "deepseek:thm_25012",
+    "deepseek:thm_25013",
+    "deepseek:thm_25014",
+    "deepseek:thm_25015",
+    "deepseek:thm_25016",
+    "deepseek:thm_25017",
+    "deepseek:thm_25018",
+    "deepseek:thm_25019",
+    "deepseek:thm_25020",
+    "deepseek:thm_25021",
+    "deepseek:thm_25022",
+    "deepseek:thm_25023",
+    "deepseek:thm_25024",
+    "deepseek:thm_25025",
+    "deepseek:thm_25026",
+    "deepseek:thm_25027",
+    "deepseek:thm_25028",
+    "deepseek:thm_25029",
+    "deepseek:thm_25030",
+    "deepseek:thm_25031",
+    "deepseek:thm_25032",
+    "deepseek:thm_25033",
+    "deepseek:thm_25034",
+    "deepseek:thm_25035",
+    "deepseek:thm_25036",
+    "deepseek:thm_25037",
+    "deepseek:thm_25038",
+    "deepseek:thm_25039",
+    "deepseek:thm_25040",
+    "deepseek:thm_25041",
+    "deepseek:thm_25042",
+    "deepseek:thm_25043",
+    "deepseek:thm_25044",
+    "deepseek:thm_25045",
+    "deepseek:thm_25046",
+    "deepseek:thm_25047"
+  ],
+  "proof_keys": [
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024950.lean\",\"25dd217600c25de1a0662ce736401cc37938fa5390688a8895b462220d13f4c8\",0,\"thm_24998\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024951.lean\",\"86e87085b5792bc41d80ed49306a63cd65a3f7ada6ca4af4dc21ef6e79044df9\",0,\"thm_24999\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024952.lean\",\"36e834d67531b37aabea82a226f5e1a2f5e2c565fe74054cba5ecdd6852babe9\",0,\"thm_25000\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024953.lean\",\"60f97ca29b1de821bcdb6ab62bbca0a510b660a06424c86973e03f0e0a408a4a\",0,\"thm_25001\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024954.lean\",\"4bab0c3958b029f08a3cc51b8baf311e9e733be965359a772736649836b7e625\",0,\"thm_25002\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024955.lean\",\"cc49449cc735eb3f216f29afce3b73a53fa12286aadb9a53f80279df571ad412\",0,\"thm_25003\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024956.lean\",\"b3043ec286d4ba46d235fc0cdd801f6865092d4afe3b2d33a908cf6ee6de8002\",0,\"thm_25004\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024957.lean\",\"31def53ddcfec7923223a357b5e510fbe942f72a8045e2e906c4a636fd78f8c4\",0,\"thm_25005\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024958.lean\",\"00bc5d445a437a2a2a1b64f021156a9675cc8f6dc2c7775acf274e7ca97da717\",0,\"thm_25006\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024959.lean\",\"8afdf63297ce70b1e3e3d5ad685f54c2d117d5c72687e4eee3a1ef987f8ff8b1\",0,\"thm_25007\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024960.lean\",\"c43781a13b57edbfb5b682d30573c9b03e14ab79e103ea6311f918ab5f9a93a8\",0,\"thm_25008\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024961.lean\",\"098b0426e46a53117e34b53be2ac9a646ce20a6d7b0221b9bfd23676065bada2\",0,\"thm_25009\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024962.lean\",\"387b3b58887dc91d1fbadefed20b088a474d4c3138fb4445759691c2003586aa\",0,\"thm_25010\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024963.lean\",\"dd53dc16a77d873a74fa4c5607ad77cb3857f1c6920d35cf3d735a2a03704e79\",0,\"thm_25011\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024964.lean\",\"e62e0d29690e7e4a53672e3a63f3d7d563d14bf4a33d4e1bbe8ca58f1fa088a8\",0,\"thm_25012\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024965.lean\",\"57fd5c1c1c74c9575cc0ea78452594ecb9433c73baecc262ce313818c58a7027\",0,\"thm_25013\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024966.lean\",\"b299857dc5ca9e41700bc43e4a845e683cbfa7c32ad306848ef76e611db3bc9a\",0,\"thm_25014\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024967.lean\",\"d019d4c59ae498ad2d0c36bef4621a8c8c14122a01d068fbd65dc60ed73e7c2a\",0,\"thm_25015\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024968.lean\",\"2aa6f18b3e8176634af983b77d5b8973d279cf57e13eb7531fdf067c276835b8\",0,\"thm_25016\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024969.lean\",\"11eba9b3bea25a1e2e1f2b2683b2226af24f1670be424aa4d8a893cf16be8ef1\",0,\"thm_25017\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024970.lean\",\"892295110700a0b1e2d0ad6012f02eddbc48f9e38cac891d71b482b0c46f77e3\",0,\"thm_25018\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024971.lean\",\"ab8589a87ee71456aca78d0695b441e3cb15007ec50e11a64ce465ccbd96286d\",0,\"thm_25019\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024972.lean\",\"7b5810b706871c63cd7425f75c30fba2d3f7b36101fd427b2e3e94be3ffffcc1\",0,\"thm_25020\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024973.lean\",\"b5b59b09b583c625afda7bf4d7185da64490ab91c9ee2d1593d8584784850195\",0,\"thm_25021\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024974.lean\",\"9dc4df942079594ea58fe5c52526ff3d3081eec8d4f0a4213c979ae4c2982951\",0,\"thm_25022\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024975.lean\",\"edd8390453dcc1a6b0e585a53ad84570e71d1a1d512276f0ee499bdd8832272a\",0,\"thm_25023\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024976.lean\",\"23f1656045007eebe638d53c6d35e498a53dbc97a8e9407d6deb8e6c6cd5e8b9\",0,\"thm_25024\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024977.lean\",\"01a6c0f53b7b28a4742731d61ea6f752978885c5b28f53fff53ae112368579f1\",0,\"thm_25025\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024978.lean\",\"642849af5677b81c1ab7e5c98e2fd3de9c942b1203a18064f73eba260edcd718\",0,\"thm_25026\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024979.lean\",\"abacffcb2da87e67d99cf25cbc78353750afd845b56f70f81cb3843a698c05f0\",0,\"thm_25027\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024980.lean\",\"f7b75b490992c5cd976679bdacdda31ffc14983705d97eb9d640e00675d7caf0\",0,\"thm_25028\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024981.lean\",\"ab6eb307fb0fa6f4d6dc1b38f58112982ae61ac3467a76866164d59113f374f3\",0,\"thm_25029\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024982.lean\",\"2d0a6b8b273c4a0dd9e3d6514e92919650528e58de18b01974598c4811f3cf5f\",0,\"thm_25030\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024983.lean\",\"733737ff36c9eca7182b01a99f7082100b7d4ac89c253f269672c94c6c36d821\",0,\"thm_25031\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024984.lean\",\"24607713097600aaca3edddbf01da97ec94ea54a2e7578c907843949735c6868\",0,\"thm_25032\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024985.lean\",\"db459cd318459ca37d93750be0d09a5f0dbeb559774e25e8dd0318299d64b732\",0,\"thm_25033\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024986.lean\",\"ed1159baa9bcc31f8ae7bb2bf9e6e96d2bfb12cc8929637a34c3d4737bb76559\",0,\"thm_25034\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024987.lean\",\"6a74468b5907ce4b73bca905221168a9ed4821738da334ecc9684cfc3560029d\",0,\"thm_25035\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024988.lean\",\"aeb1b83122579ca2b7c46d1492f9b4424e6d18c2ccdd136bd484c21505e3de59\",0,\"thm_25036\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024989.lean\",\"b6a037e303880c1ed66c1184dcaa70cb3f45b09752f168b665f02db1e607d6d7\",0,\"thm_25037\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024990.lean\",\"2db7d9b8cabede83827b4e8c887554a0d2d2657b260b50835a24e9866e53d7e2\",0,\"thm_25038\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024991.lean\",\"8a7aae79f5ec70e97a29446d3d47bfc2bec14078a004de462e4779a0dfdafbf3\",0,\"thm_25039\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024992.lean\",\"6f73404705ec10b0f1a1732107b911bf5b8a000c4607ddcc3d7b3f0c87b97ee6\",0,\"thm_25040\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024993.lean\",\"1477e290f2efff3119e9d6669cf6b7376387b0ec113caceab5a3566924f05f4b\",0,\"thm_25041\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024994.lean\",\"f33e3d7ecdfacd769da5dd0aff05901797b7af7237edf7501adf7019a9a78763\",0,\"thm_25042\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024995.lean\",\"a1bca9bcdeb5576a51a101923d65f53d0bc53b127be4f837dfedf6902a5b4d6c\",0,\"thm_25043\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024996.lean\",\"6e35d1c007bb78b3db37cd6e561cc6b5a49d782b5bd0493e7e2bb4174ee49717\",0,\"thm_25044\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024997.lean\",\"d7598614f635e35295df24493f6a72057e2c87aa7c911dc230400f813bc3ff92\",0,\"thm_25045\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024998.lean\",\"b002894fdfb6ab855908d50a73e64525cf6285e0e0d09da6a39c0cf14bd2e43b\",0,\"thm_25046\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024999.lean\",\"000c105d45ba545a4ed609ecdf331c04047c1ec5742471d7db6d5f8bbe5c8be6\",0,\"thm_25047\"]"
+  ]
+}

