{"as_of":"2026-08-18T20:51:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:df29e6059a22f41930885d451465031100b8fdaa91b1e20fe293e165a540cd56","coverage":[{"denominator":22,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":22,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-11T10:41:55.028144Z","state":"measured"},{"denominator":22,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":22,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-18T06:34:40.430872+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/2412.16517/citation-record","integrity":"/paper/2412.16517/integrity","json":"/paper/2412.16517/citation-record.json","paper":"/paper/2412.16517"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T10:41:54.956777Z","title":"Automatic sequences","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2412.16517","last_updated":"2024-12-21T07:34:40Z","snapshot_observed_at":"2026-08-11T15:54:26.674150Z","submitted_at":"2024-12-21T07:34:40Z","title":"On non-holonomicity, transcendence and $p$-adic valuations","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-11T10:41:54.956777Z"},"links":{"citing_paper":"/paper/2412.16517"},"observation_digest":"sha256:64acb4d6670273c79cbb4aa619804d818602f8b7fdb3319a4717b0bca3b1c0ea","observation_id":"f08501cf-af1e-4a42-a6dc-edd810295530","resolution":{"observed_at":"2026-08-11T10:41:54.956777Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T10:41:55.263327Z","title":"Funktionentheorie","venue":null,"work_id":"dcd62746-ab35-4d03-95c4-63b79ecbd070","year":1968},"citing_paper":{"arxiv_id":"2412.16517","last_updated":"2024-12-21T07:34:40Z","snapshot_observed_at":"2026-08-11T15:54:26.674150Z","submitted_at":"2024-12-21T07:34:40Z","title":"On non-holonomicity, transcendence and $p$-adic valuations","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-11T10:41:54.960942Z"},"links":{"citing_paper":"/paper/2412.16517"},"observation_digest":"sha256:21f6b92f404a716d0212a4b632f52673b79da570b940feab1f4210ff8806ceda","observation_id":"cf4b3009-9b2b-4dc9-a3c9-d8783a589c30","resolution":{"observed_at":"2026-08-11T10:41:55.266563Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/bf01378331","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T11:08:50.044864Z","title":"¨Uber Potenzreihen mit ganzzahligen Koeﬃzienten","venue":"Mathematische Zeitschrift","work_id":"b4317051-edc4-471e-8574-6ed992769e0d","year":1921},"citing_paper":{"arxiv_id":"2412.16517","last_updated":"2024-12-21T07:34:40Z","snapshot_observed_at":"2026-08-11T15:54:26.674150Z","submitted_at":"2024-12-21T07:34:40Z","title":"On non-holonomicity, transcendence and $p$-adic valuations","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-11T10:41:54.964640Z"},"links":{"citing_paper":"/paper/2412.16517"},"observation_digest":"sha256:124863a56e967eee2214f887934c4de1f3a77fb796abac878ee8775c250a914b","observation_id":"58cd885f-5ec8-4f9a-ac54-2b5d6715f2f2","resolution":{"observed_at":"2026-08-11T10:41:55.133090Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.24033/bsmf.1926","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T10:41:55.119995Z","title":"Christol, T","venue":null,"work_id":"756e2e32-906d-4085-bfe4-0fc6f66326da","year":1980},"citing_paper":{"arxiv_id":"2412.16517","last_updated":"2024-12-21T07:34:40Z","snapshot_observed_at":"2026-08-11T15:54:26.674150Z","submitted_at":"2024-12-21T07:34:40Z","title":"On non-holonomicity, transcendence and $p$-adic valuations","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-11T10:41:54.968465Z"},"links":{"citing_paper":"/paper/2412.16517"},"observation_digest":"sha256:ba33a722832c3abd7b9fc0c0d81f600aa1d4c31f04f10e735161f2a588ae721f","observation_id":"fbdb3de8-d4fb-44dd-b8b5-893eaa90e8ab","resolution":{"observed_at":"2026-08-11T10:41:55.123198Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T10:41:55.253388Z","title":"Algebraic power series a nd diagonals","venue":null,"work_id":"6bf6e1d0-148d-4468-9d95-b5eac2ecbf53","year":null},"citing_paper":{"arxiv_id":"2412.16517","last_updated":"2024-12-21T07:34:40Z","snapshot_observed_at":"2026-08-11T15:54:26.674150Z","submitted_at":"2024-12-21T07:34:40Z","title":"On