{"as_of":"2026-08-17T14:31:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:f954cde061d3476ec8a993732d9a66792357be57dba55a34999ec050e790dc2c","coverage":[{"denominator":49,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":49,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-16T04:40:35.190241Z","state":"measured"},{"denominator":49,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":49,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-17T06:30:58.91139+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/2505.00807/citation-record","integrity":"/paper/2505.00807/integrity","json":"/paper/2505.00807/citation-record.json","paper":"/paper/2505.00807"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T04:40:35.870023Z","title":"A nonstandard standardization theorem","venue":null,"work_id":"01044fca-32e3-4567-8274-22a6ec0ea502","year":2014},"citing_paper":{"arxiv_id":"2505.00807","last_updated":"2026-06-25T10:41:18Z","snapshot_observed_at":"2026-08-16T04:32:05.241560Z","submitted_at":"2025-05-01T19:08:22Z","title":"Categorical E-Graphs for Lambda Calculi","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-16T04:40:34.981385Z"},"links":{"citing_paper":"/paper/2505.00807"},"observation_digest":"sha256:1920391dbea5e74fb588c153ac84f332f711be8a7da996efb5e783a0475d029b","observation_id":"09549786-a6d2-477f-b8dc-ccfcc30bdf73","resolution":{"observed_at":"2026-08-16T04:40:35.874050Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T04:40:35.857409Z","title":"R., S PRUNGER , D., AND ZANASI , F","venue":null,"work_id":"0e0e517c-ec4c-4555-af98-7c9c075371a4","year":2022},"citing_paper":{"arxiv_id":"2505.00807","last_updated":"2026-06-25T10:41:18Z","snapshot_observed_at":"2026-08-16T04:32:05.241560Z","submitted_at":"2025-05-01T19:08:22Z","title":"Categorical E-Graphs for Lambda Calculi","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-16T04:40:34.986492Z"},"links":{"citing_paper":"/paper/2505.00807"},"observation_digest":"sha256:e0d3a765172f3dcf40b57e24cec561b8c1f02fbe2472a33694bbec9ccaa23246","observation_id":"215b87a7-db2f-419c-87d1-8ad940d975f6","resolution":{"observed_at":"2026-08-16T04:40:35.861473Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T04:40:35.844132Z","title":"String diagram rewrite theory i: Rewriting with frobeni us structure","venue":null,"work_id":"5e34a37c-ad27-4448-ad91-7fb484857dba","year":2022},"citing_paper":{"arxiv_id":"2505.00807","last_updated":"2026-06-25T10:41:18Z","snapshot_observed_at":"2026-08-16T04:32:05.241560Z","submitted_at":"2025-05-01T19:08:22Z","title":"Categorical E-Graphs for Lambda Calculi","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-16T04:40:34.991037Z"},"links":{"citing_paper":"/paper/2505.00807"},"observation_digest":"sha256:82df67e21eb731f1e28328253f761448f9c5e95a546a1606f698838833e2364a","observation_id":"bdfd39d6-c9d7-4ca6-b159-b11886019d57","resolution":{"observed_at":"2026-08-16T04:40:35.848424Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T04:40:35.830739Z","title":"String diagram rewrite theory i: Rewriting with frobeni us structure","venue":null,"work_id":"e39271e3-69c7-4e3b-9574-6579cceb445d","year":2022},"citing_paper":{"arxiv_id":"2505.00807","last_updated":"2026-06-25T10:41:18Z","snapshot_observed_at":"2026-08-16T04:32:05.241560Z","submitted_at":"2025-05-01T19:08:22Z","title":"Categorical E-Graphs for Lambda Calculi","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-16T04:40:34.996139Z"},"links":{"citing_paper":"/paper/2505.00807"},"observation_digest":"sha256:adc0cf8230e93e3449961dab22f7a7c57b7ca8373aa15270c9088593ce951a7a","observation_id":"589bec3a-a9cb-40ae-8184-6f9558ec47cb","resolution":{"observed_at":"2026-08-16T04:40:35.835147Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T04:40:35.816688Z","title":"String diagram rewrite theory ii: Rewriting with symmet ric monoidal structure","venue":null,"work_id":"f73f6311-292e-4eac-b614-02c48a865fae","year":2022},"citing_paper":{"arxiv_id":"2505.00807","last_updated":"2026-06-25T10:41:18Z","snapshot_observed_at":"2026-08-16T04:32:05.241560Z","submitted_at":"2025-05-01T19:08:22Z","title":"Categorical E-Graphs for Lambda Calculi","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-16T04:40:35.000913Z"},"links":{"citing_paper":"/paper/2505.00807"},"observation_digest":"sha256:eb3d483b05c340b3fc7c37679fbc8f618023758b3ed74e00361a6d969b2dcb42","observation_id":"c4263188-d2c1-47c9-a0fe-ad24a914e448","resolution":{"observed_at":"2026-08-16T04:40:35.821319Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T04:40:35.803370Z","title":"Handbook of Categorical Algebra II","venue":null,"work_id":"13f35b89-740e-40b1-88fa-24df950de0d3","year":1994},"citing_paper":{"arxiv_id":"2505.00807","last_updated":"2026-06-25T10:41:18Z","snapshot_observed_at":"2026-08-16T04:32:05.241560Z","submitted_at":"2025-05-01T19:08:22Z","title":"Categorical