{"as_of":"2026-08-17T05:39:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:6af2a5c1850306a45f8449ea3fc530dc350eb32d21612216601c67aede63ac19","coverage":[{"denominator":24,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":24,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-14T06:17:33.908292Z","state":"measured"},{"denominator":24,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":24,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-16T06:30:59.297886+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/1909.00177/citation-record","integrity":"/paper/1909.00177/integrity","json":"/paper/1909.00177/citation-record.json","paper":"/paper/1909.00177"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T06:17:34.168255Z","title":", On Joris’ theorem on diﬀerentiability of functions , Kodai Math","venue":null,"work_id":"2bc32e05-f523-41a1-a338-0104a60d8cdd","year":1989},"citing_paper":{"arxiv_id":"1909.00177","last_updated":"2019-08-31T09:36:38Z","snapshot_observed_at":"2026-08-17T00:04:14.272796Z","submitted_at":"2019-08-31T09:36:38Z","title":"Functions with ultradifferentiable powers","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-14T06:17:33.830287Z"},"links":{"citing_paper":"/paper/1909.00177"},"observation_digest":"sha256:b7945341bd6962d481126d491e86a35aa5ee651894bdfe1cab4b975ad2fe0338","observation_id":"bd50f8c7-9d3c-477d-9534-bbc560474b3c","resolution":{"observed_at":"2026-08-14T06:17:34.171464Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T06:17:34.159312Z","title":", Diﬀerentiability of a function and of its compositions with functions of one variable, Math","venue":null,"work_id":"c670622c-f791-436e-9942-9f9a08c7e777","year":1967},"citing_paper":{"arxiv_id":"1909.00177","last_updated":"2019-08-31T09:36:38Z","snapshot_observed_at":"2026-08-17T00:04:14.272796Z","submitted_at":"2019-08-31T09:36:38Z","title":"Functions with ultradifferentiable powers","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-14T06:17:33.834329Z"},"links":{"citing_paper":"/paper/1909.00177"},"observation_digest":"sha256:5114d7fefd03ace55200a302f4b1a3c03f4c6e6c4bf7f7fe278a9e5befaac9e4","observation_id":"8fde9465-1148-41bd-883a-ee285cbf88ac","resolution":{"observed_at":"2026-08-14T06:17:34.162634Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T06:17:34.149851Z","title":", Functional Analysis, Sobolev Spaces and Partial Diﬀerenti al Equations , Springer, New York, NY (2011)","venue":null,"work_id":"7150b618-92d4-4b64-a70e-3248251c62ce","year":2011},"citing_paper":{"arxiv_id":"1909.00177","last_updated":"2019-08-31T09:36:38Z","snapshot_observed_at":"2026-08-17T00:04:14.272796Z","submitted_at":"2019-08-31T09:36:38Z","title":"Functions with ultradifferentiable powers","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-14T06:17:33.837840Z"},"links":{"citing_paper":"/paper/1909.00177"},"observation_digest":"sha256:6b2a012160fea20286021574cfa25ca717c9950b8cce03e525651223cd4b3195","observation_id":"28b09f93-25b5-4c69-b9c0-05684d9e3f82","resolution":{"observed_at":"2026-08-14T06:17:34.153372Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T06:17:34.140279Z","title":", Nonlinear conditions for diﬀerentiability of functions, J","venue":null,"work_id":"629300f8-7cea-4a11-bcbc-19cfc9356edd","year":1985},"citing_paper":{"arxiv_id":"1909.00177","last_updated":"2019-08-31T09:36:38Z","snapshot_observed_at":"2026-08-17T00:04:14.272796Z","submitted_at":"2019-08-31T09:36:38Z","title":"Functions