{"as_of":"2026-08-12T03:32:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:048a857a9a6ba0a7441cc3c274eea7ba3ca8250e0dd2b22f79a656bb8dedab95","coverage":[{"denominator":21,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":21,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-09T05:12:57.119912Z","state":"measured"},{"denominator":21,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":21,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-11T06:34:44.6726+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2502.03348/citation-record","integrity":"/paper/2502.03348/integrity","json":"/paper/2502.03348/citation-record.json","paper":"/paper/2502.03348"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-09T05:12:58.011569Z","title":null,"venue":null,"work_id":"6224bc1d-7b82-478a-b665-0f21e06a6a59","year":1999},"citing_paper":{"arxiv_id":"2502.03348","last_updated":"2025-02-05T16:40:05Z","snapshot_observed_at":"2026-08-09T04:59:11.431113Z","submitted_at":"2025-02-05T16:40:05Z","title":"Values of Ducci Periods for Sequences on $\\mathbb{Z}_m^n$","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-09T05:12:56.818666Z"},"links":{"citing_paper":"/paper/2502.03348"},"observation_digest":"sha256:742c0f60b0ad8f92d91dc533765b10344e0af6b85fbee49270817e6d17c0e237","observation_id":"7beae5e6-fb0c-4186-805e-a5921a712c05","resolution":{"observed_at":"2026-08-09T05:12:58.033865Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-09T05:12:57.997247Z","title":null,"venue":null,"work_id":"84548b8e-58ec-4544-b409-2394d03decd3","year":2010},"citing_paper":{"arxiv_id":"2502.03348","last_updated":"2025-02-05T16:40:05Z","snapshot_observed_at":"2026-08-09T04:59:11.431113Z","submitted_at":"2025-02-05T16:40:05Z","title":"Values of Ducci Periods for Sequences on $\\mathbb{Z}_m^n$","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-09T05:12:56.853803Z"},"links":{"citing_paper":"/paper/2502.03348"},"observation_digest":"sha256:a44c2f59686a77d7ca0ba2d9827fe17631bcad32394d3062ce3aa3afd1ecf5ca","observation_id":"9ae0be1c-02c8-45b1-98a9-6897fac9ce73","resolution":{"observed_at":"2026-08-09T05:12:58.001732Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-09T05:12:57.982934Z","title":"& Merzel, J","venue":null,"work_id":"20418ae9-00d9-42a2-964c-aad8b698bd5d","year":2003},"citing_paper":{"arxiv_id":"2502.03348","last_updated":"2025-02-05T16:40:05Z","snapshot_observed_at":"2026-08-09T04:59:11.431113Z","submitted_at":"2025-02-05T16:40:05Z","title":"Values of Ducci Periods for Sequences on $\\mathbb{Z}_m^n$","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-09T05:12:56.890855Z"},"links":{"citing_paper":"/paper/2502.03348"},"observation_digest":"sha256:d4b65a4c932c61d9445ec3a2b202562d6ea3d5f020a38dbbdbc87907b8acf20b","observation_id":"82c8c104-e956-4364-b75d-4ca60e1c3522","resolution":{"observed_at":"2026-08-09T05:12:57.987535Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-09T05:12:57.969283Z","title":"& Merzel, J","venue":null,"work_id":"967884bd-be3f-4efd-9d43-ec44ec73c265","year":2007},"citing_paper":{"arxiv_id":"2502.03348","last_updated":"2025-02-05T16:40:05Z","snapshot_observed_at":"2026-08-09T04:59:11.431113Z","submitted_at":"2025-02-05T16:40:05Z","title":"Values of Ducci Periods for Sequences on $\\mathbb{Z}_m^n$","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-09T05:12:56.926833Z"},"links":{"citing_paper":"/paper/2502.03348"},"observation_digest":"sha256:e8c06a665b840689d861ab7daf60c11b2b5d755c38a8ae061b8746e690644b4a","observation_id":"acb2b9c5-4059-4247-a319-54122e40a927","resolution":{"observed_at":"2026-08-09T05:12:57.973519Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-09T05:12:57.954577Z","title":"(1978) Circles