{"as_of":"2026-08-16T12:21:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:4c9ad1e1ce484c507d2a849ca8b63c1d7f439aac3734d4cecd03a3a9867d1536","coverage":[{"denominator":19,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":19,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-14T13:30:05.562702Z","state":"measured"},{"denominator":19,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":19,"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/1908.05220/citation-record","integrity":"/paper/1908.05220/integrity","json":"/paper/1908.05220/citation-record.json","paper":"/paper/1908.05220"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:30:05.723673Z","title":"Dismal Arithmetic","venue":null,"work_id":"ee1e8054-d124-479a-a55c-453e58bb084c","year":2011},"citing_paper":{"arxiv_id":"1908.05220","last_updated":"2019-08-14T16:45:32Z","snapshot_observed_at":"2026-08-16T04:42:51.813173Z","submitted_at":"2019-08-14T16:45:32Z","title":"Maximally additively reducible subsets of the integers","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-14T13:30:05.510455Z"},"links":{"citing_paper":"/paper/1908.05220"},"observation_digest":"sha256:6c0858fa955ef7cb18c5715777d790310b54e4b44179ff6c14aa7da306db992d","observation_id":"305c5626-ed7b-4b02-a73e-dcfbfe960040","resolution":{"observed_at":"2026-08-14T13:30:05.726422Z","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":"2026-08-14T13:30:05.716239Z","title":"On the enumeration of certain compositions and related sequences of numbers","venue":null,"work_id":"7941300b-4eae-4095-94e3-93fcc30b6179","year":null},"citing_paper":{"arxiv_id":"1908.05220","last_updated":"2019-08-14T16:45:32Z","snapshot_observed_at":"2026-08-16T04:42:51.813173Z","submitted_at":"2019-08-14T16:45:32Z","title":"Maximally additively reducible subsets of the integers","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-14T13:30:05.514033Z"},"links":{"citing_paper":"/paper/1908.05220"},"observation_digest":"sha256:9bac73ce997d5dc68d36c33c932fdf4e40186e64663f1b11d0606c12e8bee544","observation_id":"89f77cc0-691b-43e0-b1f2-7a6d8d0f6b90","resolution":{"observed_at":"2026-08-14T13:30:05.719314Z","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":"2026-08-14T13:30:05.708897Z","title":"Additive decomposability of multiplicatively deﬁn ed sets","venue":null,"work_id":"5c3d948d-e20f-45a1-93d8-5862840d82a7","year":2006},"citing_paper":{"arxiv_id":"1908.05220","last_updated":"2019-08-14T16:45:32Z","snapshot_observed_at":"2026-08-16T04:42:51.813173Z","submitted_at":"2019-08-14T16:45:32Z","title":"Maximally additively reducible subsets of the integers","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-14T13:30:05.517110Z"},"links":{"citing_paper":"/paper/1908.05220"},"observation_digest":"sha256:29161e528d707c4d1ecd3815fa36809b553df496b0a7049780f8115ac603b9d7","observation_id":"d24e3fd8-6600-44a0-b452-8145b3395388","resolution":{"observed_at":"2026-08-14T13:30:05.711760Z","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":"2026-08-14T13:30:05.701814Z","title":"Sums and products of integers","venue":null,"work_id":"5e88aa0a-b897-41c7-a6ee-c85794012fae","year":1983},"citing_paper":{"arxiv_id":"1908.05220","last_updated":"2019-08-14T16:45:32Z","snapshot_observed_at":"2026-08-16T04:42:51.813173Z","submitted_at":"2019-08-14T16:45:32Z","title":"Maximally additively reducible subsets of the integers","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-14T13:30:05.521236Z"},"links":{"citing_paper":"/paper/1908.05220"},"observation_digest":"sha256:90e9b86e39cf0ed51ecab4caf829295e4a6cfd6499b6fc5dbfc4c734f4446f77","observation_id":"d718ab0c-1095-42b2-8377-6537d53c78ff","resolution":{"observed_at":"2026-08-14T13:30:05.704316Z","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":"2026-08-14T13:30:05.695044Z","title":"On the sequence A079500 and its c ombinatorial interpretations","venue":null,"work_id":"d3000d85-dc97-43b1-a9be-0ba89b1bfffa","year":2006},"citing_paper":{"arxiv_id":"1908.05220","last_updated":"2019-08-14T16:45:32Z","snapshot_observed_at":"2026-08-16T04:42:51.813173Z","submitted_at":"2019-08-14T16:45:32Z","title":"Maximally