with ultradifferentiable powers","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-14T06:17:33.841748Z"},"links":{"citing_paper":"/paper/1909.00177"},"observation_digest":"sha256:772d95c2a787e5dcbbe6f69fb6cefc20c0d5fadaa5d50ab11c3cb072a29ad770","observation_id":"5f1e5f1a-8377-475f-a8cc-6dec6fc2bb1f","resolution":{"observed_at":"2026-08-14T06:17:34.143821Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T06:17:34.130177Z","title":", Pseudoanalytic extension of smooth functions","venue":null,"work_id":"3739d311-b14b-4cc0-beae-57dabb74449d","year":1980},"citing_paper":{"arxiv_id":"1909.00177","last_updated":"2019-08-31T09:36:38Z","snapshot_observed_at":"2026-08-17T00:04:14.272796Z","submitted_at":"2019-08-31T09:36:38Z","title":"Functions with ultradifferentiable powers","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-14T06:17:33.845357Z"},"links":{"citing_paper":"/paper/1909.00177"},"observation_digest":"sha256:2f77ab571104ff2d8d31dd73e8cfd05a9cc354aceb4384d3052b5d5b64eee87b","observation_id":"6e3194f0-4336-4455-9b59-97bc221cbd47","resolution":{"observed_at":"2026-08-14T06:17:34.134139Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T06:17:34.120637Z","title":null,"venue":null,"work_id":"2ce52ed8-5589-4aaf-82f6-c6e4ba9bdff2","year":2018},"citing_paper":{"arxiv_id":"1909.00177","last_updated":"2019-08-31T09:36:38Z","snapshot_observed_at":"2026-08-17T00:04:14.272796Z","submitted_at":"2019-08-31T09:36:38Z","title":"Functions with ultradifferentiable powers","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-14T06:17:33.848785Z"},"links":{"citing_paper":"/paper/1909.00177"},"observation_digest":"sha256:07c0cb80b5b0ceb48546745333308052cbea3b866d43f200918388961b8a3709","observation_id":"f9191a82-911c-4a4a-bd56-db643b74e06b","resolution":{"observed_at":"2026-08-14T06:17:34.123933Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T06:17:34.110859Z","title":", Lectures on Analysis on Metric Spaces , Springer, New York (2001)","venue":null,"work_id":"bed2ebe1-c83c-44a1-aa22-54605539bdf1","year":2001},"citing_paper":{"arxiv_id":"1909.00177","last_updated":"2019-08-31T09:36:38Z","snapshot_observed_at":"2026-08-17T00:04:14.272796Z","submitted_at":"2019-08-31T09:36:38Z","title":"Functions with ultradifferentiable powers","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-14T06:17:33.852378Z"},"links":{"citing_paper":"/paper/1909.00177"},"observation_digest":"sha256:d3306b909f4babd4362cc891c099044d2162c9e70746fc794b97662447d2bb42","observation_id":"2ca4b491-655e-4801-971d-f9b1b0c23b71","resolution":{"observed_at":"2026-08-14T06:17:34.114777Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T06:17:34.100615Z","title":", Pathological phenomena in Denjoy-Carleman classes , Canad","venue":null,"work_id":"79d69aba-809f-43b9-9b91-d2a67ff56562","year":2016},"citing_paper":{"arxiv_id":"1909.00177","last_updated":"2019-08-31T09:36:38Z","snapshot_observed_at":"2026-08-17T00:04:14.272796Z","submitted_at":"2019-08-31T09:36:38Z","title":"Functions with ultradifferentiable powers","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-14T06:17:33.855501Z"},"links":{"citing_paper":"/paper/1909.00177"},"observation_digest":"sha256:8f786d07563246081563861d1b76641ea12d4bd142874f58c76c5d7717b0cdd9","observation_id":"54b08471-2f63-4827-b776-e968c910a095","resolution":{"observed_at":"2026-08-14T06:17:34.104102Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T06:17:34.090697Z","title":null,"venue":null,"work_id":"6a7c8786-0b45-473d-9537-8511b027e537","year":2018},"citing_paper":{"arxiv_id":"1909.00177","last_updated":"2019-08-31T09:36:38Z","snapshot_observed_at":"2026-08-17T00:04:14.272796Z","submitted_at":"2019-08-31T09:36:38Z","title":"Functions