o f Numbers","venue":null,"work_id":"590d36d4-f00d-4477-95e1-e1bf4fc3844c","year":1978},"citing_paper":{"arxiv_id":"2502.03348","last_updated":"2025-02-05T16:40:05Z","snapshot_observed_at":"2026-08-09T04:59:11.431113Z","submitted_at":"2025-02-05T16:40:05Z","title":"Values of Ducci Periods for Sequences on $\\mathbb{Z}_m^n$","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-09T05:12:56.975968Z"},"links":{"citing_paper":"/paper/2502.03348"},"observation_digest":"sha256:ce53b7365b5c90a0088d9c1982ef89424db902816861cc9685927019ffa26f3f","observation_id":"efe3378c-431f-4eda-a248-6c762736954d","resolution":{"observed_at":"2026-08-09T05:12:57.959279Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-09T05:12:57.939796Z","title":null,"venue":null,"work_id":"f220d5f0-bc89-4027-bcfd-c7af3e8f2480","year":2003},"citing_paper":{"arxiv_id":"2502.03348","last_updated":"2025-02-05T16:40:05Z","snapshot_observed_at":"2026-08-09T04:59:11.431113Z","submitted_at":"2025-02-05T16:40:05Z","title":"Values of Ducci Periods for Sequences on $\\mathbb{Z}_m^n$","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-09T05:12:57.016590Z"},"links":{"citing_paper":"/paper/2502.03348"},"observation_digest":"sha256:abbb9c2cb016a109166ad22531f91749caf6a745e5205e3eb3e2afb14643ca37","observation_id":"a822a62d-fa23-443a-ae85-229c20ec81ac","resolution":{"observed_at":"2026-08-09T05:12:57.944677Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-09T05:12:57.857087Z","title":"& Marengoni, A","venue":null,"work_id":"11131e50-7a60-428e-8261-d8f61be0591f","year":1937},"citing_paper":{"arxiv_id":"2502.03348","last_updated":"2025-02-05T16:40:05Z","snapshot_observed_at":"2026-08-09T04:59:11.431113Z","submitted_at":"2025-02-05T16:40:05Z","title":"Values of Ducci Periods for Sequences on $\\mathbb{Z}_m^n$","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-09T05:12:57.029925Z"},"links":{"citing_paper":"/paper/2502.03348"},"observation_digest":"sha256:51d152d86bd1e9586ab5690a92a5e0f84445224cc2acad140d71a1950b389b5a","observation_id":"a1a9eb80-f3c0-4bba-8987-c210c01e51b9","resolution":{"observed_at":"2026-08-09T05:12:57.885692Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-09T05:12:57.793063Z","title":null,"venue":null,"work_id":"aac3f963-6a89-4117-a105-ae6e2ae32c4e","year":2020},"citing_paper":{"arxiv_id":"2502.03348","last_updated":"2025-02-05T16:40:05Z","snapshot_observed_at":"2026-08-09T04:59:11.431113Z","submitted_at":"2025-02-05T16:40:05Z","title":"Values of Ducci Periods for Sequences on $\\mathbb{Z}_m^n$","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-09T05:12:57.035390Z"},"links":{"citing_paper":"/paper/2502.03348"},"observation_digest":"sha256:0ff28243ef8a138171eb3ffd4ea0e3f3157b62e6a1767c7a5d7226a6727f0e2a","observation_id":"3baac0f1-5eba-45a6-8c76-c6c98547c75a","resolution":{"observed_at":"2026-08-09T05:12:57.808783Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-09T05:12:57.768836Z","title":null,"venue":null,"work_id":"0b0d5be0-9145-4cb3-81b6-13c7ed336d12","year":1990},"citing_paper":{"arxiv_id":"2502.03348","last_updated":"2025-02-05T16:40:05Z","snapshot_observed_at":"2026-08-09T04:59:11.431113Z","submitted_at":"2025-02-05T16:40:05Z","title":"Values of Ducci Periods for Sequences on $\\mathbb{Z}_m^n$","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-09T05:12:57.039751Z"},"links":{"citing_paper":"/paper/2502.03348"},"observation_digest":"sha256:4e85c8acc9b3b816d89c1a1b854a53840de13ba0de1fab13c1a13eac1c61e77f","observation_id":"4645b1f0-6955-4560-b7e9-2396b64f40ed","resolution":{"observed_at":"2026-08-09T05:12:57.774120Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-09T05:12:57.749019Z","title":"The Four Number Game","venue":null,"work_id":"14238d74-0447-4c5e-a928-48fa2971b1ec","year":1948},"citing_paper":{"arxiv_id":"2502.03348","last_updated":"2025-02-05T16:40:05Z","snapshot_observed_at":"2026-08-09T04:59:11.431113Z","submitted_at":"2025-02-05T16:40:05Z","title":"Values of Ducci Periods for Sequences on $\\mathbb{Z}_m^n$","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-09T05:12:57.045214Z"},"links":{"citing_paper":"/paper/2502.03348"},"observation_digest":"sha256:13bcbaa34dd8837f02a5876605247fdc02de4db9e1f72736522f1751bce84283","observation_id":"d4fd627a-1590-4092-b80d-aaff6c2508df","resolution":{"observed_at":"2026-08-09T05:12:57.753021Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-09T05:12:57.734496Z","title":"& Sch¨ offl, G","venue":null,"work_id":"169ba4bd-a9f2-4574-9918-8c05f2c7aad0","year":1995},"citing_paper":{"arxiv_id":"2502.03348","last_updated":"2025-02-05T16:40:05Z","snapshot_observed_at":"2026-08-09T04:59:11.431113Z","submitted_at":"2025-02-05T16:40:05Z","title":"Values of Ducci Periods for Sequences on $\\mathbb{Z}_m^n$","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-09T05:12:57.050270Z"},"links":{"citing_paper":"/paper/2502.03348"},"observation_digest":"sha256:a59c7f382ff262ec8d6ffa1d4ac3a8097e339f66ba0fcd30295570a517f1b77c","observation_id":"b0df3f22-d803-4ae2-82b5-068809785cfa","resolution":{"observed_at":"2026-08-09T05:12:57.739364Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2401.17502","last_updated":"2024-08-29T12:51:17Z","snapshot_observed_at":"2026-07-06T17:22:49.561301Z","submitted_at":"2024-01-30T23:29:21Z","title":"The Period of Ducci Cycles on $\\mathbb{Z}_{2^l}$ for Tuples of Length $2^k$","version":2},"cited_work":{"arxiv_id":"2401.17502","doi":null,"metadata_source":"pith","pith_arxiv_id":"2401.17502","snapshot_observed_at":"2026-08-09T05:12:57.364209Z","title":"The Period of Ducci Cycles on $\\mathbb{Z}_{2^l}$ for Tuples of Length $2^k$","venue":"math.NT","work_id":"f3715e2b-c6a3-4289-aa38-43fe75a3d26f","year":2024},"citing_paper":{"arxiv_id":"2502.03348","last_updated":"2025-02-05T16:40:05Z","snapshot_observed_at":"2026-08-09T04:59:11.431113Z","submitted_at":"2025-02-05T16:40:05Z","title":"Values of Ducci Periods for Sequences on $\\mathbb{Z}_m^n$","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-09T05:12:57.055498Z"},"links":{"cited_paper":"/paper/2401.17502","citing_paper":"/paper/2502.03348"},"observation_digest":"sha256:41303c2ff5e759407a10f0d3708c548458223810e401de742e00031983f18ff8","observation_id":"9e0da464-341a-49d0-962c-abce170ccd3d","resolution":{"observed_at":"2026-08-09T05:12:57.369518Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2403.05319","last_updated":"2024-08-29T12:48:48Z","snapshot_observed_at":"2026-07-06T17:41:34.856417Z","submitted_at":"2024-03-08T13:49:42Z","title":"Ducci on $\\mathbb{Z}_m^n$ and the Maximum Length for $n$ Odd","version":2},"cited_work":{"arxiv_id":"2403.05319","doi":null,"metadata_source":"pith","pith_arxiv_id":"2403.05319","snapshot_observed_at":"2026-08-09T05:12:57.307393Z","title":"Ducci on $\\mathbb{Z}_m^n$ and the