additively reducible subsets of the integers","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-14T13:30:05.524322Z"},"links":{"citing_paper":"/paper/1908.05220"},"observation_digest":"sha256:668887805d5c51fa7dd6ec6104a0cbab4263bb94a22a4077ce151480574b7b38","observation_id":"65f89ded-8e38-4474-9afe-5977efb0b1b3","resolution":{"observed_at":"2026-08-14T13:30:05.697621Z","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":"2026-08-14T13:30:05.687770Z","title":"Concrete Mathematics","venue":null,"work_id":"792f7e0c-301d-4174-9d53-f9ec2cde0afe","year":1994},"citing_paper":{"arxiv_id":"1908.05220","last_updated":"2019-08-14T16:45:32Z","snapshot_observed_at":"2026-08-16T04:42:51.813173Z","submitted_at":"2019-08-14T16:45:32Z","title":"Maximally additively reducible subsets of the integers","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-14T13:30:05.527320Z"},"links":{"citing_paper":"/paper/1908.05220"},"observation_digest":"sha256:9432384354b26ce6d95b30ee725f8467ad641bd904328af94cd042cb9032129b","observation_id":"91063aba-6e54-4e0a-928e-bb04569b3bde","resolution":{"observed_at":"2026-08-14T13:30:05.690335Z","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":"2026-08-14T13:30:05.680272Z","title":"Primes on the Moon (Lunar Arithmetic)","venue":null,"work_id":"e0b0d947-d547-4e04-8e26-79a748a21fa2","year":2019},"citing_paper":{"arxiv_id":"1908.05220","last_updated":"2019-08-14T16:45:32Z","snapshot_observed_at":"2026-08-16T04:42:51.813173Z","submitted_at":"2019-08-14T16:45:32Z","title":"Maximally additively reducible subsets of the integers","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-14T13:30:05.530328Z"},"links":{"citing_paper":"/paper/1908.05220"},"observation_digest":"sha256:c6e33bde0342d2ed5c9de25a09b71168f4e9da5b5d1cfdb182c1ae458fefe64d","observation_id":"6238506d-7592-49c3-980e-a7f0b487fbf8","resolution":{"observed_at":"2026-08-14T13:30:05.683136Z","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":"2026-08-14T13:30:05.673366Z","title":"Combinatorics of Compositions and Words","venue":null,"work_id":"dd52be41-4dd7-471b-a563-6d347766dd0e","year":2010},"citing_paper":{"arxiv_id":"1908.05220","last_updated":"2019-08-14T16:45:32Z","snapshot_observed_at":"2026-08-16T04:42:51.813173Z","submitted_at":"2019-08-14T16:45:32Z","title":"Maximally additively reducible subsets of the integers","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-14T13:30:05.533258Z"},"links":{"citing_paper":"/paper/1908.05220"},"observation_digest":"sha256:6794e885db2acf07d7f92bb2ee201f16a82f5b58e7f70b1faa403399f3031976","observation_id":"9822d10f-8e42-48df-8557-4619ea699b75","resolution":{"observed_at":"2026-08-14T13:30:05.675883Z","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":"2026-08-14T13:30:05.666221Z","title":"Calculus of Finite Diﬀerences","venue":null,"work_id":"20d8dbaa-1b14-4f90-a1d5-9f0aca270ea6","year":1965},"citing_paper":{"arxiv_id":"1908.05220","last_updated":"2019-08-14T16:45:32Z","snapshot_observed_at":"2026-08-16T04:42:51.813173Z","submitted_at":"2019-08-14T16:45:32Z","title":"Maximally additively reducible subsets of the integers","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-14T13:30:05.536161Z"},"links":{"citing_paper":"/paper/1908.05220"},"observation_digest":"sha256:737a8367f45b38a743e621b00f9ea2c6cabd3df95c87264ba17a8c07ae94bad8","observation_id":"1bd2f4f5-6aa4-4530-881b-dd0ba235c398","resolution":{"observed_at":"2026-08-14T13:30:05.668965Z","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":"2026-08-14T13:30:05.658054Z","title":"Compositions with parts c ontrained by the leading summand","venue":null,"work_id":"afc4f8f0-9022-489d-9197-1a49e4cd7e39","year":2005},"citing_paper":{"arxiv_id":"1908.05220","last_updated":"2019-08-14T16:45:32Z","snapshot_observed_at":"2026-08-16T04:42:51.813173Z","submitted_at":"2019-08-14T16:45:32Z","title":"Maximally