E-Graphs for Lambda Calculi","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-16T04:40:35.005967Z"},"links":{"citing_paper":"/paper/2505.00807"},"observation_digest":"sha256:b2a05f69719d0a45e6ba515b762d925f3a10983d4e47189dec543d1842b8cc74","observation_id":"05f772b2-977c-487b-8215-432941eaadac","resolution":{"observed_at":"2026-08-16T04:40:35.807675Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T04:40:35.789605Z","title":"An algebra of hierarchical graphs and its application to structural encoding","venue":null,"work_id":"9407ecd9-694c-481b-bbec-a862c0346da1","year":2010},"citing_paper":{"arxiv_id":"2505.00807","last_updated":"2026-06-25T10:41:18Z","snapshot_observed_at":"2026-08-16T04:32:05.241560Z","submitted_at":"2025-05-01T19:08:22Z","title":"Categorical E-Graphs for Lambda Calculi","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-16T04:40:35.010735Z"},"links":{"citing_paper":"/paper/2505.00807"},"observation_digest":"sha256:1bccaad0ed4096241758dd28fbe7714589339c2511298641e76cf538b9e74224","observation_id":"aed180c2-25d6-43db-b2b8-56a00273b3e3","resolution":{"observed_at":"2026-08-16T04:40:35.793989Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T04:40:35.776401Z","title":"Gs.lambda theories: A syntax for higher-order graphs","venue":null,"work_id":"d43528bb-52a9-406f-bb9b-679b88f5ae22","year":2002},"citing_paper":{"arxiv_id":"2505.00807","last_updated":"2026-06-25T10:41:18Z","snapshot_observed_at":"2026-08-16T04:32:05.241560Z","submitted_at":"2025-05-01T19:08:22Z","title":"Categorical E-Graphs for Lambda Calculi","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-16T04:40:35.015219Z"},"links":{"citing_paper":"/paper/2505.00807"},"observation_digest":"sha256:ae7a505b23b0a1f7f6eb8c88a375eb310fbde48865b3c2a525ad1efc7284c28c","observation_id":"5be09371-1c70-4c58-9c0f-bf06b611ac58","resolution":{"observed_at":"2026-08-16T04:40:35.779987Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T04:40:35.764569Z","title":null,"venue":null,"work_id":"dac2ee3b-daaa-445e-8dff-7cece3b4d92c","year":1972},"citing_paper":{"arxiv_id":"2505.00807","last_updated":"2026-06-25T10:41:18Z","snapshot_observed_at":"2026-08-16T04:32:05.241560Z","submitted_at":"2025-05-01T19:08:22Z","title":"Categorical E-Graphs for Lambda Calculi","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-16T04:40:35.019360Z"},"links":{"citing_paper":"/paper/2505.00807"},"observation_digest":"sha256:783955adf7174210642ccfc47c3bde0569208cd5fa470f2bae1f9a8737a57794","observation_id":"211eedd8-66d4-4d34-a94c-2ea7087498a3","resolution":{"observed_at":"2026-08-16T04:40:35.768077Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T04:40:35.751094Z","title":"Hierarchical graph transformation","venue":null,"work_id":"3a95a37c-e87b-4b0d-b25b-cc423e157498","year":2002},"citing_paper":{"arxiv_id":"2505.00807","last_updated":"2026-06-25T10:41:18Z","snapshot_observed_at":"2026-08-16T04:32:05.241560Z","submitted_at":"2025-05-01T19:08:22Z","title":"Categorical E-Graphs for Lambda Calculi","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-16T04:40:35.022926Z"},"links":{"citing_paper":"/paper/2505.00807"},"observation_digest":"sha256:c7574a5b7d1fa1d0ddb3c2ee6d9e86328d3612f3e614ea673aa21197d492567c","observation_id":"02773295-fc53-4ac5-8864-183d69132825","resolution":{"observed_at":"2026-08-16T04:40:35.755713Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T04:40:35.737557Z","title":"Small Proofs from Congruence Closure","venue":null,"work_id":"cfb4665b-33ab-400c-8ad5-fdbb19cce114","year":2022},"citing_paper":{"arxiv_id":"2505.00807","last_updated":"2026-06-25T10:41:18Z","snapshot_observed_at":"2026-08-16T04:32:05.241560Z","submitted_at":"2025-05-01T19:08:22Z","title":"Categorical E-Graphs for Lambda Calculi","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-16T04:40:35.026508Z"},"links":{"citing_paper":"/paper/2505.00807"},"observation_digest":"sha256:3919049cbb3e9d33de455003c629b4e786825e17b76fb1e2511369ba010048f2","observation_id":"e16979cb-e6ac-4e27-a3e0-95a38a7dcee5","resolution":{"observed_at":"2026-08-16T04:40:35.741939Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T04:40:35.724582Z","title":null,"venue":null,"work_id":"8abab998-b6d2-4fed-b6d1-affd179ffa52","year":2018},"citing_paper":{"arxiv_id":"2505.00807","last_updated":"2026-06-25T10:41:18Z","snapshot_observed_at":"2026-08-16T04:32:05.241560Z","submitted_at":"2025-05-01T19:08:22Z","title":"Categorical E-Graphs for Lambda Calculi","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-16T04:40:35.030250Z"},"links":{"citing_paper":"/paper/2505.00807"},"observation_digest":"sha256:e8e8216f316655fba3456924ba4ac621e491a45602bc41bb10083b53a30fb720","observation_id":"2c409155-9dea-4ae2-8f7a-c6386d4ce649","resolution":{"observed_at":"2026-08-16T04:40:35.728620Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T04:40:35.711123Z","title":"String