{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:PNFIODEUW3IIOMNTPKSGZZMCMQ","short_pith_number":"pith:PNFIODEU","schema_version":"1.0","canonical_sha256":"7b4a870c94b6d08731b37aa46ce5826409bf70eac1f6c3bef54efc593d20fca0","source":{"kind":"arxiv","id":"2410.08343","version":1},"attestation_state":"computed","paper":{"title":"Computing Generalized Eigenfunctions in Rigged Hilbert Spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA","math.SP"],"primary_cat":"math.NA","authors_text":"Andrew Horning, Matthew J. Colbrook, Tianyiwa Xie","submitted_at":"2024-10-10T20:03:54Z","abstract_excerpt":"We introduce a simple, general, and convergent scheme to compute generalized eigenfunctions of self-adjoint operators with continuous spectra on rigged Hilbert spaces. Our approach does not require prior knowledge about the eigenfunctions, such as asymptotics or other analytic properties. Instead, we carefully sample the range of the resolvent operator to construct smooth and accurate wave packet approximations to generalized eigenfunctions. We prove high-order convergence in key topologies, including weak-star convergence for distributional eigenfunctions, uniform convergence on compact sets "},"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":"2410.08343","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2024-10-10T20:03:54Z","cross_cats_sorted":["cs.NA","math.SP"],"title_canon_sha256":"13249308f77aaf4da714e31c90493682943feb94913c9692f6ba822040d16a6c","abstract_canon_sha256":"928b5828d1fd946bde1447e52c1d89a0b591c0d8bc893bf9cccaf30e3dfef3b5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:18:56.864555Z","signature_b64":"lWcvbR0PiIdNob/VkcpzD4w8s/stVEg44deI7wdD+mj4/MHNxPaJ1UIYjeQ+o106PdbWJx1reR1JL0oc/QaHCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7b4a870c94b6d08731b37aa46ce5826409bf70eac1f6c3bef54efc593d20fca0","last_reissued_at":"2026-07-05T09:18:56.864109Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:18:56.864109Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Computing Generalized Eigenfunctions in Rigged Hilbert Spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA","math.SP"],"primary_cat":"math.NA","authors_text":"Andrew Horning, Matthew J. Colbrook, Tianyiwa Xie","submitted_at":"2024-10-10T20:03:54Z","abstract_excerpt":"We introduce a simple, general, and convergent scheme to compute generalized eigenfunctions of self-adjoint operators with continuous spectra on rigged Hilbert spaces. Our approach does not require prior knowledge about the eigenfunctions, such as asymptotics or other analytic properties. Instead, we carefully sample the range of the resolvent operator to construct smooth and accurate wave packet approximations to generalized eigenfunctions. We prove high-order convergence in key topologies, including weak-star convergence for distributional eigenfunctions, uniform convergence on compact sets "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.08343","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.08343/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":"2410.08343","created_at":"2026-07-05T09:18:56.864170+00:00"},{"alias_kind":"arxiv_version","alias_value":"2410.08343v1","created_at":"2026-07-05T09:18:56.864170+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.08343","created_at":"2026-07-05T09:18:56.864170+00:00"},{"alias_kind":"pith_short_12","alias_value":"PNFIODEUW3II","created_at":"2026-07-05T09:18:56.864170+00:00"},{"alias_kind":"pith_short_16","alias_value":"PNFIODEUW3IIOMNT","created_at":"2026-07-05T09:18:56.864170+00:00"},{"alias_kind":"pith_short_8","alias_value":"PNFIODEU","created_at":"2026-07-05T09:18:56.864170+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/PNFIODEUW3IIOMNTPKSGZZMCMQ","json":"https://pith.science/pith/PNFIODEUW3IIOMNTPKSGZZMCMQ.json","graph_json":"https://pith.science/api/pith-number/PNFIODEUW3IIOMNTPKSGZZMCMQ/graph.json","events_json":"https://pith.science/api/pith-number/PNFIODEUW3IIOMNTPKSGZZMCMQ/events.json","paper":"https://pith.science/paper/PNFIODEU"},"agent_actions":{"view_html":"https://pith.science/pith/PNFIODEUW3IIOMNTPKSGZZMCMQ","download_json":"https://pith.science/pith/PNFIODEUW3IIOMNTPKSGZZMCMQ.json","view_paper":"https://pith.science/paper/PNFIODEU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2410.08343&json=true","fetch_graph":"https://pith.science/api/pith-number/PNFIODEUW3IIOMNTPKSGZZMCMQ/graph.json","fetch_events":"https://pith.science/api/pith-number/PNFIODEUW3IIOMNTPKSGZZMCMQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PNFIODEUW3IIOMNTPKSGZZMCMQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PNFIODEUW3IIOMNTPKSGZZMCMQ/action/storage_attestation","attest_author":"https://pith.science/pith/PNFIODEUW3IIOMNTPKSGZZMCMQ/action/author_attestation","sign_citation":"https://pith.science/pith/PNFIODEUW3IIOMNTPKSGZZMCMQ/action/citation_signature","submit_replication":"https://pith.science/pith/PNFIODEUW3IIOMNTPKSGZZMCMQ/action/replication_record"}},"created_at":"2026-07-05T09:18:56.864170+00:00","updated_at":"2026-07-05T09:18:56.864170+00:00"}