{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:NUIKYQIBH4IZFVLHW3HAVASJCW","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":"23a4717b57baadc71b356505481c4b74c490898c56de30c2df070e153fe88e62","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2020-05-05T10:19:47Z","title_canon_sha256":"7af2b66bfc59d5430c1e701ddd7ec9f24d002de57e172777bb0d0e2aadf9ff5a"},"schema_version":"1.0","source":{"id":"2005.02044","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2005.02044","created_at":"2026-07-05T01:36:09Z"},{"alias_kind":"arxiv_version","alias_value":"2005.02044v2","created_at":"2026-07-05T01:36:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2005.02044","created_at":"2026-07-05T01:36:09Z"},{"alias_kind":"pith_short_12","alias_value":"NUIKYQIBH4IZ","created_at":"2026-07-05T01:36:09Z"},{"alias_kind":"pith_short_16","alias_value":"NUIKYQIBH4IZFVLH","created_at":"2026-07-05T01:36:09Z"},{"alias_kind":"pith_short_8","alias_value":"NUIKYQIB","created_at":"2026-07-05T01:36:09Z"}],"graph_snapshots":[{"event_id":"sha256:9930152cd1887ebd1d9d412465795c6b8452f09c0bb849ecaed8e73024421c63","target":"graph","created_at":"2026-07-05T01:36:09Z","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/2005.02044/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a framework to systematically address topological phases when finer partitionings of bands are taken into account, rather than only considering the two subspaces spanned by valence and conduction bands. Focusing on $C_2\\mathcal{T}$-symmetric systems that have gained recent attention, for example in the context of layered van-der-Waals graphene heterostructures, we relate these insights to homotopy groups of Grassmannians and flag varieties, which in turn correspond to cohomology classes and Wilson-flow approaches. We furthermore make use of a geometric construction, the so-called Pl","authors_text":"Adrien Bouhon, Robert-Jan Slager, Tom\\'a\\v{s} Bzdu\\v{s}ek","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2020-05-05T10:19:47Z","title":"Geometric approach to fragile topology beyond symmetry indicators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2005.02044","kind":"arxiv","version":2},"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":"sha256:876ebde2f46ac1ab6ded605e845f578321764cd0a06423642da0f882ddf5161c","target":"record","created_at":"2026-07-05T01:36:09Z","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":"23a4717b57baadc71b356505481c4b74c490898c56de30c2df070e153fe88e62","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2020-05-05T10:19:47Z","title_canon_sha256":"7af2b66bfc59d5430c1e701ddd7ec9f24d002de57e172777bb0d0e2aadf9ff5a"},"schema_version":"1.0","source":{"id":"2005.02044","kind":"arxiv","version":2}},"canonical_sha256":"6d10ac41013f1192d567b6ce0a824915b26b6877f08df014c44d81d753dac8d9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6d10ac41013f1192d567b6ce0a824915b26b6877f08df014c44d81d753dac8d9","first_computed_at":"2026-07-05T01:36:09.215261Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:36:09.215261Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yFvfGVsbRekoDKgRvzpCrsLQTekzaPDWiKh+fvy6hsvP0pDa+9ZtOd8xdoW4mHNfNflFnRRFPlPbWGHhQSGUBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T01:36:09.215749Z","signed_message":"canonical_sha256_bytes"},"source_id":"2005.02044","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:876ebde2f46ac1ab6ded605e845f578321764cd0a06423642da0f882ddf5161c","sha256:9930152cd1887ebd1d9d412465795c6b8452f09c0bb849ecaed8e73024421c63"],"state_sha256":"c128b90250dc66967c30ec1891fa1aab476e3ce875cd95ab5aa73addad0eadb0"}