non-holonomicity, transcendence and $p$-adic valuations","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-11T10:41:54.972409Z"},"links":{"citing_paper":"/paper/2412.16517"},"observation_digest":"sha256:cc41685b9bca24764e59c9c830c0dcbc5db247bde11b2f45a9a6a5989171e5a1","observation_id":"b27cf709-30ff-4116-bff6-0759d306bb92","resolution":{"observed_at":"2026-08-11T10:41:55.257009Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.37236/1894","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T10:41:55.099645Z","title":"On t he non-holonomic character of logarithms, pow- ers, and the nth prime function","venue":null,"work_id":"dcb6533e-841a-45f9-a31f-c54779bf1188","year":2005},"citing_paper":{"arxiv_id":"2412.16517","last_updated":"2024-12-21T07:34:40Z","snapshot_observed_at":"2026-08-11T15:54:26.674150Z","submitted_at":"2024-12-21T07:34:40Z","title":"On non-holonomicity, transcendence and $p$-adic valuations","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-11T10:41:54.979765Z"},"links":{"citing_paper":"/paper/2412.16517"},"observation_digest":"sha256:ee4cb14d7bb63a3f13b36a5328d2c692913a874ba4c17af1c16306b725d684ca","observation_id":"c8ccd247-7ad7-4e1e-9d33-373cf814a690","resolution":{"observed_at":"2026-08-11T10:41:55.103573Z","resolver_source":"doi_truncated","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T10:41:55.243602Z","title":"On some non-holonomic sequences","venue":null,"work_id":"90906402-49b9-4ee5-b1eb-32a1ff63223e","year":null},"citing_paper":{"arxiv_id":"2412.16517","last_updated":"2024-12-21T07:34:40Z","snapshot_observed_at":"2026-08-11T15:54:26.674150Z","submitted_at":"2024-12-21T07:34:40Z","title":"On non-holonomicity, transcendence and $p$-adic valuations","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-11T10:41:54.983091Z"},"links":{"citing_paper":"/paper/2412.16517"},"observation_digest":"sha256:d4a055ae93f747b15881b96a8306ee4bb2f1338608c7377cb66a412f4ee21a0c","observation_id":"e3a0f447-f920-49a7-8c2c-76c78ea5dbac","resolution":{"observed_at":"2026-08-11T10:41:55.247134Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T10:41:55.233149Z","title":"Applied and computational complex analysis, vol","venue":null,"work_id":"d19104f1-7e3d-4a90-886a-ed0acc00b6b8","year":1974},"citing_paper":{"arxiv_id":"2412.16517","last_updated":"2024-12-21T07:34:40Z","snapshot_observed_at":"2026-08-11T15:54:26.674150Z","submitted_at":"2024-12-21T07:34:40Z","title":"On non-holonomicity, transcendence and $p$-adic valuations","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-11T10:41:54.989137Z"},"links":{"citing_paper":"/paper/2412.16517"},"observation_digest":"sha256:9d1ca47b7f620b81025e043d81a4f124e5f48334188ba8cb956622fb18122d5b","observation_id":"f430c0c9-4c94-4572-9c01-d19a2edfcdc5","resolution":{"observed_at":"2026-08-11T10:41:55.237232Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T10:41:54.992523Z","title":"The concrete tetrahedron","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2412.16517","last_updated":"2024-12-21T07:34:40Z","snapshot_observed_at":"2026-08-11T15:54:26.674150Z","submitted_at":"2024-12-21T07:34:40Z","title":"On non-holonomicity, transcendence and $p$-adic valuations","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-11T10:41:54.992523Z"},"links":{"citing_paper":"/paper/2412.16517"},"observation_digest":"sha256:ad6d770fdefeab42a20ae088045f48f85ac3be1556104dd43d1833943cfdcc85","observation_id":"33e58b1a-ea5b-4819-8271-7dccb1f14c5a","resolution":{"observed_at":"2026-08-11T10:41:54.992523Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T10:41:55.223435Z","title":null,"venue":null,"work_id":"2fa852c7-19ca-40e5-9873-62e3d5ee8aeb","year":2006},"citing_paper":{"arxiv_id":"2412.16517","last_updated":"2024-12-21T07:34:40Z","snapshot_observed_at":"2026-08-11T15:54:26.674150Z","submitted_at":"2024-12-21T07:34:40Z","title":"On non-holonomicity, transcendence and $p$-adic