{"as_of":"2026-08-07T05:41:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:d07f2f497990d234991684d51c4995837304ffaec714bb25cf0476d296b684ab","coverage":[{"denominator":46,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":46,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-04T21:00:35.884437Z","state":"measured"},{"denominator":46,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":46,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-06T06:34:29.942622+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/2509.08264/citation-record","integrity":"/paper/2509.08264/integrity","json":"/paper/2509.08264/citation-record.json","paper":"/paper/2509.08264"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T21:00:35.644719Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2509.08264","last_updated":"2025-09-10T03:44:44Z","snapshot_observed_at":"2026-08-04T21:00:34.972904Z","submitted_at":"2025-09-10T03:44:44Z","title":"Hammering Higher Order Set Theory","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-04T21:00:35.644719Z"},"links":{"citing_paper":"/paper/2509.08264"},"observation_digest":"sha256:4e53da82cf2258a44f4c530bf03bc13857677639d97b02d05efa47e85ccc4655","observation_id":"e483177a-0563-4c20-9e2a-e64a52c6c4d3","resolution":{"observed_at":"2026-08-04T21:00:35.644719Z","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":"2026-08-04T21:00:36.630540Z","title":"Superpositionforlambda-freehigher-orderlogic.Log","venue":null,"work_id":"a60d6805-37f4-474d-b28c-e577032677e5","year":null},"citing_paper":{"arxiv_id":"2509.08264","last_updated":"2025-09-10T03:44:44Z","snapshot_observed_at":"2026-08-04T21:00:34.972904Z","submitted_at":"2025-09-10T03:44:44Z","title":"Hammering Higher Order Set Theory","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-04T21:00:35.649377Z"},"links":{"citing_paper":"/paper/2509.08264"},"observation_digest":"sha256:e2b2dabecce052095074b11f1f82967e532b9ae6455447bf2856e27a97b1cfd9","observation_id":"3d36b629-391d-4e08-9542-d0cc201733d6","resolution":{"observed_at":"2026-08-04T21:00:36.636329Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-08-04T21:00:36.601808Z","title":"THF0 - the core of the TPTP language for higher-order logic","venue":null,"work_id":"d28fbcce-7082-4f86-bbea-e6ccdf7b28ae","year":2008},"citing_paper":{"arxiv_id":"2509.08264","last_updated":"2025-09-10T03:44:44Z","snapshot_observed_at":"2026-08-04T21:00:34.972904Z","submitted_at":"2025-09-10T03:44:44Z","title":"Hammering Higher Order Set Theory","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-04T21:00:35.658573Z"},"links":{"citing_paper":"/paper/2509.08264"},"observation_digest":"sha256:c120753f17eee9011391593ddfb2f6a20c02a98bbe9b9b5c6e501020addebb0b","observation_id":"46f12512-181c-4836-a971-4e279f58a830","resolution":{"observed_at":"2026-08-04T21:00:36.606648Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T21:00:35.663990Z","title":"A higher-order vampire (short paper)","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2509.08264","last_updated":"2025-09-10T03:44:44Z","snapshot_observed_at":"2026-08-04T21:00:34.972904Z","submitted_at":"2025-09-10T03:44:44Z","title":"Hammering Higher Order Set Theory","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-04T21:00:35.663990Z"},"links":{"citing_paper":"/paper/2509.08264"},"observation_digest":"sha256:423a2186489f215064da43094f4a8bbd745785563d28de55d2896525434f4c97","observation_id":"99f45460-824d-47be-9348-9394565371d2","resolution":{"observed_at":"2026-08-04T21:00:35.663990Z","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":"2026-08-04T21:00:36.587784Z","title":"PhD thesis, Fakultät für Informatik, Technische Universität München, 2012","venue":null,"work_id":"f9cda678-d7ca-456d-bd1b-ba66daa27ef3","year":2012},"citing_paper":{"arxiv_id":"2509.08264","last_updated":"2025-09-10T03:44:44Z","snapshot_observed_at":"2026-08-04T21:00:34.972904Z","submitted_at":"2025-09-10T03:44:44Z","title":"Hammering Higher Order Set