{"as_of":"2026-08-14T13:09:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:ba8d7e7c3aeb6ea4513684de6a43d0335c7e76d240eea377dc8edb016a05fb35","coverage":[{"denominator":32,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":32,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-10T21:34:00.728056Z","state":"measured"},{"denominator":34,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":34,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-14T06:32:32.682623+00:00","state":"measured"},{"denominator":2,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":2,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-11T00:30:45.115254Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-07-04T19:30:07.618503Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2501.04990","last_updated":"2025-01-09T06:10:57Z","snapshot_observed_at":"2026-08-14T02:06:09.285801Z","submitted_at":"2025-01-09T06:10:57Z","title":"On the ascent of almost and quasi-atomicity to monoid semidomains","version":1},"cited_work":{"arxiv_id":"2501.04990","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2501.04990","snapshot_observed_at":"2026-07-04T19:30:07.618503Z","title":"Gonzalez, F","venue":null,"work_id":"c7ea40b9-ffc3-4fa2-89f9-3a8fdb38f3c2","year":null},"citing_paper":{"arxiv_id":"2606.25227","last_updated":"2026-06-23T23:08:04Z","snapshot_observed_at":"2026-08-06T15:39:21.037237Z","submitted_at":"2026-06-23T23:08:04Z","title":"On near atomicity and a characterization of the FF property","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-06-25T21:17:27.384336Z"},"links":{"cited_paper":"/paper/2501.04990","citing_paper":"/paper/2606.25227"},"observation_digest":"sha256:4a6f633e009ddba060c35812a9fa0bd397543e15a7a1f9cdcb0311bf366cbbab","observation_id":"0d473e30-7934-4add-b60e-f3afcd686038","resolution":{"observed_at":"2026-07-04T19:30:07.619802Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2501.04990","last_updated":"2025-01-09T06:10:57Z","snapshot_observed_at":"2026-08-14T02:06:09.285801Z","submitted_at":"2025-01-09T06:10:57Z","title":"On the ascent of almost and quasi-atomicity to monoid semidomains","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2501.04990","snapshot_observed_at":"2026-08-11T00:30:45.115254Z","title":"On the ascent of almost and quasi-atomicity to monoid semidomains, 2025.https://arxiv.org/abs/2501.04990","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.07741","last_updated":"2026-08-07T20:13:45Z","snapshot_observed_at":"2026-08-14T12:29:12.565553Z","submitted_at":"2026-08-07T20:13:45Z","title":"(Locally) Associated Subrings in Polynomial and Power Series Extensions","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-11T00:30:45.115254Z"},"links":{"cited_paper":"/paper/2501.04990","citing_paper":"/paper/2608.07741"},"observation_digest":"sha256:d8a3ee46be4d0f095466eb19b6617f9b97a0f4890e2534969d8c7d1f19e86674","observation_id":"307b7e1d-b995-45a0-a09a-3502040a8d06","resolution":{"observed_at":"2026-08-11T00:30:45.115254Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2501.04990/citation-record","integrity":"/paper/2501.04990/integrity","json":"/paper/2501.04990/citation-record.json","paper":"/paper/2501.04990"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T21:34:01.033409Z","title":null,"venue":null,"work_id":"ca58c23b-8fd0-4a98-8ce2-7314d794e361","year":1990},"citing_paper":{"arxiv_id":"2501.04990","last_updated":"2025-01-09T06:10:57Z","snapshot_observed_at":"2026-08-14T02:06:09.285801Z","submitted_at":"2025-01-09T06:10:57Z","title":"On the ascent of almost and