{"as_of":"2026-08-14T18:11:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:9fb986e24be8ed52f47e2c7eda3e97352cf561b84d06557ebc1d0a523b12d8b0","coverage":[{"denominator":15,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":15,"source":"paper_references, paper_reference_links","source_observed_at":"2026-07-08T20:02:53.295835Z","state":"measured"},{"denominator":15,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":15,"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/2607.05723/citation-record","integrity":"/paper/2607.05723/integrity","json":"/paper/2607.05723/citation-record.json","paper":"/paper/2607.05723"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"1402.5087","last_updated":"2015-02-25T15:48:52Z","snapshot_observed_at":"2026-07-06T03:36:32.333089Z","submitted_at":"2014-02-20T17:40:27Z","title":"Lojasiewicz inequalities and applications","version":3},"cited_work":{"arxiv_id":"1402.5087","doi":null,"metadata_source":"pith","pith_arxiv_id":"1402.5087","snapshot_observed_at":"2026-07-08T20:05:34.112906Z","title":"Lojasiewicz inequalities and applications","venue":"math.DG","work_id":"58981926-3241-4c5b-b070-5f6ad80b4914","year":2014},"citing_paper":{"arxiv_id":"2607.05723","last_updated":"2026-07-07T01:09:59Z","snapshot_observed_at":"2026-08-14T14:48:00.810263Z","submitted_at":"2026-07-07T01:09:59Z","title":"Generalized Marshall Quotients and Real Semigroups of Continuous and Differentiable Functions","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-07-08T20:02:53.295835Z"},"links":{"cited_paper":"/paper/1402.5087","citing_paper":"/paper/2607.05723"},"observation_digest":"sha256:281ecd38c680eef219ee67cbda9fdc6a12c201b570722177e15f78fbc104636c","observation_id":"c3c9db6c-65ca-4fb8-8e1e-c2bbe35e5306","resolution":{"observed_at":"2026-07-08T20:05:34.114057Z","resolver_source":"local_arxiv","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":"2026-07-08T20:05:34.407310Z","title":"Quadratic structures associated to (multi) rings.Categories and General Algebraic Structures, 16(1):105–141, 2022","venue":null,"work_id":"f7d17e86-5712-488e-a5c8-cfe0f1d91af9","year":2022},"citing_paper":{"arxiv_id":"2607.05723","last_updated":"2026-07-07T01:09:59Z","snapshot_observed_at":"2026-08-14T14:48:00.810263Z","submitted_at":"2026-07-07T01:09:59Z","title":"Generalized Marshall Quotients and Real Semigroups of Continuous and Differentiable Functions","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-07-08T20:02:53.295835Z"},"links":{"citing_paper":"/paper/2607.05723"},"observation_digest":"sha256:a5b5657fc69d0647246c19933312c7ef6eb951cb4fd9962f1bffb671516e5d3a","observation_id":"27a8abf8-232a-4111-87d9-c14003340c6f","resolution":{"observed_at":"2026-07-08T20:05:34.408499Z","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":"2026-07-08T20:05:34.409048Z","title":"Functorial relationship between multirings and the various abstract theories of quadratic forms.São Paulo Journal of Mathematical Sciences, 16:5–42, 2022","venue":null,"work_id":"7947da33-8825-48ef-91b1-926d7ac113f5","year":2022},"citing_paper":{"arxiv_id":"2607.05723","last_updated":"2026-07-07T01:09:59Z","snapshot_observed_at":"2026-08-14T14:48:00.810263Z","submitted_at":"2026-07-07T01:09:59Z","title":"Generalized Marshall Quotients and Real Semigroups of Continuous and Differentiable Functions","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-07-08T20:02:53.295835Z"},"links":{"citing_paper":"/paper/2607.05723"},"observation_digest":"sha256:cf39ee7aa106bdf4ee0a3947b9e7fda348c7074a7895b64c1fba3da78f2621b0","observation_id":"c2a669a7-d5af-4dbc-988c-7fb0b9ee4384","resolution":{"observed_at":"2026-07-08T20:05:34.410341Z","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":"2026-07-08T20:05:34.405579Z","title":"Number 