{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:W7AR5GEYXFD2OMX2KYJQHREJM5","short_pith_number":"pith:W7AR5GEY","canonical_record":{"source":{"id":"1202.2397","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2012-02-11T01:54:22Z","cross_cats_sorted":["hep-th","quant-ph"],"title_canon_sha256":"8823de42439a44abd34c9fcbd0607b8f91a6ddda520c37b80d0cf2d1d753b9a3","abstract_canon_sha256":"e8b99c9a3d7f4358d2272a138fa93a16f7abbc4847d5dd65fba86703a3df5480"},"schema_version":"1.0"},"canonical_sha256":"b7c11e9898b947a732fa561303c48967680f1e37c7f1f178f6d54f27c698bc09","source":{"kind":"arxiv","id":"1202.2397","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.2397","created_at":"2026-05-18T03:17:34Z"},{"alias_kind":"arxiv_version","alias_value":"1202.2397v3","created_at":"2026-05-18T03:17:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.2397","created_at":"2026-05-18T03:17:34Z"},{"alias_kind":"pith_short_12","alias_value":"W7AR5GEYXFD2","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"W7AR5GEYXFD2OMX2","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"W7AR5GEY","created_at":"2026-05-18T12:27:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:W7AR5GEYXFD2OMX2KYJQHREJM5","target":"record","payload":{"canonical_record":{"source":{"id":"1202.2397","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2012-02-11T01:54:22Z","cross_cats_sorted":["hep-th","quant-ph"],"title_canon_sha256":"8823de42439a44abd34c9fcbd0607b8f91a6ddda520c37b80d0cf2d1d753b9a3","abstract_canon_sha256":"e8b99c9a3d7f4358d2272a138fa93a16f7abbc4847d5dd65fba86703a3df5480"},"schema_version":"1.0"},"canonical_sha256":"b7c11e9898b947a732fa561303c48967680f1e37c7f1f178f6d54f27c698bc09","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:17:34.362195Z","signature_b64":"II7lVwMvD9xfKdYklNbG0gcWGTYnEEZOVNQnmQVwAxOXRnS/uJbhvbxdL/nTWre3BXzXTWCZdXMqZRWm/wteCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b7c11e9898b947a732fa561303c48967680f1e37c7f1f178f6d54f27c698bc09","last_reissued_at":"2026-05-18T03:17:34.361557Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:17:34.361557Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.2397","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":"2026-05-18T03:17:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z2eG4A9DQ6IEEyuxpScHUnkjJmUdKI5vJFGRHll7UVO2AmwEHpGYU/9xzR6A+hAvTpNSWhkU7WYy7f0Y16zQAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T22:11:00.612532Z"},"content_sha256":"1edefb3fa904d90d1ecb13609ad078a61fbb70d97a906d422b44082c471acfe4","schema_version":"1.0","event_id":"sha256:1edefb3fa904d90d1ecb13609ad078a61fbb70d97a906d422b44082c471acfe4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:W7AR5GEYXFD2OMX2KYJQHREJM5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Euler Number of Bloch States Manifold and the Quantum Phases in Gapped Fermionic Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","quant-ph"],"primary_cat":"cond-mat.str-el","authors_text":"Heng Fan, Shi-Jian Gu, Shu Chen, Wu-Ming Liu, Yu-Quan Ma","submitted_at":"2012-02-11T01:54:22Z","abstract_excerpt":"We propose a topological Euler number to characterize nontrivial topological phases of gapped fermionic systems, which originates from the Gauss-Bonnet theorem on the Riemannian structure of Bloch states established by the real part of the quantum geometric tensor in momentum space. Meanwhile, the imaginary part of the geometric tensor corresponds to the Berry curvature which leads to the Chern number characterization. We discuss the topological numbers induced by the geometric tensor analytically in a general two-band model. As an example, we show that the zero-temperature phase diagram of a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2397","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":""},"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":"2026-05-18T03:17:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0Q7Pf6FbyTp5bwFVNF94wVlMsS7SpwUSW6zHWhacl6l9wHsLXAT0Hhyo8lqzsBoOsw4ewyCaeDXByQJ8O8lGAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T22:11:00.613252Z"},"content_sha256":"b6bb098d993468b66337ed49cc8b88747314adb3d1ee21acd83eb69c1fc47c73","schema_version":"1.0","event_id":"sha256:b6bb098d993468b66337ed49cc8b88747314adb3d1ee21acd83eb69c1fc47c73"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W7AR5GEYXFD2OMX2KYJQHREJM5/bundle.json","