quasi-atomicity to monoid semidomains","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-10T21:34:00.630241Z"},"links":{"citing_paper":"/paper/2501.04990"},"observation_digest":"sha256:d9208a23a0862f102a82b7a4d8e4cabb5c6e6eb94b63ead2820ae7f0d93cd798","observation_id":"fbf56b26-c173-4ad1-a367-95c1ca716b1e","resolution":{"observed_at":"2026-08-10T21:34:01.036653Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T21:34:01.024805Z","title":null,"venue":null,"work_id":"30f917c2-1892-412c-b8f3-fd8f69457c66","year":2022},"citing_paper":{"arxiv_id":"2501.04990","last_updated":"2025-01-09T06:10:57Z","snapshot_observed_at":"2026-08-14T02:06:09.285801Z","submitted_at":"2025-01-09T06:10:57Z","title":"On the ascent of almost and quasi-atomicity to monoid semidomains","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-10T21:34:00.634611Z"},"links":{"citing_paper":"/paper/2501.04990"},"observation_digest":"sha256:b4dd640d78a71c5025b54544997c4384b57970c857035e855351f6d78050faa8","observation_id":"5153bbfc-a901-4ffd-b957-dab26910e886","resolution":{"observed_at":"2026-08-10T21:34:01.028048Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T21:34:01.016012Z","title":null,"venue":null,"work_id":"0e228e08-0aff-4051-8434-a2144fb07b48","year":1993},"citing_paper":{"arxiv_id":"2501.04990","last_updated":"2025-01-09T06:10:57Z","snapshot_observed_at":"2026-08-14T02:06:09.285801Z","submitted_at":"2025-01-09T06:10:57Z","title":"On the ascent of almost and quasi-atomicity to monoid semidomains","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-10T21:34:00.638319Z"},"links":{"citing_paper":"/paper/2501.04990"},"observation_digest":"sha256:ba09a1bf3f2ee1fbe2a102a494af69a42afbe4351471368eac79007ed8a24679","observation_id":"dcf6a1e4-08f9-4cdb-b00f-ea2522143603","resolution":{"observed_at":"2026-08-10T21:34:01.019171Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T21:34:01.006739Z","title":"Boynton and J","venue":null,"work_id":"278db707-1766-4e13-8d6c-7334f7c00f1e","year":2015},"citing_paper":{"arxiv_id":"2501.04990","last_updated":"2025-01-09T06:10:57Z","snapshot_observed_at":"2026-08-14T02:06:09.285801Z","submitted_at":"2025-01-09T06:10:57Z","title":"On the ascent of almost and quasi-atomicity to monoid semidomains","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-10T21:34:00.641736Z"},"links":{"citing_paper":"/paper/2501.04990"},"observation_digest":"sha256:a9dc04ee478aec0b6bee79819cb5ab45c6e87cc1aefda4311d1a58ba085c1f20","observation_id":"f5395701-8641-4332-87bc-eecdbf888e95","resolution":{"observed_at":"2026-08-10T21:34:01.009935Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T21:34:00.997353Z","title":null,"venue":null,"work_id":"e17b3ff9-cbe0-45b4-8b57-98383fe2fd0c","year":null},"citing_paper":{"arxiv_id":"2501.04990","last_updated":"2025-01-09T06:10:57Z","snapshot_observed_at":"2026-08-14T02:06:09.285801Z","submitted_at":"2025-01-09T06:10:57Z","title":"On the ascent of almost and quasi-atomicity to monoid semidomains","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-10T21:34:00.645158Z"},"links":{"citing_paper":"/paper/2501.04990"},"observation_digest":"sha256:83afffce4ee7d60d96645590225a7b45cba7aafabd7194458f2770438729d4b7","observation_id":"79c052d5-cde3-4783-9ec0-048a85f0dda5","resolution":{"observed_at":"2026-08-10T21:34:01.000579Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1017/s0004972","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T21:34:00.752744Z","title":null,"venue":null,"work_id":"d7720122-7425-4b79-b4d5-171d8e5694ac","year":null},"citing_paper":{"arxiv_id":"2501.04990","last_updated":"2025-01-09T06:10:57Z","snapshot_observed_at":"2026-08-14T02:06:09.285801Z","submitted_at":"2025-01-09T06:10:57Z","title":"On