689 in Memoirs AMS","venue":null,"work_id":"98f81ac4-1096-46ea-bce2-d376771c06af","year":2000},"citing_paper":{"arxiv_id":"2607.05723","last_updated":"2026-07-07T01:09:59Z","snapshot_observed_at":"2026-08-14T14:48:00.810263Z","submitted_at":"2026-07-07T01:09:59Z","title":"Generalized Marshall Quotients and Real Semigroups of Continuous and Differentiable Functions","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-07-08T20:02:53.295835Z"},"links":{"citing_paper":"/paper/2607.05723"},"observation_digest":"sha256:c4612090aabc81fe5a1dce04986c6e44f1e870a2659f2e62b2c61f0e49195dda","observation_id":"e1157eba-34dc-4acb-b679-3561ad47405c","resolution":{"observed_at":"2026-07-08T20:05:34.406772Z","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":"2026-07-08T20:05:34.410845Z","title":"Number 1128 in Memoirs AMS","venue":null,"work_id":"00289a4e-60a2-4fde-bdf6-211e9aa1a736","year":2015},"citing_paper":{"arxiv_id":"2607.05723","last_updated":"2026-07-07T01:09:59Z","snapshot_observed_at":"2026-08-14T14:48:00.810263Z","submitted_at":"2026-07-07T01:09:59Z","title":"Generalized Marshall Quotients and Real Semigroups of Continuous and Differentiable Functions","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-07-08T20:02:53.295835Z"},"links":{"citing_paper":"/paper/2607.05723"},"observation_digest":"sha256:b987ae9dc32343ddc4194bb1835ac5c61e36d83f2796df8cf65490a32fdb4762","observation_id":"fe3ebaae-2cb9-4627-8407-d4d2f8c11919","resolution":{"observed_at":"2026-07-08T20:05:34.411832Z","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":"2026-07-08T20:05:34.400591Z","title":"Constructions in the category of real semigroups.Contemporary Mathematics, 69:107–134, 2017","venue":null,"work_id":"278f23b0-6890-46fe-9caf-cf46221e02e1","year":2017},"citing_paper":{"arxiv_id":"2607.05723","last_updated":"2026-07-07T01:09:59Z","snapshot_observed_at":"2026-08-14T14:48:00.810263Z","submitted_at":"2026-07-07T01:09:59Z","title":"Generalized Marshall Quotients and Real Semigroups of Continuous and Differentiable Functions","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-07-08T20:02:53.295835Z"},"links":{"citing_paper":"/paper/2607.05723"},"observation_digest":"sha256:d5ca26429457b5c1120897b54ff58a8225285dd47e9ede2c7f09521bc94a8fbf","observation_id":"ac64bc15-231f-4026-b9e4-aed3227c463b","resolution":{"observed_at":"2026-07-08T20:05:34.401733Z","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":"2026-07-08T20:05:34.402252Z","title":"Real semigroups and abstract real spectra","venue":null,"work_id":"d1d2678f-e737-4631-bc1b-2566a760c374","year":2004},"citing_paper":{"arxiv_id":"2607.05723","last_updated":"2026-07-07T01:09:59Z","snapshot_observed_at":"2026-08-14T14:48:00.810263Z","submitted_at":"2026-07-07T01:09:59Z","title":"Generalized Marshall Quotients and Real Semigroups of Continuous and Differentiable Functions","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-07-08T20:02:53.295835Z"},"links":{"citing_paper":"/paper/2607.05723"},"observation_digest":"sha256:3c7e7324afbdfbec4c91e5cf18f1329100de24a9ff9a71fe201136e588502b3f","observation_id":"543aa984-84e1-4e6a-ac98-83ee7a028a21","resolution":{"observed_at":"2026-07-08T20:05:34.403354Z","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":"2026-07-08T20:05:34.412370Z","title":"Real semigroups, real spectra and quadratic forms over rings, 