manifests/batches/deepseek/000501.json

@@ -0,0 +1,148 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "deepseek/000501",
+  "batch_fingerprint": "8d5c305b88db02f24e687412cbb9cee78de89555979f48707d299cba9a382eb0",
+  "evidence": {
+    "batch_fingerprint": "8d5c305b88db02f24e687412cbb9cee78de89555979f48707d299cba9a382eb0",
+    "contamination_matches": [],
+    "failures": [],
+    "input_proofs": 50,
+    "input_units": 50,
+    "proofs": 50,
+    "published_proofs": 50,
+    "published_transitions": 125,
+    "replay_failures": [],
+    "trace_mode": "individual",
+    "transitions": 125,
+    "validation_failures": [],
+    "validation_rejected_proofs": 0,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/deepseek-000501-0000-abc720b49f80683e.parquet",
+      "sha256": "abc720b49f80683e06d008911f2d2494841c02ba16b9b639f31efef8e321248b",
+      "bytes": 334166,
+      "rows": 102,
+      "revision": "3ccd431b411f5443a88469e9af85fa5eacacb34d"
+    },
+    {
+      "path": "data/dev/deepseek-000501-0000-25f4506cd2d4990a.parquet",
+      "sha256": "25f4506cd2d4990a4319473e14c6623a826cfb2c5ca08a2266d191af27b39631",
+      "bytes": 46549,
+      "rows": 3,
+      "revision": "3ccd431b411f5443a88469e9af85fa5eacacb34d"
+    },
+    {
+      "path": "data/internal_test/deepseek-000501-0000-74a45531845b9cdd.parquet",
+      "sha256": "74a45531845b9cdd96fa82321965ff003089972f475114cff723d8905fd8c616",
+      "bytes": 68884,
+      "rows": 20,
+      "revision": "3ccd431b411f5443a88469e9af85fa5eacacb34d"
+    }
+  ],
+  "proof_ids": [
+    "deepseek:thm_25098",
+    "deepseek:thm_25099",
+    "deepseek:thm_25100",
+    "deepseek:thm_25101",
+    "deepseek:thm_25102",
+    "deepseek:thm_25103",
+    "deepseek:thm_25104",
+    "deepseek:thm_25105",
+    "deepseek:thm_25106",
+    "deepseek:thm_25107",
+    "deepseek:thm_25108",
+    "deepseek:thm_25109",
+    "deepseek:thm_25110",
+    "deepseek:thm_25111",
+    "deepseek:thm_25112",
+    "deepseek:thm_25113",
+    "deepseek:thm_25114",
+    "deepseek:thm_25115",
+    "deepseek:thm_25116",
+    "deepseek:thm_25117",
+    "deepseek:thm_25118",
+    "deepseek:thm_25119",
+    "deepseek:thm_25120",
+    "deepseek:thm_25121",
+    "deepseek:thm_25122",
+    "deepseek:thm_25123",
+    "deepseek:thm_25124",
+    "deepseek:thm_25125",
+    "deepseek:thm_25126",
+    "deepseek:thm_25127",
+    "deepseek:thm_25128",
+    "deepseek:thm_25129",
+    "deepseek:thm_25130",
+    "deepseek:thm_25131",
+    "deepseek:thm_25132",
+    "deepseek:thm_25133",
+    "deepseek:thm_25134",
+    "deepseek:thm_25135",
+    "deepseek:thm_25136",
+    "deepseek:thm_25137",
+    "deepseek:thm_25138",
+    "deepseek:thm_25139",
+    "deepseek:thm_25140",
+    "deepseek:thm_25141",
+    "deepseek:thm_25142",
+    "deepseek:thm_25143",
+    "deepseek:thm_25144",
+    "deepseek:thm_25145",
+    "deepseek:thm_25146",
+    "deepseek:thm_25147"
+  ],
+  "proof_keys": [
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_025050.lean\",\"0d66be7c35553ee5ed91f0f41a1e9d74b9a56d60344f85c56cbf671a85c46a7a\",0,\"thm_25098\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_025051.lean\",\"9e8a056c43ef2980a676a11c66ccfef4fa62e1015f0654014dd7b9bc6dc6e20e\",0,\"thm_25099\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_025052.lean\",\"9acbe22cdc4ca33b0635b800b2509377aa6b3a46f6adba37f2884d0edf07c701\",0,\"thm_25100\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_025053.lean\",\"f4365bc3f6d62bbebc0e74387c3b9166123975ff960c8301657c443be1feea68\",0,\"thm_25101\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_025054.lean\",\"0bb869a2552aca6f86d4192116529b2e6f2b695932c59732fca385e7c2d491c0\",0,\"thm_25102\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_025055.lean\",\"4ebeef615751e8bccf660eb3ead437ff98ab18be0635570661dbbcc477257437\",0,\"thm_25103\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_025056.lean\",\"35f05bf3f371eac83819ee1662befa42af97c4b2809452662c6fc55f47d3b7f7\",0,\"thm_25104\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_025057.lean\",\"48ea08d32024af8f8908e142bc8152805c2619b5c1d3be733c262755fb4d3986\",0,\"thm_25105\"]",
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+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_025079.lean\",\"51c3ae7de2c34ce4db7b3ca1dd091305be062f60fa8c169f1246228de0129c17\",0,\"thm_25127\"]",
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+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_025091.lean\",\"2ea6039b7151fd023ac68c0c872970d2fa803ff123de1dfe451fee49ff6af451\",0,\"thm_25139\"]",
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+  ]
+}

manifests/batches/deepseek/000502.json

@@ -0,0 +1,148 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "deepseek/000502",
+  "batch_fingerprint": "22b599e11e20f89a7d8316539012966d08bae9c63196a75d8d49fb7278524dcb",
+  "evidence": {
+    "batch_fingerprint": "22b599e11e20f89a7d8316539012966d08bae9c63196a75d8d49fb7278524dcb",
+    "contamination_matches": [],
+    "failures": [],
+    "input_proofs": 50,
+    "input_units": 50,
+    "proofs": 50,
+    "published_proofs": 50,
+    "published_transitions": 117,
+    "replay_failures": [],
+    "trace_mode": "individual",
+    "transitions": 117,
+    "validation_failures": [],
+    "validation_rejected_proofs": 0,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/deepseek-000502-0000-5d2f2e0ce9443fbd.parquet",
+      "sha256": "5d2f2e0ce9443fbd661b1eea41a43cec9d3e1303b4bb300a10907278c9184ab6",
+      "bytes": 319148,
+      "rows": 100,
+      "revision": "3ccd431b411f5443a88469e9af85fa5eacacb34d"
+    },
+    {
+      "path": "data/dev/deepseek-000502-0000-7b145273042d8426.parquet",
+      "sha256": "7b145273042d84261ef14fab027dfa95993447cb7e63bf7b467ac0cb51b6612c",
+      "bytes": 32948,
+      "rows": 3,
+      "revision": "3ccd431b411f5443a88469e9af85fa5eacacb34d"
+    },
+    {
+      "path": "data/internal_test/deepseek-000502-0000-838c9d97e2b2fb51.parquet",
+      "sha256": "838c9d97e2b2fb51891e66d4ba3f2367a1683841974dc4d59430396553e2654e",
+      "bytes": 65043,
+      "rows": 14,
+      "revision": "3ccd431b411f5443a88469e9af85fa5eacacb34d"
+    }
+  ],
+  "proof_ids": [
+    "deepseek:thm_25148",
+    "deepseek:thm_25149",
+    "deepseek:thm_25150",
+    "deepseek:thm_25151",
+    "deepseek:thm_25152",
+    "deepseek:thm_25153",
+    "deepseek:thm_25154",
+    "deepseek:thm_25155",
+    "deepseek:thm_25156",
+    "deepseek:thm_25157",
+    "deepseek:thm_25158",
+    "deepseek:thm_25159",
+    "deepseek:thm_25160",
+    "deepseek:thm_25161",
+    "deepseek:thm_25162",
+    "deepseek:thm_25163",
+    "deepseek:thm_25164",
+    "deepseek:thm_25165",
+    "deepseek:thm_25166",
+    "deepseek:thm_25167",
+    "deepseek:thm_25168",
+    "deepseek:thm_25169",
+    "deepseek:thm_25170",
+    "deepseek:thm_25171",
+    "deepseek:thm_25172",
+    "deepseek:thm_25173",
+    "deepseek:thm_25174",
+    "deepseek:thm_25175",
+    "deepseek:thm_25176",
+    "deepseek:thm_25177",
+    "deepseek:thm_25178",
+    "deepseek:thm_25179",
+    "deepseek:thm_25180",
+    "deepseek:thm_25181",
+    "deepseek:thm_25182",
+    "deepseek:thm_25183",
+    "deepseek:thm_25184",
+    "deepseek:thm_25185",
+    "deepseek:thm_25186",
+    "deepseek:thm_25187",
+    "deepseek:thm_25188",
+    "deepseek:thm_25189",
+    "deepseek:thm_25190",
+    "deepseek:thm_25191",
+    "deepseek:thm_25192",
+    "deepseek:thm_25193",
+    "deepseek:thm_25194",
+    "deepseek:thm_25195",
+    "deepseek:thm_25196",
+    "deepseek:thm_25197"
+  ],
+  "proof_keys": [
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+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_025123.lean\",\"a650ead39281aaad9fbf4668583b39cc7d2858f93ebb6cf3887ae5cff8c9e7fa\",0,\"thm_25171\"]",
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+  ]
+}

