{"as_of":"2026-08-16T22:38:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:64a1eab1e49a2aca990d3dd3dbf9932de9bcc8369ff3ca67d0d41905bf208755","coverage":[{"denominator":36,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":36,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-14T05:13:46.140766Z","state":"measured"},{"denominator":36,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":36,"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/1909.01935/citation-record","integrity":"/paper/1909.01935/integrity","json":"/paper/1909.01935/citation-record.json","paper":"/paper/1909.01935"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T05:13:46.659980Z","title":"Beckwith, A","venue":null,"work_id":"26f4cd92-a7dc-41db-9277-0d710eb049c8","year":2013},"citing_paper":{"arxiv_id":"1909.01935","last_updated":"2019-09-04T16:49:40Z","snapshot_observed_at":"2026-08-14T05:01:56.546825Z","submitted_at":"2019-09-04T16:49:40Z","title":"Gaps of Summands of the Zeckendorf Lattice","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-14T05:13:45.968945Z"},"links":{"citing_paper":"/paper/1909.01935"},"observation_digest":"sha256:0d71e7121aa79ba68cb5e64ec70f15df3f365dd5afc0454579c8fae5ce79e7b6","observation_id":"f1d3f208-4a8b-4e7d-aefd-b4abf784e377","resolution":{"observed_at":"2026-08-14T05:13:46.663986Z","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":"2026-08-14T05:13:46.646107Z","title":"Ben-Ari, S","venue":null,"work_id":"d0ab4fc8-68a9-4bef-9663-07afb91fbfd6","year":2016},"citing_paper":{"arxiv_id":"1909.01935","last_updated":"2019-09-04T16:49:40Z","snapshot_observed_at":"2026-08-14T05:01:56.546825Z","submitted_at":"2019-09-04T16:49:40Z","title":"Gaps of Summands of the Zeckendorf Lattice","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-14T05:13:45.973290Z"},"links":{"citing_paper":"/paper/1909.01935"},"observation_digest":"sha256:1f58a88bb4aa27a4477841dd4b0b138af1164c986a6549365f0b4a64805ff38c","observation_id":"0397e0df-f53b-474b-aede-8af1649ec516","resolution":{"observed_at":"2026-08-14T05:13:46.650130Z","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":"2026-08-14T05:13:46.633405Z","title":null,"venue":null,"work_id":"a39b77a1-b6ac-47d0-bdbd-a3ea6c97a791","year":2014},"citing_paper":{"arxiv_id":"1909.01935","last_updated":"2019-09-04T16:49:40Z","snapshot_observed_at":"2026-08-14T05:01:56.546825Z","submitted_at":"2019-09-04T16:49:40Z","title":"Gaps of Summands of the Zeckendorf Lattice","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-14T05:13:45.977320Z"},"links":{"citing_paper":"/paper/1909.01935"},"observation_digest":"sha256:e30843f45a3996f43451ccf56ceccc3aeeaf236e04ce88857c4151568cd8d63a","observation_id":"9bdc898e-a454-49b9-b045-624c73c02b3a","resolution":{"observed_at":"2026-08-14T05:13:46.637662Z","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":"2026-08-14T05:13:46.622065Z","title":"Bower, R","venue":null,"work_id":"85d28475-6f0e-4817-9b0d-9a9aa6eba5a5","year":2015},"citing_paper":{"arxiv_id":"1909.01935","last_updated":"2019-09-04T16:49:40Z","snapshot_observed_at":"2026-08-14T05:01:56.546825Z","submitted_at":"2019-09-04T16:49:40Z","title":"Gaps of Summands of the Zeckendorf Lattice","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-14T05:13:45.981979Z"},"links":{"citing_paper":"/paper/1909.01935"},"observation_digest":"sha256:79bc1027c8e1755bf81f7057bd3ff5e422e8a7946604bdda000a99ffe11e6305","observation_id":"7a2b3784-b203-4294-b3ec-3d8789b4db94","resolution":{"observed_at":"2026-08-14T05:13:46.626103Z","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":"2026-08-14T05:13:46.610616Z","title":null,"venue":null,"work_id":"212107f9-bc14-4d43-bbc5-3d6b5426e8b4","year":1964},"citing_paper":{"arxiv_id":"1909.01935","last_updated":"2019-09-04T16:49:40Z","snapshot_observed_at":"2026-08-14T05:01:56.546825Z","submitted_at":"2019-09-04T16:49:40Z","title":"Gaps