2012","venue":null,"work_id":"1ca7b4bf-0195-4349-add4-2d19fd395633","year":2012},"citing_paper":{"arxiv_id":"2607.05723","last_updated":"2026-07-07T01:09:59Z","snapshot_observed_at":"2026-08-14T14:48:00.810263Z","submitted_at":"2026-07-07T01:09:59Z","title":"Generalized Marshall Quotients and Real Semigroups of Continuous and Differentiable Functions","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-07-08T20:02:53.295835Z"},"links":{"citing_paper":"/paper/2607.05723"},"observation_digest":"sha256:71a29dcb82a740e903606f8e1c4b5a82e522b438cd404d93c8af6f968caac916","observation_id":"b0b87314-13ab-4644-b3fd-72476766a20c","resolution":{"observed_at":"2026-07-08T20:05:34.413482Z","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":"2026-07-08T20:05:34.397526Z","title":"Spectral real semigroups","venue":null,"work_id":"dba6c7b4-25f6-4e3e-b1fd-a6d2a54021ed","year":2012},"citing_paper":{"arxiv_id":"2607.05723","last_updated":"2026-07-07T01:09:59Z","snapshot_observed_at":"2026-08-14T14:48:00.810263Z","submitted_at":"2026-07-07T01:09:59Z","title":"Generalized Marshall Quotients and Real Semigroups of Continuous and Differentiable Functions","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-07-08T20:02:53.295835Z"},"links":{"citing_paper":"/paper/2607.05723"},"observation_digest":"sha256:daecd5a9fc9813047736294c6662a4c7f785c153f87c142c0e20c84bf41188c6","observation_id":"34376436-2dae-4243-8612-d790f1501f63","resolution":{"observed_at":"2026-07-08T20:05:34.398539Z","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":"2026-07-08T20:05:34.394334Z","title":"Heldermann Verlag, 1989","venue":null,"work_id":"c5631c21-216e-4056-8d57-9765dfeabacf","year":1989},"citing_paper":{"arxiv_id":"2607.05723","last_updated":"2026-07-07T01:09:59Z","snapshot_observed_at":"2026-08-14T14:48:00.810263Z","submitted_at":"2026-07-07T01:09:59Z","title":"Generalized Marshall Quotients and Real Semigroups of Continuous and Differentiable Functions","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-07-08T20:02:53.295835Z"},"links":{"citing_paper":"/paper/2607.05723"},"observation_digest":"sha256:e205a5ef9b02a4ad7ccb2694d0316fe38de1ac403157a5107e965cd161d88a2a","observation_id":"8ce8c43c-202e-4e09-8a4c-38e87b480762","resolution":{"observed_at":"2026-07-08T20:05:34.395347Z","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":"2026-07-08T20:05:34.395835Z","title":"Some applications of the łojasiewicz gradient inequality.Communications on Pure and Applied Analysis, 11:2417–2427, 2012","venue":null,"work_id":"12e161d7-b44c-4289-a978-b095c8d4b0f8","year":2012},"citing_paper":{"arxiv_id":"2607.05723","last_updated":"2026-07-07T01:09:59Z","snapshot_observed_at":"2026-08-14T14:48:00.810263Z","submitted_at":"2026-07-07T01:09:59Z","title":"Generalized Marshall Quotients and Real Semigroups of Continuous and Differentiable Functions","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-07-08T20:02:53.295835Z"},"links":{"citing_paper":"/paper/2607.05723"},"observation_digest":"sha256:64f01075e645a2a5c0bad9d5d0c19145d6fb909286ebff1c8de83ef6ad573dd0","observation_id":"c20024db-1b50-4ca5-86c3-a54e8eaeec42","resolution":{"observed_at":"2026-07-08T20:05:34.397001Z","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":"2026-07-08T20:05:34.399070Z","title":"Springer","venue":null,"work_id":"59b901bd-6693-4ab1-9207-ac7ba9b92302","year":2000},"citing_paper":{"arxiv_id":"2607.05723","last_updated":"2026-07-07T01:09:59Z","snapshot_observed_at":"2026-08-14T14:48:00.810263Z","submitted_at":"2026-07-07T01:09:59Z","title":"Generalized Marshall Quotients and Real