valuations","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-11T10:41:54.995564Z"},"links":{"citing_paper":"/paper/2412.16517"},"observation_digest":"sha256:a4c0f51f14a2aa7e7c379e78414c1fe7b396c900d809797e9d75cf8ecaba357e","observation_id":"d2d8b3be-6bbc-4426-8649-9edcb58475f0","resolution":{"observed_at":"2026-08-11T10:41:55.226930Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1002/1521-3870(200201)48:1","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T10:41:55.072781Z","title":"Plain bases for classes of primitive recursive functions","venue":null,"work_id":"d2162f24-9830-456c-bc28-f7745ac129a2","year":2002},"citing_paper":{"arxiv_id":"2412.16517","last_updated":"2024-12-21T07:34:40Z","snapshot_observed_at":"2026-08-11T15:54:26.674150Z","submitted_at":"2024-12-21T07:34:40Z","title":"On non-holonomicity, transcendence and $p$-adic valuations","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-11T10:41:54.998583Z"},"links":{"citing_paper":"/paper/2412.16517"},"observation_digest":"sha256:61ab79437a6dfb1450e01637c96bf754762c7273489f6b13e5f7c1bac077ebd0","observation_id":"8ea1ad44-87f4-4329-9f8d-87f3a5e2754c","resolution":{"observed_at":"2026-08-11T10:41:55.076661Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T10:41:55.213240Z","title":"Published electronically at http://oeis.org","venue":null,"work_id":"e7c012d2-5dbb-454d-a5d5-3343780799a8","year":2023},"citing_paper":{"arxiv_id":"2412.16517","last_updated":"2024-12-21T07:34:40Z","snapshot_observed_at":"2026-08-11T15:54:26.674150Z","submitted_at":"2024-12-21T07:34:40Z","title":"On non-holonomicity, transcendence and $p$-adic valuations","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-11T10:41:55.001675Z"},"links":{"citing_paper":"/paper/2412.16517"},"observation_digest":"sha256:2c1db2c0a32cee79fdb48c33f387482b47234ed59be63fe7cd6070d09f851b70","observation_id":"65a65462-9563-48f8-9712-4b5891cdcf08","resolution":{"observed_at":"2026-08-11T10:41:55.216881Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/bf01456965","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T11:08:50.044864Z","title":"¨Uber Potenzreihen mit ganzzahligen Koeﬃzienten","venue":"Mathematische Annalen","work_id":"e8c0981b-d8f6-4367-9432-a43ba7451822","year":1916},"citing_paper":{"arxiv_id":"2412.16517","last_updated":"2024-12-21T07:34:40Z","snapshot_observed_at":"2026-08-11T15:54:26.674150Z","submitted_at":"2024-12-21T07:34:40Z","title":"On non-holonomicity, transcendence and $p$-adic valuations","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-11T10:41:55.004581Z"},"links":{"citing_paper":"/paper/2412.16517"},"observation_digest":"sha256:b50ce24122ce75b57d83355c280fa5be7cbf3d0167fdfd5b5ad1ada81a2b99aa","observation_id":"e3b646c4-23d9-48aa-b057-b36157a3769e","resolution":{"observed_at":"2026-08-11T10:41:55.065876Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2406.06436","last_updated":"2024-06-10T16:27:17Z","snapshot_observed_at":"2026-08-16T22:47:23.859495Z","submitted_at":"2024-06-10T16:27:17Z","title":"On other two representations of the C-recursive integer sequences by terms in modular arithmetic","version":1},"cited_work":{"arxiv_id":"2406.06436","doi":null,"metadata_source":"pith","pith_arxiv_id":"2406.06436","snapshot_observed_at":"2026-08-11T10:41:55.182918Z","title":"On other two representations of the C-recursive integer sequences by terms in modular arithmetic","venue":"math.NT","work_id":"d0f9ba95-f826-4545-8da4-35efa567a226","year":2024},"citing_paper":{"arxiv_id":"2412.16517","last_updated":"2024-12-21T07:34:40Z","snapshot_observed_at":"2026-08-11T15:54:26.674150Z","submitted_at":"2024-12-21T07:34:40Z","title":"On non-holonomicity, transcendence and $p$-adic valuations","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-11T10:41:55.007646Z"},"links":{"cited_paper":"/paper/2406.06436","citing_paper":"/paper/2412.16517"},"observation_digest":"sha256:8308d8ec3c0bbb1145eef6d84c0cdd200bf54f392b4c6305a539b2795ce27927","observation_id":"587c9c4a-7542-45a9-a60c-dda69971d154","resolution":{"observed_at":"2026-08-11T10:41:55.186272Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2405.04083","last_updated":"2025-06-05T19:58:19Z","snapshot_observed_at":"2026-08-17T17:24:29.751437Z","submitted_at":"2024-05-07T07:31:42Z","title":"On