diagrams for λ -calculi and functional computation, 2024","venue":null,"work_id":"f8f7b7c6-71cc-4444-b818-d6ecd29dedeb","year":2024},"citing_paper":{"arxiv_id":"2505.00807","last_updated":"2026-06-25T10:41:18Z","snapshot_observed_at":"2026-08-16T04:32:05.241560Z","submitted_at":"2025-05-01T19:08:22Z","title":"Categorical E-Graphs for Lambda Calculi","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-16T04:40:35.033575Z"},"links":{"citing_paper":"/paper/2505.00807"},"observation_digest":"sha256:1ae81a6f2f117a8c0e8bb16d8dc33b65cd05a73fa35af0ea447337ed631278cd","observation_id":"06540d79-66ce-40b8-afc8-97fc4abf4270","resolution":{"observed_at":"2026-08-16T04:40:35.715446Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T04:40:35.697961Z","title":"R., B ARRETT , C., AND TIURIN , A","venue":null,"work_id":"1bb53816-9286-4480-bff0-2d94e43562dd","year":2024},"citing_paper":{"arxiv_id":"2505.00807","last_updated":"2026-06-25T10:41:18Z","snapshot_observed_at":"2026-08-16T04:32:05.241560Z","submitted_at":"2025-05-01T19:08:22Z","title":"Categorical E-Graphs for Lambda Calculi","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-16T04:40:35.036959Z"},"links":{"citing_paper":"/paper/2505.00807"},"observation_digest":"sha256:c1944096ba6e9235ced1021487decd323f79bf42649eb210667f4f6af7347045","observation_id":"317df629-d6ed-45cf-a473-c59599ed1130","resolution":{"observed_at":"2026-08-16T04:40:35.702208Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1907.01257","last_updated":"2025-04-23T13:57:46Z","snapshot_observed_at":"2026-08-16T10:59:28.041414Z","submitted_at":"2019-07-02T09:34:59Z","title":"A robust graph-based approach to observational equivalence","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1907.01257","snapshot_observed_at":"2026-08-16T04:40:35.041949Z","title":"R., M UROYA , K., AND AMBRIDGE , T","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2505.00807","last_updated":"2026-06-25T10:41:18Z","snapshot_observed_at":"2026-08-16T04:32:05.241560Z","submitted_at":"2025-05-01T19:08:22Z","title":"Categorical E-Graphs for Lambda Calculi","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-16T04:40:35.041949Z"},"links":{"cited_paper":"/paper/1907.01257","citing_paper":"/paper/2505.00807"},"observation_digest":"sha256:7d80d52d4f2b1b5d1881c88ef80c489a383e193a253c2d0de4e4b9f7fd16dcd0","observation_id":"d21d1f32-d539-4435-b69a-7c7b88362247","resolution":{"observed_at":"2026-08-16T04:40:35.041949Z","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":"2026-08-16T04:40:35.685355Z","title":"Proceedings of the 22nd Conference on Formal Methods in C omputer-Aided Design – FMCAD 2022","venue":null,"work_id":"7f80d3e8-131e-4790-a949-93a1a14ef1e3","year":2022},"citing_paper":{"arxiv_id":"2505.00807","last_updated":"2026-06-25T10:41:18Z","snapshot_observed_at":"2026-08-16T04:32:05.241560Z","submitted_at":"2025-05-01T19:08:22Z","title":"Categorical E-Graphs for Lambda Calculi","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-16T04:40:35.046210Z"},"links":{"citing_paper":"/paper/2505.00807"},"observation_digest":"sha256:99d1a048706eda37af23d761b341eed1373c9a88d8e0969be81e0bfb0a75ef5d","observation_id":"c6104945-8b67-4f7d-96e8-6017b14a49b9","resolution":{"observed_at":"2026-08-16T04:40:35.688973Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T04:40:35.672821Z","title":"Eine algebraisierung des syntheseproblems von schaltk reisen","venue":null,"work_id":"aa448e24-2964-4245-91d1-3636d9d7457a","year":1965},"citing_paper":{"arxiv_id":"2505.00807","last_updated":"2026-06-25T10:41:18Z","snapshot_observed_at":"2026-08-16T04:32:05.241560Z","submitted_at":"2025-05-01T19:08:22Z","title":"Categorical E-Graphs for Lambda Calculi","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-16T04:40:35.050356Z"},"links":{"citing_paper":"/paper/2505.00807"},"observation_digest":"sha256:a7ca318fac292162da8dd7604285b4aedca61348ada7ebfdade81812974a12bf","observation_id":"5aa7aabb-5905-4053-8124-fd054d7b27f4","resolution":{"observed_at":"2026-08-16T04:40:35.676630Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T04:40:35.660257Z","title":"The geometry of tensor calculus, I","venue":null,"work_id":"bd2e6c0f-cc39-44b4-89d9-13540abdb36d","year":1991},"citing_paper":{"arxiv_id":"2505.00807","last_updated":"2026-06-25T10:41:18Z","snapshot_observed_at":"2026-08-16T04:32:05.241560Z","submitted_at":"2025-05-01T19:08:22Z","title":"Categorical E-Graphs for Lambda Calculi","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-16T04:40:35.054492Z"},"links":{"citing_paper":"/paper/2505.00807"},"observation_digest":"sha256:f7e9b36ba51e760de1ecd4d417f08372224957e23729f2010da0ffb05e3b890d","observation_id":"519ec39b-ecc3-4a59-86e4-f1d668bbdd91","resolution":{"observed_at":"2026-08-16T04:40:35.664451Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T04:40:35.646439Z","title":"Sketch-guided