{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:TVBPSGCK37UDP46ECDIRQL62TN","short_pith_number":"pith:TVBPSGCK","schema_version":"1.0","canonical_sha256":"9d42f9184adfe837f3c410d1182fda9b7382f011ea6a31deba8b87b3d969472b","source":{"kind":"arxiv","id":"2201.02598","version":4},"attestation_state":"computed","paper":{"title":"Completeness of derived interleaving distances and sheaf quantization of non-smooth objects","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.SG","authors_text":"Tomohiro Asano, Yuichi Ike","submitted_at":"2022-01-07T18:49:02Z","abstract_excerpt":"We develop sheaf-theoretic methods to deal with non-smooth objects in symplectic geometry. We show the completeness of a derived category of sheaves with respect to the interleaving distance and construct a sheaf quantization of a Hamiltonian homeomorphism. We also develop Lusternik--Schnirelmann theory in the microlocal theory of sheaves. With these new sheaf-theoretic methods, we prove an Arnold-type theorem for the image of a compact exact Lagrangian submanifold under a Hamiltonian homeomorphism."},"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":"2201.02598","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2022-01-07T18:49:02Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"d1e6dddc445dde4815f789de3b154563e305f1525ba434de4e317398837ee315","abstract_canon_sha256":"001e39c5bd4f6b90804fd49b52ba25e7804ab6fb0fbe886569880ae5f85dc668"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:55:18.200745Z","signature_b64":"EfBGDdqLqFIwA5ylvmaWgvQ+A+AnLEs2rr8uiw7Yz4KPp+7sC0vl7PLEFXbfAK5WnDDbdPQpjUr2HiwyaT6MCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9d42f9184adfe837f3c410d1182fda9b7382f011ea6a31deba8b87b3d969472b","last_reissued_at":"2026-07-05T07:55:18.200344Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:55:18.200344Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Completeness of derived interleaving distances and sheaf quantization of non-smooth objects","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.SG","authors_text":"Tomohiro Asano, Yuichi Ike","submitted_at":"2022-01-07T18:49:02Z","abstract_excerpt":"We develop sheaf-theoretic methods to deal with non-smooth objects in symplectic geometry. We show the completeness of a derived category of sheaves with respect to the interleaving distance and construct a sheaf quantization of a Hamiltonian homeomorphism. We also develop Lusternik--Schnirelmann theory in the microlocal theory of sheaves. With these new sheaf-theoretic methods, we prove an Arnold-type theorem for the image of a compact exact Lagrangian submanifold under a Hamiltonian homeomorphism."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.02598","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2201.02598/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":"2201.02598","created_at":"2026-07-05T07:55:18.200405+00:00"},{"alias_kind":"arxiv_version","alias_value":"2201.02598v4","created_at":"2026-07-05T07:55:18.200405+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2201.02598","created_at":"2026-07-05T07:55:18.200405+00:00"},{"alias_kind":"pith_short_12","alias_value":"TVBPSGCK37UD","created_at":"2026-07-05T07:55:18.200405+00:00"},{"alias_kind":"pith_short_16","alias_value":"TVBPSGCK37UDP46E","created_at":"2026-07-05T07:55:18.200405+00:00"},{"alias_kind":"pith_short_8","alias_value":"TVBPSGCK","created_at":"2026-07-05T07:55:18.200405+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/TVBPSGCK37UDP46ECDIRQL62TN","json":"https://pith.science/pith/TVBPSGCK37UDP46ECDIRQL62TN.json","graph_json":"https://pith.science/api/pith-number/TVBPSGCK37UDP46ECDIRQL62TN/graph.json","events_json":"https://pith.science/api/pith-number/TVBPSGCK37UDP46ECDIRQL62TN/events.json","paper":"https://pith.science/paper/TVBPSGCK"},"agent_actions":{"view_html":"https://pith.science/pith/TVBPSGCK37UDP46ECDIRQL62TN","download_json":"https://pith.science/pith/TVBPSGCK37UDP46ECDIRQL62TN.json","view_paper":"https://pith.science/paper/TVBPSGCK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2201.02598&json=true","fetch_graph":"https://pith.science/api/pith-number/TVBPSGCK37UDP46ECDIRQL62TN/graph.json","fetch_events":"https://pith.science/api/pith-number/TVBPSGCK37UDP46ECDIRQL62TN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TVBPSGCK37UDP46ECDIRQL62TN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TVBPSGCK37UDP46ECDIRQL62TN/action/storage_attestation","attest_author":"https://pith.science/pith/TVBPSGCK37UDP46ECDIRQL62TN/action/author_attestation","sign_citation":"https://pith.science/pith/TVBPSGCK37UDP46ECDIRQL62TN/action/citation_signature","submit_replication":"https://pith.science/pith/TVBPSGCK37UDP46ECDIRQL62TN/action/replication_record"}},"created_at":"2026-07-05T07:55:18.200405+00:00","updated_at":"2026-07-05T07:55:18.200405+00:00"}