state_url":"https://pith.science/pith/W7AR5GEYXFD2OMX2KYJQHREJM5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W7AR5GEYXFD2OMX2KYJQHREJM5/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":"2026-05-27T22:11:00Z","links":{"resolver":"https://pith.science/pith/W7AR5GEYXFD2OMX2KYJQHREJM5","bundle":"https://pith.science/pith/W7AR5GEYXFD2OMX2KYJQHREJM5/bundle.json","state":"https://pith.science/pith/W7AR5GEYXFD2OMX2KYJQHREJM5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W7AR5GEYXFD2OMX2KYJQHREJM5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:W7AR5GEYXFD2OMX2KYJQHREJM5","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":"e8b99c9a3d7f4358d2272a138fa93a16f7abbc4847d5dd65fba86703a3df5480","cross_cats_sorted":["hep-th","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2012-02-11T01:54:22Z","title_canon_sha256":"8823de42439a44abd34c9fcbd0607b8f91a6ddda520c37b80d0cf2d1d753b9a3"},"schema_version":"1.0","source":{"id":"1202.2397","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.2397","created_at":"2026-05-18T03:17:34Z"},{"alias_kind":"arxiv_version","alias_value":"1202.2397v3","created_at":"2026-05-18T03:17:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.2397","created_at":"2026-05-18T03:17:34Z"},{"alias_kind":"pith_short_12","alias_value":"W7AR5GEYXFD2","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"W7AR5GEYXFD2OMX2","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"W7AR5GEY","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:b6bb098d993468b66337ed49cc8b88747314adb3d1ee21acd83eb69c1fc47c73","target":"graph","created_at":"2026-05-18T03:17:34Z","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"},"paper":{"abstract_excerpt":"We propose a topological Euler number to characterize nontrivial topological phases of gapped fermionic systems, which originates from the Gauss-Bonnet theorem on the Riemannian structure of Bloch states established by the real part of the quantum geometric tensor in momentum space. Meanwhile, the imaginary part of the geometric tensor corresponds to the Berry curvature which leads to the Chern number characterization. We discuss the topological numbers induced by the geometric tensor analytically in a general two-band model. As an example, we show that the zero-temperature phase diagram of a ","authors_text":"Heng Fan, Shi-Jian Gu, Shu Chen, Wu-Ming Liu, Yu-Quan Ma","cross_cats":["hep-th","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2012-02-11T01:54:22Z","title":"The Euler Number of Bloch States Manifold and the Quantum Phases in Gapped Fermionic Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2397","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":"sha256:1edefb3fa904d90d1ecb13609ad078a61fbb70d97a906d422b44082c471acfe4","target":"record","created_at":"2026-05-18T03:17:34Z","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":"e8b99c9a3d7f4358d2272a138fa93a16f7abbc4847d5dd65fba86703a3df5480","cross_cats_sorted":["hep-th","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2012-02-11T01:54:22Z","title_canon_sha256":"8823de42439a44abd34c9fcbd0607b8f91a6ddda520c37b80d0cf2d1d753b9a3"},"schema_version":"1.0","source":{"id":"1202.2397","kind":"arxiv","version":3}},"canonical_sha256":"b7c11e9898b947a732fa561303c48967680f1e37c7f1f178f6d54f27c698bc09","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b7c11e9898b947a732fa561303c48967680f1e37c7f1f178f6d54f27c698bc09","first_computed_at":"2026-05-18T03:17:34.361557Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:17:34.361557Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"II7lVwMvD9xfKdYklNbG0gcWGTYnEEZOVNQnmQVwAxOXRnS/uJbhvbxdL/nTWre3BXzXTWCZdXMqZRWm/wteCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:17:34.362195Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.2397","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1edefb3fa904d90d1ecb13609ad078a61fbb70d97a906d422b44082c471acfe4","sha256:b6bb098d993468b66337ed49cc8b88747314adb3d1ee21acd83eb69c1fc47c73"],"state_sha256":"aef5cfd796c1f0eb64b05712a810e919c88a9106e6af520039756b2aff87bff1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hAsp3vidhAoj6HiEteQx78mPEPPmEG0MivbGd9NPvIf9YXEDx4/ZP/Nko5N77ro9eTrnOW/bXPBiC4t0eJJuAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T22:11:00.617183Z","bundle_sha256":"e96b03ca577bd7381b00ee89c623ee24d9c5de1fe82ede6584439da146417053"}}