equality saturation: Scaling equality s aturation to complex optimizations of functional programs, 2022","venue":null,"work_id":"6b215120-0df8-4de2-b993-e9f769850616","year":2022},"citing_paper":{"arxiv_id":"2505.00807","last_updated":"2026-06-25T10:41:18Z","snapshot_observed_at":"2026-08-16T04:32:05.241560Z","submitted_at":"2025-05-01T19:08:22Z","title":"Categorical E-Graphs for Lambda Calculi","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-16T04:40:35.058590Z"},"links":{"citing_paper":"/paper/2505.00807"},"observation_digest":"sha256:e1cc7fe06eae0123ab142c574e83ff777eb8d9905e0d4023d05a92e6c7d6a899","observation_id":"35011033-72d8-40b9-a1e2-2fdc9caf82a5","resolution":{"observed_at":"2026-08-16T04:40:35.651272Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T04:40:35.633457Z","title":"Categories for the W orking Mathematician","venue":null,"work_id":"e92a49e4-2732-4cfc-97e4-4ce647fc619a","year":1971},"citing_paper":{"arxiv_id":"2505.00807","last_updated":"2026-06-25T10:41:18Z","snapshot_observed_at":"2026-08-16T04:32:05.241560Z","submitted_at":"2025-05-01T19:08:22Z","title":"Categorical E-Graphs for Lambda Calculi","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-16T04:40:35.062494Z"},"links":{"citing_paper":"/paper/2505.00807"},"observation_digest":"sha256:706c71326d8e539b87f7fd77025dd4ddad032cf5c3a1d7867203f8afcab83462","observation_id":"0f1eb6dd-9c4a-4467-a241-e6bb3cd9270f","resolution":{"observed_at":"2026-08-16T04:40:35.637558Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T04:40:35.619767Z","title":"Functorial boxes in string diagrams","venue":null,"work_id":"a488a877-6f4a-4e69-8263-d52cd06e29a9","year":2006},"citing_paper":{"arxiv_id":"2505.00807","last_updated":"2026-06-25T10:41:18Z","snapshot_observed_at":"2026-08-16T04:32:05.241560Z","submitted_at":"2025-05-01T19:08:22Z","title":"Categorical E-Graphs for Lambda Calculi","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-16T04:40:35.066543Z"},"links":{"citing_paper":"/paper/2505.00807"},"observation_digest":"sha256:7012f04d4d9f1950bf8e9a85d91791da3c48d2c99bef9a33b8a2ea0d076926a5","observation_id":"b468f16d-d7db-470a-8589-ea8bfad65b31","resolution":{"observed_at":"2026-08-16T04:40:35.624490Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T04:40:35.604877Z","title":"Monoidal categories enriched in braided monoidal categ ories","venue":null,"work_id":"e383bdc3-1817-4ee3-ab83-1ca4dd979762","year":2019},"citing_paper":{"arxiv_id":"2505.00807","last_updated":"2026-06-25T10:41:18Z","snapshot_observed_at":"2026-08-16T04:32:05.241560Z","submitted_at":"2025-05-01T19:08:22Z","title":"Categorical E-Graphs for Lambda Calculi","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-16T04:40:35.070672Z"},"links":{"citing_paper":"/paper/2505.00807"},"observation_digest":"sha256:105c6172529ce7bb93d76582177cbd1489ee064725f6aae66005c0e363cdeb0e","observation_id":"b36a7f67-9949-4ce9-8153-6dbd1287ec9c","resolution":{"observed_at":"2026-08-16T04:40:35.610197Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T04:40:35.591252Z","title":null,"venue":null,"work_id":"7a28e857-baa0-4d63-abb7-5330222281f4","year":1980},"citing_paper":{"arxiv_id":"2505.00807","last_updated":"2026-06-25T10:41:18Z","snapshot_observed_at":"2026-08-16T04:32:05.241560Z","submitted_at":"2025-05-01T19:08:22Z","title":"Categorical E-Graphs for Lambda Calculi","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-16T04:40:35.074966Z"},"links":{"citing_paper":"/paper/2505.00807"},"observation_digest":"sha256:10da5ccafe6196cca8f8c969491b8eee5f9ca0283c0e205118f61e0887b24d69","observation_id":"a4eab16f-4257-4ea8-8952-71fb38b7231a","resolution":{"observed_at":"2026-08-16T04:40:35.595652Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T04:40:35.578461Z","title":"Algebraic hierarchical graph transformation","venue":null,"work_id":"2c035614-691b-48d1-ad4a-de90bb6613f3","year":2004},"citing_paper":{"arxiv_id":"2505.00807","last_updated":"2026-06-25T10:41:18Z","snapshot_observed_at":"2026-08-16T04:32:05.241560Z","submitted_at":"2025-05-01T19:08:22Z","title":"Categorical E-Graphs for Lambda Calculi","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-16T04:40:35.080078Z"},"links":{"citing_paper":"/paper/2505.00807"},"observation_digest":"sha256:9c9c832dfac6ac25a738f3594e87b5b0658da9cc12f0a691d81b87952fc90796","observation_id":"09b3bb38-f480-42dc-91bf-5f8d45aad869","resolution":{"observed_at":"2026-08-16T04:40:35.582665Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T04:40:35.564059Z","title":"Spinors and space-time , vol","venue":null,"work_id":"1bd78250-b6fd-4b71-98ed-96f789ac4e6b","year":1984},"citing_paper":{"arxiv_id":"2505.00807","last_updated":"2026-06-25T10:41:18Z","snapshot_observed_at":"2026-08-16T04:32:05.241560Z","submitted_at":"2025-05-01T19:08:22Z","title":"Categorical E-Graphs for Lambda Calculi","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-16T04:40:35.084151Z"},"links":{"citing_paper":"/paper/2505.00807"},"observation_digest":"sha256:71731658a7658646d5c918d14c3f3b82becd80fa93fa2d852e5f69a5f954a57b","observation_id":"b0cc838b-6875-4ab7-a59e-0a23d93d6973","resolution":{"observed_at":"2026-08-16T04:40:35.569131Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T04:40:35.550303Z","title":"An introduction to string diagrams for computer scienti sts, 2023","venue":null,"work_id":"0d0164ff-4fcb-45dd-bd54-25d8a6f1ac9d","year":2023},"citing_paper":{"arxiv_id":"2505.00807","last_updated":"2026-06-25T10:41:18Z","snapshot_observed_at":"2026-08-16T04:32:05.241560Z","submitted_at":"2025-05-01T19:08:22Z","title":"Categorical E-Graphs for Lambda Calculi","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-16T04:40:35.088371Z"},"links":{"citing_paper":"/paper/2505.00807"},"observation_digest":"sha256:16a2ef276f9fde8e70752cfc06b46e97980e344811550f233c53786b483925d9","observation_id":"946ebedf-809f-43e1-a073-c2d84ae42739","resolution":{"observed_at":"2026-08-16T04:40:35.555188Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T04:40:35.534926Z","title":null,"venue":null,"work_id":"5a74e68b-ee92-475e-9235-3d3880c04d1a","year":2013},"citing_paper":{"arxiv_id":"2505.00807","last_updated":"2026-06-25T10:41:18Z","snapshot_observed_at":"2026-08-16T04:32:05.241560Z","submitted_at":"2025-05-01T19:08:22Z","title":"Categorical E-Graphs for Lambda Calculi","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-16T04:40:35.092591Z"},"links":{"citing_paper":"/paper/2505.00807"},"observation_digest":"sha256:6fddaf3879c27ef1c52f7a27e1ce60c79821bbfbf988599a833586b6ec18f9fc","observation_id":"e39ebedf-03b5-44e9-9b23-25337bbfff5b","resolution":{"observed_at":"2026-08-16T04:40:35.540167Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T04:40:35.520744Z","title":null,"venue":null,"work_id":"6d67a481-40a7-4dd4-bfc5-25b548e5045a","year":2025},"citing_paper":{"arxiv_id":"2505.00807","last_updated":"2026-06-25T10:41:18Z","snapshot_observed_at":"2026-08-16T04:32:05.241560Z","submitted_at":"2025-05-01T19:08:22Z","title":"Categorical E-Graphs for Lambda Calculi","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-16T04:40:35.096924Z"},"links":{"citing_paper":"/paper/2505.00807"},"observation_digest":"sha256:4441fca85c02236069617548cb8a5dab9455ffa99b3b85cf6b0ca3e51d4fa4e2","observation_id":"93310771-a911-44a1-bce4-21b710891c34","resolution":{"observed_at":"2026-08-16T04:40:35.525406Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T04:40:35.508695Z","title":"A Survey of Graphical Languages for Monoidal Categories","venue":null,"work_id":"16f5b08a-32ae-416a-9659-ee4adefa9d89","year":2010},"citing_paper":{"arxiv_id":"2505.00807","last_updated":"2026-06-25T10:41:18Z","snapshot_observed_at":"2026-08-16T04:32:05.241560Z","submitted_at":"2025-05-01T19:08:22Z","title":"Categorical E-Graphs for Lambda Calculi","version":2},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-16T04:40:35.100972Z"},"links":{"citing_paper":"/paper/2505.00807"},"observation_digest":"sha256:a68a8cb676420a8757ed071a0445488dc0baffac9957a5bdb6fdd40cb48ad16f","observation_id":"c6beaf4a-222a-4800-9874-bda3db729f7c","resolution":{"observed_at":"2026-08-16T04:40:35.512364Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T04:40:35.495248Z","title":"Colored e-graph: Equality reasoning with conditions, 2 023","venue":null,"work_id":"38aac16b-5b35-4abd-94ca-633851c38012","year":null},"citing_paper":{"arxiv_id":"2505.00807","last_updated":"2026-06-25T10:41:18Z","snapshot_observed_at":"2026-08-16T04:32:05.241560Z","submitted_at":"2025-05-01T19:08:22Z","title":"Categorical E-Graphs for Lambda Calculi","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-16T04:40:35.105216Z"},"links":{"citing_paper":"/paper/2505.00807"},"observation_digest":"sha256:1bec1658bc9caa836987db036475fb64b60c1fb74588e11ef8f310bfe0653a07","observation_id":"330f1ad6-5a6b-48ae-bc1b-0d70d7babb0a","resolution":{"observed_at":"2026-08-16T04:40:35.499593Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T04:40:35.481277Z","title":"Equality saturation: A new approach to optimization","venue":null,"work_id":"dac64a27-98cd-47a7-83f9-3799dd00c491","year":2009},"citing_paper":{"arxiv_id":"2505.00807","last_updated":"2026-06-25T10:41:18Z","snapshot_observed_at":"2026-08-16T04:32:05.241560Z","submitted_at":"2025-05-01T19:08:22Z","title":"Categorical E-Graphs for Lambda