Maximum Length for $n$ Odd","venue":"math.NT","work_id":"4255416f-7c10-4c8b-b8b4-6f196c767d8b","year":2024},"citing_paper":{"arxiv_id":"2502.03348","last_updated":"2025-02-05T16:40:05Z","snapshot_observed_at":"2026-08-09T04:59:11.431113Z","submitted_at":"2025-02-05T16:40:05Z","title":"Values of Ducci Periods for Sequences on $\\mathbb{Z}_m^n$","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-09T05:12:57.069657Z"},"links":{"cited_paper":"/paper/2403.05319","citing_paper":"/paper/2502.03348"},"observation_digest":"sha256:6bf09b0c1161c9653b9c36d8a6ab011eb6268dfd96c2f1d1565a8e8be40a5c56","observation_id":"0f8602f9-10df-478d-a49a-f4dd3be5194f","resolution":{"observed_at":"2026-08-09T05:12:57.324748Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"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":"2026-08-09T04:59:11.431113Z","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":"sha256:901990aa5232a8e25e9ab7eb396e306dd8371f223cb1b5715f68310d9e7d6466","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 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-09T05:12:57.706996Z","title":"Cycles of differences of inte gers","venue":null,"work_id":"36745285-1f99-4917-9d43-20632531a3d7","year":1981},"citing_paper":{"arxiv_id":"2502.03348","last_updated":"2025-02-05T16:40:05Z","snapshot_observed_at":"2026-08-09T04:59:11.431113Z","submitted_at":"2025-02-05T16:40:05Z","title":"Values of Ducci Periods for Sequences on $\\mathbb{Z}_m^n$","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-09T05:12:57.081341Z"},"links":{"citing_paper":"/paper/2502.03348"},"observation_digest":"sha256:ccf40a4074a088097ce950198383525c01d0dd862c81f75b15cee9ba0b8372b0","observation_id":"3b16c57f-6f29-4842-aa49-53bc51a5917c","resolution":{"observed_at":"2026-08-09T05:12:57.714745Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-09T05:12:57.674746Z","title":null,"venue":null,"work_id":"a4f3c247-5607-419e-ab53-35bc52bdc972","year":2023},"citing_paper":{"arxiv_id":"2502.03348","last_updated":"2025-02-05T16:40:05Z","snapshot_observed_at":"2026-08-09T04:59:11.431113Z","submitted_at":"2025-02-05T16:40:05Z","title":"Values of Ducci Periods for Sequences on $\\mathbb{Z}_m^n$","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-09T05:12:57.086472Z"},"links":{"citing_paper":"/paper/2502.03348"},"observation_digest":"sha256:52bdf67e3f7535c4b73c8e186db00f1f9dd267d5252e8c25051a0107302b210f","observation_id":"d024d9aa-7773-44b2-b252-cae590493432","resolution":{"observed_at":"2026-08-09T05:12:57.690134Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-09T05:12:57.629452Z","title":null,"venue":null,"work_id":"6a7db443-9803-4c7e-8488-456768b49420","year":1978},"citing_paper":{"arxiv_id":"2502.03348","last_updated":"2025-02-05T16:40:05Z","snapshot_observed_at":"2026-08-09T04:59:11.431113Z","submitted_at":"2025-02-05T16:40:05Z","title":"Values of Ducci Periods for Sequences on $\\mathbb{Z}_m^n$","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-09T05:12:57.091813Z"},"links":{"citing_paper":"/paper/2502.03348"},"observation_digest":"sha256:24eac77c1a413b854303e452c3ace83c700824a7227c7a18be2162568a0d393d","observation_id":"9e7d67e9-72e9-447a-846a-a1f3f938d4b2","resolution":{"observed_at":"2026-08-09T05:12:57.644796Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-09T05:12:57.580682Z","title":null,"venue":null,"work_id":"0e021fde-69a0-428d-a987-62d27b02dd40","year":1996},"citing_paper":{"arxiv_id":"2502.03348","last_updated":"2025-02-05T16:40:05Z","snapshot_observed_at":"2026-08-09T04:59:11.431113Z","submitted_at":"2025-02-05T16:40:05Z","title":"Values