of Summands of the Zeckendorf Lattice","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-14T05:13:45.986215Z"},"links":{"citing_paper":"/paper/1909.01935"},"observation_digest":"sha256:d3a9cad393f93f2d282458389bf1cec43018cf3f6973771ebc3d9c81f1e12f3f","observation_id":"506e6c0b-8ab8-4f20-ba93-5d81c7444ec5","resolution":{"observed_at":"2026-08-14T05:13:46.614799Z","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":"2026-08-14T05:13:46.599630Z","title":null,"venue":null,"work_id":"83739f5b-2118-4757-9f56-27bd6aca6d35","year":null},"citing_paper":{"arxiv_id":"1909.01935","last_updated":"2019-09-04T16:49:40Z","snapshot_observed_at":"2026-08-14T05:01:56.546825Z","submitted_at":"2019-09-04T16:49:40Z","title":"Gaps of Summands of the Zeckendorf Lattice","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-14T05:13:45.990842Z"},"links":{"citing_paper":"/paper/1909.01935"},"observation_digest":"sha256:1c83536d8c2c2f6aaa49b83e14a5df10e5400c6725e385923adb5e37fc1cf52d","observation_id":"c509b616-6e8d-4002-be61-4de0a188e69f","resolution":{"observed_at":"2026-08-14T05:13:46.603365Z","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":"2026-08-14T05:13:46.586353Z","title":"Catral, P","venue":null,"work_id":"f87e522c-9265-4f34-a967-ddc7e48fc33d","year":2014},"citing_paper":{"arxiv_id":"1909.01935","last_updated":"2019-09-04T16:49:40Z","snapshot_observed_at":"2026-08-14T05:01:56.546825Z","submitted_at":"2019-09-04T16:49:40Z","title":"Gaps of Summands of the Zeckendorf Lattice","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-14T05:13:45.995785Z"},"links":{"citing_paper":"/paper/1909.01935"},"observation_digest":"sha256:7ecbab0a9f01e5468009382ce41e1af68789b2f858a14029a2685f49d5c689b7","observation_id":"76cb20d9-5d05-43fb-a81c-41631b57587b","resolution":{"observed_at":"2026-08-14T05:13:46.590732Z","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":"2026-08-14T05:13:46.572397Z","title":"Catral, P","venue":null,"work_id":"b49f56ce-bc59-4de9-9907-c200bc937a25","year":2016},"citing_paper":{"arxiv_id":"1909.01935","last_updated":"2019-09-04T16:49:40Z","snapshot_observed_at":"2026-08-14T05:01:56.546825Z","submitted_at":"2019-09-04T16:49:40Z","title":"Gaps of Summands of the Zeckendorf Lattice","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-14T05:13:46.000966Z"},"links":{"citing_paper":"/paper/1909.01935"},"observation_digest":"sha256:7b35580838fa19a682aaa719949aa70a5c04c4764f15ca35343f36708392dade","observation_id":"2cc166c5-685d-4600-8821-abfc01218306","resolution":{"observed_at":"2026-08-14T05:13:46.576427Z","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":"1606.09309","last_updated":"2016-07-01T15:46:15Z","snapshot_observed_at":"2026-08-14T21:50:31.844374Z","submitted_at":"2016-06-29T23:51:05Z","title":"New Behavior in Legal Decompositions Arising from Non-positive Linear Recurrences","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1606.09309","snapshot_observed_at":"2026-08-14T05:13:46.007156Z","title":"Catral, P","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"1909.01935","last_updated":"2019-09-04T16:49:40Z","snapshot_observed_at":"2026-08-14T05:01:56.546825Z","submitted_at":"2019-09-04T16:49:40Z","title":"Gaps of Summands of the Zeckendorf