the ascent of almost and quasi-atomicity to monoid semidomains","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-10T21:34:00.648398Z"},"links":{"citing_paper":"/paper/2501.04990"},"observation_digest":"sha256:05e1bc88b5704d31b2fadf7e0d2835351a724939970efef190eb072aef2cb744","observation_id":"6c2b04ba-61e7-464c-a366-b506a600bd1b","resolution":{"observed_at":"2026-08-10T21:34:00.757279Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T21:34:00.989004Z","title":"Chouinard, Krull semigroups and divisor class groups , Canad","venue":null,"work_id":"9bf25733-054a-4b3b-a353-ad809575f361","year":1981},"citing_paper":{"arxiv_id":"2501.04990","last_updated":"2025-01-09T06:10:57Z","snapshot_observed_at":"2026-08-14T02:06:09.285801Z","submitted_at":"2025-01-09T06:10:57Z","title":"On the ascent of almost and quasi-atomicity to monoid semidomains","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-10T21:34:00.651811Z"},"links":{"citing_paper":"/paper/2501.04990"},"observation_digest":"sha256:7ea36d2c8a17312cdab54430c6f13726afbf2d46c92ac936cd6ded5519a70d6e","observation_id":"d0e4db41-6a21-45a1-8e3d-a36fd61237ef","resolution":{"observed_at":"2026-08-10T21:34:00.992195Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T21:34:00.980258Z","title":null,"venue":null,"work_id":"b82a0d60-dca1-4140-be54-0c0241301658","year":1968},"citing_paper":{"arxiv_id":"2501.04990","last_updated":"2025-01-09T06:10:57Z","snapshot_observed_at":"2026-08-14T02:06:09.285801Z","submitted_at":"2025-01-09T06:10:57Z","title":"On the ascent of almost and quasi-atomicity to monoid semidomains","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-10T21:34:00.654949Z"},"links":{"citing_paper":"/paper/2501.04990"},"observation_digest":"sha256:30fd2063099dc8159dd2e068f0bee71c27f3aad493724c754a7a496f5222e93d","observation_id":"287eb995-d062-48c1-bb0f-b5e724c14b86","resolution":{"observed_at":"2026-08-10T21:34:00.983426Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T21:34:00.971660Z","title":"Coykendall and F","venue":null,"work_id":"37dbcb1e-1e35-4a0f-843b-72a37d728575","year":2024},"citing_paper":{"arxiv_id":"2501.04990","last_updated":"2025-01-09T06:10:57Z","snapshot_observed_at":"2026-08-14T02:06:09.285801Z","submitted_at":"2025-01-09T06:10:57Z","title":"On the ascent of almost and quasi-atomicity to monoid semidomains","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-10T21:34:00.658007Z"},"links":{"citing_paper":"/paper/2501.04990"},"observation_digest":"sha256:1c3b7feade4c3e23d64f5569db964b52deae00f6c2e5e3584feade4daf76f19a","observation_id":"682858c3-1c2c-43c7-80af-62d8f4ca991e","resolution":{"observed_at":"2026-08-10T21:34:00.974786Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T21:34:00.962708Z","title":"Coykendall and F","venue":null,"work_id":"53a51326-e945-46ab-9cd1-a84e4204bbb5","year":2019},"citing_paper":{"arxiv_id":"2501.04990","last_updated":"2025-01-09T06:10:57Z","snapshot_observed_at":"2026-08-14T02:06:09.285801Z","submitted_at":"2025-01-09T06:10:57Z","title":"On the ascent of almost and quasi-atomicity to monoid semidomains","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-10T21:34:00.661054Z"},"links":{"citing_paper":"/paper/2501.04990"},"observation_digest":"sha256:87f78edbb782b9495f3c4028f0f41ecfa3074401b36b3d42614d4beb650813ea","observation_id":"8d3f2220-34ef-4859-ba64-55db7c8ec4a2","resolution":{"observed_at":"2026-08-10T21:34:00.966071Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T21:34:00.954162Z","title":"Coykendall, F","venue":null,"work_id":"e1bfe4d9-cd5c-44e4-b3c2-1909e9a38b11","year":2023},"citing_paper":{"arxiv_id":"2501.04990","last_updated":"2025-01-09T06:10:57Z","snapshot_observed_at":"2026-08-14T02:06:09.285801Z","submitted_at":"2025-01-09T06:10:57Z","title":"On