{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:SHC4J7RIEC6YFNXT6MTQBUYQ2S","short_pith_number":"pith:SHC4J7RI","canonical_record":{"source":{"id":"2412.18796","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2024-12-25T06:35:04Z","cross_cats_sorted":["hep-lat"],"title_canon_sha256":"1b474aae9c5826614c542da5e7e6442de6e8f39050f8bf3605b3c38e9dfdcace","abstract_canon_sha256":"08db568bec2e7ce4a657cd33185913a0500561d6ccbf34aeb9b5d18f88f8b7e8"},"schema_version":"1.0"},"canonical_sha256":"91c5c4fe2820bd82b6f3f32700d310d4890ceffb4bec38a7bdc1a4c8ce0aca42","source":{"kind":"arxiv","id":"2412.18796","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.18796","created_at":"2026-07-05T09:54:10Z"},{"alias_kind":"arxiv_version","alias_value":"2412.18796v1","created_at":"2026-07-05T09:54:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.18796","created_at":"2026-07-05T09:54:10Z"},{"alias_kind":"pith_short_12","alias_value":"SHC4J7RIEC6Y","created_at":"2026-07-05T09:54:10Z"},{"alias_kind":"pith_short_16","alias_value":"SHC4J7RIEC6YFNXT","created_at":"2026-07-05T09:54:10Z"},{"alias_kind":"pith_short_8","alias_value":"SHC4J7RI","created_at":"2026-07-05T09:54:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:SHC4J7RIEC6YFNXT6MTQBUYQ2S","target":"record","payload":{"canonical_record":{"source":{"id":"2412.18796","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2024-12-25T06:35:04Z","cross_cats_sorted":["hep-lat"],"title_canon_sha256":"1b474aae9c5826614c542da5e7e6442de6e8f39050f8bf3605b3c38e9dfdcace","abstract_canon_sha256":"08db568bec2e7ce4a657cd33185913a0500561d6ccbf34aeb9b5d18f88f8b7e8"},"schema_version":"1.0"},"canonical_sha256":"91c5c4fe2820bd82b6f3f32700d310d4890ceffb4bec38a7bdc1a4c8ce0aca42","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:54:10.964109Z","signature_b64":"QNeeAEUn5DVS7n5ztOWQkFdUsggCLGFfc3/VeM2xoeb3UlD/bXuIknbWm2vQNPDUHJxYGUw3NpFaeiCF4SGgBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"91c5c4fe2820bd82b6f3f32700d310d4890ceffb4bec38a7bdc1a4c8ce0aca42","last_reissued_at":"2026-07-05T09:54:10.963665Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:54:10.963665Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2412.18796","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:54:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IxIe4IM0OkrDlXGJ0HT5LeJGG6w7Z+RObkO3e+OfQjL32iNQ3/RyKZboEijK0jovDE26nl4SaODCSr8fMwmnCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T10:34:29.306003Z"},"content_sha256":"690aef09f918a98d348d41bc6716d78c7939b07149096e3f842e555029f5b1e6","schema_version":"1.0","event_id":"sha256:690aef09f918a98d348d41bc6716d78c7939b07149096e3f842e555029f5b1e6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:SHC4J7RIEC6YFNXT6MTQBUYQ2S","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Discrete Formulation of Second Stiefel-Whitney Class for Band Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-lat"],"primary_cat":"cond-mat.mes-hall","authors_text":"Jing-Yuan Chen, Ken Shiozaki","submitted_at":"2024-12-25T06:35:04Z","abstract_excerpt":"Topological invariants in band theory are often formulated assuming that Bloch wave functions are smoothly defined over the Brillouin zone (BZ). However, first-principles band calculations typically provide Bloch states only at discrete points in the BZ, rendering standard continuum-based approaches inapplicable. In this work, we focus on the second Stiefel-Whitney class $w_2$, a key $\\mathbb{Z}_2$ topological invariant under PT symmetry that characterizes various higher-order topological insulators and nodal-line semimetals. We develop a fully discrete, gauge-fixing-free formula for $w_2$ whi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.18796","kind":"arxiv","version":1},"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/2412.18796/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":"2026-07-05T09:54:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RXgvHd/8S3wGjUkiiFbhS1Vkoow9NWeOKYGY46w/WOTsR2AqM75XR/Ry90cgY/sfKnDQL0sOGjopuQryvCyQDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T10:34:29.306889Z"},"content_sha256":"d04f82b344f4e298fd767fcab0c480da2c87c454fd6a6f58d0f45517ec01c070","schema_version":"1.0","event_id":"sha256:d04f82b344f4e298fd767fcab0c480da2c87c454fd6a6f58d0f45517ec01c070"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SHC4J7RIEC6YFNXT6MTQBUYQ2S/bundle.json","state_url":"https://pith.science/pith/SHC