Lattice","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-14T05:13:46.007156Z"},"links":{"cited_paper":"/paper/1606.09309","citing_paper":"/paper/1909.01935"},"observation_digest":"sha256:d03c959f4a8d7a24241ea124c9a5ff4eaa80449b383271ad3d208d2d64a9849b","observation_id":"4cd86519-f5f2-4a93-8826-8ba175b6b7f1","resolution":{"observed_at":"2026-08-14T05:13:46.007156Z","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":"2026-08-14T05:13:46.559995Z","title":null,"venue":null,"work_id":"92e11ecb-819f-454a-bdc8-4f474adeebcc","year":1960},"citing_paper":{"arxiv_id":"1909.01935","last_updated":"2019-09-04T16:49:40Z","snapshot_observed_at":"2026-08-14T05:01:56.546825Z","submitted_at":"2019-09-04T16:49:40Z","title":"Gaps of Summands of the Zeckendorf Lattice","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-14T05:13:46.013498Z"},"links":{"citing_paper":"/paper/1909.01935"},"observation_digest":"sha256:eda482efe291bde9b25fa37eab5b625b228a995f6ba5b49e4418446b071659a9","observation_id":"b18f0287-345f-4cce-9f5b-3ad1a5ac2917","resolution":{"observed_at":"2026-08-14T05:13:46.564597Z","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":"2026-08-14T05:13:46.544975Z","title":"Demontigny, T","venue":null,"work_id":"07632d18-3951-41ba-aee8-77ac717ecdd7","year":2014},"citing_paper":{"arxiv_id":"1909.01935","last_updated":"2019-09-04T16:49:40Z","snapshot_observed_at":"2026-08-14T05:01:56.546825Z","submitted_at":"2019-09-04T16:49:40Z","title":"Gaps of Summands of the Zeckendorf Lattice","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-14T05:13:46.018548Z"},"links":{"citing_paper":"/paper/1909.01935"},"observation_digest":"sha256:b0447145202edff008bec1502e44ef69014133a12e6ed02482d757073dde7577","observation_id":"fd2bad64-949a-48d0-b7b1-9d3350db10c8","resolution":{"observed_at":"2026-08-14T05:13:46.549135Z","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":"2026-08-14T05:13:46.530229Z","title":"Dorward, P","venue":null,"work_id":"df0ce91a-b6bb-45a3-ae54-bd3e6c543a74","year":2017},"citing_paper":{"arxiv_id":"1909.01935","last_updated":"2019-09-04T16:49:40Z","snapshot_observed_at":"2026-08-14T05:01:56.546825Z","submitted_at":"2019-09-04T16:49:40Z","title":"Gaps of Summands of the Zeckendorf Lattice","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-14T05:13:46.028092Z"},"links":{"citing_paper":"/paper/1909.01935"},"observation_digest":"sha256:7f0aac5fcc343d4034df16d8e4351d76e8daaee830e73e2b8e69caf647ade82d","observation_id":"3896f894-5798-417d-89a5-ffee1b4da940","resolution":{"observed_at":"2026-08-14T05:13:46.536059Z","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":"2026-08-14T05:13:46.516104Z","title":"Drmota and J","venue":null,"work_id":"8d722a25-4834-4e6f-ae85-5a1f8da5a6b5","year":1998},"citing_paper":{"arxiv_id":"1909.01935","last_updated":"2019-09-04T16:49:40Z","snapshot_observed_at":"2026-08-14T05:01:56.546825Z","submitted_at":"2019-09-04T16:49:40Z","title":"Gaps of Summands of the Zeckendorf Lattice","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-14T05:13:46.032793Z"},"links":{"citing_paper":"/paper/1909.01935"},"observation_digest":"sha256:5dcda34ac4472501c31c8eb43d0f2bcf56c84383a194def6cbe770726ebbb41a","observation_id":"c205adee-307c-49d1-b554-327a29f0610e","resolution":{"observed_at":"2026-08-14T05:13:46.520723Z","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":"2026-08-14T05:13:46.501467Z","title":"Eger, Stirling's Approximation for Central Extended Binomial Coefficients, American Mathematical Monthly, 121 (2014), no","venue":null,"work_id":"7a496ff3-cdc5-4c24-ab80-83c842f7a6c6","year":2014},"citing_paper":{"arxiv_id":"1909.01935","last_updated":"2019-09-04T16:49:40Z","snapshot_observed_at":"2026-08-14T05:01:56.546825Z","submitted_at":"2019-09-04T16:49:40Z","title":"Gaps of Summands of the Zeckendorf