the ascent of almost and quasi-atomicity to monoid semidomains","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-10T21:34:00.663933Z"},"links":{"citing_paper":"/paper/2501.04990"},"observation_digest":"sha256:1c7170ab57693e839b95f9c5c487c131104e2e256f78d0a275926ad4a9b7c412","observation_id":"c489002b-4fc3-44f4-b7be-f3e027f64237","resolution":{"observed_at":"2026-08-10T21:34:00.957353Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T21:34:00.945596Z","title":"Fuchs, Inﬁnite Abelian Groups I , Academic Press, 1970","venue":null,"work_id":"ee94e1f5-27eb-4230-b00d-4caec195e2e1","year":1970},"citing_paper":{"arxiv_id":"2501.04990","last_updated":"2025-01-09T06:10:57Z","snapshot_observed_at":"2026-08-14T02:06:09.285801Z","submitted_at":"2025-01-09T06:10:57Z","title":"On the ascent of almost and quasi-atomicity to monoid semidomains","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-10T21:34:00.666920Z"},"links":{"citing_paper":"/paper/2501.04990"},"observation_digest":"sha256:7b1094e8e2048571221754d5ede3339222abfcd8580da7f250015949c12dc7f5","observation_id":"7e307a41-df90-4dce-948e-994d739b3fd0","resolution":{"observed_at":"2026-08-10T21:34:00.948749Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T21:34:00.936952Z","title":null,"venue":null,"work_id":"6ab67705-100f-4f8f-815b-2796aee3d433","year":null},"citing_paper":{"arxiv_id":"2501.04990","last_updated":"2025-01-09T06:10:57Z","snapshot_observed_at":"2026-08-14T02:06:09.285801Z","submitted_at":"2025-01-09T06:10:57Z","title":"On the ascent of almost and quasi-atomicity to monoid semidomains","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-10T21:34:00.669849Z"},"links":{"citing_paper":"/paper/2501.04990"},"observation_digest":"sha256:a72c10fd40091058bdf4f35e49ccd94ce92f150a171ed59d2bff8f4f6d754fbe","observation_id":"cf32f482-8071-4419-9132-76171a8f8e44","resolution":{"observed_at":"2026-08-10T21:34:00.940020Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2404.11494","last_updated":"2024-04-17T15:49:18Z","snapshot_observed_at":"2026-08-13T00:28:06.123116Z","submitted_at":"2024-04-17T15:49:18Z","title":"On monoid algebras having every nonempty subset of $\\mathbb{N}_{\\ge 2}$ as a length set","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2404.11494","snapshot_observed_at":"2026-08-10T21:34:00.672952Z","title":"Geroldinger and F","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2501.04990","last_updated":"2025-01-09T06:10:57Z","snapshot_observed_at":"2026-08-14T02:06:09.285801Z","submitted_at":"2025-01-09T06:10:57Z","title":"On the ascent of almost and quasi-atomicity to monoid semidomains","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-10T21:34:00.672952Z"},"links":{"cited_paper":"/paper/2404.11494","citing_paper":"/paper/2501.04990"},"observation_digest":"sha256:49441f6750f21ecd945795b552ecc021a26a255828aea5b14a0dbb9daceb3217","observation_id":"1339afbb-9ea8-459c-9f23-67e53cf25eab","resolution":{"observed_at":"2026-08-10T21:34:00.672952Z","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":"2026-08-10T21:34:00.928589Z","title":"Geroldinger and Q","venue":null,"work_id":"54717ead-63c4-4c99-b936-49fec356c81c","year":2020},"citing_paper":{"arxiv_id":"2501.04990","last_updated":"2025-01-09T06:10:57Z","snapshot_observed_at":"2026-08-14T02:06:09.285801Z","submitted_at":"2025-01-09T06:10:57Z","title":"On