manifests/batches/deepseek/000505.json

@@ -0,0 +1,148 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "deepseek/000505",
+  "batch_fingerprint": "82459663729abd76dcd7fc13c472c92b343955cdded930b81d8ebfd186bfa6da",
+  "evidence": {
+    "batch_fingerprint": "82459663729abd76dcd7fc13c472c92b343955cdded930b81d8ebfd186bfa6da",
+    "contamination_matches": [],
+    "failures": [],
+    "input_proofs": 50,
+    "input_units": 50,
+    "proofs": 50,
+    "published_proofs": 50,
+    "published_transitions": 117,
+    "replay_failures": [],
+    "trace_mode": "individual",
+    "transitions": 117,
+    "validation_failures": [],
+    "validation_rejected_proofs": 0,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/deepseek-000505-0000-408e8bdf19adbdc5.parquet",
+      "sha256": "408e8bdf19adbdc53af39cf78c96d64e0785fcdd51d0c00d79bead52a0c43408",
+      "bytes": 284398,
+      "rows": 94,
+      "revision": "3ccd431b411f5443a88469e9af85fa5eacacb34d"
+    },
+    {
+      "path": "data/dev/deepseek-000505-0000-2de7f2bf94999766.parquet",
+      "sha256": "2de7f2bf9499976649f0b61d6a0106d942093478823a154cbb5cfa33f6ea6a98",
+      "bytes": 46052,
+      "rows": 10,
+      "revision": "3ccd431b411f5443a88469e9af85fa5eacacb34d"
+    },
+    {
+      "path": "data/internal_test/deepseek-000505-0000-66f10222aa978694.parquet",
+      "sha256": "66f10222aa978694681090f53ba4d3d6de755031f9809159c4eec5c6d1f9c95b",
+      "bytes": 49765,
+      "rows": 13,
+      "revision": "3ccd431b411f5443a88469e9af85fa5eacacb34d"
+    }
+  ],
+  "proof_ids": [
+    "deepseek:thm_25298",
+    "deepseek:thm_25299",
+    "deepseek:thm_25300",
+    "deepseek:thm_25301",
+    "deepseek:thm_25302",
+    "deepseek:thm_25303",
+    "deepseek:thm_25304",
+    "deepseek:thm_25305",
+    "deepseek:thm_25306",
+    "deepseek:thm_25307",
+    "deepseek:thm_25308",
+    "deepseek:thm_25309",
+    "deepseek:thm_25310",
+    "deepseek:thm_25311",
+    "deepseek:thm_25312",
+    "deepseek:thm_25313",
+    "deepseek:thm_25314",
+    "deepseek:thm_25315",
+    "deepseek:thm_25316",
+    "deepseek:thm_25317",
+    "deepseek:thm_25318",
+    "deepseek:thm_25319",
+    "deepseek:thm_25320",
+    "deepseek:thm_25321",
+    "deepseek:thm_25322",
+    "deepseek:thm_25323",
+    "deepseek:thm_25324",
+    "deepseek:thm_25325",
+    "deepseek:thm_25326",
+    "deepseek:thm_25327",
+    "deepseek:thm_25328",
+    "deepseek:thm_25329",
+    "deepseek:thm_25330",
+    "deepseek:thm_25331",
+    "deepseek:thm_25332",
+    "deepseek:thm_25333",
+    "deepseek:thm_25334",
+    "deepseek:thm_25335",
+    "deepseek:thm_25336",
+    "deepseek:thm_25337",
+    "deepseek:thm_25338",
+    "deepseek:thm_25339",
+    "deepseek:thm_25340",
+    "deepseek:thm_25341",
+    "deepseek:thm_25342",
+    "deepseek:thm_25343",
+    "deepseek:thm_25344",
+    "deepseek:thm_25345",
+    "deepseek:thm_25346",
+    "deepseek:thm_25347"
+  ],
+  "proof_keys": [
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+}