Calculi","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-16T04:40:35.108932Z"},"links":{"citing_paper":"/paper/2505.00807"},"observation_digest":"sha256:9c30a90074e52001eac4c221ac13d62c506fc960040469862a38f4a6307a22f2","observation_id":"d842767c-bfcb-4794-a19b-bda970c6935c","resolution":{"observed_at":"2026-08-16T04:40:35.485658Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T04:40:35.468028Z","title":"R., F LATT, O., T ATLOCK , Z., AND PANCHEKHA , P","venue":null,"work_id":"683538bd-f4f4-4bab-a56a-ea7e45df5bdf","year":2021},"citing_paper":{"arxiv_id":"2505.00807","last_updated":"2026-06-25T10:41:18Z","snapshot_observed_at":"2026-08-16T04:32:05.241560Z","submitted_at":"2025-05-01T19:08:22Z","title":"Categorical E-Graphs for Lambda Calculi","version":2},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-16T04:40:35.112425Z"},"links":{"citing_paper":"/paper/2505.00807"},"observation_digest":"sha256:c2423b8231f06396f4a23f531bb60302e2a71c397da6d071c5c795401ff4323c","observation_id":"5f448f5a-f1dc-4c34-bd84-e14059f950de","resolution":{"observed_at":"2026-08-16T04:40:35.472220Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T04:40:35.454651Z","title":"R., W ILLSEY , M., AND TATLOCK , Z","venue":null,"work_id":"17ddaefc-51ae-4766-a698-464af38b1282","year":2022},"citing_paper":{"arxiv_id":"2505.00807","last_updated":"2026-06-25T10:41:18Z","snapshot_observed_at":"2026-08-16T04:32:05.241560Z","submitted_at":"2025-05-01T19:08:22Z","title":"Categorical E-Graphs for Lambda Calculi","version":2},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-16T04:40:35.116178Z"},"links":{"citing_paper":"/paper/2505.00807"},"observation_digest":"sha256:0aedfd1023ed53596f6f404463beabd1d2d6304ddc2477ffd5c4874208f1deff","observation_id":"59dbbc63-81aa-467a-8b4e-67835f77f784","resolution":{"observed_at":"2026-08-16T04:40:35.458915Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T04:40:35.442879Z","title":null,"venue":null,"work_id":"da7fabbf-1d82-4b64-b2c6-25923c4b2a96","year":null},"citing_paper":{"arxiv_id":"2505.00807","last_updated":"2026-06-25T10:41:18Z","snapshot_observed_at":"2026-08-16T04:32:05.241560Z","submitted_at":"2025-05-01T19:08:22Z","title":"Categorical E-Graphs for Lambda Calculi","version":2},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-16T04:40:35.120078Z"},"links":{"citing_paper":"/paper/2505.00807"},"observation_digest":"sha256:d6d015b237a6896e3c1d74bbe1c2b2c8df337239812ac1435348d07617e6e250","observation_id":"e563b8d8-ba47-4c70-bf52-a692b0f7cd21","resolution":{"observed_at":"2026-08-16T04:40:35.446367Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T04:40:35.429237Z","title":null,"venue":null,"work_id":"3a4a55ca-1010-4867-92ef-fd92259d8c13","year":null},"citing_paper":{"arxiv_id":"2505.00807","last_updated":"2026-06-25T10:41:18Z","snapshot_observed_at":"2026-08-16T04:32:05.241560Z","submitted_at":"2025-05-01T19:08:22Z","title":"Categorical E-Graphs for Lambda Calculi","version":2},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-16T04:40:35.129115Z"},"links":{"citing_paper":"/paper/2505.00807"},"observation_digest":"sha256:6119383e6a3d99f301e96a57d66c046088b38e77b3fb0c653b77cc204728f532","observation_id":"b6d5893d-f602-431b-81ee-e31ca87fe06b","resolution":{"observed_at":"2026-08-16T04:40:35.433866Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T04:40:35.416159Z","title":null,"venue":null,"work_id":"11c14be7-a39a-43c9-ae4a-11357ea3e3be","year":null},"citing_paper":{"arxiv_id":"2505.00807","last_updated":"2026-06-25T10:41:18Z","snapshot_observed_at":"2026-08-16T04:32:05.241560Z","submitted_at":"2025-05-01T19:08:22Z","title":"Categorical E-Graphs for Lambda Calculi","version":2},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-16T04:40:35.133475Z"},"links":{"citing_paper":"/paper/2505.00807"},"observation_digest":"sha256:1bca861e61fed5f87f926e71a00de0bfbe688e6a3b5611b9046d1b01dc13e9bc","observation_id":"5991b908-17ee-4b80-ba47-584e50f37424","resolution":{"observed_at":"2026-08-16T04:40:35.420402Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T04:40:35.402698Z","title":"Theorem A.10 (Existence of pushouts in EHyp(Σ) )","venue":null,"work_id":"49ba643f-b5b2-4a1f-a30e-5b67bbfa1d81","year":null},"citing_paper":{"arxiv_id":"2505.00807","last_updated":"2026-06-25T10:41:18Z","snapshot_observed_at":"2026-08-16T04:32:05.241560Z","submitted_at":"2025-05-01T19:08:22Z","title":"Categorical E-Graphs for Lambda Calculi","version":2},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-16T04:40:35.137858Z"},"links":{"citing_paper":"/paper/2505.00807"},"observation_digest":"sha256:6fe2810666b1ccac0a3f0bf8a5bb96822f529aee45e888f850feb28c76a65ea7","observation_id":"5a7e18af-4eb1-4946-99c2-da7f1dcc8717","resolution":{"observed_at":"2026-08-16T04:40:35.407273Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T04:40:35.389220Z","title":null,"venue":null,"work_id":"5712bc61-9f0f-4ca4-94ba-6cee474d55dc","year":null},"citing_paper":{"arxiv_id":"2505.00807","last_updated":"2026-06-25T10:41:18Z","snapshot_observed_at":"2026-08-16T04:32:05.241560Z","submitted_at":"2025-05-01T19:08:22Z","title":"Categorical