{"as_of":"2026-08-14T22:44:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:94afe496bcccea0071ae394743fe746275cb2cd996ce05eca56464222857e52c","coverage":[{"denominator":14,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":14,"source":"paper_references, paper_reference_links","source_observed_at":"2026-07-14T07:06:35.322813Z","state":"measured"},{"denominator":14,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":14,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-14T06:32:32.682623+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/2607.11093/citation-record","integrity":"/paper/2607.11093/integrity","json":"/paper/2607.11093/citation-record.json","paper":"/paper/2607.11093"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T07:06:35.322813Z","title":"Delgado, P","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.11093","last_updated":"2026-07-13T05:00:13Z","snapshot_observed_at":"2026-08-14T09:03:12.317637Z","submitted_at":"2026-07-13T05:00:13Z","title":"Existence of a far-flung Gorenstein numerical semigroup attaining the Herzog--Kumashiro--Stamate bound","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-07-14T07:06:35.322813Z"},"links":{"citing_paper":"/paper/2607.11093"},"observation_digest":"sha256:51c93bc5814d98b46d8f913c3a200007291a07798f49b6bdf035fb16701e47ec","observation_id":"9d1f041c-b6e6-4ea2-82f8-605224a6384d","resolution":{"observed_at":"2026-07-14T07:06:35.322813Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T07:06:35.322813Z","title":"Fr¨ oberg, C","venue":null,"work_id":null,"year":1987},"citing_paper":{"arxiv_id":"2607.11093","last_updated":"2026-07-13T05:00:13Z","snapshot_observed_at":"2026-08-14T09:03:12.317637Z","submitted_at":"2026-07-13T05:00:13Z","title":"Existence of a far-flung Gorenstein numerical semigroup attaining the Herzog--Kumashiro--Stamate bound","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-07-14T07:06:35.322813Z"},"links":{"citing_paper":"/paper/2607.11093"},"observation_digest":"sha256:15036f2e3726019ad51f8027e702472d2b673a7fb3b5183b67b174067dcbf009","observation_id":"1d2c71d4-362d-4822-8990-816187a475fb","resolution":{"observed_at":"2026-07-14T07:06:35.322813Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T07:06:35.322813Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.11093","last_updated":"2026-07-13T05:00:13Z","snapshot_observed_at":"2026-08-14T09:03:12.317637Z","submitted_at":"2026-07-13T05:00:13Z","title":"Existence of a far-flung Gorenstein numerical semigroup attaining the Herzog--Kumashiro--Stamate bound","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-07-14T07:06:35.322813Z"},"links":{"citing_paper":"/paper/2607.11093"},"observation_digest":"sha256:c36a6dcf562bc7b7831f7dacafa92122826195f3a68329ef1fa709522cdadd79","observation_id":"10aa171b-b74d-4729-b4a8-19f9c305601e","resolution":{"observed_at":"2026-07-14T07:06:35.322813Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T07:06:35.322813Z","title":"Herzog, T","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.11093","last_updated":"2026-07-13T05:00:13Z","snapshot_observed_at":"2026-08-14T09:03:12.317637Z","submitted_at":"2026-07-13T05:00:13Z","title":"Existence of a far-flung Gorenstein numerical semigroup attaining the Herzog--Kumashiro--Stamate bound","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-07-14T07:06:35.322813Z"},"links":{"citing_paper":"/paper/2607.11093"},"observation_digest":"sha256:b7951505f4076ce390e8fa1caf3f3f5b8c6b95d6ae5b5e0669229c13929e0dad","observation_id":"36e271c6-8b1f-4cf7-9bd1-ed744e979c10","resolution":{"observed_at":"2026-07-14T07:06:35.322813Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T07:06:35.322813Z","title":"Herzog and S","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.11093","last_updated":"2026-07-13T05:00:13Z","snapshot_observed_at":"2026-08-14T09:03:12.317637Z","submitted_at":"2026-07-13T05:00:13Z","title":"Existence of a far-flung Gorenstein numerical semigroup attaining the