{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:BA4URRYWW7HGKOISSA26EZZQSW","short_pith_number":"pith:BA4URRYW","schema_version":"1.0","canonical_sha256":"083948c716b7ce6539129035e26730959a32afd577d703ede5036d82dcc99337","source":{"kind":"arxiv","id":"1510.04367","version":4},"attestation_state":"computed","paper":{"title":"On the structure of band edges of 2d periodic elliptic operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Ilya Kachkovskiy, Nikolay Filonov","submitted_at":"2015-10-15T01:19:08Z","abstract_excerpt":"For a wide class of 2D periodic elliptic operators, we show that the global extrema of all spectral band functions are isolated."},"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":"1510.04367","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-10-15T01:19:08Z","cross_cats_sorted":["math.AP","math.MP","math.SP"],"title_canon_sha256":"2c9b8c5db759bf56009a4eaf9af13b9a975f05500f72812ae20cfa546772a5ba","abstract_canon_sha256":"81594d4b303b8c5b5ca0c445e312ca59a3c96d0e27da6e48b9c59c587f65e1f4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:19.469067Z","signature_b64":"EC5MGEyCnk619bZ/Bx5yVWCD3zWcPDrnxHe0bOR9gr1nyzvO3hHObBwj2NYgzGhq/hDl6KnQ1MSl+UuH0laUAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"083948c716b7ce6539129035e26730959a32afd577d703ede5036d82dcc99337","last_reissued_at":"2026-05-18T00:11:19.468400Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:19.468400Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the structure of band edges of 2d periodic elliptic operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Ilya Kachkovskiy, Nikolay Filonov","submitted_at":"2015-10-15T01:19:08Z","abstract_excerpt":"For a wide class of 2D periodic elliptic operators, we show that the global extrema of all spectral band functions are isolated."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.04367","kind":"arxiv","version":4},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1510.04367","created_at":"2026-05-18T00:11:19.468505+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.04367v4","created_at":"2026-05-18T00:11:19.468505+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.04367","created_at":"2026-05-18T00:11:19.468505+00:00"},{"alias_kind":"pith_short_12","alias_value":"BA4URRYWW7HG","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_16","alias_value":"BA4URRYWW7HGKOIS","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_8","alias_value":"BA4URRYW","created_at":"2026-05-18T12:29:14.074870+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BA4URRYWW7HGKOISSA26EZZQSW","json":"https://pith.science/pith/BA4URRYWW7HGKOISSA26EZZQSW.json","graph_json":"https://pith.science/api/pith-number/BA4URRYWW7HGKOISSA26EZZQSW/graph.json","events_json":"https://pith.science/api/pith-number/BA4URRYWW7HGKOISSA26EZZQSW/events.json","paper":"https://pith.science/paper/BA4URRYW"},"agent_actions":{"view_html":"https://pith.science/pith/BA4URRYWW7HGKOISSA26EZZQSW","download_json":"https://pith.science/pith/BA4URRYWW7HGKOISSA26EZZQSW.json","view_paper":"https://pith.science/paper/BA4URRYW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.04367&json=true","fetch_graph":"https://pith.science/api/pith-number/BA4URRYWW7HGKOISSA26EZZQSW/graph.json","fetch_events":"https://pith.science/api/pith-number/BA4URRYWW7HGKOISSA26EZZQSW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BA4URRYWW7HGKOISSA26EZZQSW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BA4URRYWW7HGKOISSA26EZZQSW/action/storage_attestation","attest_author":"https://pith.science/pith/BA4URRYWW7HGKOISSA26EZZQSW/action/author_attestation","sign_citation":"https://pith.science/pith/BA4URRYWW7HGKOISSA26EZZQSW/action/citation_signature","submit_replication":"https://pith.science/pith/BA4URRYWW7HGKOISSA26EZZQSW/action/replication_record"}},"created_at":"2026-05-18T00:11:19.468505+00:00","updated_at":"2026-05-18T00:11:19.468505+00:00"}