E-Graphs for Lambda Calculi","version":2},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-16T04:40:35.142616Z"},"links":{"citing_paper":"/paper/2505.00807"},"observation_digest":"sha256:4308c7995ded146bb5b9243038ab1a705716927e7ccd962818a45d6d8ec566a3","observation_id":"a2e17fe2-ad0d-4b07-afa4-7323326a556f","resolution":{"observed_at":"2026-08-16T04:40:35.393387Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T04:40:35.376235Z","title":null,"venue":null,"work_id":"82219700-2408-429b-ab02-83311f6ca42d","year":null},"citing_paper":{"arxiv_id":"2505.00807","last_updated":"2026-06-25T10:41:18Z","snapshot_observed_at":"2026-08-16T04:32:05.241560Z","submitted_at":"2025-05-01T19:08:22Z","title":"Categorical E-Graphs for Lambda Calculi","version":2},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-16T04:40:35.146821Z"},"links":{"citing_paper":"/paper/2505.00807"},"observation_digest":"sha256:0919eafb94af19ecd7873a75af6c8349c045c2db9b724638ac8faf8008dcedd7","observation_id":"26cb576e-18e4-4820-881d-bb6dc16f7655","resolution":{"observed_at":"2026-08-16T04:40:35.380296Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T04:40:35.362782Z","title":null,"venue":null,"work_id":"f63b032e-a16e-4a4c-804a-2d12d2eb01b3","year":null},"citing_paper":{"arxiv_id":"2505.00807","last_updated":"2026-06-25T10:41:18Z","snapshot_observed_at":"2026-08-16T04:32:05.241560Z","submitted_at":"2025-05-01T19:08:22Z","title":"Categorical E-Graphs for Lambda Calculi","version":2},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-16T04:40:35.152067Z"},"links":{"citing_paper":"/paper/2505.00807"},"observation_digest":"sha256:240afa08ecbdcff5922157599c8d8e534c61e4d3bfc3078ec8be28b282849bcd","observation_id":"a4e6b8d4-57a7-4015-8251-93d1c16bd426","resolution":{"observed_at":"2026-08-16T04:40:35.366989Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T04:40:35.349632Z","title":"then the pushout X +f,g Y exists","venue":null,"work_id":"b8b26de9-050d-46cb-b5bc-bcd3af69378d","year":null},"citing_paper":{"arxiv_id":"2505.00807","last_updated":"2026-06-25T10:41:18Z","snapshot_observed_at":"2026-08-16T04:32:05.241560Z","submitted_at":"2025-05-01T19:08:22Z","title":"Categorical E-Graphs for Lambda Calculi","version":2},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-16T04:40:35.156152Z"},"links":{"citing_paper":"/paper/2505.00807"},"observation_digest":"sha256:eae90b9117796edf5696b9b8f2cf2ff993c51b5d16c11b6227bdf295c0a29835","observation_id":"d3446458-1300-40f7-9146-763765d17888","resolution":{"observed_at":"2026-08-16T04:40:35.353423Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T04:40:35.336549Z","title":null,"venue":null,"work_id":"9fce0466-6007-436e-a239-d28f7fe5d659","year":null},"citing_paper":{"arxiv_id":"2505.00807","last_updated":"2026-06-25T10:41:18Z","snapshot_observed_at":"2026-08-16T04:32:05.241560Z","submitted_at":"2025-05-01T19:08:22Z","title":"Categorical E-Graphs for Lambda Calculi","version":2},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-16T04:40:35.160499Z"},"links":{"citing_paper":"/paper/2505.00807"},"observation_digest":"sha256:ec09dba81b2fd1dd01f86e598b7f0a5650405fc4d0cedcfcb80de023f7142d35","observation_id":"151c69ef-2dbd-40c6-8f57-c59f5d7f319e","resolution":{"observed_at":"2026-08-16T04:40:35.340832Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T04:40:35.321448Z","title":null,"venue":null,"work_id":"47d4524b-99b6-4f6c-a0f4-e3c6897e17c5","year":null},"citing_paper":{"arxiv_id":"2505.00807","last_updated":"2026-06-25T10:41:18Z","snapshot_observed_at":"2026-08-16T04:32:05.241560Z","submitted_at":"2025-05-01T19:08:22Z","title":"Categorical E-Graphs for Lambda Calculi","version":2},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-16T04:40:35.165390Z"},"links":{"citing_paper":"/paper/2505.00807"},"observation_digest":"sha256:8f8ac4571b51bf17d08e029ac4fa0c4d615001dce97c25b5301ffddd44712da2","observation_id":"60e321bf-46bf-4c67-9ad0-8454bf88a185","resolution":{"observed_at":"2026-08-16T04:40:35.326999Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T04:40:35.306581Z","title":"Then we deﬁne <µ X + Y / ∼ (ιEX + EY / ∼[e]) = [ <µ X+Y (ιEX +EY (e))]","venue":null,"work_id":"a78d19de-1fcb-4f1d-959a-c8244fc707eb","year":null},"citing_paper":{"arxiv_id":"2505.00807","last_updated":"2026-06-25T10:41:18Z","snapshot_observed_at":"2026-08-16T04:32:05.241560Z","submitted_at":"2025-05-01T19:08:22Z","title":"Categorical E-Graphs for Lambda