{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:2SC4NLYWGYAFL3YXWKVCZATHPX","short_pith_number":"pith:2SC4NLYW","schema_version":"1.0","canonical_sha256":"d485c6af16360055ef17b2aa2c82677dfa127400c84f38d710e5bfa18d3ce2d0","source":{"kind":"arxiv","id":"math/0606125","version":12},"attestation_state":"computed","paper":{"title":"Limiting absorption principle on manifolds having ends with various measure growth rate limits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.DG","authors_text":"Hironori Kumura","submitted_at":"2006-06-06T06:49:41Z","abstract_excerpt":"The purpose of this paper is to study the property of the resolvent of the Laplace-Beltrami operator on a noncompact complete Riemannian manifold with various ends each of which has a different limit of the growth rate of the Riemannian measure at infinity, in particular, focusing on the limiting absorption principle. As a result, we will obtain the absolute continuity of the Laplace-Beltrami operator."},"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":"math/0606125","kind":"arxiv","version":12},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2006-06-06T06:49:41Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"307f7c315260069607d03add1007159adccfcedc2a23dd30f86c1ad178e93197","abstract_canon_sha256":"c1ce8f65f52081f11af2db1de1ec7c0e26092d9554401095bbaa2673a8fcef31"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:57:45.577358Z","signature_b64":"1CothOMmz5czuwMfKbo5FPS/3ycnaLsB9qMAe2kYuxc4QxB9vQKlHMBFcVCBfX3r9qD/YeV6Z9bdzVn2CvEhCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d485c6af16360055ef17b2aa2c82677dfa127400c84f38d710e5bfa18d3ce2d0","last_reissued_at":"2026-05-18T02:57:45.576883Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:57:45.576883Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Limiting absorption principle on manifolds having ends with various measure growth rate limits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.DG","authors_text":"Hironori Kumura","submitted_at":"2006-06-06T06:49:41Z","abstract_excerpt":"The purpose of this paper is to study the property of the resolvent of the Laplace-Beltrami operator on a noncompact complete Riemannian manifold with various ends each of which has a different limit of the growth rate of the Riemannian measure at infinity, in particular, focusing on the limiting absorption principle. As a result, we will obtain the absolute continuity of the Laplace-Beltrami operator."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0606125","kind":"arxiv","version":12},"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":"math/0606125","created_at":"2026-05-18T02:57:45.576955+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0606125v12","created_at":"2026-05-18T02:57:45.576955+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0606125","created_at":"2026-05-18T02:57:45.576955+00:00"},{"alias_kind":"pith_short_12","alias_value":"2SC4NLYWGYAF","created_at":"2026-05-18T12:25:53.939244+00:00"},{"alias_kind":"pith_short_16","alias_value":"2SC4NLYWGYAFL3YX","created_at":"2026-05-18T12:25:53.939244+00:00"},{"alias_kind":"pith_short_8","alias_value":"2SC4NLYW","created_at":"2026-05-18T12:25:53.939244+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/2SC4NLYWGYAFL3YXWKVCZATHPX","json":"https://pith.science/pith/2SC4NLYWGYAFL3YXWKVCZATHPX.json","graph_json":"https://pith.science/api/pith-number/2SC4NLYWGYAFL3YXWKVCZATHPX/graph.json","events_json":"https://pith.science/api/pith-number/2SC4NLYWGYAFL3YXWKVCZATHPX/events.json","paper":"https://pith.science/paper/2SC4NLYW"},"agent_actions":{"view_html":"https://pith.science/pith/2SC4NLYWGYAFL3YXWKVCZATHPX","download_json":"https://pith.science/pith/2SC4NLYWGYAFL3YXWKVCZATHPX.json","view_paper":"https://pith.science/paper/2SC4NLYW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0606125&json=true","fetch_graph":"https://pith.science/api/pith-number/2SC4NLYWGYAFL3YXWKVCZATHPX/graph.json","fetch_events":"https://pith.science/api/pith-number/2SC4NLYWGYAFL3YXWKVCZATHPX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2SC4NLYWGYAFL3YXWKVCZATHPX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2SC4NLYWGYAFL3YXWKVCZATHPX/action/storage_attestation","attest_author":"https://pith.science/pith/2SC4NLYWGYAFL3YXWKVCZATHPX/action/author_attestation","sign_citation":"https://pith.science/pith/2SC4NLYWGYAFL3YXWKVCZATHPX/action/citation_signature","submit_replication":"https://pith.science/pith/2SC4NLYWGYAFL3YXWKVCZATHPX/action/replication_record"}},"created_at":"2026-05-18T02:57:45.576955+00:00","updated_at":"2026-05-18T02:57:45.576955+00:00"}