the representation of C-recursive integer sequences by arithmetic terms","version":2},"cited_work":{"arxiv_id":"2405.04083","doi":null,"metadata_source":"pith","pith_arxiv_id":"2405.04083","snapshot_observed_at":"2026-08-11T10:41:55.170300Z","title":"On the representation of C-recursive integer sequences by arithmetic terms","venue":"math.LO","work_id":"e03bbe68-3a35-4444-a4d1-da08cd1f952b","year":2024},"citing_paper":{"arxiv_id":"2412.16517","last_updated":"2024-12-21T07:34:40Z","snapshot_observed_at":"2026-08-11T15:54:26.674150Z","submitted_at":"2024-12-21T07:34:40Z","title":"On non-holonomicity, transcendence and $p$-adic valuations","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-11T10:41:55.010975Z"},"links":{"cited_paper":"/paper/2405.04083","citing_paper":"/paper/2412.16517"},"observation_digest":"sha256:534b12928931df752bfc2847e84f68f28b74e8be231775de5aa9d88335e08050","observation_id":"fce38123-2cfc-4ee7-aa3f-23a3e8ab19bb","resolution":{"observed_at":"2026-08-11T10:41:55.173724Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2407.12928","last_updated":"2024-07-17T18:02:37Z","snapshot_observed_at":"2026-08-16T18:33:46.536298Z","submitted_at":"2024-07-17T18:02:37Z","title":"On the representation of number-theoretic functions by arithmetic terms","version":1},"cited_work":{"arxiv_id":"2407.12928","doi":null,"metadata_source":"pith","pith_arxiv_id":"2407.12928","snapshot_observed_at":"2026-08-11T10:41:55.157331Z","title":"On the representation of number-theoretic functions by arithmetic terms","venue":"math.NT","work_id":"5aac3692-126f-4073-bc95-cae450aec84a","year":2024},"citing_paper":{"arxiv_id":"2412.16517","last_updated":"2024-12-21T07:34:40Z","snapshot_observed_at":"2026-08-11T15:54:26.674150Z","submitted_at":"2024-12-21T07:34:40Z","title":"On non-holonomicity, transcendence and $p$-adic valuations","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-11T10:41:55.014103Z"},"links":{"cited_paper":"/paper/2407.12928","citing_paper":"/paper/2412.16517"},"observation_digest":"sha256:d64ba1659ef4e919ac1706fda966f71daf4044f23858ac85b0ff00b20ef2fe64","observation_id":"91f05088-ed32-4622-a77c-46644c48d91c","resolution":{"observed_at":"2026-08-11T10:41:55.161100Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T10:41:55.202853Z","title":"Arithmetic-term rep resentations for the greatest common divisor,","venue":null,"work_id":"84c554fa-44a6-44ca-a688-ce3936ee549a","year":null},"citing_paper":{"arxiv_id":"2412.16517","last_updated":"2024-12-21T07:34:40Z","snapshot_observed_at":"2026-08-11T15:54:26.674150Z","submitted_at":"2024-12-21T07:34:40Z","title":"On non-holonomicity, transcendence and $p$-adic valuations","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-11T10:41:55.017359Z"},"links":{"citing_paper":"/paper/2412.16517"},"observation_digest":"sha256:278544efa171397005d1a6e597d81d2b606addf1566ce392525ca1e00fd7a712","observation_id":"d4a2c083-6400-4b19-95ba-ad6231c468fa","resolution":{"observed_at":"2026-08-11T10:41:55.206348Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T10:41:55.024799Z","title":null,"venue":null,"work_id":null,"year":1955},"citing_paper":{"arxiv_id":"2412.16517","last_updated":"2024-12-21T07:34:40Z","snapshot_observed_at":"2026-08-11T15:54:26.674150Z","submitted_at":"2024-12-21T07:34:40Z","title":"On non-holonomicity, transcendence and $p$-adic valuations","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-11T10:41:55.024799Z"},"links":{"citing_paper":"/paper/2412.16517"},"observation_digest":"sha256:6d835061aa16e5f306d65ef5d7f3eff40dc03e3b979872cfbc492fd2cb7f96b2","observation_id":"72ad6ebb-2c8a-46f3-a1b2-acd2e2f2c8b4","resolution":{"observed_at":"2026-08-11T10:41:55.024799Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T10:41:55.193007Z","title":"Simion Stoilow","venue":null,"work_id":"78f8034d-4213-4107-a040-03d1e714a658","year":null},"citing_paper":{"arxiv_id":"2412.16517","last_updated":"2024-12-21T07:34:40Z","snapshot_observed_at":"2026-08-11T15:54:26.674150Z","submitted_at":"2024-12-21T07:34:40Z","title":"On