of Ducci Periods for Sequences on $\\mathbb{Z}_m^n$","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-09T05:12:57.099165Z"},"links":{"citing_paper":"/paper/2502.03348"},"observation_digest":"sha256:195ebdbc3d81477cf0bbcc314ca4c6f0624d61e6694a1bda99ec011b7157e6ba","observation_id":"765c549c-7385-4260-b788-094e242963a2","resolution":{"observed_at":"2026-08-09T05:12:57.599842Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-09T05:12:57.494748Z","title":"[Review of Su una interessante curiosit a numerica, by Ciamberlini, C","venue":null,"work_id":"741c0a82-088c-49f0-b7d8-b9d4e97512b5","year":null},"citing_paper":{"arxiv_id":"2502.03348","last_updated":"2025-02-05T16:40:05Z","snapshot_observed_at":"2026-08-09T04:59:11.431113Z","submitted_at":"2025-02-05T16:40:05Z","title":"Values of Ducci Periods for Sequences on $\\mathbb{Z}_m^n$","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-09T05:12:57.103935Z"},"links":{"citing_paper":"/paper/2502.03348"},"observation_digest":"sha256:c603688d40dd56a1a83e987fabd430725907d5c985ccaa5ae056375fab9f74c4","observation_id":"af457c61-776a-46c6-8517-817fec83fd73","resolution":{"observed_at":"2026-08-09T05:12:57.545882Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-09T05:12:57.460964Z","title":null,"venue":null,"work_id":"061bcf9f-f23a-462d-9d68-fd7d05e6916d","year":1988},"citing_paper":{"arxiv_id":"2502.03348","last_updated":"2025-02-05T16:40:05Z","snapshot_observed_at":"2026-08-09T04:59:11.431113Z","submitted_at":"2025-02-05T16:40:05Z","title":"Values of Ducci Periods for Sequences on $\\mathbb{Z}_m^n$","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-09T05:12:57.114762Z"},"links":{"citing_paper":"/paper/2502.03348"},"observation_digest":"sha256:7c51f9cc995340713b785d8caf805cb8668144455c62717be1721af4c9261a71","observation_id":"3fcec81d-e06a-4e23-8b18-5c4ba7b1e8da","resolution":{"observed_at":"2026-08-09T05:12:57.468911Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-09T05:12:57.404756Z","title":null,"venue":null,"work_id":"db75f9b6-45b6-4b6d-8f44-8bc449b16f29","year":1982},"citing_paper":{"arxiv_id":"2502.03348","last_updated":"2025-02-05T16:40:05Z","snapshot_observed_at":"2026-08-09T04:59:11.431113Z","submitted_at":"2025-02-05T16:40:05Z","title":"Values of Ducci Periods for Sequences on $\\mathbb{Z}_m^n$","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-09T05:12:57.119912Z"},"links":{"citing_paper":"/paper/2502.03348"},"observation_digest":"sha256:87e2e24a4ac0e4b81f9f2dacdd324294d10e967b284c1067029d5730fe607972","observation_id":"d97d0713-01e7-47eb-b701-d0e66a4c77b2","resolution":{"observed_at":"2026-08-09T05:12:57.409690Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2502.03348","last_updated":"2025-02-05T16:40:05Z","latest_version":1,"primary_category":"math.NT","snapshot_observed_at":"2026-08-09T04:59:11.431113Z","submitted_at":"2025-02-05T16:40:05Z","title":"Values of Ducci Periods for Sequences on $\\mathbb{Z}_m^n$"},"reference_resolution":{"displayed":21,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":10,"verified_exact":3,"verified_fuzzy":8},"total_outbound_references":21},"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":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"thesis":"As of 12 August 2026, this Paper Citation Record lists 21 of 21 outbound references and 0 inbound Pith citation observations for arXiv:2502.03348."}