with ultradifferentiable powers","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-14T06:17:33.858658Z"},"links":{"citing_paper":"/paper/1909.00177"},"observation_digest":"sha256:19c947bb04c4b3d66f6b55b3a8e7c7e524d38c702425e41c6f5f2719bdc72dda","observation_id":"32e13e77-4a88-4a16-8e5f-658f8dae1a99","resolution":{"observed_at":"2026-08-14T06:17:34.094346Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T06:17:34.080851Z","title":", Log-convex sequences and nonzero proxi- mate orders, J","venue":null,"work_id":"4d4567e2-e76e-43b0-ba7f-315e6e2aa4c4","year":2017},"citing_paper":{"arxiv_id":"1909.00177","last_updated":"2019-08-31T09:36:38Z","snapshot_observed_at":"2026-08-17T00:04:14.272796Z","submitted_at":"2019-08-31T09:36:38Z","title":"Functions with ultradifferentiable powers","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-14T06:17:33.861593Z"},"links":{"citing_paper":"/paper/1909.00177"},"observation_digest":"sha256:c8aa4570b55050765d17e8e203227bc1cb919f1c555f453b946013638fd2e338","observation_id":"5d97d1cd-5a3c-43d6-8794-df50ef4db685","resolution":{"observed_at":"2026-08-14T06:17:34.084274Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1806.01605","last_updated":"2018-06-05T10:55:09Z","snapshot_observed_at":"2026-08-14T19:07:24.163397Z","submitted_at":"2018-06-05T10:55:09Z","title":"Indices of O-regular variation for weight functions and weight sequences","version":1},"cited_work":{"arxiv_id":"1806.01605","doi":null,"metadata_source":"pith","pith_arxiv_id":"1806.01605","snapshot_observed_at":"2026-08-14T06:17:33.950972Z","title":"Indices of O-regular variation for weight functions and weight sequences","venue":"math.FA","work_id":"db447f8b-0c2a-4457-aea0-878cfe63020f","year":2018},"citing_paper":{"arxiv_id":"1909.00177","last_updated":"2019-08-31T09:36:38Z","snapshot_observed_at":"2026-08-17T00:04:14.272796Z","submitted_at":"2019-08-31T09:36:38Z","title":"Functions with ultradifferentiable powers","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-14T06:17:33.864742Z"},"links":{"cited_paper":"/paper/1806.01605","citing_paper":"/paper/1909.00177"},"observation_digest":"sha256:0bb893c19d691bebe0eb46641e61dbce015a642aca80fc73344a3e7c92547b35","observation_id":"ebd9d2c6-e82c-4f3e-813b-db69dd28ded8","resolution":{"observed_at":"2026-08-14T06:17:33.954637Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T06:17:34.070386Z","title":", Une C ∞-application non immersive qui possède la propriété univer selle des immersions, Arch","venue":null,"work_id":"c9ba5da5-d609-4f53-a0aa-54c869e54c64","year":1982},"citing_paper":{"arxiv_id":"1909.00177","last_updated":"2019-08-31T09:36:38Z","snapshot_observed_at":"2026-08-17T00:04:14.272796Z","submitted_at":"2019-08-31T09:36:38Z","title":"Functions with ultradifferentiable powers","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-14T06:17:33.868299Z"},"links":{"citing_paper":"/paper/1909.00177"},"observation_digest":"sha256:046b0888672c5ad41a110b74f904d851435f2f3587acd123483d8deff090ef7f","observation_id":"6ca4eb85-bcc2-45b5-bb33-cd9855fab2c7","resolution":{"observed_at":"2026-08-14T06:17:34.074829Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T06:17:34.060193Z","title":", Pseudo-immersions, Ann","venue":null,"work_id":"83e4f1cf-a854-41cb-889a-1687d0fc3c81","year":1987},"citing_paper":{"arxiv_id":"1909.00177","last_updated":"2019-08-31T09:36:38Z","snapshot_observed_at":"2026-08-17T00:04:14.272796Z","submitted_at":"2019-08-31T09:36:38Z","title":"Functions