Theory","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-04T21:00:35.668872Z"},"links":{"citing_paper":"/paper/2509.08264"},"observation_digest":"sha256:842dc177a61f2aaa7ecb173c4e6de1c2309109f876e73a9506091bc4945f2c17","observation_id":"d539da97-6c96-4bfc-a38c-2d9ab263e7a0","resolution":{"observed_at":"2026-08-04T21:00:36.591756Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-08-04T21:00:36.573330Z","title":null,"venue":null,"work_id":"9b00847c-80cd-4130-b273-fe43e5988834","year":2011},"citing_paper":{"arxiv_id":"2509.08264","last_updated":"2025-09-10T03:44:44Z","snapshot_observed_at":"2026-08-04T21:00:34.972904Z","submitted_at":"2025-09-10T03:44:44Z","title":"Hammering Higher Order Set Theory","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-04T21:00:35.675331Z"},"links":{"citing_paper":"/paper/2509.08264"},"observation_digest":"sha256:11a56f4329e029f9fe42c3341f24ea5735a495ecfa2dc266e9165ca5ce2dc215","observation_id":"6705cfb3-dad2-4caf-8832-be356ff25b4c","resolution":{"observed_at":"2026-08-04T21:00:36.578093Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.2168/lmcs-12(4:13)2016","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Encoding monomorphic and polymorphic types.Log","venue":"Logical Methods in Computer Science","work_id":"003faf55-d7c0-40e4-9cfa-d0357be9ab4f","year":2016},"citing_paper":{"arxiv_id":"2509.08264","last_updated":"2025-09-10T03:44:44Z","snapshot_observed_at":"2026-08-04T21:00:34.972904Z","submitted_at":"2025-09-10T03:44:44Z","title":"Hammering Higher Order Set Theory","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-04T21:00:35.682404Z"},"links":{"citing_paper":"/paper/2509.08264"},"observation_digest":"sha256:608a04358462984495b583344270f8bb67eadda3556ca3828735d8ac3a0bf9b0","observation_id":"05b0297d-5d60-48f1-8e80-6787e87fd479","resolution":{"observed_at":"2026-08-04T21:00:36.084650Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s10817-016-9362-8","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"A learning-based fact selector for Isabelle/HOL","venue":"Journal of Automated Reasoning","work_id":"5fbcfcf2-d5bf-423a-bf0c-db9efa191fbb","year":2016},"citing_paper":{"arxiv_id":"2509.08264","last_updated":"2025-09-10T03:44:44Z","snapshot_observed_at":"2026-08-04T21:00:34.972904Z","submitted_at":"2025-09-10T03:44:44Z","title":"Hammering Higher Order Set Theory","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-04T21:00:35.689523Z"},"links":{"citing_paper":"/paper/2509.08264"},"observation_digest":"sha256:1e040104a35fdf888ee490cdb60fdc31b6911e9bcd0143ebcbbd70af863d0db7","observation_id":"9f2f35f1-b2b9-4b84-bb5e-794d9f6599e1","resolution":{"observed_at":"2026-08-04T21:00:36.070744Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-08-04T21:00:36.556213Z","title":"Paulson, and Josef Urban","venue":null,"work_id":"ae67a7e2-59e0-49c5-ad6c-4e705f966b40","year":null},"citing_paper":{"arxiv_id":"2509.08264","last_updated":"2025-09-10T03:44:44Z","snapshot_observed_at":"2026-08-04T21:00:34.972904Z","submitted_at":"2025-09-10T03:44:44Z","title":"Hammering Higher Order Set Theory","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-04T21:00:35.693991Z"},"links":{"citing_paper":"/paper/2509.08264"},"observation_digest":"sha256:868cf414b948e3b74754053d8e8e996118c69c2743fed72314e7def342fe994a","observation_id":"59ab1fe0-a174-494d-8adb-be94c7d26e87","resolution":{"observed_at":"2026-08-04T21:00:36.562726Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-08-04T21:00:36.533020Z","title":null,"venue":null,"work_id":"084652be-b47a-4432-bcec-7f5b56ac787a","year":2015},"citing_paper":{"arxiv_id":"2509.08264","last_updated":"2025-09-10T03:44:44Z","snapshot_observed_at":"2026-08-04T21:00:34.972904Z","submitted_at":"2025-09-10T03:44:44Z","title":"Hammering Higher Order Set Theory","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-04T21:00:35.704746Z"},"links":{"citing_paper":"/paper/2509.08264"},"observation_digest":"sha256:9cdf79c6cf9b47b6a2e19656beb4dc4cbdfd8dafb2fd11f2a85d42e8fb744a1d","observation_id":"4f435b0e-7913-40dd-b7ba-1fda6f12196d","resolution":{"observed_at":"2026-08-04T21:00:36.537304Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T21:00:35.710717Z","title":"Brown, Thibault Gauthier, Cezary Kaliszyk, Geoff Sutcliffe, and Josef Urban","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2509.08264","last_updated":"2025-09-10T03:44:44Z","snapshot_observed_at":"2026-08-04T21:00:34.972904Z","submitted_at":"2025-09-10T03:44:44Z","title":"Hammering Higher Order Set