Herzog--Kumashiro--Stamate bound","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-07-14T07:06:35.322813Z"},"links":{"citing_paper":"/paper/2607.11093"},"observation_digest":"sha256:b802d766679157ddbce0c9a466698dc8ed3cb02101e08b206989658dd25b9bb0","observation_id":"0cfc830b-4f01-4155-bcd4-97976bbde839","resolution":{"observed_at":"2026-07-14T07:06:35.322813Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T07:06:35.322813Z","title":"Herzog, S","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.11093","last_updated":"2026-07-13T05:00:13Z","snapshot_observed_at":"2026-08-14T09:03:12.317637Z","submitted_at":"2026-07-13T05:00:13Z","title":"Existence of a far-flung Gorenstein numerical semigroup attaining the Herzog--Kumashiro--Stamate bound","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-07-14T07:06:35.322813Z"},"links":{"citing_paper":"/paper/2607.11093"},"observation_digest":"sha256:a921479a8f7c0a14f45ea8e5fd429da1390551ec11285a49ed295582f33f1efb","observation_id":"0ac1d427-9fe0-46aa-9bcd-9a050d8f731b","resolution":{"observed_at":"2026-07-14T07:06:35.322813Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T07:06:35.322813Z","title":"Huneke, S","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.11093","last_updated":"2026-07-13T05:00:13Z","snapshot_observed_at":"2026-08-14T09:03:12.317637Z","submitted_at":"2026-07-13T05:00:13Z","title":"Existence of a far-flung Gorenstein numerical semigroup attaining the Herzog--Kumashiro--Stamate bound","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-07-14T07:06:35.322813Z"},"links":{"citing_paper":"/paper/2607.11093"},"observation_digest":"sha256:35c8a351c8920b6b314f5b44dc20f6cc970876af18ce517b4088ebca03f9de9c","observation_id":"67c0dfe4-58ef-4d3d-a17c-1751534e1972","resolution":{"observed_at":"2026-07-14T07:06:35.322813Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T07:06:35.322813Z","title":"Kohonen and J","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2607.11093","last_updated":"2026-07-13T05:00:13Z","snapshot_observed_at":"2026-08-14T09:03:12.317637Z","submitted_at":"2026-07-13T05:00:13Z","title":"Existence of a far-flung Gorenstein numerical semigroup attaining the Herzog--Kumashiro--Stamate bound","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-07-14T07:06:35.322813Z"},"links":{"citing_paper":"/paper/2607.11093"},"observation_digest":"sha256:a8fa8e691bf2dbcce3bc83afd6cfb697bb836596019b01849ff7bf49d0f9fb05","observation_id":"db6b3f1c-32d7-4627-a6ce-8530bcfab7ad","resolution":{"observed_at":"2026-07-14T07:06:35.322813Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2306.17069","last_updated":"2023-06-29T16:16:54Z","snapshot_observed_at":"2026-08-13T11:05:57.394633Z","submitted_at":"2023-06-29T16:16:54Z","title":"Extremal behavior of reduced type of one dimensional rings","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2306.17069","snapshot_observed_at":"2026-07-14T07:06:35.322813Z","title":"Maitra and V","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.11093","last_updated":"2026-07-13T05:00:13Z","snapshot_observed_at":"2026-08-14T09:03:12.317637Z","submitted_at":"2026-07-13T05:00:13Z","title":"Existence of a far-flung Gorenstein numerical semigroup attaining the Herzog--Kumashiro--Stamate bound","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-07-14T07:06:35.322813Z"},"links":{"cited_paper":"/paper/2306.17069","citing_paper":"/paper/2607.11093"},"observation_digest":"sha256:5f4aa5a2cc927c2472879038bdf80c35d24c50da85161d99612efa14a034c4a1","observation_id":"9384e67f-aedd-4537-86ca-f7b6605df3f6","resolution":{"observed_at":"2026-07-14T07:06:35.322813Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T07:06:35.322813Z","title":"Rohrbach","venue":null,"work_id":null,"year":1937},"citing_paper":{"arxiv_id":"2607.11093","last_updated":"2026-07-13T05:00:13Z","snapshot_observed_at":"2026-08-14T09:03:12.317637Z","submitted_at":"2026-07-13T05:00:13Z","title":"Existence of a far-flung Gorenstein numerical