Semigroups of Continuous and Differentiable Functions","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-07-08T20:02:53.295835Z"},"links":{"citing_paper":"/paper/2607.05723"},"observation_digest":"sha256:d985c3b0e05f7d3b2d2222f3205f99b171b5dc5a1593ccf6963f2862ab736394","observation_id":"e7d9faeb-40c4-43f6-b3fe-4121035f3b21","resolution":{"observed_at":"2026-07-08T20:05:34.400065Z","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":"2026-07-08T20:05:34.403866Z","title":"Real reduced multirings and multifields.Journal of Pure and Applied Algebra, 205(2):452–468, 2006","venue":null,"work_id":"f185302a-749f-4adf-8e80-c5e891a10f41","year":2006},"citing_paper":{"arxiv_id":"2607.05723","last_updated":"2026-07-07T01:09:59Z","snapshot_observed_at":"2026-08-14T14:48:00.810263Z","submitted_at":"2026-07-07T01:09:59Z","title":"Generalized Marshall Quotients and Real Semigroups of Continuous and Differentiable Functions","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-07-08T20:02:53.295835Z"},"links":{"citing_paper":"/paper/2607.05723"},"observation_digest":"sha256:43c8e8929e43ba4fa5b3522ce97d26687d8eb332ecea50efd8fa14804343a2ce","observation_id":"aed6d40b-8fff-4c35-a6b8-9e79b5121a00","resolution":{"observed_at":"2026-07-08T20:05:34.405032Z","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":"2026-07-08T20:05:34.392543Z","title":"Lecture Notes in Mathematics 1636, Springer, 1996","venue":null,"work_id":"b3a41a59-0a3f-4d0f-bea7-97540c12bbaa","year":1996},"citing_paper":{"arxiv_id":"2607.05723","last_updated":"2026-07-07T01:09:59Z","snapshot_observed_at":"2026-08-14T14:48:00.810263Z","submitted_at":"2026-07-07T01:09:59Z","title":"Generalized Marshall Quotients and Real Semigroups of Continuous and Differentiable Functions","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-07-08T20:02:53.295835Z"},"links":{"citing_paper":"/paper/2607.05723"},"observation_digest":"sha256:887807a518ab0b4c3e07605c3f47aac1757ddca3e29908813a6269a415cdf8cc","observation_id":"d1686e74-43c5-41a9-bab2-ce12b7b1a2ed","resolution":{"observed_at":"2026-07-08T20:05:34.393801Z","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":"2026-07-08T20:05:34.390656Z","title":"Boolean real semigroups.Tribute Series, 44:136–175, 2021","venue":null,"work_id":"a0eb4ab3-56de-4d7f-9590-b85b40e6cdc1","year":2021},"citing_paper":{"arxiv_id":"2607.05723","last_updated":"2026-07-07T01:09:59Z","snapshot_observed_at":"2026-08-14T14:48:00.810263Z","submitted_at":"2026-07-07T01:09:59Z","title":"Generalized Marshall Quotients and Real Semigroups of Continuous and Differentiable Functions","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-07-08T20:02:53.295835Z"},"links":{"citing_paper":"/paper/2607.05723"},"observation_digest":"sha256:f8ba10d40fe67b19f74a5734a20fc422791c7404b956d5fe24cf651c940e1068","observation_id":"6cce9c18-b802-4f13-9c11-9ad0186da674","resolution":{"observed_at":"2026-07-08T20:05:34.391980Z","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":"2607.05723","last_updated":"2026-07-07T01:09:59Z","latest_version":1,"primary_category":"math.AC","snapshot_observed_at":"2026-08-14T14:48:00.810263Z","submitted_at":"2026-07-07T01:09:59Z","title":"Generalized Marshall Quotients and Real Semigroups of Continuous and Differentiable Functions"},"reference_resolution":{"displayed":15,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":1,"verified_fuzzy":14},"total_outbound_references":15},"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 15 of 15 outbound references and 0 inbound Pith citation observations for arXiv:2607.05723."}