Theory","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-04T21:00:35.710717Z"},"links":{"citing_paper":"/paper/2509.08264"},"observation_digest":"sha256:c4908cb4b8c84071e6c9a75d689fa727153dd4b1b85177710e7b12d40a7e2155","observation_id":"88e0e719-43c0-439b-be75-6a23242c19fd","resolution":{"observed_at":"2026-08-04T21:00:35.710717Z","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":"2026-08-04T21:00:35.714576Z","title":"Brown and Cezary Kaliszyk","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2509.08264","last_updated":"2025-09-10T03:44:44Z","snapshot_observed_at":"2026-08-04T21:00:34.972904Z","submitted_at":"2025-09-10T03:44:44Z","title":"Hammering Higher Order Set Theory","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-04T21:00:35.714576Z"},"links":{"citing_paper":"/paper/2509.08264"},"observation_digest":"sha256:02e1676040f7a86c590fa06b26b210feca44c0ad8d48f25ab97c4ce8bc500954","observation_id":"628fb0f9-753d-4f06-993a-b63bc0318303","resolution":{"observed_at":"2026-08-04T21:00:35.714576Z","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":"2026-08-04T21:00:35.717957Z","title":"Brown, Cezary Kaliszyk, Thibault Gauthier, and Josef Urban","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2509.08264","last_updated":"2025-09-10T03:44:44Z","snapshot_observed_at":"2026-08-04T21:00:34.972904Z","submitted_at":"2025-09-10T03:44:44Z","title":"Hammering Higher Order Set Theory","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-04T21:00:35.717957Z"},"links":{"citing_paper":"/paper/2509.08264"},"observation_digest":"sha256:16e03f8f4ff67977906805464b9a8b778da049020594795ec6d688c6edd19084","observation_id":"c4c1c186-678b-49cb-b1eb-e5da2ffcdd7c","resolution":{"observed_at":"2026-08-04T21:00:35.717957Z","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":"2026-08-04T21:00:36.519769Z","title":"Brown, Cezary Kaliszyk, and Josef Urban","venue":null,"work_id":"7332d1db-bb51-4f38-a67d-18118365fb9e","year":2025},"citing_paper":{"arxiv_id":"2509.08264","last_updated":"2025-09-10T03:44:44Z","snapshot_observed_at":"2026-08-04T21:00:34.972904Z","submitted_at":"2025-09-10T03:44:44Z","title":"Hammering Higher Order Set Theory","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-04T21:00:35.722541Z"},"links":{"citing_paper":"/paper/2509.08264"},"observation_digest":"sha256:b63b622ef47744a35d91eafb91bdee7659608d73d65697364bc09e38617f0679","observation_id":"10f10f53-137e-4d94-ad62-0765b38674d5","resolution":{"observed_at":"2026-08-04T21:00:36.523332Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-08-04T21:00:36.507988Z","title":"Brown and Karol Pąk","venue":null,"work_id":"8da90e15-7d5b-45c9-a6af-1d59832e88e7","year":2019},"citing_paper":{"arxiv_id":"2509.08264","last_updated":"2025-09-10T03:44:44Z","snapshot_observed_at":"2026-08-04T21:00:34.972904Z","submitted_at":"2025-09-10T03:44:44Z","title":"Hammering Higher Order Set Theory","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-04T21:00:35.727067Z"},"links":{"citing_paper":"/paper/2509.08264"},"observation_digest":"sha256:6cc059880259cbdf2c116ed7b16169fc69d14b3a8854d70b89ce65f7f69340ed","observation_id":"adaf0eb8-8911-4a56-a8c8-11a97fbed045","resolution":{"observed_at":"2026-08-04T21:00:36.511716Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-08-04T21:00:36.492892Z","title":"Brown and Josef Urban","venue":null,"work_id":"381258ad-7447-4e52-b9f9-d979bf8b1461","year":2016},"citing_paper":{"arxiv_id":"2509.08264","last_updated":"2025-09-10T03:44:44Z","snapshot_observed_at":"2026-08-04T21:00:34.972904Z","submitted_at":"2025-09-10T03:44:44Z","title":"Hammering Higher Order Set Theory","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-04T21:00:35.733295Z"},"links":{"citing_paper":"/paper/2509.08264"},"observation_digest":"sha256:1151fbc99e8d0cc59672d732b9db317bdb6fd3be46e30e1df45e5561bf17f950","observation_id":"9bd93719-28b9-4d3d-a3ea-c4cfad857c09","resolution":{"observed_at":"2026-08-04T21:00:36.498341Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T21:00:35.743737Z","title":"Brown, and Josef Urban","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2509.08264","last_updated":"2025-09-10T03:44:44Z","snapshot_observed_at":"2026-08-04T21:00:34.972904Z","submitted_at":"2025-09-10T03:44:44Z","title":"Hammering Higher Order Set