Lattice","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-14T05:13:46.037470Z"},"links":{"citing_paper":"/paper/1909.01935"},"observation_digest":"sha256:0f3ebf97792b8c7a17cf64275279db1aeea445b51cfa62104c13f2127a6922cd","observation_id":"39770fbf-443c-4e09-827e-e838e3c39cca","resolution":{"observed_at":"2026-08-14T05:13:46.506759Z","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":"1906.10645","last_updated":"2020-05-21T19:35:15Z","snapshot_observed_at":"2026-08-16T20:08:30.126040Z","submitted_at":"2019-06-25T16:37:28Z","title":"Central Limit Theorems for Compound Paths on the 2-Dimensional Lattice","version":2},"cited_work":{"arxiv_id":"1906.10645","doi":null,"metadata_source":"pith","pith_arxiv_id":"1906.10645","snapshot_observed_at":"2026-08-14T05:13:46.199590Z","title":"Central Limit Theorems for Compound Paths on the 2-Dimensional Lattice","venue":"math.NT","work_id":"17391e12-c131-4386-b2fc-f2cb544f7386","year":2019},"citing_paper":{"arxiv_id":"1909.01935","last_updated":"2019-09-04T16:49:40Z","snapshot_observed_at":"2026-08-14T05:01:56.546825Z","submitted_at":"2019-09-04T16:49:40Z","title":"Gaps of Summands of the Zeckendorf Lattice","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-14T05:13:46.042546Z"},"links":{"cited_paper":"/paper/1906.10645","citing_paper":"/paper/1909.01935"},"observation_digest":"sha256:9695777c5b0d27611642ba9b60496f115e3e9a9682d19319411b038c1692443f","observation_id":"78a06959-e8ac-4e70-8f01-a76636c4272a","resolution":{"observed_at":"2026-08-14T05:13:46.203746Z","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":"2026-08-14T05:13:46.488642Z","title":"Filipponi, P","venue":null,"work_id":"dc00242e-97e2-4034-b0ff-0cb2ad045e5d","year":1994},"citing_paper":{"arxiv_id":"1909.01935","last_updated":"2019-09-04T16:49:40Z","snapshot_observed_at":"2026-08-14T05:01:56.546825Z","submitted_at":"2019-09-04T16:49:40Z","title":"Gaps of Summands of the Zeckendorf Lattice","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-14T05:13:46.048280Z"},"links":{"citing_paper":"/paper/1909.01935"},"observation_digest":"sha256:b783c11a04968cc595575eb39e04d40fb587f4c9f26b29a22dbb0728d7e163f9","observation_id":"7f37a2e2-c74a-49b4-9ec8-2f6f883d60fd","resolution":{"observed_at":"2026-08-14T05:13:46.492686Z","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":"2026-08-14T05:13:46.474407Z","title":null,"venue":null,"work_id":"cf5df2e7-60d2-4c30-9f76-5c0f24496d17","year":1985},"citing_paper":{"arxiv_id":"1909.01935","last_updated":"2019-09-04T16:49:40Z","snapshot_observed_at":"2026-08-14T05:01:56.546825Z","submitted_at":"2019-09-04T16:49:40Z","title":"Gaps of Summands of the Zeckendorf Lattice","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-14T05:13:46.053076Z"},"links":{"citing_paper":"/paper/1909.01935"},"observation_digest":"sha256:6bfe1962a1e66fdbbf21302614ef96e1901666935837c37708cc2d3bc73f9f9d","observation_id":"bed51976-1118-4636-9f4b-ee827282a15f","resolution":{"observed_at":"2026-08-14T05:13:46.479613Z","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":"2026-08-14T05:13:46.461354Z","title":"Gordon, M","venue":null,"work_id":"c54ec0de-b4f1-4500-af0f-9050564203f9","year":1986},"citing_paper":{"arxiv_id":"1909.01935","last_updated":"2019-09-04T16:49:40Z","snapshot_observed_at":"2026-08-14T05:01:56.546825Z","submitted_at":"2019-09-04T16:49:40Z","title":"Gaps of Summands of the Zeckendorf Lattice","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-14T05:13:46.057937Z"},"links":{"citing_paper":"/paper/1909.01935"},"observation_digest":"sha256:5abcce2773b2f327195e629ccf065925e1f0769eb65df4efe05e0a5a74fc240b","observation_id":"ff1130bd-3532-49f0-b68e-0e3a6d97ded8","resolution":{"observed_at":"2026-08-14T05:13:46.465750Z","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":"2026-08-14T05:13:46.448305Z","title":null,"venue":null,"work_id":"00f19062-3e2a-4142-9ecf-e94e34fa9369","year":1994},"citing_paper":{"arxiv_id":"1909.01935","last_updated":"2019-09-04T16:49:40Z","snapshot_observed_at":"2026-08-14T05:01:56.546825Z","submitted_at":"2019-09-04T16:49:40Z","title":"Gaps