{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:2NXPPPNT64XNNSIKBNVOT2U5T3","short_pith_number":"pith:2NXPPPNT","canonical_record":{"source":{"id":"2211.15534","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"gr-qc","submitted_at":"2022-11-28T16:42:37Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"ee43e464fc28867304e1609f48b98c4827a76b12de92eeb403edfc0693c7379d","abstract_canon_sha256":"fe488a980c80126a05b3c57288ebd6f4b95ef1e1d7ca2ad95dc5759e4782cbf4"},"schema_version":"1.0"},"canonical_sha256":"d36ef7bdb3f72ed6c90a0b6ae9ea9d9ec930121e62c7685bf9486545c688e6ad","source":{"kind":"arxiv","id":"2211.15534","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.15534","created_at":"2026-07-05T05:39:26Z"},{"alias_kind":"arxiv_version","alias_value":"2211.15534v3","created_at":"2026-07-05T05:39:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.15534","created_at":"2026-07-05T05:39:26Z"},{"alias_kind":"pith_short_12","alias_value":"2NXPPPNT64XN","created_at":"2026-07-05T05:39:26Z"},{"alias_kind":"pith_short_16","alias_value":"2NXPPPNT64XNNSIK","created_at":"2026-07-05T05:39:26Z"},{"alias_kind":"pith_short_8","alias_value":"2NXPPPNT","created_at":"2026-07-05T05:39:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:2NXPPPNT64XNNSIKBNVOT2U5T3","target":"record","payload":{"canonical_record":{"source":{"id":"2211.15534","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"gr-qc","submitted_at":"2022-11-28T16:42:37Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"ee43e464fc28867304e1609f48b98c4827a76b12de92eeb403edfc0693c7379d","abstract_canon_sha256":"fe488a980c80126a05b3c57288ebd6f4b95ef1e1d7ca2ad95dc5759e4782cbf4"},"schema_version":"1.0"},"canonical_sha256":"d36ef7bdb3f72ed6c90a0b6ae9ea9d9ec930121e62c7685bf9486545c688e6ad","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:39:26.104343Z","signature_b64":"4qB9AViuR5P+lJpsiz+b4h5k8pSJwzgh190BZP9Nbjlh6o6xnZQvlmDg5kv5ktSiwMQLxRZv3cZt0IMrM7LXAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d36ef7bdb3f72ed6c90a0b6ae9ea9d9ec930121e62c7685bf9486545c688e6ad","last_reissued_at":"2026-07-05T05:39:26.103840Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:39:26.103840Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2211.15534","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":"2026-07-05T05:39:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VUhA8664McJZsr8kLSAOyJY+FYfEuOna3UyXGOFRm3EIvL5WUuzL2RhOZwg3q2D03kd9tOPQTFOVNIspmdBGDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T12:16:18.831765Z"},"content_sha256":"da320bf66ec3e0bdc024d477aa9389d08dd73b2d5fd8dbc607261fb4fac1b7bc","schema_version":"1.0","event_id":"sha256:da320bf66ec3e0bdc024d477aa9389d08dd73b2d5fd8dbc607261fb4fac1b7bc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:2NXPPPNT64XNNSIKBNVOT2U5T3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Revisiting thermodynamic topologies of black holes","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"gr-qc","authors_text":"Chaoxi Fang, Jie Jiang, Ming Zhang","submitted_at":"2022-11-28T16:42:37Z","abstract_excerpt":"In the generalized off-shell free energy landscape, black holes can be treated as thermodynamic topological defects. The local topological properties of the spacetime can be reflected by the winding numbers at the defects, while the global topological nature can be classified by the topological number which is the sum of all local winding numbers. We propose that the winding numbers can be calculated via the residues of isolated one-order pole points of characterized functions constructed from the off-shell free energy. Using the residue method, we show that the topologies of black holes can b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.15534","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/2211.15534/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":"2026-07-05T05:39:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k1ywi8EjlDyYrKInP94U39bQ97pfK4tyJe0tlgBbbvl18Rwcn2YOP8qm2dpMmq9fwh0zfpgtqt8bguFy9HROAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T12:16:18.832258Z"},"content_sha256":"a41ad7c903f88d190bc32fe14691979d5241001fc07dfd119aa10a23b3f82961","schema_version":"1.0","event_id":"sha256:a41ad7c903f88d190bc32fe14691979d5241001fc07dfd119aa10a23b3f82961"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2NXPPPNT64XNNSIKBNVOT2U5T3/bundle.json","state_url":"https://pith.science/pith/2NXPPPNT64XNNSIKBNVOT2U