{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:NFBZURSNQKEUFHBGYH2X5I6XHX","short_pith_number":"pith:NFBZURSN","canonical_record":{"source":{"id":"1709.04235","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-09-13T10:17:49Z","cross_cats_sorted":["math.NT","math.RT"],"title_canon_sha256":"246085c1298eab6a9b106f4b2e96b1f50b56c85e0a2a2acf89626c51f098500e","abstract_canon_sha256":"d48a2510e61bd3a917e4f002cdff47ee9e871e81e50ddd9949a4be7842d82119"},"schema_version":"1.0"},"canonical_sha256":"69439a464d8289429c26c1f57ea3d73dfccf49da8f660fc64fd05b95f83eb9f3","source":{"kind":"arxiv","id":"1709.04235","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.04235","created_at":"2026-07-05T04:38:39Z"},{"alias_kind":"arxiv_version","alias_value":"1709.04235v3","created_at":"2026-07-05T04:38:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.04235","created_at":"2026-07-05T04:38:39Z"},{"alias_kind":"pith_short_12","alias_value":"NFBZURSNQKEU","created_at":"2026-07-05T04:38:39Z"},{"alias_kind":"pith_short_16","alias_value":"NFBZURSNQKEUFHBG","created_at":"2026-07-05T04:38:39Z"},{"alias_kind":"pith_short_8","alias_value":"NFBZURSN","created_at":"2026-07-05T04:38:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:NFBZURSNQKEUFHBGYH2X5I6XHX","target":"record","payload":{"canonical_record":{"source":{"id":"1709.04235","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-09-13T10:17:49Z","cross_cats_sorted":["math.NT","math.RT"],"title_canon_sha256":"246085c1298eab6a9b106f4b2e96b1f50b56c85e0a2a2acf89626c51f098500e","abstract_canon_sha256":"d48a2510e61bd3a917e4f002cdff47ee9e871e81e50ddd9949a4be7842d82119"},"schema_version":"1.0"},"canonical_sha256":"69439a464d8289429c26c1f57ea3d73dfccf49da8f660fc64fd05b95f83eb9f3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:38:39.553540Z","signature_b64":"avIkwW6K1TAMFpNo1CA6o5qMOXO/HxIN38iUhkocQDNnV3Jk+Hh5lle6sUidrWs1oP45EAAi8fLHUmB5LEjfCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"69439a464d8289429c26c1f57ea3d73dfccf49da8f660fc64fd05b95f83eb9f3","last_reissued_at":"2026-07-05T04:38:39.553079Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:38:39.553079Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.04235","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:38:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EiEpFaP7ydaOHbTTpT7BlQAn+iMxOw0gLjyCAl7F1awjsAY5096GvdLwy2KULNAs9HoTM0oOC81mDmJOMVwTBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T16:59:30.618541Z"},"content_sha256":"8d90a0819e27162bb9209666559c35cc2cd884213f9116a346b3cda36b147c92","schema_version":"1.0","event_id":"sha256:8d90a0819e27162bb9209666559c35cc2cd884213f9116a346b3cda36b147c92"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:NFBZURSNQKEUFHBGYH2X5I6XHX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Topological quantum field theory for dormant opers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT","math.RT"],"primary_cat":"math.AG","authors_text":"Yasuhiro Wakabayashi","submitted_at":"2017-09-13T10:17:49Z","abstract_excerpt":"The purpose of the present paper is to develop the enumerative geometry of dormant $G$-opers for a semisimple algebraic group $G$. In the present paper, we construct a compact moduli stack admitting a perfect obstruction theory by introducing the notion of a dormant faithful twisted $G$-oper (or a \"$G$-do'per\", for short). The resulting virtual fundamental class induces a semisimple $2$d TQFT (= $2$-dimensional topological quantum field theory) counting the number of $G$-do'pers. This $2$d TQFT gives an analogue of the Witten-Kontsevich theorem describing the intersection numbers of psi classe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.04235","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1709.04235/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:38:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OZa+mkt+H8g47ZiA57tDndsEh95N+kFtxs8DI6e2mw0Bdtq0df4a5wcGnGwi5BUjJX5zx0Im3LHNQ+YtRpihCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T16:59:30.619179Z"},"content_sha256":"55c87dc3fae8180c52834dd3afce78188b3e78ff32867581a2e5571fba5a9b9b","schema_version":"1.0","event_id":"sha256:55c87dc3fae8180c52834dd3afce78188b3e78ff32867581a2e5571fba5a9b9b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NFBZURSNQKEUFHBGYH2X5I6XHX/bundle.json","state_url":"https://pith.