with ultradifferentiable powers","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-14T06:17:33.871877Z"},"links":{"citing_paper":"/paper/1909.00177"},"observation_digest":"sha256:85a68bdeb32e57295ab5208050239912b2e00c4612350d75348ecb5cd1f8ac7a","observation_id":"d58d4ad2-e2dc-4660-816c-29648bbccad4","resolution":{"observed_at":"2026-08-14T06:17:34.064280Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T06:17:34.050807Z","title":", The convenient setting for non-quasianalytic Denjoy-Carleman Diﬀerentiable Mappings , J","venue":null,"work_id":"ed346485-3079-4e79-8255-f79f83ab723c","year":2009},"citing_paper":{"arxiv_id":"1909.00177","last_updated":"2019-08-31T09:36:38Z","snapshot_observed_at":"2026-08-17T00:04:14.272796Z","submitted_at":"2019-08-31T09:36:38Z","title":"Functions with ultradifferentiable powers","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-14T06:17:33.874948Z"},"links":{"citing_paper":"/paper/1909.00177"},"observation_digest":"sha256:72fbc269a5fe3993c2b9fad1e9cdde84a6e814fb7cf1ce156db221a4f95bf5d0","observation_id":"b41da8f6-912a-496b-a45f-9220a01b1154","resolution":{"observed_at":"2026-08-14T06:17:34.054381Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T06:17:34.040711Z","title":", The convenient setting for quasianalytic Denjoy-Carleman Diﬀerentiable Mappings , J","venue":null,"work_id":"8f35a327-f901-4da4-8efc-dd27d78f72dd","year":2011},"citing_paper":{"arxiv_id":"1909.00177","last_updated":"2019-08-31T09:36:38Z","snapshot_observed_at":"2026-08-17T00:04:14.272796Z","submitted_at":"2019-08-31T09:36:38Z","title":"Functions with ultradifferentiable powers","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-14T06:17:33.878224Z"},"links":{"citing_paper":"/paper/1909.00177"},"observation_digest":"sha256:0f76ee0786de40fd52bc23d9c71883e569b8102a5d0a8c4988b9a445d16201ae","observation_id":"527bf527-ab9c-4e4a-83ef-13c6bebc2bea","resolution":{"observed_at":"2026-08-14T06:17:34.044202Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T06:17:34.030690Z","title":"Structure theorems and a character ization, J","venue":null,"work_id":"b5ff0454-a5f1-4aa0-b334-8df84c894db5","year":1973},"citing_paper":{"arxiv_id":"1909.00177","last_updated":"2019-08-31T09:36:38Z","snapshot_observed_at":"2026-08-17T00:04:14.272796Z","submitted_at":"2019-08-31T09:36:38Z","title":"Functions with ultradifferentiable powers","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-14T06:17:33.881481Z"},"links":{"citing_paper":"/paper/1909.00177"},"observation_digest":"sha256:0f8036745ae24f2591080e2064857a1f44c8ad3f2fc4504b3faacfe48b974a16","observation_id":"a6af1c66-81df-437b-a20f-e1149473dd5b","resolution":{"observed_at":"2026-08-14T06:17:34.034194Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1810.10767","last_updated":"2019-03-11T13:14:29Z","snapshot_observed_at":"2026-08-14T18:09:33.185215Z","submitted_at":"2018-10-25T08:36:22Z","title":"Quasianalytic ultradifferentiability cannot be tested in lower dimensions","version":2},"cited_work":{"arxiv_id":"1810.10767","doi":null,"metadata_source":"pith","pith_arxiv_id":"1810.10767","snapshot_observed_at":"2026-08-14T06:17:33.934919Z","title":"Quasianalytic