{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:O4R6TOYDH3F5TDFYHPOO4SBJ7A","short_pith_number":"pith:O4R6TOYD","schema_version":"1.0","canonical_sha256":"7723e9bb033ecbd98cb83bdcee4829f828adc45340d8886b86042f7e6f4e31e7","source":{"kind":"arxiv","id":"1401.3553","version":1},"attestation_state":"computed","paper":{"title":"A note on the arithmetic properties of Stern Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Maciej Gawron","submitted_at":"2014-01-15T11:58:22Z","abstract_excerpt":"We investigate the Stern polynomials defined by $B_0 ( t ) =0,B_1 ( t ) =1$, and for $n \\geq 2$ by the recurrence relations $B_{2n}( t) =tB_{n}( t) ,$ $B_{2n+1}( t) =B_n( t) +B_{n+1}( t) $. We prove that all possible rational roots of that polynomials are $0,-1,-1/2,-1/3$. We give complete characterization of $n$ such that $deg( B_n) = deg( B_{n+1}) $ and $deg( B_n) =deg( B_{n+1}) =deg( B_{n+2}) $. Moreover, we present some result concerning reciprocal Stern polynomials."},"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":"1401.3553","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-01-15T11:58:22Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"0b3f3461b8fca4c0e31e77fe5adc9f82f7437057800c424d132579ab57ef5385","abstract_canon_sha256":"4935129510e97f5682838cb9dc32508584ea594e4098752003d5ee6c41cb0aae"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:02:08.446124Z","signature_b64":"rwPUZHkTfbMf1+uA8ISnS5T1OZa1yU6i4XuEa6X8UQAZTNOjfPCNoJum+BzY3NleFUe7RBZWeu54zyCjRkiMCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7723e9bb033ecbd98cb83bdcee4829f828adc45340d8886b86042f7e6f4e31e7","last_reissued_at":"2026-05-18T03:02:08.445440Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:02:08.445440Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A note on the arithmetic properties of Stern Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Maciej Gawron","submitted_at":"2014-01-15T11:58:22Z","abstract_excerpt":"We investigate the Stern polynomials defined by $B_0 ( t ) =0,B_1 ( t ) =1$, and for $n \\geq 2$ by the recurrence relations $B_{2n}( t) =tB_{n}( t) ,$ $B_{2n+1}( t) =B_n( t) +B_{n+1}( t) $. We prove that all possible rational roots of that polynomials are $0,-1,-1/2,-1/3$. We give complete characterization of $n$ such that $deg( B_n) = deg( B_{n+1}) $ and $deg( B_n) =deg( B_{n+1}) =deg( B_{n+2}) $. Moreover, we present some result concerning reciprocal Stern polynomials."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.3553","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":""},"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":"1401.3553","created_at":"2026-05-18T03:02:08.445553+00:00"},{"alias_kind":"arxiv_version","alias_value":"1401.3553v1","created_at":"2026-05-18T03:02:08.445553+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.3553","created_at":"2026-05-18T03:02:08.445553+00:00"},{"alias_kind":"pith_short_12","alias_value":"O4R6TOYDH3F5","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_16","alias_value":"O4R6TOYDH3F5TDFY","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_8","alias_value":"O4R6TOYD","created_at":"2026-05-18T12:28:41.024544+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/O4R6TOYDH3F5TDFYHPOO4SBJ7A","json":"https://pith.science/pith/O4R6TOYDH3F5TDFYHPOO4SBJ7A.json","graph_json":"https://pith.science/api/pith-number/O4R6TOYDH3F5TDFYHPOO4SBJ7A/graph.json","events_json":"https://pith.science/api/pith-number/O4R6TOYDH3F5TDFYHPOO4SBJ7A/events.json","paper":"https://pith.science/paper/O4R6TOYD"},"agent_actions":{"view_html":"https://pith.science/pith/O4R6TOYDH3F5TDFYHPOO4SBJ7A","download_json":"https://pith.science/pith/O4R6TOYDH3F5TDFYHPOO4SBJ7A.json","view_paper":"https://pith.science/paper/O4R6TOYD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1401.3553&json=true","fetch_graph":"https://pith.science/api/pith-number/O4R6TOYDH3F5TDFYHPOO4SBJ7A/graph.json","fetch_events":"https://pith.science/api/pith-number/O4R6TOYDH3F5TDFYHPOO4SBJ7A/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/O4R6TOYDH3F5TDFYHPOO4SBJ7A/action/timestamp_anchor","attest_storage":"https://pith.science/pith/O4R6TOYDH3F5TDFYHPOO4SBJ7A/action/storage_attestation","attest_author":"https://pith.science/pith/O4R6TOYDH3F5TDFYHPOO4SBJ7A/action/author_attestation","sign_citation":"https://pith.science/pith/O4R6TOYDH3F5TDFYHPOO4SBJ7A/action/citation_signature","submit_replication":"https://pith.science/pith/O4R6TOYDH3F5TDFYHPOO4SBJ7A/action/replication_record"}},"created_at":"2026-05-18T03:02:08.445553+00:00","updated_at":"2026-05-18T03:02:08.445553+00:00"}