manifests/batches/deepseek/000506.json

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+  ]
+}

manifests/batches/mathlib/000429.json

@@ -0,0 +1,634 @@
+{
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+  "batch": "mathlib/000429",
+  "batch_fingerprint": "041deda29e564f2dae3615a7c0c571403240d441c796d9a4d764b4ee9608f4a0",
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+    "failures": [
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+        "full_name": "IsLocalExtr.deriv_eq_zero",
+        "id": "IsLocalExtr.deriv_eq_zero",
+        "reason": "import_failure",
+        "selection": {
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+          "full_name": "IsLocalExtr.deriv_eq_zero",
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+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/LocalExtr/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsLocalExtr.fderiv_eq_zero",
+        "id": "IsLocalExtr.fderiv_eq_zero",
+        "reason": "import_failure",
+        "selection": {
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+          "full_name": "IsLocalExtr.fderiv_eq_zero",
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+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/LocalExtr/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsLocalExtr.hasDerivAt_eq_zero",
+        "id": "IsLocalExtr.hasDerivAt_eq_zero",
+        "reason": "import_failure",
+        "selection": {
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+          "end": [
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+          "full_name": "IsLocalExtr.hasDerivAt_eq_zero",
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+        },
+        "source_file": "Mathlib/Analysis/Calculus/LocalExtr/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsLocalExtr.hasFDerivAt_eq_zero",
+        "id": "IsLocalExtr.hasFDerivAt_eq_zero",
+        "reason": "import_failure",
+        "selection": {
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+          "full_name": "IsLocalExtr.hasFDerivAt_eq_zero",
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+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
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+        "source_file": "Mathlib/Analysis/Calculus/LocalExtr/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsLocalMax.deriv_eq_zero",
+        "id": "IsLocalMax.deriv_eq_zero",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
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+          ],
+          "file_path": "Mathlib/Analysis/Calculus/LocalExtr/Basic.lean",
+          "full_name": "IsLocalMax.deriv_eq_zero",
+          "start": [
+            248,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/LocalExtr/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsLocalMax.fderiv_eq_zero",
+        "id": "IsLocalMax.fderiv_eq_zero",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            208,
+            46
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/LocalExtr/Basic.lean",
+          "full_name": "IsLocalMax.fderiv_eq_zero",
+          "start": [
+            206,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/LocalExtr/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsLocalMax.hasDerivAt_eq_zero",
+        "id": "IsLocalMax.hasDerivAt_eq_zero",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            244,
+            51
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/LocalExtr/Basic.lean",
+          "full_name": "IsLocalMax.hasDerivAt_eq_zero",
+          "start": [
+            243,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/LocalExtr/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsLocalMax.hasFDerivAt_eq_zero",
+        "id": "IsLocalMax.hasFDerivAt_eq_zero",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            202,
+            52
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/LocalExtr/Basic.lean",
+          "full_name": "IsLocalMax.hasFDerivAt_eq_zero",
+          "start": [
+            201,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/LocalExtr/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsLocalMin.deriv_eq_zero",
+        "id": "IsLocalMin.deriv_eq_zero",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            239,
+            45
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/LocalExtr/Basic.lean",
+          "full_name": "IsLocalMin.deriv_eq_zero",
+          "start": [
+            237,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/LocalExtr/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsLocalMin.fderiv_eq_zero",
+        "id": "IsLocalMin.fderiv_eq_zero",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            197,
+            46
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/LocalExtr/Basic.lean",
+          "full_name": "IsLocalMin.fderiv_eq_zero",
+          "start": [
+            195,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/LocalExtr/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "posTangentConeAt_univ",
+        "id": "posTangentConeAt_univ",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            105,
+            85
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/LocalExtr/Basic.lean",
+          "full_name": "posTangentConeAt_univ",
+          "start": [
+            104,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/LocalExtr/Basic.lean"
+      },
+      {
+        "error": "no internal trace for tactic \"rw [eq_C_of_derivative_eq_zero hp', roots_C, Multiset.toFinset_zero, Finset.card_empty]\"",
+        "full_name": "Polynomial.card_roots_toFinset_le_card_roots_derivative_diff_roots_succ",
+        "id": "Polynomial.card_roots_toFinset_le_card_roots_derivative_diff_roots_succ",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            47,
+            64
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/LocalExtr/Polynomial.lean",
+          "full_name": "Polynomial.card_roots_toFinset_le_card_roots_derivative_diff_roots_succ",
+          "start": [
+            37,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"rcases <a>eq_or_ne<\\/a> (<a>derivative<\\/a> p) 0 with hp' | hp'\"",
+                "[{\"full_name\":\"eq_or_ne\",\"def_path\":\"Mathlib\\/Logic\\/Basic.lean\",\"def_pos\":[212,9],\"def_end_pos\":[212,17]},{\"full_name\":\"Polynomial.derivative\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Derivative.lean\",\"def_pos\":[40,5],\"def_end_pos\":[40,15]}]"
+              ],
+              "state_after": "case inl\np : \u211d[X]\nhp' : derivative p = 0\n\u22a2 p.roots.toFinset.card \u2264 ((derivative p).roots.toFinset \\ p.roots.toFinset).card + 1\n\ncase inr\np : \u211d[X]\nhp' : derivative p \u2260 0\n\u22a2 p.roots.toFinset.card \u2264 ((derivative p).roots.toFinset \\ p.roots.toFinset).card + 1",
+              "state_before": "p : \u211d[X]\n\u22a2 p.roots.toFinset.card \u2264 ((derivative p).roots.toFinset \\ p.roots.toFinset).card + 1",
+              "tactic": "rcases eq_or_ne (derivative p) 0 with hp' | hp'"
+            },
+            {
+              "annotated_tactic": [
+                "\"have hp : p \\u2260 0 := <a>ne_of_apply_ne<\\/a> <a>derivative<\\/a> (by rwa [<a>derivative_zero<\\/a>])\"",
+                "[{\"full_name\":\"ne_of_apply_ne\",\"def_path\":\".lake\\/packages\\/batteries\\/Batteries\\/Logic.lean\",\"def_pos\":[66,9],\"def_end_pos\":[66,23]},{\"full_name\":\"Polynomial.derivative\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Derivative.lean\",\"def_pos\":[40,5],\"def_end_pos\":[40,15]},{\"full_name\":\"Polynomial.derivative_zero\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Derivative.lean\",\"def_pos\":[77,9],\"def_end_pos\":[77,24]}]"
+              ],
+              "state_after": "case inr\np : \u211d[X]\nhp' : derivative p \u2260 0\nhp : p \u2260 0\n\u22a2 p.roots.toFinset.card \u2264 ((derivative p).roots.toFinset \\ p.roots.toFinset).card + 1",
+              "state_before": "case inr\np : \u211d[X]\nhp' : derivative p \u2260 0\n\u22a2 p.roots.toFinset.card \u2264 ((derivative p).roots.toFinset \\ p.roots.toFinset).card + 1",
+              "tactic": "have hp : p \u2260 0 := ne_of_apply_ne derivative (by rwa [derivative_zero])"
+            },
+            {
+              "annotated_tactic": [
+                "\"refine <a>Finset.card_le_diff_of_interleaved<\\/a> fun x hx y hy hxy hxy' => ?_\"",
+                "[{\"full_name\":\"Finset.card_le_diff_of_interleaved\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Lattice.lean\",\"def_pos\":[1850,9],\"def_end_pos\":[1850,36]}]"
+              ],
+              "state_after": "case inr\np : \u211d[X]\nhp' : derivative p \u2260 0\nhp : p \u2260 0\nx : \u211d\nhx : x \u2208 p.roots.toFinset\ny : \u211d\nhy : y \u2208 p.roots.toFinset\nhxy : x < y\nhxy' : \u2200 z \u2208 p.roots.toFinset, z \u2209 Set.Ioo x y\n\u22a2 \u2203 z \u2208 (derivative p).roots.toFinset, x < z \u2227 z < y",
+              "state_before": "case inr\np : \u211d[X]\nhp' : derivative p \u2260 0\nhp : p \u2260 0\n\u22a2 p.roots.toFinset.card \u2264 ((derivative p).roots.toFinset \\ p.roots.toFinset).card + 1",
+              "tactic": "refine Finset.card_le_diff_of_interleaved fun x hx y hy hxy hxy' => ?_"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>Multiset.mem_toFinset<\\/a>, <a>mem_roots<\\/a> hp] at hx hy\"",
+                "[{\"full_name\":\"Multiset.mem_toFinset\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Basic.lean\",\"def_pos\":[3100,9],\"def_end_pos\":[3100,21]},{\"full_name\":\"Polynomial.mem_roots\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Roots.lean\",\"def_pos\":[114,9],\"def_end_pos\":[114,18]}]"
+              ],
+              "state_after": "case inr\np : \u211d[X]\nhp' : derivative p \u2260 0\nhp : p \u2260 0\nx : \u211d\nhx : p.IsRoot x\ny : \u211d\nhy : p.IsRoot y\nhxy : x < y\nhxy' : \u2200 z \u2208 p.roots.toFinset, z \u2209 Set.Ioo x y\n\u22a2 \u2203 z \u2208 (derivative p).roots.toFinset, x < z \u2227 z < y",