of Summands of the Zeckendorf Lattice","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-14T05:13:46.062590Z"},"links":{"citing_paper":"/paper/1909.01935"},"observation_digest":"sha256:8d224f80d036b05fe3bfc19ab67f59483eb847410f13a366212ae8893aa506e6","observation_id":"a3410c39-9106-4da2-9689-792e046167ff","resolution":{"observed_at":"2026-08-14T05:13:46.452151Z","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":"2026-08-14T05:13:46.435395Z","title":"Hamlin, Representing Positive Integers as a Sum of Linear Recurrence Sequences, Fibonacci Quarterly 50 (2012), no","venue":null,"work_id":"07f2534a-ba5a-4986-9ff0-4d6f1a9e07f8","year":2012},"citing_paper":{"arxiv_id":"1909.01935","last_updated":"2019-09-04T16:49:40Z","snapshot_observed_at":"2026-08-14T05:01:56.546825Z","submitted_at":"2019-09-04T16:49:40Z","title":"Gaps of Summands of the Zeckendorf Lattice","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-14T05:13:46.067219Z"},"links":{"citing_paper":"/paper/1909.01935"},"observation_digest":"sha256:52f903d62a291cb0dc7af2faf2007b66d4744b80bce83670218740b9fb3021ce","observation_id":"d87737e0-7a3c-49d3-a5c3-fe247b7149dc","resolution":{"observed_at":"2026-08-14T05:13:46.439926Z","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":"2026-08-14T05:13:46.416879Z","title":null,"venue":null,"work_id":"eeb9b900-cf7d-46bc-bd7f-8120eeda26d4","year":1972},"citing_paper":{"arxiv_id":"1909.01935","last_updated":"2019-09-04T16:49:40Z","snapshot_observed_at":"2026-08-14T05:01:56.546825Z","submitted_at":"2019-09-04T16:49:40Z","title":"Gaps of Summands of the Zeckendorf Lattice","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-14T05:13:46.071164Z"},"links":{"citing_paper":"/paper/1909.01935"},"observation_digest":"sha256:a23ffb190c1b4e348ba8aa6217211b586ca92c1155c168fb6041566fc8587e46","observation_id":"b3fb3ef6-acf7-4592-8379-f54cb0db8a32","resolution":{"observed_at":"2026-08-14T05:13:46.423226Z","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":"2026-08-14T05:13:46.402580Z","title":"Hamlin and W","venue":null,"work_id":"25464c0e-79de-4b51-80a7-e746e34ff3b4","year":2012},"citing_paper":{"arxiv_id":"1909.01935","last_updated":"2019-09-04T16:49:40Z","snapshot_observed_at":"2026-08-14T05:01:56.546825Z","submitted_at":"2019-09-04T16:49:40Z","title":"Gaps of Summands of the Zeckendorf Lattice","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-14T05:13:46.075640Z"},"links":{"citing_paper":"/paper/1909.01935"},"observation_digest":"sha256:65a75c388dc689507393c7e59c8a5487023375fe5cc995d550dd95ab8f4d9b41","observation_id":"7296287a-2d59-4ee6-9ace-f9c5d61677af","resolution":{"observed_at":"2026-08-14T05:13:46.408731Z","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":"2026-08-14T05:13:46.389208Z","title":null,"venue":null,"work_id":"11f2fb03-b4e4-4b2b-b855-f38898dc468a","year":1972},"citing_paper":{"arxiv_id":"1909.01935","last_updated":"2019-09-04T16:49:40Z","snapshot_observed_at":"2026-08-14T05:01:56.546825Z","submitted_at":"2019-09-04T16:49:40Z","title":"Gaps of Summands of the Zeckendorf Lattice","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-14T05:13:46.079908Z"},"links":{"citing_paper":"/paper/1909.01935"},"observation_digest":"sha256:f595670c3c1d426efbeb756e0035ad6d659f2dba2dfba696736638c415fd772e","observation_id":"f6e1dab0-d398-427d-a738-f2964cf67d0e","resolution":{"observed_at":"2026-08-14T05:13:46.393315Z","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":"2026-08-14T05:13:46.376665Z","title":"Kologlu, G","venue":null,"work_id":"8ff37aa9-8a5c-4113-9d95-a8b7636016d9","year":2011},"citing_paper":{"arxiv_id":"1909.01935","last_updated":"2019-09-04T16:49:40Z","snapshot_observed_at":"2026-08-14T05:01:56.546825Z","submitted_at":"2019-09-04T16:49:40Z","title":"Gaps