the ascent of almost and quasi-atomicity to monoid semidomains","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-10T21:34:00.676339Z"},"links":{"citing_paper":"/paper/2501.04990"},"observation_digest":"sha256:bd9ddea8b2dfe9c15965eeab00a01f53ea1550e3da0441cc66772385f61f2f4f","observation_id":"d0e1f761-1b5e-49e6-b853-d271e9ca5859","resolution":{"observed_at":"2026-08-10T21:34:00.931674Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T21:34:00.919807Z","title":"Gilmer, Commutative Semigroup Rings , The University of Chicago Press, 1984","venue":null,"work_id":"69c0f7ca-3ab7-4062-9f32-86c3f34155f4","year":1984},"citing_paper":{"arxiv_id":"2501.04990","last_updated":"2025-01-09T06:10:57Z","snapshot_observed_at":"2026-08-14T02:06:09.285801Z","submitted_at":"2025-01-09T06:10:57Z","title":"On the ascent of almost and quasi-atomicity to monoid semidomains","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-10T21:34:00.679357Z"},"links":{"citing_paper":"/paper/2501.04990"},"observation_digest":"sha256:664564f845e3c1e65a8fc07f9f2f015704115624cd437a913fe75d2a23e1c263","observation_id":"f3ea491a-cf4f-42ad-886b-074ff3ca7704","resolution":{"observed_at":"2026-08-10T21:34:00.923264Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T21:34:00.911020Z","title":"Gilmer and T","venue":null,"work_id":"47ee7746-6bfd-4fd7-aabf-de37b395edd6","year":1974},"citing_paper":{"arxiv_id":"2501.04990","last_updated":"2025-01-09T06:10:57Z","snapshot_observed_at":"2026-08-14T02:06:09.285801Z","submitted_at":"2025-01-09T06:10:57Z","title":"On the ascent of almost and quasi-atomicity to monoid semidomains","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-10T21:34:00.682617Z"},"links":{"citing_paper":"/paper/2501.04990"},"observation_digest":"sha256:3e08d5b012b0ea1d04dce6313d77008d2fe8ab791314d4b85e2e409c14b2ed38","observation_id":"1843c686-8d0c-489d-8b0f-4b27e6c97563","resolution":{"observed_at":"2026-08-10T21:34:00.914209Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T21:34:00.902057Z","title":"Gotti, Increasing positive monoids of ordered ﬁelds are FF-monoid s, J","venue":null,"work_id":"02029ed8-e9d0-4391-ab08-f5428ba33e36","year":2019},"citing_paper":{"arxiv_id":"2501.04990","last_updated":"2025-01-09T06:10:57Z","snapshot_observed_at":"2026-08-14T02:06:09.285801Z","submitted_at":"2025-01-09T06:10:57Z","title":"On the ascent of almost and quasi-atomicity to monoid semidomains","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-10T21:34:00.685690Z"},"links":{"citing_paper":"/paper/2501.04990"},"observation_digest":"sha256:5c30fb0620e08efa78742c4536b5549cf6cda56b6363596223bb86d68694aa33","observation_id":"b1ba9ac4-eef1-4a7e-a45d-3f9a023ac1b6","resolution":{"observed_at":"2026-08-10T21:34:00.905419Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T21:34:00.892894Z","title":"Gotti and B","venue":null,"work_id":"a815baa5-8f6e-4b1f-a1ba-b721e8011b13","year":2023},"citing_paper":{"arxiv_id":"2501.04990","last_updated":"2025-01-09T06:10:57Z","snapshot_observed_at":"2026-08-14T02:06:09.285801Z","submitted_at":"2025-01-09T06:10:57Z","title":"On the ascent of almost and quasi-atomicity to monoid semidomains","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-10T21:34:00.688768Z"},"links":{"citing_paper":"/paper/2501.04990"},"observation_digest":"sha256:77aa147bd398f3cd1439cd1eb4581dcdafae932ad1829db347204d8a838fa708","observation_id":"5efc2f87-594f-4102-9506-821114e01c38","resolution":{"observed_at":"2026-08-10T21:34:00.896361Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T21:34:00.883680Z","title":"Gotti