+              "state_before": "case inr\np : \u211d[X]\nhp' : derivative p \u2260 0\nhp : p \u2260 0\nx : \u211d\nhx : x \u2208 p.roots.toFinset\ny : \u211d\nhy : y \u2208 p.roots.toFinset\nhxy : x < y\nhxy' : \u2200 z \u2208 p.roots.toFinset, z \u2209 Set.Ioo x y\n\u22a2 \u2203 z \u2208 (derivative p).roots.toFinset, x < z \u2227 z < y",
+              "tactic": "rw [Multiset.mem_toFinset, mem_roots hp] at hx hy"
+            },
+            {
+              "annotated_tactic": [
+                "\"obtain \\u27e8z, hz1, hz2\\u27e9 := <a>exists_deriv_eq_zero<\\/a> hxy p.continuousOn (hx.trans hy.symm)\"",
+                "[{\"full_name\":\"exists_deriv_eq_zero\",\"def_path\":\"Mathlib\\/Analysis\\/Calculus\\/LocalExtr\\/Rolle.lean\",\"def_pos\":[57,9],\"def_end_pos\":[57,29]}]"
+              ],
+              "state_after": "case inr.intro.intro\np : \u211d[X]\nhp' : derivative p \u2260 0\nhp : p \u2260 0\nx : \u211d\nhx : p.IsRoot x\ny : \u211d\nhy : p.IsRoot y\nhxy : x < y\nhxy' : \u2200 z \u2208 p.roots.toFinset, z \u2209 Set.Ioo x y\nz : \u211d\nhz1 : z \u2208 Set.Ioo x y\nhz2 : deriv (fun x => eval x p) z = 0\n\u22a2 \u2203 z \u2208 (derivative p).roots.toFinset, x < z \u2227 z < y",
+              "state_before": "case inr\np : \u211d[X]\nhp' : derivative p \u2260 0\nhp : p \u2260 0\nx : \u211d\nhx : p.IsRoot x\ny : \u211d\nhy : p.IsRoot y\nhxy : x < y\nhxy' : \u2200 z \u2208 p.roots.toFinset, z \u2209 Set.Ioo x y\n\u22a2 \u2203 z \u2208 (derivative p).roots.toFinset, x < z \u2227 z < y",
+              "tactic": "obtain \u27e8z, hz1, hz2\u27e9 := exists_deriv_eq_zero hxy p.continuousOn (hx.trans hy.symm)"
+            },
+            {
+              "annotated_tactic": [
+                "\"refine \\u27e8z, ?_, hz1\\u27e9\"",
+                "[]"
+              ],
+              "state_after": "case inr.intro.intro\np : \u211d[X]\nhp' : derivative p \u2260 0\nhp : p \u2260 0\nx : \u211d\nhx : p.IsRoot x\ny : \u211d\nhy : p.IsRoot y\nhxy : x < y\nhxy' : \u2200 z \u2208 p.roots.toFinset, z \u2209 Set.Ioo x y\nz : \u211d\nhz1 : z \u2208 Set.Ioo x y\nhz2 : deriv (fun x => eval x p) z = 0\n\u22a2 z \u2208 (derivative p).roots.toFinset",
+              "state_before": "case inr.intro.intro\np : \u211d[X]\nhp' : derivative p \u2260 0\nhp : p \u2260 0\nx : \u211d\nhx : p.IsRoot x\ny : \u211d\nhy : p.IsRoot y\nhxy : x < y\nhxy' : \u2200 z \u2208 p.roots.toFinset, z \u2209 Set.Ioo x y\nz : \u211d\nhz1 : z \u2208 Set.Ioo x y\nhz2 : deriv (fun x => eval x p) z = 0\n\u22a2 \u2203 z \u2208 (derivative p).roots.toFinset, x < z \u2227 z < y",
+              "tactic": "refine \u27e8z, ?_, hz1\u27e9"
+            },
+            {
+              "annotated_tactic": [
+                "\"rwa [<a>Multiset.mem_toFinset<\\/a>, <a>mem_roots<\\/a> hp', <a>IsRoot<\\/a>, \\u2190 p.deriv]\"",
+                "[{\"full_name\":\"Multiset.mem_toFinset\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Basic.lean\",\"def_pos\":[3100,9],\"def_end_pos\":[3100,21]},{\"full_name\":\"Polynomial.mem_roots\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Roots.lean\",\"def_pos\":[114,9],\"def_end_pos\":[114,18]},{\"full_name\":\"Polynomial.IsRoot\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Eval.lean\",\"def_pos\":[488,5],\"def_end_pos\":[488,11]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case inr.intro.intro\np : \u211d[X]\nhp' : derivative p \u2260 0\nhp : p \u2260 0\nx : \u211d\nhx : p.IsRoot x\ny : \u211d\nhy : p.IsRoot y\nhxy : x < y\nhxy' : \u2200 z \u2208 p.roots.toFinset, z \u2209 Set.Ioo x y\nz : \u211d\nhz1 : z \u2208 Set.Ioo x y\nhz2 : deriv (fun x => eval x p) z = 0\n\u22a2 z \u2208 (derivative p).roots.toFinset",
+              "tactic": "rwa [Multiset.mem_toFinset, mem_roots hp', IsRoot, \u2190 p.deriv]"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>eq_C_of_derivative_eq_zero<\\/a> hp', <a>roots_C<\\/a>, <a>Multiset.toFinset_zero<\\/a>, <a>Finset.card_empty<\\/a>]\"",
+                "[{\"full_name\":\"Polynomial.eq_C_of_derivative_eq_zero\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Derivative.lean\",\"def_pos\":[281,9],\"def_end_pos\":[281,35]},{\"full_name\":\"Polynomial.roots_C\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Roots.lean\",\"def_pos\":[197,9],\"def_end_pos\":[197,16]},{\"full_name\":\"Multiset.toFinset_zero\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Basic.lean\",\"def_pos\":[3105,9],\"def_end_pos\":[3105,22]},{\"full_name\":\"Finset.card_empty\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Card.lean\",\"def_pos\":[59,9],\"def_end_pos\":[59,19]}]"
+              ],
+              "state_after": "case inl\np : \u211d[X]\nhp' : derivative p = 0\n\u22a2 0 \u2264 ((derivative (C (p.coeff 0))).roots.toFinset \\ \u2205).card + 1",
+              "state_before": "case inl\np : \u211d[X]\nhp' : derivative p = 0\n\u22a2 p.roots.toFinset.card \u2264 ((derivative p).roots.toFinset \\ p.roots.toFinset).card + 1",
+              "tactic": "rw [eq_C_of_derivative_eq_zero hp', roots_C, Multiset.toFinset_zero, Finset.card_empty]"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact <a>zero_le<\\/a> _\"",
+                "[{\"full_name\":\"zero_le\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Monoid\\/Canonical\\/Defs.lean\",\"def_pos\":[204,30],\"def_end_pos\":[204,37]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case inl\np : \u211d[X]\nhp' : derivative p = 0\n\u22a2 0 \u2264 ((derivative (C (p.coeff 0))).roots.toFinset \\ \u2205).card + 1",
+              "tactic": "exact zero_le _"
+            },
+            {
+              "annotated_tactic": [
+                "\"rwa [<a>derivative_zero<\\/a>]\"",
+                "[{\"full_name\":\"Polynomial.derivative_zero\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Derivative.lean\",\"def_pos\":[77,9],\"def_end_pos\":[77,24]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "p : \u211d[X]\nhp' : derivative p \u2260 0\n\u22a2 derivative p \u2260 derivative 0",
+              "tactic": "rwa [derivative_zero]"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/LocalExtr/Polynomial.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Polynomial.card_roots_toFinset_le_derivative",
+        "id": "Polynomial.card_roots_toFinset_le_derivative",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            55,
+            62
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/LocalExtr/Polynomial.lean",
+          "full_name": "Polynomial.card_roots_toFinset_le_derivative",
+          "start": [
+            52,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/LocalExtr/Polynomial.lean"
+      }
+    ],
+    "input_proofs": 27,
+    "input_units": 2,
+    "proofs": 14,
+    "published_proofs": 12,
+    "published_transitions": 18,
+    "replay_failures": [],
+    "transitions": 34,
+    "validation_failures": [
+      {
+        "errors": [
+          "internal transition boundary mismatch",
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/Analysis/Calculus/LocalExtr/Basic.lean",
+        "proof_id": "mathlib:mem_posTangentConeAt_of_segment_subset",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              96,
+              95
+            ],
+            "file_path": "Mathlib/Analysis/Calculus/LocalExtr/Basic.lean",
+            "full_name": "mem_posTangentConeAt_of_segment_subset",
+            "start": [
+              86,
+              1
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"let c := fun n : \\u2115 => (2 : \\u211d) ^ n\"",
+                  "[]"
+                ],
+                "state_after": "E : Type u\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \u211d E\nf : E \u2192 \u211d\na : E\nf' : E \u2192L[\u211d] \u211d\ns : Set E\nx y : E\nh : segment \u211d x y \u2286 s\nc : \u2115 \u2192 \u211d := fun n => 2 ^ n\n\u22a2 y - x \u2208 posTangentConeAt s x",
+                "state_before": "E : Type u\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \u211d E\nf : E \u2192 \u211d\na : E\nf' : E \u2192L[\u211d] \u211d\ns : Set E\nx y : E\nh : segment \u211d x y \u2286 s\n\u22a2 y - x \u2208 posTangentConeAt s x",
+                "tactic": "let c := fun n : \u2115 => (2 : \u211d) ^ n"
+              },
+              {
+                "annotated_tactic": [
+                  "\"let d := fun n : \\u2115 => (c n)\\u207b\\u00b9 \\u2022 (y - x)\"",
+                  "[]"
+                ],
+                "state_after": "E : Type u\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \u211d E\nf : E \u2192 \u211d\na : E\nf' : E \u2192L[\u211d] \u211d\ns : Set E\nx y : E\nh : segment \u211d x y \u2286 s\nc : \u2115 \u2192 \u211d := fun n => 2 ^ n\nd : \u2115 \u2192 E := fun n => (c n)\u207b\u00b9 \u2022 (y - x)\n\u22a2 y - x \u2208 posTangentConeAt s x",
+                "state_before": "E : Type u\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \u211d E\nf : E \u2192 \u211d\na : E\nf' : E \u2192L[\u211d] \u211d\ns : Set E\nx y : E\nh : segment \u211d x y \u2286 s\nc : \u2115 \u2192 \u211d := fun n => 2 ^ n\n\u22a2 y - x \u2208 posTangentConeAt s x",
+                "tactic": "let d := fun n : \u2115 => (c n)\u207b\u00b9 \u2022 (y - x)"
+              },
+              {
+                "annotated_tactic": [
+                  "\"refine \\u27e8c, d, <a>Filter.univ_mem'<\\/a> fun n => h ?_, <a>tendsto_pow_atTop_atTop_of_one_lt<\\/a> <a>one_lt_two<\\/a>, ?_\\u27e9\"",
+                  "[{\"full_name\":\"Filter.univ_mem'\",\"def_path\":\"Mathlib\\/Order\\/Filter\\/Basic.lean\",\"def_pos\":[172,9],\"def_end_pos\":[172,18]},{\"full_name\":\"tendsto_pow_atTop_atTop_of_one_lt\",\"def_path\":\"Mathlib\\/Analysis\\/SpecificLimits\\/Basic.lean\",\"def_pos\":[125,9],\"def_end_pos\":[125,42]},{\"full_name\":\"one_lt_two\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Monoid\\/NatCast.lean\",\"def_pos\":[106,7],\"def_end_pos\":[106,17]}]"