of Summands of the Zeckendorf Lattice","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-14T05:13:46.083769Z"},"links":{"citing_paper":"/paper/1909.01935"},"observation_digest":"sha256:7ca97fe5301cc166368bf66f64649f181ab69d2f6635f5ade45a90657f37ab1a","observation_id":"dc4c76fc-f763-46b3-b406-3e92dde54220","resolution":{"observed_at":"2026-08-14T05:13:46.380953Z","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":"2026-08-14T05:13:46.363359Z","title":"Lamberger and J","venue":null,"work_id":"c1dc1cb6-1a57-4eb0-94da-9489b9ccfb73","year":2003},"citing_paper":{"arxiv_id":"1909.01935","last_updated":"2019-09-04T16:49:40Z","snapshot_observed_at":"2026-08-14T05:01:56.546825Z","submitted_at":"2019-09-04T16:49:40Z","title":"Gaps of Summands of the Zeckendorf Lattice","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-14T05:13:46.088287Z"},"links":{"citing_paper":"/paper/1909.01935"},"observation_digest":"sha256:80cdb03aadcb15bda70d52a86cf996b4df58b686cf69de2d3cc12be837e6bd31","observation_id":"e75523fc-dc4d-451b-8381-5d8f71e0bb7d","resolution":{"observed_at":"2026-08-14T05:13:46.368393Z","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":"2026-08-14T05:13:46.351030Z","title":null,"venue":null,"work_id":"d3c4e524-741c-41eb-b304-ed21faf602f7","year":1951},"citing_paper":{"arxiv_id":"1909.01935","last_updated":"2019-09-04T16:49:40Z","snapshot_observed_at":"2026-08-14T05:01:56.546825Z","submitted_at":"2019-09-04T16:49:40Z","title":"Gaps of Summands of the Zeckendorf Lattice","version":1},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-14T05:13:46.092775Z"},"links":{"citing_paper":"/paper/1909.01935"},"observation_digest":"sha256:14e4fd3369b8e23b7a061286309b20d9c761b5f3118dfa5d5b0c2c7adc54c2ed","observation_id":"deb791f1-2d69-4d44-bed8-8505b74f3d2b","resolution":{"observed_at":"2026-08-14T05:13:46.354572Z","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":"2026-08-14T05:13:46.339134Z","title":"Lengyel, A Counting Based Proof of the Generalized Zeckendorf's Theorem, Fibonacci Quarterly 44 (2006), no","venue":null,"work_id":"5e69de90-d6ce-4b65-9c76-6bfe728a4fd0","year":2006},"citing_paper":{"arxiv_id":"1909.01935","last_updated":"2019-09-04T16:49:40Z","snapshot_observed_at":"2026-08-14T05:01:56.546825Z","submitted_at":"2019-09-04T16:49:40Z","title":"Gaps of Summands of the Zeckendorf Lattice","version":1},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-14T05:13:46.097273Z"},"links":{"citing_paper":"/paper/1909.01935"},"observation_digest":"sha256:bbd19d5d9cf216386eb9a0b23672a1490d834f243a1278f1c1edf14d135e9d3c","observation_id":"dcdd9b4d-41f5-41d6-88d0-7b806a16b096","resolution":{"observed_at":"2026-08-14T05:13:46.342935Z","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":"2026-08-14T05:13:46.326922Z","title":"Li and S","venue":null,"work_id":"3f2b52ad-8930-40a3-860b-3cf474c77535","year":2017},"citing_paper":{"arxiv_id":"1909.01935","last_updated":"2019-09-04T16:49:40Z","snapshot_observed_at":"2026-08-14T05:01:56.546825Z","submitted_at":"2019-09-04T16:49:40Z","title":"Gaps of Summands of the Zeckendorf