and H","venue":null,"work_id":"40d0b8e6-5bb3-4c61-804a-ed6a809d7ef2","year":2023},"citing_paper":{"arxiv_id":"2501.04990","last_updated":"2025-01-09T06:10:57Z","snapshot_observed_at":"2026-08-14T02:06:09.285801Z","submitted_at":"2025-01-09T06:10:57Z","title":"On the ascent of almost and quasi-atomicity to monoid semidomains","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-10T21:34:00.691643Z"},"links":{"citing_paper":"/paper/2501.04990"},"observation_digest":"sha256:37fabf994388f3971004010cc7600d061ff49f67d5107ef6e5f7afb4237d481f","observation_id":"f209945f-97df-438a-a7c2-e3bb47e54687","resolution":{"observed_at":"2026-08-10T21:34:00.886889Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T21:34:00.875342Z","title":"Gotti and H","venue":null,"work_id":"3e1173a1-8803-4c62-aef7-ddc4e48d5e35","year":null},"citing_paper":{"arxiv_id":"2501.04990","last_updated":"2025-01-09T06:10:57Z","snapshot_observed_at":"2026-08-14T02:06:09.285801Z","submitted_at":"2025-01-09T06:10:57Z","title":"On the ascent of almost and quasi-atomicity to monoid semidomains","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-10T21:34:00.694731Z"},"links":{"citing_paper":"/paper/2501.04990"},"observation_digest":"sha256:9e8612e2a0534521bbe15c6f688ebef355d2487a12fcde851d2e3feb357fedee","observation_id":"daf94dec-be6d-4095-9de4-6f95cfe2f40a","resolution":{"observed_at":"2026-08-10T21:34:00.878367Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T21:34:00.867080Z","title":"Gotti and H","venue":null,"work_id":"b49ce6d0-8923-4c98-b202-fd846d96749d","year":2025},"citing_paper":{"arxiv_id":"2501.04990","last_updated":"2025-01-09T06:10:57Z","snapshot_observed_at":"2026-08-14T02:06:09.285801Z","submitted_at":"2025-01-09T06:10:57Z","title":"On the ascent of almost and quasi-atomicity to monoid semidomains","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-10T21:34:00.697592Z"},"links":{"citing_paper":"/paper/2501.04990"},"observation_digest":"sha256:825d84bc92d853b206fab4541100e3cf3beed00f945e828f710a9b70cb2e8028","observation_id":"33ac1b7b-df10-4801-9188-146f62465d22","resolution":{"observed_at":"2026-08-10T21:34:00.870000Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T21:34:00.858149Z","title":"Grams, Atomic rings and the ascending chain condition for principa l ideals , Math","venue":null,"work_id":"1a1bb56d-3a46-46c6-a498-c2e5486a8595","year":1974},"citing_paper":{"arxiv_id":"2501.04990","last_updated":"2025-01-09T06:10:57Z","snapshot_observed_at":"2026-08-14T02:06:09.285801Z","submitted_at":"2025-01-09T06:10:57Z","title":"On the ascent of almost and quasi-atomicity to monoid semidomains","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-10T21:34:00.700510Z"},"links":{"citing_paper":"/paper/2501.04990"},"observation_digest":"sha256:3d1277689f667989f1b6929900f628f445ee173c13d3f0732b5106aaeffebe9e","observation_id":"a16f803b-0d18-4031-9bfc-a112271b25e7","resolution":{"observed_at":"2026-08-10T21:34:00.861586Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T21:34:00.849330Z","title":"Hilbert, ¨Uber die Theorie der algebraischen Formen , Mathematische Annalen 36 (1890) 473–534","venue":null,"work_id":"ba6149d8-43d5-4c39-bad7-d6f1ffc5f44e","year":null},"citing_paper":{"arxiv_id":"2501.04990","last_updated":"2025-01-09T06:10:57Z","snapshot_observed_at":"2026-08-14T02:06:09.285801Z","submitted_at":"2025-01-09T06:10:57Z","title":"On the ascent of almost and quasi-atomicity to monoid