+                ],
+                "state_after": "case refine_1\nE : Type u\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \u211d E\nf : E \u2192 \u211d\na : E\nf' : E \u2192L[\u211d] \u211d\ns : Set E\nx y : E\nh : segment \u211d x y \u2286 s\nc : \u2115 \u2192 \u211d := fun n => 2 ^ n\nd : \u2115 \u2192 E := fun n => (c n)\u207b\u00b9 \u2022 (y - x)\nn : \u2115\n\u22a2 x + d n \u2208 segment \u211d x y\n\ncase refine_2\nE : Type u\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \u211d E\nf : E \u2192 \u211d\na : E\nf' : E \u2192L[\u211d] \u211d\ns : Set E\nx y : E\nh : segment \u211d x y \u2286 s\nc : \u2115 \u2192 \u211d := fun n => 2 ^ n\nd : \u2115 \u2192 E := fun n => (c n)\u207b\u00b9 \u2022 (y - x)\n\u22a2 Tendsto (fun n => c n \u2022 d n) atTop (\ud835\udcdd (y - x))",
+                "state_before": "E : Type u\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \u211d E\nf : E \u2192 \u211d\na : E\nf' : E \u2192L[\u211d] \u211d\ns : Set E\nx y : E\nh : segment \u211d x y \u2286 s\nc : \u2115 \u2192 \u211d := fun n => 2 ^ n\nd : \u2115 \u2192 E := fun n => (c n)\u207b\u00b9 \u2022 (y - x)\n\u22a2 y - x \u2208 posTangentConeAt s x",
+                "tactic": "refine \u27e8c, d, Filter.univ_mem' fun n => h ?_, tendsto_pow_atTop_atTop_of_one_lt one_lt_two, ?_\u27e9"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rw [<a>segment_eq_image'<\\/a>]\"",
+                  "[{\"full_name\":\"segment_eq_image'\",\"def_path\":\"Mathlib\\/Analysis\\/Convex\\/Segment.lean\",\"def_pos\":[207,9],\"def_end_pos\":[207,26]}]"
+                ],
+                "state_after": "case refine_1\nE : Type u\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \u211d E\nf : E \u2192 \u211d\na : E\nf' : E \u2192L[\u211d] \u211d\ns : Set E\nx y : E\nh : segment \u211d x y \u2286 s\nc : \u2115 \u2192 \u211d := fun n => 2 ^ n\nd : \u2115 \u2192 E := fun n => (c n)\u207b\u00b9 \u2022 (y - x)\nn : \u2115\n\u22a2 x + d n \u2208 (fun \u03b8 => x + \u03b8 \u2022 (y - x)) '' Icc 0 1",
+                "state_before": "case refine_1\nE : Type u\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \u211d E\nf : E \u2192 \u211d\na : E\nf' : E \u2192L[\u211d] \u211d\ns : Set E\nx y : E\nh : segment \u211d x y \u2286 s\nc : \u2115 \u2192 \u211d := fun n => 2 ^ n\nd : \u2115 \u2192 E := fun n => (c n)\u207b\u00b9 \u2022 (y - x)\nn : \u2115\n\u22a2 x + d n \u2208 segment \u211d x y",
+                "tactic": "rw [segment_eq_image']"
+              },
+              {
+                "annotated_tactic": [
+                  "\"refine \\u27e8(c n)\\u207b\\u00b9, \\u27e8?_, ?_\\u27e9, <a>rfl<\\/a>\\u27e9\"",
+                  "[{\"full_name\":\"rfl\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[294,22],\"def_end_pos\":[294,25]}]"
+                ],
+                "state_after": "case refine_1.refine_1\nE : Type u\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \u211d E\nf : E \u2192 \u211d\na : E\nf' : E \u2192L[\u211d] \u211d\ns : Set E\nx y : E\nh : segment \u211d x y \u2286 s\nc : \u2115 \u2192 \u211d := fun n => 2 ^ n\nd : \u2115 \u2192 E := fun n => (c n)\u207b\u00b9 \u2022 (y - x)\nn : \u2115\n\u22a2 0 \u2264 (c n)\u207b\u00b9\n\ncase refine_1.refine_2\nE : Type u\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \u211d E\nf : E \u2192 \u211d\na : E\nf' : E \u2192L[\u211d] \u211d\ns : Set E\nx y : E\nh : segment \u211d x y \u2286 s\nc : \u2115 \u2192 \u211d := fun n => 2 ^ n\nd : \u2115 \u2192 E := fun n => (c n)\u207b\u00b9 \u2022 (y - x)\nn : \u2115\n\u22a2 (c n)\u207b\u00b9 \u2264 1",
+                "state_before": "case refine_1\nE : Type u\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \u211d E\nf : E \u2192 \u211d\na : E\nf' : E \u2192L[\u211d] \u211d\ns : Set E\nx y : E\nh : segment \u211d x y \u2286 s\nc : \u2115 \u2192 \u211d := fun n => 2 ^ n\nd : \u2115 \u2192 E := fun n => (c n)\u207b\u00b9 \u2022 (y - x)\nn : \u2115\n\u22a2 x + d n \u2208 (fun \u03b8 => x + \u03b8 \u2022 (y - x)) '' Icc 0 1",
+                "tactic": "refine \u27e8(c n)\u207b\u00b9, \u27e8?_, ?_\u27e9, rfl\u27e9"
+              },
+              {
+                "annotated_tactic": [
+                  "\"exacts [<a>inv_nonneg<\\/a>.2 (<a>pow_nonneg<\\/a> <a>zero_le_two<\\/a> _), <a>inv_le_one<\\/a> (<a>one_le_pow_of_one_le<\\/a> <a>one_le_two<\\/a> _)]\"",
+                  "[{\"full_name\":\"inv_nonneg\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Field\\/Defs.lean\",\"def_pos\":[55,15],\"def_end_pos\":[55,25]},{\"full_name\":\"pow_nonneg\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Ring\\/Defs.lean\",\"def_pos\":[241,9],\"def_end_pos\":[241,19]},{\"full_name\":\"zero_le_two\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Monoid\\/NatCast.lean\",\"def_pos\":[32,7],\"def_end_pos\":[32,18]},{\"full_name\":\"inv_le_one\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Field\\/Basic.lean\",\"def_pos\":[235,9],\"def_end_pos\":[235,19]},{\"full_name\":\"one_le_pow_of_one_le\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Ring\\/Basic.lean\",\"def_pos\":[82,9],\"def_end_pos\":[82,29]},{\"full_name\":\"one_le_two\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Monoid\\/NatCast.lean\",\"def_pos\":[50,7],\"def_end_pos\":[50,17]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case refine_1.refine_1\nE : Type u\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \u211d E\nf : E \u2192 \u211d\na : E\nf' : E \u2192L[\u211d] \u211d\ns : Set E\nx y : E\nh : segment \u211d x y \u2286 s\nc : \u2115 \u2192 \u211d := fun n => 2 ^ n\nd : \u2115 \u2192 E := fun n => (c n)\u207b\u00b9 \u2022 (y - x)\nn : \u2115\n\u22a2 0 \u2264 (c n)\u207b\u00b9\n\ncase refine_1.refine_2\nE : Type u\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \u211d E\nf : E \u2192 \u211d\na : E\nf' : E \u2192L[\u211d] \u211d\ns : Set E\nx y : E\nh : segment \u211d x y \u2286 s\nc : \u2115 \u2192 \u211d := fun n => 2 ^ n\nd : \u2115 \u2192 E := fun n => (c n)\u207b\u00b9 \u2022 (y - x)\nn : \u2115\n\u22a2 (c n)\u207b\u00b9 \u2264 1",
+                "tactic": "exacts [inv_nonneg.2 (pow_nonneg zero_le_two _), inv_le_one (one_le_pow_of_one_le one_le_two _)]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"exact tendsto_const_nhds.congr fun n \\u21a6 (<a>smul_inv_smul\\u2080<\\/a> (<a>pow_ne_zero<\\/a> _ <a>two_ne_zero<\\/a>) _).<a>symm<\\/a>\"",
+                  "[{\"full_name\":\"smul_inv_smul\\u2080\",\"def_path\":\"Mathlib\\/GroupTheory\\/GroupAction\\/Group.lean\",\"def_pos\":[212,9],\"def_end_pos\":[212,23]},{\"full_name\":\"pow_ne_zero\",\"def_path\":\"Mathlib\\/Algebra\\/GroupWithZero\\/Basic.lean\",\"def_pos\":[200,7],\"def_end_pos\":[200,18]},{\"full_name\":\"two_ne_zero\",\"def_path\":\"Mathlib\\/Algebra\\/NeZero.lean\",\"def_pos\":[65,7],\"def_end_pos\":[65,18]},{\"full_name\":\"Eq.symm\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[323,9],\"def_end_pos\":[323,16]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case refine_2\nE : Type u\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \u211d E\nf : E \u2192 \u211d\na : E\nf' : E \u2192L[\u211d] \u211d\ns : Set E\nx y : E\nh : segment \u211d x y \u2286 s\nc : \u2115 \u2192 \u211d := fun n => 2 ^ n\nd : \u2115 \u2192 E := fun n => (c n)\u207b\u00b9 \u2022 (y - x)\n\u22a2 Tendsto (fun n => c n \u2022 d n) atTop (\ud835\udcdd (y - x))",
+                "tactic": "exact tendsto_const_nhds.congr fun n \u21a6 (smul_inv_smul\u2080 (pow_ne_zero _ two_ne_zero) _).symm"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "mem_posTangentConeAt_of_segment_subset"
+      },
+      {
+        "errors": [
+          "internal transition boundary mismatch",
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/Analysis/Calculus/LocalExtr/Polynomial.lean",
+        "proof_id": "mathlib:Polynomial.card_roots_le_derivative",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              87,
+              75
+            ],
+            "file_path": "Mathlib/Analysis/Calculus/LocalExtr/Polynomial.lean",
+            "full_name": "Polynomial.card_roots_le_derivative",
+            "start": [
+              60,
+              1
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"simp only [<a>Finset.sum_add_distrib<\\/a>, <a>Finset.card_eq_sum_ones<\\/a>, <a>count_roots<\\/a>]\"",
+                  "[{\"full_name\":\"Finset.sum_add_distrib\",\"def_path\":\"Mathlib\\/Algebra\\/BigOperators\\/Group\\/Finset.lean\",\"def_pos\":[876,3],\"def_end_pos\":[876,14]},{\"full_name\":\"Finset.card_eq_sum_ones\",\"def_path\":\"Mathlib\\/Algebra\\/BigOperators\\/Group\\/Finset.lean\",\"def_pos\":[2076,9],\"def_end_pos\":[2076,25]},{\"full_name\":\"Polynomial.count_roots\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Roots.lean\",\"def_pos\":[100,9],\"def_end_pos\":[100,20]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "p : \u211d[X]\n\u22a2 \u2211 x \u2208 p.roots.toFinset, (Multiset.count x p.roots - 1 + 1) =\n    \u2211 x \u2208 p.roots.toFinset, (rootMultiplicity x p - 1) + p.roots.toFinset.card",
+                "tactic": "simp only [Finset.sum_add_distrib, Finset.card_eq_sum_ones, count_roots]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"simp only [\\u2190 <a>count_roots<\\/a>]\"",
+                  "[{\"full_name\":\"Polynomial.count_roots\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Roots.lean\",\"def_pos\":[100,9],\"def_end_pos\":[100,20]}]"
+                ],
+                "state_after": "p : \u211d[X]\n\u22a2 \u2211 x \u2208 p.roots.toFinset, Multiset.count x (derivative p).roots +\n      (((derivative p).roots.toFinset \\ p.roots.toFinset).card + 1) \u2264\n    \u2211 x \u2208 p.roots.toFinset, Multiset.count x (derivative p).roots +\n      (\u2211 x \u2208 (derivative p).roots.toFinset \\ p.roots.toFinset, Multiset.count x (derivative p).roots + 1)",