Lattice","version":1},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-08-14T05:13:46.101911Z"},"links":{"citing_paper":"/paper/1909.01935"},"observation_digest":"sha256:7cac12151151a7641543c039114ab7bfe28a892faa3be66466d05f4bf7d29de3","observation_id":"f95ab015-bfd1-407f-b2fd-6c425907a241","resolution":{"observed_at":"2026-08-14T05:13:46.330951Z","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":"1606.08110","last_updated":"2016-07-27T20:17:17Z","snapshot_observed_at":"2026-08-14T21:51:05.789229Z","submitted_at":"2016-06-27T02:00:17Z","title":"Central Limit Theorems for Gaps of Generalized Zeckendorf Decompositions","version":2},"cited_work":{"arxiv_id":"1606.08110","doi":null,"metadata_source":"pith","pith_arxiv_id":"1606.08110","snapshot_observed_at":"2026-08-14T05:13:46.176414Z","title":"Central Limit Theorems for Gaps of Generalized Zeckendorf Decompositions","venue":"math.NT","work_id":"1d407479-a04e-4b09-bd95-b9ba05d7cb40","year":2016},"citing_paper":{"arxiv_id":"1909.01935","last_updated":"2019-09-04T16:49:40Z","snapshot_observed_at":"2026-08-14T05:01:56.546825Z","submitted_at":"2019-09-04T16:49:40Z","title":"Gaps of Summands of the Zeckendorf Lattice","version":1},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-08-14T05:13:46.107147Z"},"links":{"cited_paper":"/paper/1606.08110","citing_paper":"/paper/1909.01935"},"observation_digest":"sha256:ba2996148fa48610cfd20c9e6e5caa9e14544a0b709f9275d9c8806fbf3b34fa","observation_id":"f4e1ff9c-525d-4cae-b984-9e63fb893499","resolution":{"observed_at":"2026-08-14T05:13:46.183996Z","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":"2026-08-14T05:13:46.313219Z","title":null,"venue":null,"work_id":"40aca514-8045-4024-9c6b-2c36b31249e1","year":2017},"citing_paper":{"arxiv_id":"1909.01935","last_updated":"2019-09-04T16:49:40Z","snapshot_observed_at":"2026-08-14T05:01:56.546825Z","submitted_at":"2019-09-04T16:49:40Z","title":"Gaps of Summands of the Zeckendorf Lattice","version":1},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-08-14T05:13:46.112427Z"},"links":{"citing_paper":"/paper/1909.01935"},"observation_digest":"sha256:b5455d9f3a543ca16d12ab54c2aaea72137f6ded2209b8323ef8d565c381fcb5","observation_id":"756f8fab-3958-4fc7-a884-5ea24239c08a","resolution":{"observed_at":"2026-08-14T05:13:46.317496Z","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":"2026-08-14T05:13:46.298532Z","title":"Miller, Y","venue":null,"work_id":"4f7b83b5-1837-4c20-a249-dcee09d2dac3","year":2012},"citing_paper":{"arxiv_id":"1909.01935","last_updated":"2019-09-04T16:49:40Z","snapshot_observed_at":"2026-08-14T05:01:56.546825Z","submitted_at":"2019-09-04T16:49:40Z","title":"Gaps of Summands of the Zeckendorf Lattice","version":1},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-08-14T05:13:46.116918Z"},"links":{"citing_paper":"/paper/1909.01935"},"observation_digest":"sha256:0ca63cf87445d1cbb510ec7e909f3d9ddc5444bcd08cc7af8ee95e51631bee9d","observation_id":"d23f829a-6891-4e8c-a7c2-e33bafb93bc0","resolution":{"observed_at":"2026-08-14T05:13:46.303688Z","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":"2026-08-14T05:13:46.284192Z","title":"Miller, Y","venue":null,"work_id":"2a8db2ea-b460-44a4-802f-2989846189c7","year":2014},"citing_paper":{"arxiv_id":"1909.01935","last_updated":"2019-09-04T16:49:40Z","snapshot_observed_at":"2026-08-14T05:01:56.546825Z","submitted_at":"2019-09-04T16:49:40Z","title":"Gaps of Summands of the Zeckendorf Lattice","version":1},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-08-14T05:13:46.121385Z"},"links":{"citing_paper":"/paper/1909.01935"},"observation_digest":"sha256:438d707caa28eb23eeb193948f186c0e028d879e6561bff7114abed64b943176","observation_id":"16333102-72c1-49b6-b993-aa431c69911d","resolution":{"observed_at":"2026-08-14T05:13:46.288714Z","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":"2026-08-14T05:13:46.271296Z","title":null,"venue":null,"work_id":"86eb69ee-c5ce-4135-b3c4-abb08b3ae7b4","year":1990},"citing_paper":{"arxiv_id":"1909.01935","last_updated":"2019-09-04T16:49:40Z","snapshot_observed_at":"2026-08-14T05:01:56.546825Z","submitted_at":"2019-09-04T16:49:40Z","title":"Gaps