semidomains","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-10T21:34:00.703418Z"},"links":{"citing_paper":"/paper/2501.04990"},"observation_digest":"sha256:7df274b05d18e763d9a306a8b7f14b76d1044ce778ed5505124cf7c10a2a3730","observation_id":"5998ef2a-8842-4064-ad60-990d052ad389","resolution":{"observed_at":"2026-08-10T21:34:00.852638Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T21:34:00.840839Z","title":null,"venue":null,"work_id":"f0dbb282-6e46-411d-ab75-81bd42e40088","year":null},"citing_paper":{"arxiv_id":"2501.04990","last_updated":"2025-01-09T06:10:57Z","snapshot_observed_at":"2026-08-14T02:06:09.285801Z","submitted_at":"2025-01-09T06:10:57Z","title":"On the ascent of almost and quasi-atomicity to monoid semidomains","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-10T21:34:00.706541Z"},"links":{"citing_paper":"/paper/2501.04990"},"observation_digest":"sha256:6301cd6b9fb5e960d58d4f2d748c50b8fca1cb655f4a7f05e53fefa4fca1c32d","observation_id":"5e32f9e2-9231-44db-ade7-04694bc6f15a","resolution":{"observed_at":"2026-08-10T21:34:00.843841Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T21:34:00.832017Z","title":null,"venue":null,"work_id":"537891ae-4ec1-41b2-9387-c16a3624e27c","year":null},"citing_paper":{"arxiv_id":"2501.04990","last_updated":"2025-01-09T06:10:57Z","snapshot_observed_at":"2026-08-14T02:06:09.285801Z","submitted_at":"2025-01-09T06:10:57Z","title":"On the ascent of almost and quasi-atomicity to monoid semidomains","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-10T21:34:00.709503Z"},"links":{"citing_paper":"/paper/2501.04990"},"observation_digest":"sha256:8cc1a129af60c7c18905da582ec2a06dec81298ae38b69ce3f1003f791f74043","observation_id":"85fdcd5d-9b74-4c4a-8baf-2015ddb500b3","resolution":{"observed_at":"2026-08-10T21:34:00.835275Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T21:34:00.821789Z","title":"Lebowitz-Lockard, On domains with properties weaker than atomicity , Comm","venue":null,"work_id":"a27b1c08-b5a7-494e-a59b-e3921394abf9","year":2019},"citing_paper":{"arxiv_id":"2501.04990","last_updated":"2025-01-09T06:10:57Z","snapshot_observed_at":"2026-08-14T02:06:09.285801Z","submitted_at":"2025-01-09T06:10:57Z","title":"On the ascent of almost and quasi-atomicity to monoid semidomains","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-10T21:34:00.712537Z"},"links":{"citing_paper":"/paper/2501.04990"},"observation_digest":"sha256:c0f6b17358696455900de8363d546d175cae118e2c8e0d9c25a9d41fd60c35c9","observation_id":"33fb628d-c243-404c-b9b7-67097e18b645","resolution":{"observed_at":"2026-08-10T21:34:00.825936Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T21:34:00.811944Z","title":"Lidl and H","venue":null,"work_id":"f20b93cd-5a92-44df-ab80-f8eee7a370d4","year":1994},"citing_paper":{"arxiv_id":"2501.04990","last_updated":"2025-01-09T06:10:57Z","snapshot_observed_at":"2026-08-14T02:06:09.285801Z","submitted_at":"2025-01-09T06:10:57Z","title":"On the ascent of almost and quasi-atomicity to monoid semidomains","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-10T21:34:00.715487Z"},"links":{"citing_paper":"/paper/2501.04990"},"observation_digest":"sha256:0611e082a92b5543261f1aea85d52a625ee0b3f8f9435d7779ea910f9394e1a7","observation_id":"97564c6c-8219-4bd3-befd-a5f04ccc5e2e","resolution":{"observed_at":"2026-08-10T21:34:00.815237Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T21:34:00.802176Z","title":null,"venue":null,"work_id":"4da29f48-29f3-4d62-bb03-4020312fda92","year":1913},"citing_paper":{"arxiv_id":"2501.04990","last_updated":"2025-01-09T06:10:57Z","snapshot_observed_at":"2026-08-14T02:06:09.285801Z","submitted_at":"2025-01-09T06:10:57Z","title":"On