Theory","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-04T21:00:35.743737Z"},"links":{"citing_paper":"/paper/2509.08264"},"observation_digest":"sha256:3ae93fb8d354211052ac080835c654b3370f9364d9180cfe066b0a47b9fb7f62","observation_id":"9ab7f1ae-6aa8-4592-a7fd-10f7618927e4","resolution":{"observed_at":"2026-08-04T21:00:35.743737Z","resolver_source":null,"status":"malformed_identifier"},"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":"2026-08-04T21:00:36.472207Z","title":"Conway.On numbers and games, Second Edition","venue":null,"work_id":"e18129b8-19eb-482f-a489-1a69ed2ed495","year":2001},"citing_paper":{"arxiv_id":"2509.08264","last_updated":"2025-09-10T03:44:44Z","snapshot_observed_at":"2026-08-04T21:00:34.972904Z","submitted_at":"2025-09-10T03:44:44Z","title":"Hammering Higher Order Set Theory","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-04T21:00:35.751084Z"},"links":{"citing_paper":"/paper/2509.08264"},"observation_digest":"sha256:d9b9d815335fc55162b9508ba9e3df2701ac99b166b7ba6f54c5e25bee5061a6","observation_id":"e2d03619-4bf4-48d9-87bb-6e9aea3db9ae","resolution":{"observed_at":"2026-08-04T21:00:36.480176Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-08-04T21:00:36.457718Z","title":"The Naproche system: Proof-checking mathematical texts in controlled natural language","venue":null,"work_id":"3091dd42-4cbf-4950-a466-aaebb51c773f","year":2014},"citing_paper":{"arxiv_id":"2509.08264","last_updated":"2025-09-10T03:44:44Z","snapshot_observed_at":"2026-08-04T21:00:34.972904Z","submitted_at":"2025-09-10T03:44:44Z","title":"Hammering Higher Order Set Theory","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-04T21:00:35.755104Z"},"links":{"citing_paper":"/paper/2509.08264"},"observation_digest":"sha256:b569d18fdfba4882720b14be1d6f7c8d1c2e07912b7a5102f275fd571c2c2507","observation_id":"da436cc4-ab56-4aa6-bd7e-275e6ef8410a","resolution":{"observed_at":"2026-08-04T21:00:36.461972Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-08-04T21:00:36.442684Z","title":"Hammer for Coq: Automation for depen- dent type theory.J","venue":null,"work_id":"f477b1a4-0f7f-47b8-b898-d16e255d7a1f","year":2018},"citing_paper":{"arxiv_id":"2509.08264","last_updated":"2025-09-10T03:44:44Z","snapshot_observed_at":"2026-08-04T21:00:34.972904Z","submitted_at":"2025-09-10T03:44:44Z","title":"Hammering Higher Order Set Theory","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-04T21:00:35.760425Z"},"links":{"citing_paper":"/paper/2509.08264"},"observation_digest":"sha256:644ee7adad6e7df879abe85421e919be04f776dde50fb9c6daa325ff52bd56b8","observation_id":"c878d1b7-2035-4913-a131-713994ce3f43","resolution":{"observed_at":"2026-08-04T21:00:36.447324Z","resolver_source":"raw_fallback","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-08-04T21:00:36.424991Z","title":"Interpretation of a Mizar-like logic in first-order logic","venue":null,"work_id":"b4adbd58-3c15-402a-99f6-f21d4c30eca7","year":1998},"citing_paper":{"arxiv_id":"2509.08264","last_updated":"2025-09-10T03:44:44Z","snapshot_observed_at":"2026-08-04T21:00:34.972904Z","submitted_at":"2025-09-10T03:44:44Z","title":"Hammering Higher Order Set Theory","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-04T21:00:35.764972Z"},"links":{"citing_paper":"/paper/2509.08264"},"observation_digest":"sha256:e2d385f908d6ede4451ede12757768f3825d643f96a91bb6b9b2e32e8f526688","observation_id":"2ecec6a3-544f-489c-8de4-ba4cb8548f23","resolution":{"observed_at":"2026-08-04T21:00:36.428665Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-08-04T21:00:36.405650Z","title":null,"venue":null,"work_id":"42b9cd20-5baf-4709-aeec-400c6f96b87f","year":null},"citing_paper":{"arxiv_id":"2509.08264","last_updated":"2025-09-10T03:44:44Z","snapshot_observed_at":"2026-08-04T21:00:34.972904Z","submitted_at":"2025-09-10T03:44:44Z","title":"Hammering Higher Order Set Theory","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-04T21:00:35.768727Z"},"links":{"citing_paper":"/paper/2509.08264"},"observation_digest":"sha256:b75d3f2bb557b53541b1ac8f926e31ac6408fa909f32c6811be41b7fc5cb90ce","observation_id":"252511d4-8da4-4737-85ea-b692351e075f","resolution":{"observed_at":"2026-08-04T21:00:36.415368Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T21:00:35.772915Z","title":"Seventeen provers under the hammer","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2509.08264","last_updated":"2025-09-10T03:44:44Z","snapshot_observed_at":"2026-08-04T21:00:34.972904Z","submitted_at":"2025-09-10T03:44:44Z","title":"Hammering