5T3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2NXPPPNT64XNNSIKBNVOT2U5T3/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":"2026-08-09T12:16:18Z","links":{"resolver":"https://pith.science/pith/2NXPPPNT64XNNSIKBNVOT2U5T3","bundle":"https://pith.science/pith/2NXPPPNT64XNNSIKBNVOT2U5T3/bundle.json","state":"https://pith.science/pith/2NXPPPNT64XNNSIKBNVOT2U5T3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2NXPPPNT64XNNSIKBNVOT2U5T3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:2NXPPPNT64XNNSIKBNVOT2U5T3","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":"fe488a980c80126a05b3c57288ebd6f4b95ef1e1d7ca2ad95dc5759e4782cbf4","cross_cats_sorted":["hep-th"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"gr-qc","submitted_at":"2022-11-28T16:42:37Z","title_canon_sha256":"ee43e464fc28867304e1609f48b98c4827a76b12de92eeb403edfc0693c7379d"},"schema_version":"1.0","source":{"id":"2211.15534","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.15534","created_at":"2026-07-05T05:39:26Z"},{"alias_kind":"arxiv_version","alias_value":"2211.15534v3","created_at":"2026-07-05T05:39:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.15534","created_at":"2026-07-05T05:39:26Z"},{"alias_kind":"pith_short_12","alias_value":"2NXPPPNT64XN","created_at":"2026-07-05T05:39:26Z"},{"alias_kind":"pith_short_16","alias_value":"2NXPPPNT64XNNSIK","created_at":"2026-07-05T05:39:26Z"},{"alias_kind":"pith_short_8","alias_value":"2NXPPPNT","created_at":"2026-07-05T05:39:26Z"}],"graph_snapshots":[{"event_id":"sha256:a41ad7c903f88d190bc32fe14691979d5241001fc07dfd119aa10a23b3f82961","target":"graph","created_at":"2026-07-05T05:39:26Z","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/2211.15534/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In the generalized off-shell free energy landscape, black holes can be treated as thermodynamic topological defects. The local topological properties of the spacetime can be reflected by the winding numbers at the defects, while the global topological nature can be classified by the topological number which is the sum of all local winding numbers. We propose that the winding numbers can be calculated via the residues of isolated one-order pole points of characterized functions constructed from the off-shell free energy. Using the residue method, we show that the topologies of black holes can b","authors_text":"Chaoxi Fang, Jie Jiang, Ming Zhang","cross_cats":["hep-th"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"gr-qc","submitted_at":"2022-11-28T16:42:37Z","title":"Revisiting thermodynamic topologies of black holes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.15534","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:da320bf66ec3e0bdc024d477aa9389d08dd73b2d5fd8dbc607261fb4fac1b7bc","target":"record","created_at":"2026-07-05T05:39:26Z","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":"fe488a980c80126a05b3c57288ebd6f4b95ef1e1d7ca2ad95dc5759e4782cbf4","cross_cats_sorted":["hep-th"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"gr-qc","submitted_at":"2022-11-28T16:42:37Z","title_canon_sha256":"ee43e464fc28867304e1609f48b98c4827a76b12de92eeb403edfc0693c7379d"},"schema_version":"1.0","source":{"id":"2211.15534","kind":"arxiv","version":3}},"canonical_sha256":"d36ef7bdb3f72ed6c90a0b6ae9ea9d9ec930121e62c7685bf9486545c688e6ad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d36ef7bdb3f72ed6c90a0b6ae9ea9d9ec930121e62c7685bf9486545c688e6ad","first_computed_at":"2026-07-05T05:39:26.103840Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:39:26.103840Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4qB9AViuR5P+lJpsiz+b4h5k8pSJwzgh190BZP9Nbjlh6o6xnZQvlmDg5kv5ktSiwMQLxRZv3cZt0IMrM7LXAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T05:39:26.104343Z","signed_message":"canonical_sha256_bytes"},"source_id":"2211.15534","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:da320bf66ec3e0bdc024d477aa9389d08dd73b2d5fd8dbc607261fb4fac1b7bc","sha256:a41ad7c903f88d190bc32fe14691979d5241001fc07dfd119aa10a23b3f82961"],"state_sha256":"f64a67427e8bffa75c3d1af9c68cd0ad00234fb50dd3d6215db646695507eaa4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TR1vKJ4Gsm6lAGf0uc9wPyEtCOJpl1IWRHlwR90bkbSPmcCMePCnCyrefJ7zwej3XLPLT75ZmrRHLs8Ox6f8CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T12:16:18.836000Z","bundle_sha256":"b3e0c6bd887e847eeb7f2647b84ca73abd980432d5cfce53e4f774bd5da90b62"}}