additively reducible subsets of the integers","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-14T13:30:05.538770Z"},"links":{"citing_paper":"/paper/1908.05220"},"observation_digest":"sha256:c95328edba0d7b691e97033d0d8b1e47b472098404d29de0fb5e01e8160bf06b","observation_id":"e9329836-c74c-4292-909b-cd056fd113c3","resolution":{"observed_at":"2026-08-14T13:30:05.660787Z","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":"2026-08-14T13:30:05.649735Z","title":"Combinatory Analysis I","venue":null,"work_id":"82608628-b67f-448c-88a0-c83639c4fc8c","year":1915},"citing_paper":{"arxiv_id":"1908.05220","last_updated":"2019-08-14T16:45:32Z","snapshot_observed_at":"2026-08-16T04:42:51.813173Z","submitted_at":"2019-08-14T16:45:32Z","title":"Maximally additively reducible subsets of the integers","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-14T13:30:05.541333Z"},"links":{"citing_paper":"/paper/1908.05220"},"observation_digest":"sha256:a5d9e8856534a96490f3392c58453fe2cde91c222790471bc16476b24ff547d2","observation_id":"3930e71c-ee20-4f2f-a237-4b09e26694fa","resolution":{"observed_at":"2026-08-14T13:30:05.652561Z","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":"2026-08-14T13:30:05.641873Z","title":"Additive Number Theory: The Classical Bases","venue":null,"work_id":"8018c641-5a84-4390-af0b-e705ca13c253","year":1996},"citing_paper":{"arxiv_id":"1908.05220","last_updated":"2019-08-14T16:45:32Z","snapshot_observed_at":"2026-08-16T04:42:51.813173Z","submitted_at":"2019-08-14T16:45:32Z","title":"Maximally additively reducible subsets of the integers","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-14T13:30:05.544054Z"},"links":{"citing_paper":"/paper/1908.05220"},"observation_digest":"sha256:2eb7dda0c7ae4464ba6e3939a2f21907f30fddc110d2bcc37437972704af380f","observation_id":"51c9544a-ce82-4b78-970a-490889811d46","resolution":{"observed_at":"2026-08-14T13:30:05.644523Z","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":"2026-08-14T13:30:05.634141Z","title":"Additive Number Theory: Inverse Problems and the Geometry of Sumsets","venue":null,"work_id":"11aebc49-873a-46b2-a8ee-70cc371d322c","year":1996},"citing_paper":{"arxiv_id":"1908.05220","last_updated":"2019-08-14T16:45:32Z","snapshot_observed_at":"2026-08-16T04:42:51.813173Z","submitted_at":"2019-08-14T16:45:32Z","title":"Maximally additively reducible subsets of the integers","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-14T13:30:05.546774Z"},"links":{"citing_paper":"/paper/1908.05220"},"observation_digest":"sha256:9189420dc5cdff357106403eba8e055a36dfa28761a443c05e89a2d509988f48","observation_id":"5a7fe611-7acc-4d3b-9d3a-58f9182176c8","resolution":{"observed_at":"2026-08-14T13:30:05.637225Z","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":"2026-08-14T13:30:05.626199Z","title":"Additive Zahlentheorie","venue":null,"work_id":"aaa895f1-32bd-4d47-89d0-1d4436954fec","year":1956},"citing_paper":{"arxiv_id":"1908.05220","last_updated":"2019-08-14T16:45:32Z","snapshot_observed_at":"2026-08-16T04:42:51.813173Z","submitted_at":"2019-08-14T16:45:32Z","title":"Maximally additively reducible subsets of the integers","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-14T13:30:05.549171Z"},"links":{"citing_paper":"/paper/1908.05220"},"observation_digest":"sha256:37663c687085e18804f35ead35c3d01033ee0b514eccc47e4a1de59aa412536c","observation_id":"00ef1eab-8761-42f5-958a-c299e059790c","resolution":{"observed_at":"2026-08-14T13:30:05.628858Z","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":"2026-08-14T13:30:05.617864Z","title":"The online encyclopedia of integer sequences","venue":null,"work_id":"4a104ed5-8cb4-461b-8467-e518b1b47688","year":null},"citing_paper":{"arxiv_id":"1908.05220","last_updated":"2019-08-14T16:45:32Z","snapshot_observed_at":"2026-08-16T04:42:51.813173Z","submitted_at":"2019-08-14T16:45:32Z","title":"Maximally additively reducible subsets of the