semigroup attaining the Herzog--Kumashiro--Stamate bound","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-07-14T07:06:35.322813Z"},"links":{"citing_paper":"/paper/2607.11093"},"observation_digest":"sha256:d341b635a312ff51efb5ef9a56e32dbfedf492fd02d28d099fe5b86a327981b3","observation_id":"5aaf944b-5b39-41f1-a4f3-0ec998d78dae","resolution":{"observed_at":"2026-07-14T07:06:35.322813Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T07:06:35.322813Z","title":null,"venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2607.11093","last_updated":"2026-07-13T05:00:13Z","snapshot_observed_at":"2026-08-14T09:03:12.317637Z","submitted_at":"2026-07-13T05:00:13Z","title":"Existence of a far-flung Gorenstein numerical semigroup attaining the Herzog--Kumashiro--Stamate bound","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-07-14T07:06:35.322813Z"},"links":{"citing_paper":"/paper/2607.11093"},"observation_digest":"sha256:c3b138c7634fcd4a43126f64c73ec9eae9c3f7dfeb182c9d59116bb06017aec9","observation_id":"e06340d5-824f-4c70-ad60-6b7111d947e9","resolution":{"observed_at":"2026-07-14T07:06:35.322813Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T07:06:35.322813Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.11093","last_updated":"2026-07-13T05:00:13Z","snapshot_observed_at":"2026-08-14T09:03:12.317637Z","submitted_at":"2026-07-13T05:00:13Z","title":"Existence of a far-flung Gorenstein numerical semigroup attaining the Herzog--Kumashiro--Stamate bound","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-07-14T07:06:35.322813Z"},"links":{"citing_paper":"/paper/2607.11093"},"observation_digest":"sha256:ed5951750c95659c8d6842fdcff08c849669e7b49e07260b051b17037e7c5d8f","observation_id":"e753ebb9-f7ee-49d3-831f-dc2e4c585579","resolution":{"observed_at":"2026-07-14T07:06:35.322813Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T07:06:35.322813Z","title":"Sugawara","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.11093","last_updated":"2026-07-13T05:00:13Z","snapshot_observed_at":"2026-08-14T09:03:12.317637Z","submitted_at":"2026-07-13T05:00:13Z","title":"Existence of a far-flung Gorenstein numerical semigroup attaining the Herzog--Kumashiro--Stamate bound","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-07-14T07:06:35.322813Z"},"links":{"citing_paper":"/paper/2607.11093"},"observation_digest":"sha256:3bda05b36c663a790b0802b41b02f05299b883cf194ecd1dc89c0a437e33267b","observation_id":"c1e73b56-c55f-4355-886a-462b1eae948d","resolution":{"observed_at":"2026-07-14T07:06:35.322813Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T07:06:35.322813Z","title":"GAP – Groups, Algorithms, and Programming, Version 4.12.1, 2022","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.11093","last_updated":"2026-07-13T05:00:13Z","snapshot_observed_at":"2026-08-14T09:03:12.317637Z","submitted_at":"2026-07-13T05:00:13Z","title":"Existence of a far-flung Gorenstein numerical semigroup attaining the Herzog--Kumashiro--Stamate bound","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-07-14T07:06:35.322813Z"},"links":{"citing_paper":"/paper/2607.11093"},"observation_digest":"sha256:d8b3981100507950f03fcaba855d26d73a040dab403f6624788583ae5c6677c8","observation_id":"e5f5daf9-8038-448a-89a6-d7601fa6f32e","resolution":{"observed_at":"2026-07-14T07:06:35.322813Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.11093","last_updated":"2026-07-13T05:00:13Z","latest_version":1,"primary_category":"math.AC","snapshot_observed_at":"2026-08-14T09:03:12.317637Z","submitted_at":"2026-07-13T05:00:13Z","title":"Existence of a far-flung Gorenstein numerical semigroup attaining the Herzog--Kumashiro--Stamate bound"},"reference_resolution":{"displayed":14,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":14,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":14},"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 14 of 14 outbound references and 0 inbound Pith citation observations for arXiv:2607.11093."}