{"as_of":"2026-08-12T10:57:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:545223ffbf2a484e27fb72d597f02e1c2d3dda21956c4d5572f46d62f6153f0a","coverage":[{"denominator":0,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":2,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":2,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-12T06:34:41.77262+00:00","state":"measured"},{"denominator":2,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":2,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-09T05:17:33.712965Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-08-09T05:12:57.198511Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2410.18204","last_updated":"2024-10-23T18:16:45Z","snapshot_observed_at":"2026-07-06T19:38:44.045121Z","submitted_at":"2024-10-23T18:16:45Z","title":"The Maximum Length for Ducci Sequences on $\\mathbb{}Z_m^n$ when $n$ is Even","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2410.18204","snapshot_observed_at":"2026-08-09T05:17:33.712965Z","title":"& Tefft, S.M","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2502.03345","last_updated":"2025-02-05T16:38:49Z","snapshot_observed_at":"2026-08-09T04:59:57.840121Z","submitted_at":"2025-02-05T16:38:49Z","title":"Examining $H$-Closed Ducci Sequences on $\\mathbb{Z}_m^n$","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-09T05:17:33.712965Z"},"links":{"cited_paper":"/paper/2410.18204","citing_paper":"/paper/2502.03345"},"observation_digest":"sha256:cfb7e34800e3b089e189968bea418cca677ef1adbd0d67ed3dc9def602a83520","observation_id":"7e3be7e9-6ab1-479f-b520-9704909b5da8","resolution":{"observed_at":"2026-08-09T05:17:33.712965Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2410.18204","last_updated":"2024-10-23T18:16:45Z","snapshot_observed_at":"2026-07-06T19:38:44.045121Z","submitted_at":"2024-10-23T18:16:45Z","title":"The Maximum Length for Ducci Sequences on $\\mathbb{}Z_m^n$ when $n$ is Even","version":1},"cited_work":{"arxiv_id":"2410.18204","doi":null,"metadata_source":"pith","pith_arxiv_id":"2410.18204","snapshot_observed_at":"2026-08-09T05:12:57.198511Z","title":"The Maximum Length for Ducci Sequences on $\\mathbb{}Z_m^n$ when $n$ is Even","venue":"math.NT","work_id":"ee39e2f3-39dc-4990-8b35-baaf27374bb9","year":2024},"citing_paper":{"arxiv_id":"2502.03348","last_updated":"2025-02-05T16:40:05Z","snapshot_observed_at":"2026-08-12T10:54:11.053709Z","submitted_at":"2025-02-05T16:40:05Z","title":"Values of Ducci Periods for Sequences on $\\mathbb{Z}_m^n$","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-09T05:12:57.075286Z"},"links":{"cited_paper":"/paper/2410.18204","citing_paper":"/paper/2502.03348"},"observation_digest":"sha256:d5db8f55d34cf58ef39a3822eb399c45f156e716be8b3b687493e73a41420d13","observation_id":"a86b5b55-205d-4d4a-acb6-80b0204f417e","resolution":{"observed_at":"2026-08-09T05:12:57.232183Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2410.18204/citation-record","integrity":"/paper/2410.18204/integrity","json":"/paper/2410.18204/citation-record.json","paper":"/paper/2410.18204"},"outbound":[],"paper":{"arxiv_id":"2410.18204","last_updated":"2024-10-23T18:16:45Z","latest_version":1,"primary_category":"math.NT","snapshot_observed_at":"2026-07-06T19:38:44.045121Z","submitted_at":"2024-10-23T18:16:45Z","title":"The Maximum Length for Ducci Sequences on $\\mathbb{}Z_m^n$ when $n$ is Even"},"reference_resolution":{"displayed":0,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":0},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"thesis":"As of 12 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 2 inbound Pith citation observations for arXiv:2410.18204."}