{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:7GLM35YIQMOY4SAEMIY7WB2IX4","short_pith_number":"pith:7GLM35YI","schema_version":"1.0","canonical_sha256":"f996cdf708831d8e48046231fb0748bf26a0ac8da976f7e48c98283079d7866f","source":{"kind":"arxiv","id":"1406.0317","version":1},"attestation_state":"computed","paper":{"title":"A lower bound for the number of negative eigenvalues of Schr\\\"{o}dinger operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Alexander Grigor'yan, Nikolai Nadirashvili, Yannick Sire","submitted_at":"2014-06-02T10:31:11Z","abstract_excerpt":"We prove a lower bound for the number of negative eigenvalues for a Schr\\\"{o}dinger operator on a Riemannian manifold via the integral of the potential."},"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":"1406.0317","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-06-02T10:31:11Z","cross_cats_sorted":[],"title_canon_sha256":"c4957fd0e0413a574941e4154821775a36b59a6865c81cbe3e749f40da29fbb7","abstract_canon_sha256":"0028feddf8fd67410b27a82da76ca13f3352e034a29a5795b620468f05a0de88"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:50:41.169459Z","signature_b64":"lSOH6lOudLA1j7vR8JueEbCoJd7Ga51kYPZJzaU7zikTY0lhb57q+EoUxElbMQyU8vmCMWT9pxroyCMN6GpdAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f996cdf708831d8e48046231fb0748bf26a0ac8da976f7e48c98283079d7866f","last_reissued_at":"2026-05-18T02:50:41.168881Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:50:41.168881Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A lower bound for the number of negative eigenvalues of Schr\\\"{o}dinger operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Alexander Grigor'yan, Nikolai Nadirashvili, Yannick Sire","submitted_at":"2014-06-02T10:31:11Z","abstract_excerpt":"We prove a lower bound for the number of negative eigenvalues for a Schr\\\"{o}dinger operator on a Riemannian manifold via the integral of the potential."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.0317","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":"1406.0317","created_at":"2026-05-18T02:50:41.168956+00:00"},{"alias_kind":"arxiv_version","alias_value":"1406.0317v1","created_at":"2026-05-18T02:50:41.168956+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.0317","created_at":"2026-05-18T02:50:41.168956+00:00"},{"alias_kind":"pith_short_12","alias_value":"7GLM35YIQMOY","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_16","alias_value":"7GLM35YIQMOY4SAE","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_8","alias_value":"7GLM35YI","created_at":"2026-05-18T12:28:16.859392+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/7GLM35YIQMOY4SAEMIY7WB2IX4","json":"https://pith.science/pith/7GLM35YIQMOY4SAEMIY7WB2IX4.json","graph_json":"https://pith.science/api/pith-number/7GLM35YIQMOY4SAEMIY7WB2IX4/graph.json","events_json":"https://pith.science/api/pith-number/7GLM35YIQMOY4SAEMIY7WB2IX4/events.json","paper":"https://pith.science/paper/7GLM35YI"},"agent_actions":{"view_html":"https://pith.science/pith/7GLM35YIQMOY4SAEMIY7WB2IX4","download_json":"https://pith.science/pith/7GLM35YIQMOY4SAEMIY7WB2IX4.json","view_paper":"https://pith.science/paper/7GLM35YI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1406.0317&json=true","fetch_graph":"https://pith.science/api/pith-number/7GLM35YIQMOY4SAEMIY7WB2IX4/graph.json","fetch_events":"https://pith.science/api/pith-number/7GLM35YIQMOY4SAEMIY7WB2IX4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7GLM35YIQMOY4SAEMIY7WB2IX4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7GLM35YIQMOY4SAEMIY7WB2IX4/action/storage_attestation","attest_author":"https://pith.science/pith/7GLM35YIQMOY4SAEMIY7WB2IX4/action/author_attestation","sign_citation":"https://pith.science/pith/7GLM35YIQMOY4SAEMIY7WB2IX4/action/citation_signature","submit_replication":"https://pith.science/pith/7GLM35YIQMOY4SAEMIY7WB2IX4/action/replication_record"}},"created_at":"2026-05-18T02:50:41.168956+00:00","updated_at":"2026-05-18T02:50:41.168956+00:00"}