Higher Order Set Theory","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-04T21:00:35.772915Z"},"links":{"citing_paper":"/paper/2509.08264"},"observation_digest":"sha256:33593f57053d6327f0a1154627d4ae85c2d914b293af3d6bae1297fc03c93209","observation_id":"c373ebfa-bac9-4751-8ca7-677ca7861e8c","resolution":{"observed_at":"2026-08-04T21:00:35.772915Z","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":"6724.26931","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T21:00:36.137466Z","title":"Premise selection and external provers for HOL4","venue":null,"work_id":"61efff44-4214-4881-9b9f-978ac97ba805","year":2015},"citing_paper":{"arxiv_id":"2509.08264","last_updated":"2025-09-10T03:44:44Z","snapshot_observed_at":"2026-08-04T21:00:34.972904Z","submitted_at":"2025-09-10T03:44:44Z","title":"Hammering Higher Order Set Theory","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-04T21:00:35.777114Z"},"links":{"citing_paper":"/paper/2509.08264"},"observation_digest":"sha256:94998ba7759321873cb3ff77860d3395e208a549eb3d8c046cd5b0afd5b438da","observation_id":"6fe72b8d-ef10-434e-b8b7-9dd17f35bc83","resolution":{"observed_at":"2026-08-04T21:00:36.144574Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-08-04T21:00:36.390077Z","title":null,"venue":null,"work_id":"821c5aa3-dfdf-4c5d-a811-305c2b2b69fb","year":1996},"citing_paper":{"arxiv_id":"2509.08264","last_updated":"2025-09-10T03:44:44Z","snapshot_observed_at":"2026-08-04T21:00:34.972904Z","submitted_at":"2025-09-10T03:44:44Z","title":"Hammering Higher Order Set Theory","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-04T21:00:35.781182Z"},"links":{"citing_paper":"/paper/2509.08264"},"observation_digest":"sha256:04574092efd66baeeeabd12882609e58eb946365b4ad48bc4a8a879c8270874a","observation_id":"260d14a1-28cb-436a-b8f3-eb42101abe8d","resolution":{"observed_at":"2026-08-04T21:00:36.395865Z","resolver_source":"raw_fallback","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-08-04T21:00:36.366169Z","title":"Integrating Gandalf and HOL","venue":null,"work_id":"958c92ed-f28e-404a-91c8-1da6884c60a6","year":1999},"citing_paper":{"arxiv_id":"2509.08264","last_updated":"2025-09-10T03:44:44Z","snapshot_observed_at":"2026-08-04T21:00:34.972904Z","submitted_at":"2025-09-10T03:44:44Z","title":"Hammering Higher Order Set Theory","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-04T21:00:35.786283Z"},"links":{"citing_paper":"/paper/2509.08264"},"observation_digest":"sha256:e22bac94715509093cfd287a2cf45bac60e898b39c3e42b309e1f2be2687d7ed","observation_id":"55156448-e352-48cc-af99-eb53ee05efb0","resolution":{"observed_at":"2026-08-04T21:00:36.371088Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-08-04T21:00:36.340401Z","title":"An LCF-style interface between HOL and first-order logic","venue":null,"work_id":"ba2bae15-4fc2-4df0-b8b8-9215caf020ff","year":2002},"citing_paper":{"arxiv_id":"2509.08264","last_updated":"2025-09-10T03:44:44Z","snapshot_observed_at":"2026-08-04T21:00:34.972904Z","submitted_at":"2025-09-10T03:44:44Z","title":"Hammering Higher Order Set Theory","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-04T21:00:35.790313Z"},"links":{"citing_paper":"/paper/2509.08264"},"observation_digest":"sha256:c54a3618d0c794ada25fba9309ab671e8b38ffc1b6f43fce371e6a64789debbc","observation_id":"673f1c0b-5322-406d-9db3-b38b991de6f6","resolution":{"observed_at":"2026-08-04T21:00:36.344167Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-08-04T21:00:36.325138Z","title":"First-order proof tactics in higher-order logic theorem provers","venue":null,"work_id":"5acd7425-60f6-4620-ad28-d62e2b263195","year":2003},"citing_paper":{"arxiv_id":"2509.08264","last_updated":"2025-09-10T03:44:44Z","snapshot_observed_at":"2026-08-04T21:00:34.972904Z","submitted_at":"2025-09-10T03:44:44Z","title":"Hammering Higher Order Set Theory","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-04T21:00:35.793960Z"},"links":{"citing_paper":"/paper/2509.08264"},"observation_digest":"sha256:7e8944af584edd5250a86a9dda8318edf853713f56fe6ba4cc3c7148aa5c2c62","observation_id":"23b6b8af-3221-4f85-acdd-521d835bb35f","resolution":{"observed_at":"2026-08-04T21:00:36.330555Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-08-04T21:00:36.312231Z","title":"Learning-assisted