4J7RIEC6YFNXT6MTQBUYQ2S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SHC4J7RIEC6YFNXT6MTQBUYQ2S/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":"2026-08-13T10:34:29Z","links":{"resolver":"https://pith.science/pith/SHC4J7RIEC6YFNXT6MTQBUYQ2S","bundle":"https://pith.science/pith/SHC4J7RIEC6YFNXT6MTQBUYQ2S/bundle.json","state":"https://pith.science/pith/SHC4J7RIEC6YFNXT6MTQBUYQ2S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SHC4J7RIEC6YFNXT6MTQBUYQ2S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:SHC4J7RIEC6YFNXT6MTQBUYQ2S","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":"08db568bec2e7ce4a657cd33185913a0500561d6ccbf34aeb9b5d18f88f8b7e8","cross_cats_sorted":["hep-lat"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2024-12-25T06:35:04Z","title_canon_sha256":"1b474aae9c5826614c542da5e7e6442de6e8f39050f8bf3605b3c38e9dfdcace"},"schema_version":"1.0","source":{"id":"2412.18796","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.18796","created_at":"2026-07-05T09:54:10Z"},{"alias_kind":"arxiv_version","alias_value":"2412.18796v1","created_at":"2026-07-05T09:54:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.18796","created_at":"2026-07-05T09:54:10Z"},{"alias_kind":"pith_short_12","alias_value":"SHC4J7RIEC6Y","created_at":"2026-07-05T09:54:10Z"},{"alias_kind":"pith_short_16","alias_value":"SHC4J7RIEC6YFNXT","created_at":"2026-07-05T09:54:10Z"},{"alias_kind":"pith_short_8","alias_value":"SHC4J7RI","created_at":"2026-07-05T09:54:10Z"}],"graph_snapshots":[{"event_id":"sha256:d04f82b344f4e298fd767fcab0c480da2c87c454fd6a6f58d0f45517ec01c070","target":"graph","created_at":"2026-07-05T09:54:10Z","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/2412.18796/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Topological invariants in band theory are often formulated assuming that Bloch wave functions are smoothly defined over the Brillouin zone (BZ). However, first-principles band calculations typically provide Bloch states only at discrete points in the BZ, rendering standard continuum-based approaches inapplicable. In this work, we focus on the second Stiefel-Whitney class $w_2$, a key $\\mathbb{Z}_2$ topological invariant under PT symmetry that characterizes various higher-order topological insulators and nodal-line semimetals. We develop a fully discrete, gauge-fixing-free formula for $w_2$ whi","authors_text":"Jing-Yuan Chen, Ken Shiozaki","cross_cats":["hep-lat"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2024-12-25T06:35:04Z","title":"A Discrete Formulation of Second Stiefel-Whitney Class for Band Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.18796","kind":"arxiv","version":1},"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":"sha256:690aef09f918a98d348d41bc6716d78c7939b07149096e3f842e555029f5b1e6","target":"record","created_at":"2026-07-05T09:54:10Z","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":"08db568bec2e7ce4a657cd33185913a0500561d6ccbf34aeb9b5d18f88f8b7e8","cross_cats_sorted":["hep-lat"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2024-12-25T06:35:04Z","title_canon_sha256":"1b474aae9c5826614c542da5e7e6442de6e8f39050f8bf3605b3c38e9dfdcace"},"schema_version":"1.0","source":{"id":"2412.18796","kind":"arxiv","version":1}},"canonical_sha256":"91c5c4fe2820bd82b6f3f32700d310d4890ceffb4bec38a7bdc1a4c8ce0aca42","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"91c5c4fe2820bd82b6f3f32700d310d4890ceffb4bec38a7bdc1a4c8ce0aca42","first_computed_at":"2026-07-05T09:54:10.963665Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:54:10.963665Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QNeeAEUn5DVS7n5ztOWQkFdUsggCLGFfc3/VeM2xoeb3UlD/bXuIknbWm2vQNPDUHJxYGUw3NpFaeiCF4SGgBA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:54:10.964109Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.18796","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:690aef09f918a98d348d41bc6716d78c7939b07149096e3f842e555029f5b1e6","sha256:d04f82b344f4e298fd767fcab0c480da2c87c454fd6a6f58d0f45517ec01c070"],"state_sha256":"ae37eb048a7b795e6cdde3cb9721a7220e8f39964babc09e883f5bf6e92cf1ba"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"If1mIxNJN0mPQ7g0TH5QBmgsWUSKi2UkpIyDQojayCXOUDI+X8sRItmqs8AQLJZZZlhbacMYRAWA0hGYQtIoAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T10:34:29.312621Z","bundle_sha256":"f63cfcf4631586484bc56684cd964a296627783336e94e66e48acf38862790e1"}}