science/pith/NFBZURSNQKEUFHBGYH2X5I6XHX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NFBZURSNQKEUFHBGYH2X5I6XHX/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-12T16:59:30Z","links":{"resolver":"https://pith.science/pith/NFBZURSNQKEUFHBGYH2X5I6XHX","bundle":"https://pith.science/pith/NFBZURSNQKEUFHBGYH2X5I6XHX/bundle.json","state":"https://pith.science/pith/NFBZURSNQKEUFHBGYH2X5I6XHX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NFBZURSNQKEUFHBGYH2X5I6XHX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:NFBZURSNQKEUFHBGYH2X5I6XHX","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"d48a2510e61bd3a917e4f002cdff47ee9e871e81e50ddd9949a4be7842d82119","cross_cats_sorted":["math.NT","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-09-13T10:17:49Z","title_canon_sha256":"246085c1298eab6a9b106f4b2e96b1f50b56c85e0a2a2acf89626c51f098500e"},"schema_version":"1.0","source":{"id":"1709.04235","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.04235","created_at":"2026-07-05T04:38:39Z"},{"alias_kind":"arxiv_version","alias_value":"1709.04235v3","created_at":"2026-07-05T04:38:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.04235","created_at":"2026-07-05T04:38:39Z"},{"alias_kind":"pith_short_12","alias_value":"NFBZURSNQKEU","created_at":"2026-07-05T04:38:39Z"},{"alias_kind":"pith_short_16","alias_value":"NFBZURSNQKEUFHBG","created_at":"2026-07-05T04:38:39Z"},{"alias_kind":"pith_short_8","alias_value":"NFBZURSN","created_at":"2026-07-05T04:38:39Z"}],"graph_snapshots":[{"event_id":"sha256:55c87dc3fae8180c52834dd3afce78188b3e78ff32867581a2e5571fba5a9b9b","target":"graph","created_at":"2026-07-05T04:38:39Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1709.04235/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The purpose of the present paper is to develop the enumerative geometry of dormant $G$-opers for a semisimple algebraic group $G$. In the present paper, we construct a compact moduli stack admitting a perfect obstruction theory by introducing the notion of a dormant faithful twisted $G$-oper (or a \"$G$-do'per\", for short). The resulting virtual fundamental class induces a semisimple $2$d TQFT (= $2$-dimensional topological quantum field theory) counting the number of $G$-do'pers. This $2$d TQFT gives an analogue of the Witten-Kontsevich theorem describing the intersection numbers of psi classe","authors_text":"Yasuhiro Wakabayashi","cross_cats":["math.NT","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-09-13T10:17:49Z","title":"Topological quantum field theory for dormant opers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.04235","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8d90a0819e27162bb9209666559c35cc2cd884213f9116a346b3cda36b147c92","target":"record","created_at":"2026-07-05T04:38:39Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"d48a2510e61bd3a917e4f002cdff47ee9e871e81e50ddd9949a4be7842d82119","cross_cats_sorted":["math.NT","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-09-13T10:17:49Z","title_canon_sha256":"246085c1298eab6a9b106f4b2e96b1f50b56c85e0a2a2acf89626c51f098500e"},"schema_version":"1.0","source":{"id":"1709.04235","kind":"arxiv","version":3}},"canonical_sha256":"69439a464d8289429c26c1f57ea3d73dfccf49da8f660fc64fd05b95f83eb9f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"69439a464d8289429c26c1f57ea3d73dfccf49da8f660fc64fd05b95f83eb9f3","first_computed_at":"2026-07-05T04:38:39.553079Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:38:39.553079Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"avIkwW6K1TAMFpNo1CA6o5qMOXO/HxIN38iUhkocQDNnV3Jk+Hh5lle6sUidrWs1oP45EAAi8fLHUmB5LEjfCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:38:39.553540Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.04235","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8d90a0819e27162bb9209666559c35cc2cd884213f9116a346b3cda36b147c92","sha256:55c87dc3fae8180c52834dd3afce78188b3e78ff32867581a2e5571fba5a9b9b"],"state_sha256":"88f8dca4f4937a1a25700aea1e125a74b3654483ae0d942e7eb5cd04625a936e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F6cfFgxWhbk5HIg9GnveDFfKFUhOkMpKwukFb/sopLrc0KSZVI5HJDYFVRCIWHMMUm0om/ejSkKuZEJGN91dAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T16:59:30.625717Z","bundle_sha256":"fbeb9ef92e85c74a8f63542dc764e3ee207b55959738dd539f773d609029dff4"}}