the ascent of almost and quasi-atomicity to monoid semidomains","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-10T21:34:00.718475Z"},"links":{"citing_paper":"/paper/2501.04990"},"observation_digest":"sha256:5a64a16d9eaeeee83824ab058762b2a9dcb4b27a5423a07dcb04596b999379a3","observation_id":"1bcc5b70-0c5c-4abb-a1dd-586285a34022","resolution":{"observed_at":"2026-08-10T21:34:00.805524Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T21:34:00.792382Z","title":"Malcolmson and F","venue":null,"work_id":"1bd79ce8-8a79-4114-9089-33273854fbc1","year":2009},"citing_paper":{"arxiv_id":"2501.04990","last_updated":"2025-01-09T06:10:57Z","snapshot_observed_at":"2026-08-14T02:06:09.285801Z","submitted_at":"2025-01-09T06:10:57Z","title":"On the ascent of almost and quasi-atomicity to monoid semidomains","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-10T21:34:00.721731Z"},"links":{"citing_paper":"/paper/2501.04990"},"observation_digest":"sha256:d417e05b69716ba15fd36e72e1dc668fca447922ad43bdb69f9d729a82c22075","observation_id":"aaea4238-1777-4c58-9e18-acc82e31eede","resolution":{"observed_at":"2026-08-10T21:34:00.795639Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T21:34:00.782735Z","title":"Roitman, On the atomic property for power series rings , J","venue":null,"work_id":"6f72aac5-af72-41ce-a909-87a08c9200e8","year":2000},"citing_paper":{"arxiv_id":"2501.04990","last_updated":"2025-01-09T06:10:57Z","snapshot_observed_at":"2026-08-14T02:06:09.285801Z","submitted_at":"2025-01-09T06:10:57Z","title":"On the ascent of almost and quasi-atomicity to monoid semidomains","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-10T21:34:00.724894Z"},"links":{"citing_paper":"/paper/2501.04990"},"observation_digest":"sha256:231c7727539c9b284505c980e9b4af0fa5e33512ab952240034b4c716fbf68cd","observation_id":"c1da706d-8537-47b5-9422-1e65c63c7f53","resolution":{"observed_at":"2026-08-10T21:34:00.785970Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T21:34:00.772791Z","title":"Roitman, Polynomial extensions of atomic domains , J","venue":null,"work_id":"f612eb94-92a8-47f3-a251-04ea9f2cce79","year":1993},"citing_paper":{"arxiv_id":"2501.04990","last_updated":"2025-01-09T06:10:57Z","snapshot_observed_at":"2026-08-14T02:06:09.285801Z","submitted_at":"2025-01-09T06:10:57Z","title":"On the ascent of almost and quasi-atomicity to monoid semidomains","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-10T21:34:00.728056Z"},"links":{"citing_paper":"/paper/2501.04990"},"observation_digest":"sha256:3dad4dc7a3e0009b3556b9d8d5c415862623fefb5b512db06a513dfd3ab8cf42","observation_id":"3342ab76-aea2-4f54-982f-2a0d5b5660c7","resolution":{"observed_at":"2026-08-10T21:34:00.776682Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2501.04990","last_updated":"2025-01-09T06:10:57Z","latest_version":1,"primary_category":"math.AC","snapshot_observed_at":"2026-08-14T02:06:09.285801Z","submitted_at":"2025-01-09T06:10:57Z","title":"On the ascent of almost and quasi-atomicity to monoid semidomains"},"reference_resolution":{"displayed":32,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":10,"verified_exact":1,"verified_fuzzy":21},"total_outbound_references":32},"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":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"thesis":"As of 14 August 2026, this Paper Citation Record lists 32 of 32 outbound references and 2 inbound Pith citation observations for arXiv:2501.04990."}