+                "state_before": "p : \u211d[X]\n\u22a2 \u2211 x \u2208 p.roots.toFinset, rootMultiplicity x (derivative p) +\n      (((derivative p).roots.toFinset \\ p.roots.toFinset).card + 1) \u2264\n    \u2211 x \u2208 p.roots.toFinset, Multiset.count x (derivative p).roots +\n      (\u2211 x \u2208 (derivative p).roots.toFinset \\ p.roots.toFinset, Multiset.count x (derivative p).roots + 1)",
+                "tactic": "simp only [\u2190 count_roots]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"refine <a>add_le_add_left<\\/a> (<a>add_le_add_right<\\/a> ((<a>Finset.card_eq_sum_ones<\\/a> _).<a>trans_le<\\/a> ?_) _) _\"",
+                  "[{\"full_name\":\"add_le_add_left\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Monoid\\/Unbundled\\/Basic.lean\",\"def_pos\":[49,32],\"def_end_pos\":[49,47]},{\"full_name\":\"add_le_add_right\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Monoid\\/Unbundled\\/Basic.lean\",\"def_pos\":[66,32],\"def_end_pos\":[66,48]},{\"full_name\":\"Finset.card_eq_sum_ones\",\"def_path\":\"Mathlib\\/Algebra\\/BigOperators\\/Group\\/Finset.lean\",\"def_pos\":[2076,9],\"def_end_pos\":[2076,25]},{\"full_name\":\"Eq.trans_le\",\"def_path\":\"Mathlib\\/Order\\/Basic.lean\",\"def_pos\":[198,7],\"def_end_pos\":[198,18]}]"
+                ],
+                "state_after": "p : \u211d[X]\n\u22a2 \u2211 x \u2208 (derivative p).roots.toFinset \\ p.roots.toFinset, 1 \u2264\n    \u2211 x \u2208 (derivative p).roots.toFinset \\ p.roots.toFinset, Multiset.count x (derivative p).roots",
+                "state_before": "p : \u211d[X]\n\u22a2 \u2211 x \u2208 p.roots.toFinset, Multiset.count x (derivative p).roots +\n      (((derivative p).roots.toFinset \\ p.roots.toFinset).card + 1) \u2264\n    \u2211 x \u2208 p.roots.toFinset, Multiset.count x (derivative p).roots +\n      (\u2211 x \u2208 (derivative p).roots.toFinset \\ p.roots.toFinset, Multiset.count x (derivative p).roots + 1)",
+                "tactic": "refine add_le_add_left (add_le_add_right ((Finset.card_eq_sum_ones _).trans_le ?_) _) _"
+              },
+              {
+                "annotated_tactic": [
+                  "\"refine <a>Finset.sum_le_sum<\\/a> fun x hx => <a>Nat.succ_le_iff<\\/a>.2 <| ?_\"",
+                  "[{\"full_name\":\"Finset.sum_le_sum\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/BigOperators\\/Group\\/Finset.lean\",\"def_pos\":[109,15],\"def_end_pos\":[109,25]},{\"full_name\":\"Nat.succ_le_iff\",\"def_path\":\"Mathlib\\/Data\\/Nat\\/Defs.lean\",\"def_pos\":[128,7],\"def_end_pos\":[128,18]}]"
+                ],
+                "state_after": "p : \u211d[X]\nx : \u211d\nhx : x \u2208 (derivative p).roots.toFinset \\ p.roots.toFinset\n\u22a2 0 < Multiset.count x (derivative p).roots",
+                "state_before": "p : \u211d[X]\n\u22a2 \u2211 x \u2208 (derivative p).roots.toFinset \\ p.roots.toFinset, 1 \u2264\n    \u2211 x \u2208 (derivative p).roots.toFinset \\ p.roots.toFinset, Multiset.count x (derivative p).roots",
+                "tactic": "refine Finset.sum_le_sum fun x hx => Nat.succ_le_iff.2 <| ?_"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rw [<a>Multiset.count_pos<\\/a>, \\u2190 <a>Multiset.mem_toFinset<\\/a>]\"",
+                  "[{\"full_name\":\"Multiset.count_pos\",\"def_path\":\"Mathlib\\/Data\\/Multiset\\/Basic.lean\",\"def_pos\":[2514,9],\"def_end_pos\":[2514,18]},{\"full_name\":\"Multiset.mem_toFinset\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Basic.lean\",\"def_pos\":[3100,9],\"def_end_pos\":[3100,21]}]"
+                ],
+                "state_after": "p : \u211d[X]\nx : \u211d\nhx : x \u2208 (derivative p).roots.toFinset \\ p.roots.toFinset\n\u22a2 x \u2208 (derivative p).roots.toFinset",
+                "state_before": "p : \u211d[X]\nx : \u211d\nhx : x \u2208 (derivative p).roots.toFinset \\ p.roots.toFinset\n\u22a2 0 < Multiset.count x (derivative p).roots",
+                "tactic": "rw [Multiset.count_pos, \u2190 Multiset.mem_toFinset]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"exact (<a>Finset.mem_sdiff<\\/a>.1 hx).1\"",
+                  "[{\"full_name\":\"Finset.mem_sdiff\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Basic.lean\",\"def_pos\":[2102,9],\"def_end_pos\":[2102,18]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "p : \u211d[X]\nx : \u211d\nhx : x \u2208 (derivative p).roots.toFinset \\ p.roots.toFinset\n\u22a2 x \u2208 (derivative p).roots.toFinset",
+                "tactic": "exact (Finset.mem_sdiff.1 hx).1"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rw [\\u2190 <a>add_assoc<\\/a>, \\u2190 <a>Finset.sum_union<\\/a> <a>Finset.disjoint_sdiff<\\/a>, <a>Finset.union_sdiff_self_eq_union<\\/a>, \\u2190\\n        <a>Multiset.toFinset_sum_count_eq<\\/a>, \\u2190 <a>Finset.sum_subset<\\/a> <a>Finset.subset_union_right<\\/a>]\"",
+                  "[{\"full_name\":\"add_assoc\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[288,3],\"def_end_pos\":[288,14]},{\"full_name\":\"Finset.sum_union\",\"def_path\":\"Mathlib\\/Algebra\\/BigOperators\\/Group\\/Finset.lean\",\"def_pos\":[460,3],\"def_end_pos\":[460,14]},{\"full_name\":\"Finset.disjoint_sdiff\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Basic.lean\",\"def_pos\":[2435,9],\"def_end_pos\":[2435,23]},{\"full_name\":\"Finset.union_sdiff_self_eq_union\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Basic.lean\",\"def_pos\":[2182,9],\"def_end_pos\":[2182,34]},{\"full_name\":\"Multiset.toFinset_sum_count_eq\",\"def_path\":\"Mathlib\\/Algebra\\/BigOperators\\/Group\\/Finset.lean\",\"def_pos\":[2466,9],\"def_end_pos\":[2466,30]},{\"full_name\":\"Finset.sum_subset\",\"def_path\":\"Mathlib\\/Algebra\\/BigOperators\\/Group\\/Finset.lean\",\"def_pos\":[594,3],\"def_end_pos\":[594,14]},{\"full_name\":\"Finset.subset_union_right\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Basic.lean\",\"def_pos\":[1441,9],\"def_end_pos\":[1441,27]}]"
+                ],
+                "state_after": "p : \u211d[X]\n\u22a2 \u2200 x \u2208 p.roots.toFinset \u222a (derivative p).roots.toFinset,\n    x \u2209 (derivative p).roots.toFinset \u2192 Multiset.count x (derivative p).roots = 0",
+                "state_before": "p : \u211d[X]\n\u22a2 \u2211 x \u2208 p.roots.toFinset, Multiset.count x (derivative p).roots +\n      (\u2211 x \u2208 (derivative p).roots.toFinset \\ p.roots.toFinset, Multiset.count x (derivative p).roots + 1) =\n    Multiset.card (derivative p).roots + 1",
+                "tactic": "rw [\u2190 add_assoc, \u2190 Finset.sum_union Finset.disjoint_sdiff, Finset.union_sdiff_self_eq_union, \u2190\n  Multiset.toFinset_sum_count_eq, \u2190 Finset.sum_subset Finset.subset_union_right]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"intro x _ hx\\u2082\"",
+                  "[]"
+                ],
+                "state_after": "p : \u211d[X]\nx : \u211d\na\u271d : x \u2208 p.roots.toFinset \u222a (derivative p).roots.toFinset\nhx\u2082 : x \u2209 (derivative p).roots.toFinset\n\u22a2 Multiset.count x (derivative p).roots = 0",
+                "state_before": "p : \u211d[X]\n\u22a2 \u2200 x \u2208 p.roots.toFinset \u222a (derivative p).roots.toFinset,\n    x \u2209 (derivative p).roots.toFinset \u2192 Multiset.count x (derivative p).roots = 0",
+                "tactic": "intro x _ hx\u2082"
+              },
+              {
+                "annotated_tactic": [
+                  "\"simpa only [<a>Multiset.mem_toFinset<\\/a>, <a>Multiset.count_eq_zero<\\/a>] using hx\\u2082\"",
+                  "[{\"full_name\":\"Multiset.mem_toFinset\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Basic.lean\",\"def_pos\":[3100,9],\"def_end_pos\":[3100,21]},{\"full_name\":\"Multiset.count_eq_zero\",\"def_path\":\"Mathlib\\/Data\\/Multiset\\/Basic.lean\",\"def_pos\":[2529,15],\"def_end_pos\":[2529,28]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "p : \u211d[X]\nx : \u211d\na\u271d : x \u2208 p.roots.toFinset \u222a (derivative p).roots.toFinset\nhx\u2082 : x \u2209 (derivative p).roots.toFinset\n\u22a2 Multiset.count x (derivative p).roots = 0",
+                "tactic": "simpa only [Multiset.mem_toFinset, Multiset.count_eq_zero] using hx\u2082"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "Polynomial.card_roots_le_derivative"
+      }
+    ],
+    "validation_rejected_proofs": 2,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
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+  ],
+  "proof_ids": [
+    "mathlib:IsLocalMaxOn.fderivWithin_eq_zero",
+    "mathlib:IsLocalMaxOn.fderivWithin_nonpos",
+    "mathlib:IsLocalMaxOn.hasFDerivWithinAt_eq_zero",
+    "mathlib:IsLocalMin.hasDerivAt_eq_zero",
+    "mathlib:IsLocalMin.hasFDerivAt_eq_zero",
+    "mathlib:IsLocalMinOn.fderivWithin_eq_zero",
+    "mathlib:IsLocalMinOn.fderivWithin_nonneg",
+    "mathlib:IsLocalMinOn.hasFDerivWithinAt_eq_zero",
+    "mathlib:IsLocalMinOn.hasFDerivWithinAt_nonneg",
+    "mathlib:Polynomial.card_rootSet_le_derivative",
+    "mathlib:mem_posTangentConeAt_of_segment_subset'",
+    "mathlib:posTangentConeAt_mono"
+  ],
+  "proof_keys": [
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+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Analysis/Calculus/LocalExtr/Basic.lean\",null,null,\"IsLocalMinOn.fderivWithin_nonneg\"]",
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+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Analysis/Calculus/LocalExtr/Basic.lean\",null,null,\"IsLocalMinOn.hasFDerivWithinAt_nonneg\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Analysis/Calculus/LocalExtr/Basic.lean\",null,null,\"mem_posTangentConeAt_of_segment_subset'\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Analysis/Calculus/LocalExtr/Basic.lean\",null,null,\"posTangentConeAt_mono\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Analysis/Calculus/LocalExtr/Polynomial.lean\",null,null,\"Polynomial.card_rootSet_le_derivative\"]"
+  ]
+}