Calculi","version":2},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-16T04:40:35.169608Z"},"links":{"citing_paper":"/paper/2505.00807"},"observation_digest":"sha256:cad404b1347b97b5427d796669ec7abee92c726d43105ec474fecac5863c822f","observation_id":"f8f42f39-f822-4b88-a29e-6571068e8718","resolution":{"observed_at":"2026-08-16T04:40:35.311376Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T04:40:35.291478Z","title":"Clearly, all the cases above are disjoint","venue":null,"work_id":"f20c05b4-d8ad-499f-b4b9-911f63f0cef6","year":null},"citing_paper":{"arxiv_id":"2505.00807","last_updated":"2026-06-25T10:41:18Z","snapshot_observed_at":"2026-08-16T04:32:05.241560Z","submitted_at":"2025-05-01T19:08:22Z","title":"Categorical E-Graphs for Lambda Calculi","version":2},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-16T04:40:35.173771Z"},"links":{"citing_paper":"/paper/2505.00807"},"observation_digest":"sha256:7fef2ccd82f77fd89e08c36f6061c93f97171ac8cb8bf9d930e21766a572f11f","observation_id":"89e42421-ed74-4650-9612-d3db1e7b82b4","resolution":{"observed_at":"2026-08-16T04:40:35.296123Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T04:40:35.277498Z","title":null,"venue":null,"work_id":"aed89999-95d6-4218-a25f-d0c0d9870211","year":null},"citing_paper":{"arxiv_id":"2505.00807","last_updated":"2026-06-25T10:41:18Z","snapshot_observed_at":"2026-08-16T04:32:05.241560Z","submitted_at":"2025-05-01T19:08:22Z","title":"Categorical E-Graphs for Lambda Calculi","version":2},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-16T04:40:35.177780Z"},"links":{"citing_paper":"/paper/2505.00807"},"observation_digest":"sha256:01fc1c536d2b9186be1e4dedda41d6b25aef36247126ec53681be1d33f67cec8","observation_id":"a6738679-7db4-4fce-a9f4-bdbcf1eca177","resolution":{"observed_at":"2026-08-16T04:40:35.281859Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T04:40:35.263778Z","title":"Then we let ⌣# X + Y / ∼(ιVX + VY / ∼([u])) = ⌣# X + Y / ∼(ιVX + VY / ∼([v])) Next we deﬁne ⌣# X + Y / ∼ for edges","venue":null,"work_id":"f924ce25-be2d-4a84-a6d6-11b1a0c2eb36","year":null},"citing_paper":{"arxiv_id":"2505.00807","last_updated":"2026-06-25T10:41:18Z","snapshot_observed_at":"2026-08-16T04:32:05.241560Z","submitted_at":"2025-05-01T19:08:22Z","title":"Categorical E-Graphs for Lambda Calculi","version":2},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-16T04:40:35.181885Z"},"links":{"citing_paper":"/paper/2505.00807"},"observation_digest":"sha256:b510a80d7b7c2dc1c424eeeb23a790959622ab061fbfa8b0f43459d69aa89d18","observation_id":"28988a9e-7273-47a2-beaa-104abe8e6acb","resolution":{"observed_at":"2026-08-16T04:40:35.268240Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T04:40:35.249880Z","title":null,"venue":null,"work_id":"73f677cb-be31-4d59-9c52-2d2679cdd151","year":null},"citing_paper":{"arxiv_id":"2505.00807","last_updated":"2026-06-25T10:41:18Z","snapshot_observed_at":"2026-08-16T04:32:05.241560Z","submitted_at":"2025-05-01T19:08:22Z","title":"Categorical E-Graphs for Lambda Calculi","version":2},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-16T04:40:35.186053Z"},"links":{"citing_paper":"/paper/2505.00807"},"observation_digest":"sha256:d96c3a9004a0191f036c9bb5c6ee4006b1a23e2dbd9d014c516acc55ada02c22","observation_id":"63e56d2e-8d99-4994-8f2b-9b1cacdb47fd","resolution":{"observed_at":"2026-08-16T04:40:35.254265Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T04:40:35.235227Z","title":"Then we deﬁne ⌣X + Y / ∼(ιVX + VY / ∼([v])) and ⌣X + Y / ∼(ιEX + EY / ∼([e])) as closures of ⌣# X + Y / ∼ as below","venue":null,"work_id":"60a36f94-76ba-4e9f-9d3a-a378c9015d68","year":null},"citing_paper":{"arxiv_id":"2505.00807","last_updated":"2026-06-25T10:41:18Z","snapshot_observed_at":"2026-08-16T04:32:05.241560Z","submitted_at":"2025-05-01T19:08:22Z","title":"Categorical E-Graphs for Lambda Calculi","version":2},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-16T04:40:35.190241Z"},"links":{"citing_paper":"/paper/2505.00807"},"observation_digest":"sha256:6c26ab1a768834023f5bcce5b0df34906dfdc13be719f1d2fa5808cb06db8381","observation_id":"76b0829d-9be9-4669-a5a0-7361a6b2378c","resolution":{"observed_at":"2026-08-16T04:40:35.240071Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2505.00807","last_updated":"2026-06-25T10:41:18Z","latest_version":2,"primary_category":"cs.LO","snapshot_observed_at":"2026-08-16T04:32:05.241560Z","submitted_at":"2025-05-01T19:08:22Z","title":"Categorical E-Graphs for Lambda Calculi"},"reference_resolution":{"displayed":49,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":16,"verified_exact":0,"verified_fuzzy":33},"total_outbound_references":49},"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":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"thesis":"As of 17 August 2026, this Paper Citation Record lists 49 of 49 outbound references and 0 inbound Pith citation observations for arXiv:2505.00807."}