{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:S4AWKS36TMHELM55BZWPAKIWFO","short_pith_number":"pith:S4AWKS36","schema_version":"1.0","canonical_sha256":"9701654b7e9b0e45b3bd0e6cf029162bba0bfb28bb53be44422fb1640a56d59c","source":{"kind":"arxiv","id":"1503.02998","version":3},"attestation_state":"computed","paper":{"title":"Spectral theory of von Neumann algebra valued differential operators over non-compact manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.SP"],"primary_cat":"math.OA","authors_text":"Maxim Braverman, Simone Cecchini","submitted_at":"2015-03-10T17:31:58Z","abstract_excerpt":"We provide criteria for self-adjointness and {\\tau}-Fredhomness of first and second order differential operators acting on sections of infinite dimensional bundles, whose fibers are modules of finite type over a von Neumann algebra A endowed with a trace {\\tau}. We extend the Callias-type index to operators acting on sections of such bundles and show that this index is stable under compact perturbations."},"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":"1503.02998","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-03-10T17:31:58Z","cross_cats_sorted":["math.DG","math.SP"],"title_canon_sha256":"149c509464315653750426e16d05563b0ded6bb0896832b5b0597da8aac0d000","abstract_canon_sha256":"c0c14c83f9ea4a8e97dd11ee11e505270a210d0f6db345e743a5d25e8c5b3524"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:25:47.217898Z","signature_b64":"8tJF8WQVEApr2fQM3fHyHwcP3X0D1lQjZ/BUO0KwOtJI8sVlPR3iO4TjLAxG/D5KqbiTgJX3u/kN2TKLbBn3Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9701654b7e9b0e45b3bd0e6cf029162bba0bfb28bb53be44422fb1640a56d59c","last_reissued_at":"2026-05-18T01:25:47.217407Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:25:47.217407Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spectral theory of von Neumann algebra valued differential operators over non-compact manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.SP"],"primary_cat":"math.OA","authors_text":"Maxim Braverman, Simone Cecchini","submitted_at":"2015-03-10T17:31:58Z","abstract_excerpt":"We provide criteria for self-adjointness and {\\tau}-Fredhomness of first and second order differential operators acting on sections of infinite dimensional bundles, whose fibers are modules of finite type over a von Neumann algebra A endowed with a trace {\\tau}. We extend the Callias-type index to operators acting on sections of such bundles and show that this index is stable under compact perturbations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02998","kind":"arxiv","version":3},"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":"1503.02998","created_at":"2026-05-18T01:25:47.217467+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.02998v3","created_at":"2026-05-18T01:25:47.217467+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.02998","created_at":"2026-05-18T01:25:47.217467+00:00"},{"alias_kind":"pith_short_12","alias_value":"S4AWKS36TMHE","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_16","alias_value":"S4AWKS36TMHELM55","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_8","alias_value":"S4AWKS36","created_at":"2026-05-18T12:29:39.896362+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/S4AWKS36TMHELM55BZWPAKIWFO","json":"https://pith.science/pith/S4AWKS36TMHELM55BZWPAKIWFO.json","graph_json":"https://pith.science/api/pith-number/S4AWKS36TMHELM55BZWPAKIWFO/graph.json","events_json":"https://pith.science/api/pith-number/S4AWKS36TMHELM55BZWPAKIWFO/events.json","paper":"https://pith.science/paper/S4AWKS36"},"agent_actions":{"view_html":"https://pith.science/pith/S4AWKS36TMHELM55BZWPAKIWFO","download_json":"https://pith.science/pith/S4AWKS36TMHELM55BZWPAKIWFO.json","view_paper":"https://pith.science/paper/S4AWKS36","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.02998&json=true","fetch_graph":"https://pith.science/api/pith-number/S4AWKS36TMHELM55BZWPAKIWFO/graph.json","fetch_events":"https://pith.science/api/pith-number/S4AWKS36TMHELM55BZWPAKIWFO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S4AWKS36TMHELM55BZWPAKIWFO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S4AWKS36TMHELM55BZWPAKIWFO/action/storage_attestation","attest_author":"https://pith.science/pith/S4AWKS36TMHELM55BZWPAKIWFO/action/author_attestation","sign_citation":"https://pith.science/pith/S4AWKS36TMHELM55BZWPAKIWFO/action/citation_signature","submit_replication":"https://pith.science/pith/S4AWKS36TMHELM55BZWPAKIWFO/action/replication_record"}},"created_at":"2026-05-18T01:25:47.217467+00:00","updated_at":"2026-05-18T01:25:47.217467+00:00"}