{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:HLSBXPZ3Q44XZDJPO7MVMRWGP5","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"514188852f3f4ac8ae5e554c6462d94bb30a6fa9282225d77edb2abc84e95b5f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-01-10T02:37:22Z","title_canon_sha256":"3ca2d0037373649fc9a8ef7f0838253067658e3155a4f4acb588d65e73724722"},"schema_version":"1.0","source":{"id":"1701.02420","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.02420","created_at":"2026-05-18T00:53:04Z"},{"alias_kind":"arxiv_version","alias_value":"1701.02420v1","created_at":"2026-05-18T00:53:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.02420","created_at":"2026-05-18T00:53:04Z"},{"alias_kind":"pith_short_12","alias_value":"HLSBXPZ3Q44X","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"HLSBXPZ3Q44XZDJP","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"HLSBXPZ3","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:beb037c75172690ccd317adbc4d0e076315c926c5e1184d99d9f3e3fa9cec88a","target":"graph","created_at":"2026-05-18T00:53:04Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We prove that every multiplier sequence for the Legendre basis which can be interpolated by a polynomial has the form $\\{h(k^2+k)\\}_{k=0}^{\\infty}$, where $h\\in\\mathbb{R}[x]$. We also prove that a non-trivial collection of polynomials of a certain form interpolate multiplier sequences for the Legendre basis, and we state conjectures on how to extend these results.","authors_text":"Andrzej Piotrowski, Matthew Chasse, Tam\\'as Forg\\'acs","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-01-10T02:37:22Z","title":"Polynomially Interpolated Legendre Multiplier Sequences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02420","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:09af54b9293509c34c1039e82b983b56bc1117782d0fe11f0ce55c7223127a67","target":"record","created_at":"2026-05-18T00:53:04Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"514188852f3f4ac8ae5e554c6462d94bb30a6fa9282225d77edb2abc84e95b5f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-01-10T02:37:22Z","title_canon_sha256":"3ca2d0037373649fc9a8ef7f0838253067658e3155a4f4acb588d65e73724722"},"schema_version":"1.0","source":{"id":"1701.02420","kind":"arxiv","version":1}},"canonical_sha256":"3ae41bbf3b87397c8d2f77d95646c67f7ceb4924ee413297cf6013c358cace25","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3ae41bbf3b87397c8d2f77d95646c67f7ceb4924ee413297cf6013c358cace25","first_computed_at":"2026-05-18T00:53:04.297880Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:04.297880Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YHCgsEyUHwrznzX9hyTlRX1bJccxbXD/XMBTtDAGpBv0AtGF26KRo78KnEp+YXdsCc/6gUGMy5/gdwyRecgRCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:04.298476Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.02420","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:09af54b9293509c34c1039e82b983b56bc1117782d0fe11f0ce55c7223127a67","sha256:beb037c75172690ccd317adbc4d0e076315c926c5e1184d99d9f3e3fa9cec88a"],"state_sha256":"6d74c7f6e95e5327534c362cb0fc4c6845a1d650a402c5900c908944875b9ca1"}