{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:66QTTF5LL2HHBPS66PIUN47Q4R","short_pith_number":"pith:66QTTF5L","schema_version":"1.0","canonical_sha256":"f7a13997ab5e8e70be5ef3d146f3f0e479df3a97d6c8392c3bcb5fe68ded4602","source":{"kind":"arxiv","id":"2505.09697","version":1},"attestation_state":"computed","paper":{"title":"Stable Real-Space Invariants and Topology Beyond Symmetry Indicators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mtrl-sci"],"primary_cat":"cond-mat.mes-hall","authors_text":"B. Andrei Bernevig, Barry Bradlyn, Frank Schindler, Luis Elcoro, Vaibhav Gupta, Yoonseok Hwang, Zhida Song","submitted_at":"2025-05-14T18:00:54Z","abstract_excerpt":"We show that certain band gaps, which appear topologically trivial from the perspective of symmetry indicators (SIs), must instead be topological, as guaranteed by real-space information that follows from Topological Quantum Chemistry (TQC). To address this, we introduce stable real-space invariants (SRSIs) that generalize the previously discovered local and composite real-space invariants to global topological invariants of a given set of bands. These are linear combinations of Wannier state multiplicities at Wyckoff positions and take the form of $\\mathbb{Z}$- and $\\mathbb{Z}_n$-valued quant"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2505.09697","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2025-05-14T18:00:54Z","cross_cats_sorted":["cond-mat.mtrl-sci"],"title_canon_sha256":"b45b0fb5dec2b6bdc0662095239f7a845722dd83adff299d89cc4093fdcc9d34","abstract_canon_sha256":"4147d4060e8f4f4727c037012bd21fd145f75067adaa1f4da56f08d5ae8f9302"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:03:27.171639Z","signature_b64":"KbyBkEFhxC920rsPaS5Ysp5jI58H3hQVhNRbCmceYCL8AH8mkhV3Kk/3vJFrpvzNOYSUjeL8VkQnXMho154QDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f7a13997ab5e8e70be5ef3d146f3f0e479df3a97d6c8392c3bcb5fe68ded4602","last_reissued_at":"2026-07-05T11:03:27.171152Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:03:27.171152Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stable Real-Space Invariants and Topology Beyond Symmetry Indicators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mtrl-sci"],"primary_cat":"cond-mat.mes-hall","authors_text":"B. Andrei Bernevig, Barry Bradlyn, Frank Schindler, Luis Elcoro, Vaibhav Gupta, Yoonseok Hwang, Zhida Song","submitted_at":"2025-05-14T18:00:54Z","abstract_excerpt":"We show that certain band gaps, which appear topologically trivial from the perspective of symmetry indicators (SIs), must instead be topological, as guaranteed by real-space information that follows from Topological Quantum Chemistry (TQC). To address this, we introduce stable real-space invariants (SRSIs) that generalize the previously discovered local and composite real-space invariants to global topological invariants of a given set of bands. These are linear combinations of Wannier state multiplicities at Wyckoff positions and take the form of $\\mathbb{Z}$- and $\\mathbb{Z}_n$-valued quant"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.09697","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/2505.09697/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2505.09697","created_at":"2026-07-05T11:03:27.171209+00:00"},{"alias_kind":"arxiv_version","alias_value":"2505.09697v1","created_at":"2026-07-05T11:03:27.171209+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.09697","created_at":"2026-07-05T11:03:27.171209+00:00"},{"alias_kind":"pith_short_12","alias_value":"66QTTF5LL2HH","created_at":"2026-07-05T11:03:27.171209+00:00"},{"alias_kind":"pith_short_16","alias_value":"66QTTF5LL2HHBPS6","created_at":"2026-07-05T11:03:27.171209+00:00"},{"alias_kind":"pith_short_8","alias_value":"66QTTF5L","created_at":"2026-07-05T11:03:27.171209+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":3,"sample":[{"citing_arxiv_id":"2606.12525","citing_title":"Composite Quantum Geometry and Semiclassical Dynamics","ref_index":10,"is_internal_anchor":true},{"citing_arxiv_id":"2604.21643","citing_title":"Stable Wave-Function Zeros Indicate Exciton Topology","ref_index":15,"is_internal_anchor":true},{"citing_arxiv_id":"2604.10338","citing_title":"Crystalline topological invariants in quantum many-body systems","ref_index":53,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/66QTTF5LL2HHBPS66PIUN47Q4R","json":"https://pith.science/pith/66QTTF5LL2HHBPS66PIUN47Q4R.json","graph_json":"https://pith.science/api/pith-number/66QTTF5LL2HHBPS66PIUN47Q4R/graph.json","events_json":"https://pith.science/api/pith-number/66QTTF5LL2HHBPS66PIUN47Q4R/events.json","paper":"https://pith.science/paper/66QTTF5L"},"agent_actions":{"view_html":"https://pith.science/pith/66QTTF5LL2HHBPS66PIUN47Q4R","download_json":"https://pith.science/pith/66QTTF5LL2HHBPS66PIUN47Q4R.json","view_paper":"https://pith.science/paper/66QTTF5L","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2505.09697&json=true","fetch_graph":"https://pith.science/api/pith-number/66QTTF5LL2HHBPS66PIUN47Q4R/graph.json","fetch_events":"https://pith.science/api/pith-number/66QTTF5LL2HHBPS66PIUN47Q4R/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/66QTTF5LL2HHBPS66PIUN47Q4R/action/timestamp_anchor","attest_storage":"https://pith.science/pith/66QTTF5LL2HHBPS66PIUN47Q4R/action/storage_attestation","attest_author":"https://pith.science/pith/66QTTF5LL2HHBPS66PIUN47Q4R/action/author_attestation","sign_citation":"https://pith.science/pith/66QTTF5LL2HHBPS66PIUN47Q4R/action/citation_signature","submit_replication":"https://pith.science/pith/66QTTF5LL2HHBPS66PIUN47Q4R/action/replication_record"}},"created_at":"2026-07-05T11:03:27.171209+00:00","updated_at":"2026-07-05T11:03:27.171209+00:00"}