of Summands of the Zeckendorf Lattice","version":1},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-08-14T05:13:46.125845Z"},"links":{"citing_paper":"/paper/1909.01935"},"observation_digest":"sha256:e7f06a61783950620f84a58ed22a2b5f18b53e53fb7ac7898c91207dee611ca3","observation_id":"041c95c2-6113-43b0-89a3-daf947a2e06f","resolution":{"observed_at":"2026-08-14T05:13:46.275237Z","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":"2026-08-14T05:13:46.257362Z","title":"Steiner, Parry expansions of polynomial sequences, Integers, 2 (2002), Paper A14","venue":null,"work_id":"d76a2608-beb8-4abb-9c9a-9c61ce8b42ef","year":2002},"citing_paper":{"arxiv_id":"1909.01935","last_updated":"2019-09-04T16:49:40Z","snapshot_observed_at":"2026-08-14T05:01:56.546825Z","submitted_at":"2019-09-04T16:49:40Z","title":"Gaps of Summands of the Zeckendorf Lattice","version":1},"reference_index":34,"source":"arxiv_source","source_observed_at":"2026-08-14T05:13:46.131377Z"},"links":{"citing_paper":"/paper/1909.01935"},"observation_digest":"sha256:a6b82f5e4eb643c9ca1fe08126760e8fac893c93b24accbaf8e03ce0f19c08e5","observation_id":"67d20905-c3ea-4adf-87a0-3cf42c45dcee","resolution":{"observed_at":"2026-08-14T05:13:46.261863Z","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":"2026-08-14T05:13:46.242712Z","title":"Steiner, The Joint Distribution of Greedy and Lazy Fibonacci Expansions, Fibonacci Quarterly, 43 (2005), 60--69","venue":null,"work_id":"e435bfd2-2ad2-4687-b76e-6579b1ed4156","year":2005},"citing_paper":{"arxiv_id":"1909.01935","last_updated":"2019-09-04T16:49:40Z","snapshot_observed_at":"2026-08-14T05:01:56.546825Z","submitted_at":"2019-09-04T16:49:40Z","title":"Gaps of Summands of the Zeckendorf Lattice","version":1},"reference_index":35,"source":"arxiv_source","source_observed_at":"2026-08-14T05:13:46.136232Z"},"links":{"citing_paper":"/paper/1909.01935"},"observation_digest":"sha256:e11281a4c11b0f919f58cbe1a0c870c88ae0b67603a1814ba480008183b04803","observation_id":"342e82c4-e35c-4e16-8805-30e828197fc3","resolution":{"observed_at":"2026-08-14T05:13:46.247696Z","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":"2026-08-14T05:13:46.228395Z","title":null,"venue":null,"work_id":"31bd3052-a39a-476d-ae89-590737b450d1","year":1972},"citing_paper":{"arxiv_id":"1909.01935","last_updated":"2019-09-04T16:49:40Z","snapshot_observed_at":"2026-08-14T05:01:56.546825Z","submitted_at":"2019-09-04T16:49:40Z","title":"Gaps of Summands of the Zeckendorf Lattice","version":1},"reference_index":36,"source":"arxiv_source","source_observed_at":"2026-08-14T05:13:46.140766Z"},"links":{"citing_paper":"/paper/1909.01935"},"observation_digest":"sha256:8784b5fea9acc5b81fee7e39e80fb7cb9aacdcb8830a586aa263849c402e1c04","observation_id":"bc99419a-6f08-41c3-a6a2-dcce38c68cc5","resolution":{"observed_at":"2026-08-14T05:13:46.232786Z","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"}}],"paper":{"arxiv_id":"1909.01935","last_updated":"2019-09-04T16:49:40Z","latest_version":1,"primary_category":"math.NT","snapshot_observed_at":"2026-08-14T05:01:56.546825Z","submitted_at":"2019-09-04T16:49:40Z","title":"Gaps of Summands of the Zeckendorf Lattice"},"reference_resolution":{"displayed":36,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":13,"verified_exact":2,"verified_fuzzy":21},"total_outbound_references":36},"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 36 of 36 outbound references and 0 inbound Pith citation observations for arXiv:1909.01935."}