automated reasoning with Flyspeck.J","venue":null,"work_id":"07817bf9-74d0-4f22-a505-11c7e43d91fe","year":2014},"citing_paper":{"arxiv_id":"2509.08264","last_updated":"2025-09-10T03:44:44Z","snapshot_observed_at":"2026-08-04T21:00:34.972904Z","submitted_at":"2025-09-10T03:44:44Z","title":"Hammering Higher Order Set Theory","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-04T21:00:35.797685Z"},"links":{"citing_paper":"/paper/2509.08264"},"observation_digest":"sha256:9985cff5a8124ace386c76f85e1f8e338b0f1ca3ce1b81faef59e811bfaa95e3","observation_id":"44f0cbac-7a41-4ea3-ac44-609cea168e1e","resolution":{"observed_at":"2026-08-04T21:00:36.316598Z","resolver_source":"raw_fallback","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T21:00:35.808173Z","title":"Learning-assisted automated reasoning with Flyspeck.J","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2509.08264","last_updated":"2025-09-10T03:44:44Z","snapshot_observed_at":"2026-08-04T21:00:34.972904Z","submitted_at":"2025-09-10T03:44:44Z","title":"Hammering Higher Order Set Theory","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-04T21:00:35.808173Z"},"links":{"citing_paper":"/paper/2509.08264"},"observation_digest":"sha256:12055ba8c2a6db1aa429fce537a6314068a52326c9e14e75a59c275595a9d80e","observation_id":"a2bdde78-8840-4aaa-9aeb-e932d1ec2369","resolution":{"observed_at":"2026-08-04T21:00:35.808173Z","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":"2026-08-04T21:00:35.812609Z","title":"Case study: Verified vampire proofs in the lambdapi-calculus modulo, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2509.08264","last_updated":"2025-09-10T03:44:44Z","snapshot_observed_at":"2026-08-04T21:00:34.972904Z","submitted_at":"2025-09-10T03:44:44Z","title":"Hammering Higher Order Set Theory","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-04T21:00:35.812609Z"},"links":{"citing_paper":"/paper/2509.08264"},"observation_digest":"sha256:661d236083de1fb5eda746d4081eb7704157655db1ebc185fccc4d382e28468b","observation_id":"365bc92e-c9a7-414f-9166-54994a5bc817","resolution":{"observed_at":"2026-08-04T21:00:35.812609Z","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":"2026-08-04T21:00:36.295831Z","title":null,"venue":null,"work_id":"c7da491b-6f05-4362-97d9-a7d14be17783","year":2005},"citing_paper":{"arxiv_id":"2509.08264","last_updated":"2025-09-10T03:44:44Z","snapshot_observed_at":"2026-08-04T21:00:34.972904Z","submitted_at":"2025-09-10T03:44:44Z","title":"Hammering Higher Order Set Theory","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-04T21:00:35.817718Z"},"links":{"citing_paper":"/paper/2509.08264"},"observation_digest":"sha256:bd565a732dc04c33810a97ad099a62b518cb22c175503a77201cbff0b7d26ce4","observation_id":"4576d800-c2b7-49ae-9b34-8d604004f0ae","resolution":{"observed_at":"2026-08-04T21:00:36.301342Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-08-04T21:00:36.278174Z","title":null,"venue":null,"work_id":"27c8389d-8329-4b7d-8aa8-644d30a90e8d","year":2009},"citing_paper":{"arxiv_id":"2509.08264","last_updated":"2025-09-10T03:44:44Z","snapshot_observed_at":"2026-08-04T21:00:34.972904Z","submitted_at":"2025-09-10T03:44:44Z","title":"Hammering Higher Order Set Theory","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-04T21:00:35.821322Z"},"links":{"citing_paper":"/paper/2509.08264"},"observation_digest":"sha256:4d4e5aba867aa2b61ab646a99c18f26e25e933623b7a755d5746f3e4fcdcee14","observation_id":"133a82c0-e634-4a13-af1b-c73efa5f320e","resolution":{"observed_at":"2026-08-04T21:00:36.283107Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-08-04T21:00:36.260948Z","title":null,"venue":null,"work_id":"b0378d54-93f7-43e2-9b10-afe847702628","year":1978},"citing_paper":{"arxiv_id":"2509.08264","last_updated":"2025-09-10T03:44:44Z","snapshot_observed_at":"2026-08-04T21:00:34.972904Z","submitted_at":"2025-09-10T03:44:44Z","title":"Hammering Higher Order Set Theory","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-04T21:00:35.826112Z"},"links":{"citing_paper":"/paper/2509.08264"},"observation_digest":"sha256:6085c22a9299283ce1480abf5cb76efb3e00c51c9313f3f2b70a76b330b03154","observation_id":"5bab2c53-b5e9-4ecf-af88-c092d9fb42db","resolution":{"observed_at":"2026-08-04T21:00:36.265699Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.4230/lipics.itp.2024.29","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Conway