integers","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-14T13:30:05.551800Z"},"links":{"citing_paper":"/paper/1908.05220"},"observation_digest":"sha256:6c93f1481c551c18593bc140662ff211b4196e6da1e6a7fabce233c715dd45b0","observation_id":"d8709bd7-e1b0-4402-8d1f-10a7603d169c","resolution":{"observed_at":"2026-08-14T13:30:05.620723Z","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":"2026-08-14T13:30:05.609147Z","title":"On a generalized compos ition func- tion","venue":null,"work_id":"d7a8a757-f66d-4599-bec7-ddcd19855d02","year":2000},"citing_paper":{"arxiv_id":"1908.05220","last_updated":"2019-08-14T16:45:32Z","snapshot_observed_at":"2026-08-16T04:42:51.813173Z","submitted_at":"2019-08-14T16:45:32Z","title":"Maximally additively reducible subsets of the integers","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-14T13:30:05.554597Z"},"links":{"citing_paper":"/paper/1908.05220"},"observation_digest":"sha256:41d87faa1df2548df768cc5dd6c02aaca694f172adbde4d00dbe214ecaf0932d","observation_id":"423161df-4495-4443-a557-5bb37310c966","resolution":{"observed_at":"2026-08-14T13:30:05.611922Z","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":"2026-08-14T13:30:05.600054Z","title":"Additive Combinatorics","venue":null,"work_id":"0a2ef73f-5a50-455f-8929-30e99acd3f2b","year":2010},"citing_paper":{"arxiv_id":"1908.05220","last_updated":"2019-08-14T16:45:32Z","snapshot_observed_at":"2026-08-16T04:42:51.813173Z","submitted_at":"2019-08-14T16:45:32Z","title":"Maximally additively reducible subsets of the integers","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-14T13:30:05.557140Z"},"links":{"citing_paper":"/paper/1908.05220"},"observation_digest":"sha256:d29d3e57541b5c530b234dd2a1627d67c66b3a2e005360f69540fac2da947b48","observation_id":"e53b17a5-1aac-4523-9ba3-0b2306c2de08","resolution":{"observed_at":"2026-08-14T13:30:05.603218Z","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":"2026-08-14T13:30:05.590661Z","title":"Ein metrischer Satz ber Mengen ganzer Zahle n","venue":null,"work_id":"0d054230-64ec-4c53-bd6e-30a57e757795","year":1953},"citing_paper":{"arxiv_id":"1908.05220","last_updated":"2019-08-14T16:45:32Z","snapshot_observed_at":"2026-08-16T04:42:51.813173Z","submitted_at":"2019-08-14T16:45:32Z","title":"Maximally additively reducible subsets of the integers","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-14T13:30:05.559687Z"},"links":{"citing_paper":"/paper/1908.05220"},"observation_digest":"sha256:715fb43497a8f1b7645afe5ffa030d68dda03a10614cee118ecc8b18c495a334","observation_id":"f47fac13-2468-4c2c-8a90-d6f477c831dd","resolution":{"observed_at":"2026-08-14T13:30:05.593793Z","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":"2026-08-14T13:30:05.580113Z","title":"Solving generalized Fibonacci recurrenc es","venue":null,"work_id":"6571a642-4f8f-4d04-917a-893452dbe971","year":1998},"citing_paper":{"arxiv_id":"1908.05220","last_updated":"2019-08-14T16:45:32Z","snapshot_observed_at":"2026-08-16T04:42:51.813173Z","submitted_at":"2019-08-14T16:45:32Z","title":"Maximally additively reducible subsets of the integers","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-14T13:30:05.562702Z"},"links":{"citing_paper":"/paper/1908.05220"},"observation_digest":"sha256:3bc2224d93bca01e5f0519aa09fcd52ce51d631c0dadcb653416b195bab08c1c","observation_id":"4d7b2b94-838f-41a7-8c39-852de3268e12","resolution":{"observed_at":"2026-08-14T13:30:05.584641Z","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":"1908.05220","last_updated":"2019-08-14T16:45:32Z","latest_version":1,"primary_category":"math.CO","snapshot_observed_at":"2026-08-16T04:42:51.813173Z","submitted_at":"2019-08-14T16:45:32Z","title":"Maximally additively reducible subsets of the integers"},"reference_resolution":{"displayed":19,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":0,"verified_fuzzy":19},"total_outbound_references":19},"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 16 August 2026, this Paper Citation Record lists 19 of 19 outbound references and 0 inbound Pith citation observations for arXiv:1908.05220."}