{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:VPDAE3BPCHHEWLPUM4L2YZT63I","short_pith_number":"pith:VPDAE3BP","schema_version":"1.0","canonical_sha256":"abc6026c2f11ce4b2df46717ac667eda37049130025ff50fe687995879730908","source":{"kind":"arxiv","id":"2412.16752","version":1},"attestation_state":"computed","paper":{"title":"Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.SP","authors_text":"Petr Zem\\'anek","submitted_at":"2024-12-21T20:06:03Z","abstract_excerpt":"Eigenfunctions expansion for discrete symplectic systems on a finite discrete interval is established in the case of a general linear dependence on the spectral parameter as a significant generalization of the Expansion theorem given by Bohner, Do\\v{s}l\\'{y} and Kratz in [Trans. Amer. Math. Soc. 361 (2009), 3109--3123]. Subsequently, an integral representation of the Weyl--Titchmarsh $M({\\lambda})$-function is derived explicitly by using a suitable spectral function and a possible extension to the half-line case is discussed. The main results are illustrated by several 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":"2412.16752","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.SP","submitted_at":"2024-12-21T20:06:03Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"c351415e3cf89d591527bf850ce7cb85816108dceee35b09d4427326dc14d97d","abstract_canon_sha256":"77cc512579ffd9fa1a769d9e9856d3432642dfa045c21eea304d24a9c2e6cb6b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:53:12.591102Z","signature_b64":"4/csYH0LgAyb1TU6HOGHuJrCrNKp/+laGUVrHiQ0gYUgiNMI63ELlxDm4tjUnie7g648ygEBDOX9JNljKdGkDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"abc6026c2f11ce4b2df46717ac667eda37049130025ff50fe687995879730908","last_reissued_at":"2026-07-05T09:53:12.590699Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:53:12.590699Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.SP","authors_text":"Petr Zem\\'anek","submitted_at":"2024-12-21T20:06:03Z","abstract_excerpt":"Eigenfunctions expansion for discrete symplectic systems on a finite discrete interval is established in the case of a general linear dependence on the spectral parameter as a significant generalization of the Expansion theorem given by Bohner, Do\\v{s}l\\'{y} and Kratz in [Trans. Amer. Math. Soc. 361 (2009), 3109--3123]. Subsequently, an integral representation of the Weyl--Titchmarsh $M({\\lambda})$-function is derived explicitly by using a suitable spectral function and a possible extension to the half-line case is discussed. The main results are illustrated by several examples."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.16752","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/2412.16752/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":"2412.16752","created_at":"2026-07-05T09:53:12.590744+00:00"},{"alias_kind":"arxiv_version","alias_value":"2412.16752v1","created_at":"2026-07-05T09:53:12.590744+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.16752","created_at":"2026-07-05T09:53:12.590744+00:00"},{"alias_kind":"pith_short_12","alias_value":"VPDAE3BPCHHE","created_at":"2026-07-05T09:53:12.590744+00:00"},{"alias_kind":"pith_short_16","alias_value":"VPDAE3BPCHHEWLPU","created_at":"2026-07-05T09:53:12.590744+00:00"},{"alias_kind":"pith_short_8","alias_value":"VPDAE3BP","created_at":"2026-07-05T09:53:12.590744+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/VPDAE3BPCHHEWLPUM4L2YZT63I","json":"https://pith.science/pith/VPDAE3BPCHHEWLPUM4L2YZT63I.json","graph_json":"https://pith.science/api/pith-number/VPDAE3BPCHHEWLPUM4L2YZT63I/graph.json","events_json":"https://pith.science/api/pith-number/VPDAE3BPCHHEWLPUM4L2YZT63I/events.json","paper":"https://pith.science/paper/VPDAE3BP"},"agent_actions":{"view_html":"https://pith.science/pith/VPDAE3BPCHHEWLPUM4L2YZT63I","download_json":"https://pith.science/pith/VPDAE3BPCHHEWLPUM4L2YZT63I.json","view_paper":"https://pith.science/paper/VPDAE3BP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2412.16752&json=true","fetch_graph":"https://pith.science/api/pith-number/VPDAE3BPCHHEWLPUM4L2YZT63I/graph.json","fetch_events":"https://pith.science/api/pith-number/VPDAE3BPCHHEWLPUM4L2YZT63I/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VPDAE3BPCHHEWLPUM4L2YZT63I/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VPDAE3BPCHHEWLPUM4L2YZT63I/action/storage_attestation","attest_author":"https://pith.science/pith/VPDAE3BPCHHEWLPUM4L2YZT63I/action/author_attestation","sign_citation":"https://pith.science/pith/VPDAE3BPCHHEWLPUM4L2YZT63I/action/citation_signature","submit_replication":"https://pith.science/pith/VPDAE3BPCHHEWLPUM4L2YZT63I/action/replication_record"}},"created_at":"2026-07-05T09:53:12.590744+00:00","updated_at":"2026-07-05T09:53:12.590744+00:00"}