manifests/batches/numina/001188.json

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+  ]
+}

manifests/batches/numina/001189.json

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manifests/batches/numina/001192.json

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+}

manifests/batches/numina/001193.json

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manifests/batches/numina/001194.json

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+    "numina:afd93506-b1e3-571d-821b-96bcb7baf197",
+    "numina:ee48fdfd-43b5-554b-825c-f93c183bd07a"
+  ],
+  "proof_keys": [
+    "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_005970.lean\",\"ba27029401a7dedbafdb40e4518ce189d3bc8666ad7f5576083a6ae3c34f53e7\",0,\"algebra_64758\"]",
+    "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_005971.lean\",\"317d470c9d09d6c28efc4e7980721322d0048123d0ae8c6c781565471593d938\",0,\"algebra_299469\"]",
+    "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_005972.lean\",\"c737adc8519a099e47c7b1793111d1a264c0435630f791118214240d0f866199\",0,\"algebra_171194\"]",
+    "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_005973.lean\",\"0ec38d16a12e4312e0de72f9231529483d3c39a533c0f6443b0fe916bcb5d513\",0,\"algebra_160505\"]",
+    "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_005974.lean\",\"513fc0727e69d8dfeb35b1f081b63e90edbd92e59567f9832cb154d78d1f4056\",0,\"number_theory_305984\"]"
+  ]
+}

manifests/batches/numina/001195.json

@@ -0,0 +1,73 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "numina/001195",
+  "batch_fingerprint": "ef3d67c5bc32215173b551ee949c5c3d9bd9390f69d756aff7b5a6103fd155a8",
+  "evidence": {
+    "batch_fingerprint": "ef3d67c5bc32215173b551ee949c5c3d9bd9390f69d756aff7b5a6103fd155a8",
+    "contamination_matches": [],
+    "failures": [],
+    "input_proofs": 5,
+    "input_units": 5,
+    "proofs": 5,
+    "published_proofs": 4,
+    "published_transitions": 20,
+    "replay_failures": [],
+    "trace_mode": "bundle",
+    "transitions": 29,
+    "validation_failures": [
+      {
+        "errors": [
+          "internal transition boundary mismatch",
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Full/Proof_005977.lean",
+        "proof_id": "numina:37b1149f-91aa-5972-a084-fb35f346fa83",
+        "provenance": {
+          "atomic_transition_count": 28,
+          "bundle_ordinal": 2,
+          "compound_transition_count": 10,
+          "declaration_kind": "theorem",
+          "metadata": {
+            "bundle_ordinal": 2,
+            "declaration_kind": "theorem",
+            "original_file_path": "Full/Proof_005977.lean",
+            "source_dataset": "numina",
+            "theorem_name": "number_theory_165219",
+            "theorem_ordinal": 0
+          },
+          "original_file_path": "Full/Proof_005977.lean",
+          "selection_index": 5977,
+          "source_dataset": "numina",
+          "source_id": "37b1149f-91aa-5972-a084-fb35f346fa83",
+          "source_sha256": "2757c0eb2e99fb59da6784970e87350d268ea9b0cebfc58ba5852e5f3d2b6803",
+          "theorem_name": "number_theory_165219",
+          "theorem_ordinal": 0
+        },
+        "theorem_name": "number_theory_165219"
+      }
+    ],
+    "validation_rejected_proofs": 1,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/numina-001195-0000-4773fb7c5591910b.parquet",
+      "sha256": "4773fb7c5591910bafa6411a3a3d271ad89a47baedb50e68091a718758ed31a8",
+      "bytes": 168736,
+      "rows": 20,
+      "revision": "3ccd431b411f5443a88469e9af85fa5eacacb34d"
+    }
+  ],
+  "proof_ids": [
+    "numina:1708a5f0-9da6-53e5-aa73-20a292d4d4ef",
+    "numina:af0b76ff-55e2-5749-adc0-53b5b08b6c44",
+    "numina:eef8c7dd-b47b-5c3c-bcbe-68431076aca8",
+    "numina:f8226547-ae41-57b2-a97e-8c3bb6be6f1a"
+  ],
+  "proof_keys": [
+    "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_005975.lean\",\"0d352c71ba9ff050243d13341724fd5e98e5d4b82c280981c51a56f84414865e\",0,\"algebra_291533\"]",
+    "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_005976.lean\",\"24e9282552ca1da96059ad259fecde9febf59a638fd369d8824735eef5a0a730\",0,\"algebra_155560\"]",
+    "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_005978.lean\",\"a189a2d28575fae53f51f5251f5f575be318edabd3a6075178a00ad1ed266ae9\",0,\"algebra_291755\"]",
+    "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_005979.lean\",\"65eaa77f26ba77c4739fc8ca5bff42d3a62db917c78be37a640d7ab069ab608b\",0,\"number_theory_156842\"]"
+  ]
+}