{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:M6UUDNN43GPY37KQ6GFTNH7MHX","short_pith_number":"pith:M6UUDNN4","schema_version":"1.0","canonical_sha256":"67a941b5bcd99f8dfd50f18b369fec3dc0e677663414854d7d7dd1bd553cff4e","source":{"kind":"arxiv","id":"0909.1107","version":1},"attestation_state":"computed","paper":{"title":"Generalized eigenfunctions and spectral theory for strongly local Dirichlet forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Daniel Lenz, Ivan Veselic, Peter Stollmann","submitted_at":"2009-09-06T20:29:23Z","abstract_excerpt":"We present an introduction to the framework of strongly local Dirichlet forms and discuss connections between the existence of certain generalized eigenfunctions and spectral properties within this framework. The range of applications is illustrated by a list of examples."},"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":"0909.1107","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2009-09-06T20:29:23Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"9df43c16a9ee9ca1cf7fd53736c84c4ffad73d034e7820b2799d4c9f61b0bc86","abstract_canon_sha256":"2c8a4836b02edc4f2dc22531e25f92e0d8c20d60615b57bee8d725c0b0e059c9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:37.774121Z","signature_b64":"Bu/jfwubClbIyb/A1uLgBowP0//eUaCYcxkNZirO9kkQEE8nklCyU9M/EiKlyzNSCcWPU40qOR2nrDhH5F3ZCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"67a941b5bcd99f8dfd50f18b369fec3dc0e677663414854d7d7dd1bd553cff4e","last_reissued_at":"2026-05-18T00:04:37.773600Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:37.773600Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generalized eigenfunctions and spectral theory for strongly local Dirichlet forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Daniel Lenz, Ivan Veselic, Peter Stollmann","submitted_at":"2009-09-06T20:29:23Z","abstract_excerpt":"We present an introduction to the framework of strongly local Dirichlet forms and discuss connections between the existence of certain generalized eigenfunctions and spectral properties within this framework. The range of applications is illustrated by a list of examples."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.1107","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":""},"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":"0909.1107","created_at":"2026-05-18T00:04:37.773698+00:00"},{"alias_kind":"arxiv_version","alias_value":"0909.1107v1","created_at":"2026-05-18T00:04:37.773698+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.1107","created_at":"2026-05-18T00:04:37.773698+00:00"},{"alias_kind":"pith_short_12","alias_value":"M6UUDNN43GPY","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_16","alias_value":"M6UUDNN43GPY37KQ","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_8","alias_value":"M6UUDNN4","created_at":"2026-05-18T12:26:00.592388+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/M6UUDNN43GPY37KQ6GFTNH7MHX","json":"https://pith.science/pith/M6UUDNN43GPY37KQ6GFTNH7MHX.json","graph_json":"https://pith.science/api/pith-number/M6UUDNN43GPY37KQ6GFTNH7MHX/graph.json","events_json":"https://pith.science/api/pith-number/M6UUDNN43GPY37KQ6GFTNH7MHX/events.json","paper":"https://pith.science/paper/M6UUDNN4"},"agent_actions":{"view_html":"https://pith.science/pith/M6UUDNN43GPY37KQ6GFTNH7MHX","download_json":"https://pith.science/pith/M6UUDNN43GPY37KQ6GFTNH7MHX.json","view_paper":"https://pith.science/paper/M6UUDNN4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0909.1107&json=true","fetch_graph":"https://pith.science/api/pith-number/M6UUDNN43GPY37KQ6GFTNH7MHX/graph.json","fetch_events":"https://pith.science/api/pith-number/M6UUDNN43GPY37KQ6GFTNH7MHX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/M6UUDNN43GPY37KQ6GFTNH7MHX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/M6UUDNN43GPY37KQ6GFTNH7MHX/action/storage_attestation","attest_author":"https://pith.science/pith/M6UUDNN43GPY37KQ6GFTNH7MHX/action/author_attestation","sign_citation":"https://pith.science/pith/M6UUDNN43GPY37KQ6GFTNH7MHX/action/citation_signature","submit_replication":"https://pith.science/pith/M6UUDNN43GPY37KQ6GFTNH7MHX/action/replication_record"}},"created_at":"2026-05-18T00:04:37.773698+00:00","updated_at":"2026-05-18T00:04:37.773698+00:00"}