ultradifferentiability cannot be tested in lower dimensions","venue":"math.CA","work_id":"c3804071-be3f-4afb-ae38-29cc73453354","year":2018},"citing_paper":{"arxiv_id":"1909.00177","last_updated":"2019-08-31T09:36:38Z","snapshot_observed_at":"2026-08-17T00:04:14.272796Z","submitted_at":"2019-08-31T09:36:38Z","title":"Functions with ultradifferentiable powers","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-14T06:17:33.884607Z"},"links":{"cited_paper":"/paper/1810.10767","citing_paper":"/paper/1909.00177"},"observation_digest":"sha256:2669896a2220a0bdc2643ea32bf180df1f4085352c3619323a201bbfe087b872","observation_id":"be05d1f0-a50f-4518-8c28-04dce62ed91c","resolution":{"observed_at":"2026-08-14T06:17:33.940337Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T06:17:34.021185Z","title":", Arc-smooth functions on closed sets , Compositio Math","venue":null,"work_id":"c9fa9d2a-4e43-4ab7-9427-f28c95a43170","year":2019},"citing_paper":{"arxiv_id":"1909.00177","last_updated":"2019-08-31T09:36:38Z","snapshot_observed_at":"2026-08-17T00:04:14.272796Z","submitted_at":"2019-08-31T09:36:38Z","title":"Functions with ultradifferentiable powers","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-14T06:17:33.888350Z"},"links":{"citing_paper":"/paper/1909.00177"},"observation_digest":"sha256:e9e34dd30504f00efc287224f1f7a6435ace99c1cac6dfb25e92beeb11168de8","observation_id":"a08d0b22-ed87-4704-b57d-820053bc22df","resolution":{"observed_at":"2026-08-14T06:17:34.024700Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T06:17:34.011454Z","title":", Methods of modern mathematical physics, Vol","venue":null,"work_id":"1b1a94af-0dac-4a76-a361-3f178ec7f4e8","year":1975},"citing_paper":{"arxiv_id":"1909.00177","last_updated":"2019-08-31T09:36:38Z","snapshot_observed_at":"2026-08-17T00:04:14.272796Z","submitted_at":"2019-08-31T09:36:38Z","title":"Functions with ultradifferentiable powers","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-14T06:17:33.891878Z"},"links":{"citing_paper":"/paper/1909.00177"},"observation_digest":"sha256:9d572ece621e50f4ef136797e43008061d3d3af4cb98c5aabbe3f31371d3f685","observation_id":"6a10b728-d07a-4362-82c5-0581c60bd7eb","resolution":{"observed_at":"2026-08-14T06:17:34.014923Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T06:17:34.001079Z","title":", Flat functions in Carleman ultraholomorphic classes via pr oximate orders , J","venue":null,"work_id":"0b973cea-5004-45ab-9930-77db14d16a31","year":2014},"citing_paper":{"arxiv_id":"1909.00177","last_updated":"2019-08-31T09:36:38Z","snapshot_observed_at":"2026-08-17T00:04:14.272796Z","submitted_at":"2019-08-31T09:36:38Z","title":"Functions with ultradifferentiable powers","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-14T06:17:33.895374Z"},"links":{"citing_paper":"/paper/1909.00177"},"observation_digest":"sha256:90f50ee588873623a4acbcc74782d3863dd7f024b5e77ae1436724aeb30b3a24","observation_id":"b06619cd-1a56-4d26-81f4-1cd5c12d0500","resolution":{"observed_at":"2026-08-14T06:17:34.004487Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T06:17:33.990327Z","title":", Germes de détermination inﬁnie dans des classes lisses , Manuscripta Math","venue":null,"work_id":"41b67f3e-20ff-44d2-bbcd-045478b85298","year":1999},"citing_paper":{"arxiv_id":"1909.00177","last_updated":"2019-08-31T09:36:38Z","snapshot_observed_at":"2026-08-17T00:04:14.272796Z","submitted_at":"2019-08-31T09:36:38Z","title":"Functions