{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:LSHA75F6S3YMDFUSHJBKGVRMJH","short_pith_number":"pith:LSHA75F6","schema_version":"1.0","canonical_sha256":"5c8e0ff4be96f0c196923a42a3562c49e2c93d679925cbf54a71ee92e6f5782d","source":{"kind":"arxiv","id":"0803.4171","version":2},"attestation_state":"computed","paper":{"title":"Average growth of the spectral function on a Riemannian manifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.SP","authors_text":"Hugues Lapointe, Iosif Polterovich, Yuri Safarov","submitted_at":"2008-03-28T17:23:05Z","abstract_excerpt":"We study average growth of the spectral function of the Laplacian on a Riemannian manifold. Two types of averaging are considered: with respect to the spectral parameter and with respect to a point on a manifold. We obtain as well related estimates of the growth of the pointwise zeta-function along vertical lines in the complex plane. Some examples and open problems regarding almost periodic properties of the spectral function are also discussed."},"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":"0803.4171","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2008-03-28T17:23:05Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"373858454f56a92ed47e0254fc3227bbef1027d4910795cd7d786e33bd2319cf","abstract_canon_sha256":"e3637c61a3b0d68b406fb6ab2df83ba44037b96ce40df2feac1f1c1a7548c95e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:14:29.288459Z","signature_b64":"lAAu05bpAItRgRpqgnMLEOw2FUeDeOqSfJtMQl55fS1i80GTEXOu3CwOqJmvc6M0Cw+Gvzm1OfFMvph5sbIqCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5c8e0ff4be96f0c196923a42a3562c49e2c93d679925cbf54a71ee92e6f5782d","last_reissued_at":"2026-07-04T15:14:29.288101Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:14:29.288101Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Average growth of the spectral function on a Riemannian manifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.SP","authors_text":"Hugues Lapointe, Iosif Polterovich, Yuri Safarov","submitted_at":"2008-03-28T17:23:05Z","abstract_excerpt":"We study average growth of the spectral function of the Laplacian on a Riemannian manifold. Two types of averaging are considered: with respect to the spectral parameter and with respect to a point on a manifold. We obtain as well related estimates of the growth of the pointwise zeta-function along vertical lines in the complex plane. Some examples and open problems regarding almost periodic properties of the spectral function are also discussed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0803.4171","kind":"arxiv","version":2},"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/0803.4171/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":"0803.4171","created_at":"2026-07-04T15:14:29.288164+00:00"},{"alias_kind":"arxiv_version","alias_value":"0803.4171v2","created_at":"2026-07-04T15:14:29.288164+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0803.4171","created_at":"2026-07-04T15:14:29.288164+00:00"},{"alias_kind":"pith_short_12","alias_value":"LSHA75F6S3YM","created_at":"2026-07-04T15:14:29.288164+00:00"},{"alias_kind":"pith_short_16","alias_value":"LSHA75F6S3YMDFUS","created_at":"2026-07-04T15:14:29.288164+00:00"},{"alias_kind":"pith_short_8","alias_value":"LSHA75F6","created_at":"2026-07-04T15:14:29.288164+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/LSHA75F6S3YMDFUSHJBKGVRMJH","json":"https://pith.science/pith/LSHA75F6S3YMDFUSHJBKGVRMJH.json","graph_json":"https://pith.science/api/pith-number/LSHA75F6S3YMDFUSHJBKGVRMJH/graph.json","events_json":"https://pith.science/api/pith-number/LSHA75F6S3YMDFUSHJBKGVRMJH/events.json","paper":"https://pith.science/paper/LSHA75F6"},"agent_actions":{"view_html":"https://pith.science/pith/LSHA75F6S3YMDFUSHJBKGVRMJH","download_json":"https://pith.science/pith/LSHA75F6S3YMDFUSHJBKGVRMJH.json","view_paper":"https://pith.science/paper/LSHA75F6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0803.4171&json=true","fetch_graph":"https://pith.science/api/pith-number/LSHA75F6S3YMDFUSHJBKGVRMJH/graph.json","fetch_events":"https://pith.science/api/pith-number/LSHA75F6S3YMDFUSHJBKGVRMJH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LSHA75F6S3YMDFUSHJBKGVRMJH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LSHA75F6S3YMDFUSHJBKGVRMJH/action/storage_attestation","attest_author":"https://pith.science/pith/LSHA75F6S3YMDFUSHJBKGVRMJH/action/author_attestation","sign_citation":"https://pith.science/pith/LSHA75F6S3YMDFUSHJBKGVRMJH/action/citation_signature","submit_replication":"https://pith.science/pith/LSHA75F6S3YMDFUSHJBKGVRMJH/action/replication_record"}},"created_at":"2026-07-04T15:14:29.288164+00:00","updated_at":"2026-07-04T15:14:29.288164+00:00"}