normal form: Bridging approaches for comprehensive formalization of surreal numbers","venue":"arXiv (Cornell University)","work_id":"f86341fe-81f7-4194-8d4d-93395d57e0b9","year":2024},"citing_paper":{"arxiv_id":"2509.08264","last_updated":"2025-09-10T03:44:44Z","snapshot_observed_at":"2026-08-04T21:00:34.972904Z","submitted_at":"2025-09-10T03:44:44Z","title":"Hammering Higher Order Set Theory","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-04T21:00:35.834736Z"},"links":{"citing_paper":"/paper/2509.08264"},"observation_digest":"sha256:7290ee2f8a894d48e914346d8ac1d8403f63e2a8a76556d1356afd32bc6e04b1","observation_id":"0daa6cc6-c8cb-4e7b-941c-5e3ef1516be5","resolution":{"observed_at":"2026-08-04T21:00:35.957876Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-08-04T21:00:36.244256Z","title":null,"venue":null,"work_id":"05b71e45-4ecc-4b44-934f-38e7dc8f08e9","year":1993},"citing_paper":{"arxiv_id":"2509.08264","last_updated":"2025-09-10T03:44:44Z","snapshot_observed_at":"2026-08-04T21:00:34.972904Z","submitted_at":"2025-09-10T03:44:44Z","title":"Hammering Higher Order Set Theory","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-04T21:00:35.840712Z"},"links":{"citing_paper":"/paper/2509.08264"},"observation_digest":"sha256:14ec7455849d8f2abaaaec76a87b582c1a654074cce90b13ac312b8491e9ef6d","observation_id":"66c330e7-f16f-46ba-8dcb-ccb4ed4ae1cd","resolution":{"observed_at":"2026-08-04T21:00:36.248682Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T21:00:35.845623Z","title":null,"venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2509.08264","last_updated":"2025-09-10T03:44:44Z","snapshot_observed_at":"2026-08-04T21:00:34.972904Z","submitted_at":"2025-09-10T03:44:44Z","title":"Hammering Higher Order Set Theory","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-04T21:00:35.845623Z"},"links":{"citing_paper":"/paper/2509.08264"},"observation_digest":"sha256:9c9370d18330ba312a6d76f69a9235dd0b1584e0db2edcb248feff6caa7867fa","observation_id":"24467f26-39d3-456b-a8e2-74436878a3b2","resolution":{"observed_at":"2026-08-04T21:00:35.845623Z","resolver_source":null,"status":"malformed_identifier"},"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":"2026-08-04T21:00:36.228657Z","title":"Dover, 2006","venue":null,"work_id":"46cb0f5d-0a44-4831-9e99-7456c1de6ae0","year":2006},"citing_paper":{"arxiv_id":"2509.08264","last_updated":"2025-09-10T03:44:44Z","snapshot_observed_at":"2026-08-04T21:00:34.972904Z","submitted_at":"2025-09-10T03:44:44Z","title":"Hammering Higher Order Set Theory","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-04T21:00:35.850459Z"},"links":{"citing_paper":"/paper/2509.08264"},"observation_digest":"sha256:15f6a008c622d46419c03b6df746aff9619483620573cba860f7f969ca52c6eb","observation_id":"7b307597-4cd0-4605-b41e-1c9223c9f9c3","resolution":{"observed_at":"2026-08-04T21:00:36.233234Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-08-04T21:00:36.203900Z","title":"Axiomofchoiceandcomplementation.Proceedings of the American Mathematical Society, 51:176–178, 1975","venue":null,"work_id":"21bff2fc-82e4-413a-8ca4-9ea4ac4ce15d","year":1975},"citing_paper":{"arxiv_id":"2509.08264","last_updated":"2025-09-10T03:44:44Z","snapshot_observed_at":"2026-08-04T21:00:34.972904Z","submitted_at":"2025-09-10T03:44:44Z","title":"Hammering Higher Order Set Theory","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-04T21:00:35.855826Z"},"links":{"citing_paper":"/paper/2509.08264"},"observation_digest":"sha256:4649d46f4e0aedf6b6b16fcaf7346184ae66bc1b754dec00f06046da337b22d1","observation_id":"aeafb364-35a6-44a4-87d3-42d86bfd1047","resolution":{"observed_at":"2026-08-04T21:00:36.209690Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-08-04T21:00:36.185959Z","title":"Cambridge University Press, 1903","venue":null,"work_id":"e3f2545a-50ef-4788-a781-885bb531b50a","year":1903},"citing_paper":{"arxiv_id":"2509.08264","last_updated":"2025-09-10T03:44:44Z","snapshot_observed_at":"2026-08-04T21:00:34.972904Z","submitted_at":"2025-09-10T03:44:44Z","title":"Hammering Higher Order Set