{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:PG6IFXGHHMODILLSPXW275U7OD","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":"fb45a732831a90fe11d885621a5e1694191587534f1322a392942fb8acc32c02","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2026-07-15T04:58:49Z","title_canon_sha256":"acee504e8485c76944d72bebcbdc5e5cd715f91dd129d221104b2073d13c8595"},"schema_version":"1.0","source":{"id":"2607.13442","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.13442","created_at":"2026-07-16T01:22:12Z"},{"alias_kind":"arxiv_version","alias_value":"2607.13442v1","created_at":"2026-07-16T01:22:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.13442","created_at":"2026-07-16T01:22:12Z"},{"alias_kind":"pith_short_12","alias_value":"PG6IFXGHHMOD","created_at":"2026-07-16T01:22:12Z"},{"alias_kind":"pith_short_16","alias_value":"PG6IFXGHHMODILLS","created_at":"2026-07-16T01:22:12Z"},{"alias_kind":"pith_short_8","alias_value":"PG6IFXGH","created_at":"2026-07-16T01:22:12Z"}],"graph_snapshots":[{"event_id":"sha256:6bd4f81fb20c7b5453d5bf6e7a18d88bffbbd43851c3aff1de47f6280522d283","target":"graph","created_at":"2026-07-16T01:22:12Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.13442/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study periodicity properties of the 2-D $\\bigl(p_1(t)/p_2(t),\\, tp_3(t)\\bigr)$ and 3-D $\\bigl(p_1(t)/p_2(t),\\, tp_3(t),\\, p_4(t)\\bigr)$ Riordan arrays over a finite field ${\\mathbb F}_q$, where each $p_i(t)$ is a polynomial with $p_i(0)\\neq 0$. We show that the columns of the 2-D Riordan array are eventually periodic sequences, where a circulant matrix generated by the coefficients of $p_3(t)$ determines the behavior of this periodicity as the column index grows indefinitely. Furthermore, we prove that the preperiodic column partial sums of the 2-D array are periodic, and present a family o","authors_text":"Derek E. Bellamy, Eva N. Pflomm, Nikolai A. Krylov","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2026-07-15T04:58:49Z","title":"Periodicities in the Riordan arrays of polynomials over finite fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.13442","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":"sha256:45b19c3b449d651f2d3f6dc2d224537b1a2b23b7dbbfe73a7696294101748be3","target":"record","created_at":"2026-07-16T01:22:12Z","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":"fb45a732831a90fe11d885621a5e1694191587534f1322a392942fb8acc32c02","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2026-07-15T04:58:49Z","title_canon_sha256":"acee504e8485c76944d72bebcbdc5e5cd715f91dd129d221104b2073d13c8595"},"schema_version":"1.0","source":{"id":"2607.13442","kind":"arxiv","version":1}},"canonical_sha256":"79bc82dcc73b1c342d727dedaff69f70f7ae19ae8b7e193c8fe78ff359b8fa57","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"79bc82dcc73b1c342d727dedaff69f70f7ae19ae8b7e193c8fe78ff359b8fa57","first_computed_at":"2026-07-16T01:22:12.943531Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-16T01:22:12.943531Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xbVZkhwktqKISRkJHl7+lnWnquT4W7EBJrhIkdx3BvBpKZhky7nSC2ueT9kcV1QfwPoF0icjF4+5ZPLMI4GtBw==","signature_status":"signed_v1","signed_at":"2026-07-16T01:22:12.944491Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.13442","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:45b19c3b449d651f2d3f6dc2d224537b1a2b23b7dbbfe73a7696294101748be3","sha256:6bd4f81fb20c7b5453d5bf6e7a18d88bffbbd43851c3aff1de47f6280522d283"],"state_sha256":"2e21c2b5cae3b7ea6e5c0083a1594e36217b52993a887290b046969494e56c5b"}