non-holonomicity, transcendence and $p$-adic valuations","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-11T10:41:55.028144Z"},"links":{"citing_paper":"/paper/2412.16517"},"observation_digest":"sha256:fe4f7bdbd4bdd93036f408a606e191225917a060bb43f85ba4ccf38550089d19","observation_id":"6c59c53f-b383-427e-a89b-97d353e18d71","resolution":{"observed_at":"2026-08-11T10:41:55.196540Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/0022-314x(87)90095-3","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T10:41:55.110310Z","title":"(page 11)","venue":null,"work_id":"3df5ae14-74ba-419f-8165-3825779495e0","year":null},"citing_paper":{"arxiv_id":"2412.16517","last_updated":"2024-12-21T07:34:40Z","snapshot_observed_at":"2026-08-11T15:54:26.674150Z","submitted_at":"2024-12-21T07:34:40Z","title":"On non-holonomicity, transcendence and $p$-adic valuations","version":1},"reference_index":1987,"source":"pdf_text","source_observed_at":"2026-08-11T10:41:54.976082Z"},"links":{"citing_paper":"/paper/2412.16517"},"observation_digest":"sha256:352759e0c28e03fa0aa24bcf1fa6aa8c082944c9364ee93eafea4d2cfee0761b","observation_id":"b3cc0f25-cd13-4f7d-a593-9396e1189302","resolution":{"observed_at":"2026-08-11T10:41:55.113740Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.37236/1840","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T10:41:55.089676Z","title":"(page 3)","venue":null,"work_id":"bfe2844b-ca8d-44dc-bcb5-922ad8439324","year":null},"citing_paper":{"arxiv_id":"2412.16517","last_updated":"2024-12-21T07:34:40Z","snapshot_observed_at":"2026-08-11T15:54:26.674150Z","submitted_at":"2024-12-21T07:34:40Z","title":"On non-holonomicity, transcendence and $p$-adic valuations","version":1},"reference_index":2004,"source":"pdf_text","source_observed_at":"2026-08-11T10:41:54.986170Z"},"links":{"citing_paper":"/paper/2412.16517"},"observation_digest":"sha256:fe4740413264778a761124a9e147134bb7653d312e53c17f811da427f93248a5","observation_id":"7a0b5691-97a6-41f0-8ec7-c505fad21f8b","resolution":{"observed_at":"2026-08-11T10:41:55.093054Z","resolver_source":"doi_truncated","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2411.06430","last_updated":"2025-06-11T15:48:58Z","snapshot_observed_at":"2026-08-16T13:01:26.268401Z","submitted_at":"2024-11-10T11:21:39Z","title":"Arithmetic-term representations for the greatest common divisor","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2411.06430","snapshot_observed_at":"2026-08-11T10:41:55.020665Z","title":"(page 1)","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2412.16517","last_updated":"2024-12-21T07:34:40Z","snapshot_observed_at":"2026-08-11T15:54:26.674150Z","submitted_at":"2024-12-21T07:34:40Z","title":"On non-holonomicity, transcendence and $p$-adic valuations","version":1},"reference_index":2024,"source":"pdf_text","source_observed_at":"2026-08-11T10:41:55.020665Z"},"links":{"cited_paper":"/paper/2411.06430","citing_paper":"/paper/2412.16517"},"observation_digest":"sha256:9de88ebfef36d0b5970ed2d61d67254adbf4b5503ca8312dfdc8762d5b88f1df","observation_id":"5dc93509-6bc0-48ac-b361-6a77778f556a","resolution":{"observed_at":"2026-08-11T10:41:55.020665Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2412.16517","last_updated":"2024-12-21T07:34:40Z","latest_version":1,"primary_category":"math.NT","snapshot_observed_at":"2026-08-11T15:54:26.674150Z","submitted_at":"2024-12-21T07:34:40Z","title":"On non-holonomicity, transcendence and $p$-adic valuations"},"reference_resolution":{"displayed":22,"state_counts":{"malformed_identifier":2,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":5,"verified_exact":8,"verified_fuzzy":7},"total_outbound_references":22},"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":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"thesis":"As of 18 August 2026, this Paper Citation Record lists 22 of 22 outbound references and 0 inbound Pith citation observations for arXiv:2412.16517."}