with ultradifferentiable powers","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-14T06:17:33.898725Z"},"links":{"citing_paper":"/paper/1909.00177"},"observation_digest":"sha256:73b5df1ed8089cdb943166769100ce360a911bdc58dfc1f528aeb16e16714423","observation_id":"09cb9d94-0919-435f-a45e-bb8db03c9300","resolution":{"observed_at":"2026-08-14T06:17:33.994084Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T06:17:33.980875Z","title":", On closed ideals in smooth classes , Math","venue":null,"work_id":"83fcd49c-ebe9-4538-97fe-355416156605","year":2001},"citing_paper":{"arxiv_id":"1909.00177","last_updated":"2019-08-31T09:36:38Z","snapshot_observed_at":"2026-08-17T00:04:14.272796Z","submitted_at":"2019-08-31T09:36:38Z","title":"Functions with ultradifferentiable powers","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-14T06:17:33.901854Z"},"links":{"citing_paper":"/paper/1909.00177"},"observation_digest":"sha256:82e76599d15c9c3ea0b38de328dfbbd6c066028021f3455b3df1be9a2634f7ae","observation_id":"273f1f30-afcf-4abf-8f99-a7308531416d","resolution":{"observed_at":"2026-08-14T06:17:33.984212Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T06:17:33.971158Z","title":", On quasianalytic local rings , Expo","venue":null,"work_id":"48b7e51d-5ebf-43fb-9f4d-f9dfb5bf77c0","year":2008},"citing_paper":{"arxiv_id":"1909.00177","last_updated":"2019-08-31T09:36:38Z","snapshot_observed_at":"2026-08-17T00:04:14.272796Z","submitted_at":"2019-08-31T09:36:38Z","title":"Functions with ultradifferentiable powers","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-14T06:17:33.905239Z"},"links":{"citing_paper":"/paper/1909.00177"},"observation_digest":"sha256:79aa40e3e8c096994f61de0d42f40dbb87d66cf051f018f38e5a7ebaadd1e720","observation_id":"2f27794d-91c3-48bd-8d97-492bb19c10e2","resolution":{"observed_at":"2026-08-14T06:17:33.974604Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T06:17:33.961123Z","title":", Smooth solutions of quasianalytic or ultraholomorphic equ ations, Monatsh","venue":null,"work_id":"a24457d2-af25-494c-bb9c-da8da00627df","year":2010},"citing_paper":{"arxiv_id":"1909.00177","last_updated":"2019-08-31T09:36:38Z","snapshot_observed_at":"2026-08-17T00:04:14.272796Z","submitted_at":"2019-08-31T09:36:38Z","title":"Functions with ultradifferentiable powers","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-14T06:17:33.908292Z"},"links":{"citing_paper":"/paper/1909.00177"},"observation_digest":"sha256:352c85a5ea3f9c2f234afc6e2f8eae7028146ab44c686b04a819264fadcd0ca2","observation_id":"f5d92a69-c2c4-4793-acb7-0a2b06490d76","resolution":{"observed_at":"2026-08-14T06:17:33.964601Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"1909.00177","last_updated":"2019-08-31T09:36:38Z","latest_version":1,"primary_category":"math.CA","snapshot_observed_at":"2026-08-17T00:04:14.272796Z","submitted_at":"2019-08-31T09:36:38Z","title":"Functions with ultradifferentiable powers"},"reference_resolution":{"displayed":24,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":2,"verified_exact":2,"verified_fuzzy":20},"total_outbound_references":24},"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":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"thesis":"As of 17 August 2026, this Paper Citation Record lists 24 of 24 outbound references and 0 inbound Pith citation observations for arXiv:1909.00177."}