Theory","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-04T21:00:35.860004Z"},"links":{"citing_paper":"/paper/2509.08264"},"observation_digest":"sha256:0a5f9b49250ea6237becbc8fcca0dd2ae22f519d3458461ae0b87baa90992b79","observation_id":"ac9d368d-0449-44a7-bd7b-05c994f6db74","resolution":{"observed_at":"2026-08-04T21:00:36.191750Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-08-04T21:00:36.173144Z","title":null,"venue":null,"work_id":"24075d26-d833-47ac-8d89-f63ca0f308c5","year":2003},"citing_paper":{"arxiv_id":"2509.08264","last_updated":"2025-09-10T03:44:44Z","snapshot_observed_at":"2026-08-04T21:00:34.972904Z","submitted_at":"2025-09-10T03:44:44Z","title":"Hammering Higher Order Set Theory","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-04T21:00:35.864466Z"},"links":{"citing_paper":"/paper/2509.08264"},"observation_digest":"sha256:c790accaf7f9421dac8aec5db66257a912acd1e80b33aa6fb2aa31ec28a9ba83","observation_id":"ab4ba324-019e-48be-ac5f-09912aae47b3","resolution":{"observed_at":"2026-08-04T21:00:36.176747Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s10817-004-6245-1","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"MPTP – Motivation, Implementation, First Experiments.J","venue":"Journal of Automated Reasoning","work_id":"14a54196-9222-4090-81ba-0d1ca8a017f9","year":2004},"citing_paper":{"arxiv_id":"2509.08264","last_updated":"2025-09-10T03:44:44Z","snapshot_observed_at":"2026-08-04T21:00:34.972904Z","submitted_at":"2025-09-10T03:44:44Z","title":"Hammering Higher Order Set Theory","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-04T21:00:35.879835Z"},"links":{"citing_paper":"/paper/2509.08264"},"observation_digest":"sha256:656d8c5f01a2c3ada7363aacb02e730026b9f8850e01be578553d4c8752235bf","observation_id":"59960382-e8ab-45c8-9212-d8be373444e7","resolution":{"observed_at":"2026-08-04T21:00:35.927341Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-08-04T21:00:36.156784Z","title":"Extending a high- performance prover to higher-order logic","venue":null,"work_id":"3341e18f-918c-4991-9893-cd09f3260155","year":2023},"citing_paper":{"arxiv_id":"2509.08264","last_updated":"2025-09-10T03:44:44Z","snapshot_observed_at":"2026-08-04T21:00:34.972904Z","submitted_at":"2025-09-10T03:44:44Z","title":"Hammering Higher Order Set Theory","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-04T21:00:35.884437Z"},"links":{"citing_paper":"/paper/2509.08264"},"observation_digest":"sha256:d42c2365f910392ebe1780fb357c7846f226fed6dc7ea364e3b08350068c9c09","observation_id":"8218697a-9308-4922-b945-35c38a7e4fd7","resolution":{"observed_at":"2026-08-04T21:00:36.161781Z","resolver_source":"raw_fallback","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/978-3-319-42547-4","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"Lecture notes in computer science","work_id":"83c9cc7d-a7da-4e51-b1c8-80b168e0757f","year":2016},"citing_paper":{"arxiv_id":"2509.08264","last_updated":"2025-09-10T03:44:44Z","snapshot_observed_at":"2026-08-04T21:00:34.972904Z","submitted_at":"2025-09-10T03:44:44Z","title":"Hammering Higher Order Set Theory","version":1},"reference_index":114,"source":"pdf_text","source_observed_at":"2026-08-04T21:00:35.739291Z"},"links":{"citing_paper":"/paper/2509.08264"},"observation_digest":"sha256:e742c056fbecc1e1a1c6dae9c2967968dd20525b8dc9aa747a2abe1ed4fa7894","observation_id":"cfc310f6-18f7-4749-baf4-8880dc809029","resolution":{"observed_at":"2026-08-04T21:00:36.009634Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T21:00:35.699138Z","title":null,"venue":null,"work_id":null,"year":1972},"citing_paper":{"arxiv_id":"2509.08264","last_updated":"2025-09-10T03:44:44Z","snapshot_observed_at":"2026-08-04T21:00:34.972904Z","submitted_at":"2025-09-10T03:44:44Z","title":"Hammering Higher Order Set Theory","version":1},"reference_index":2016,"source":"pdf_text","source_observed_at":"2026-08-04T21:00:35.699138Z"},"links":{"citing_paper":"/paper/2509.08264"},"observation_digest":"sha256:598b637698b27c4501ad9247ff8b94466dde760345e00106a83a5e0e8287b219","observation_id":"cdd2e710-b526-4633-b790-da8dcf77ba20","resolution":{"observed_at":"2026-08-04T21:00:35.699138Z","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":"2026-08-04T21:00:36.615777Z","title":null,"venue":null,"work_id":"caec413f-585e-4650-a9ca-387060a932cc","year":null},"citing_paper":{"arxiv_id":"2509.08264","last_updated":"2025-09-10T03:44:44Z","snapshot_observed_at":"2026-08-04T21:00:34.972904Z","submitted_at":"2025-09-10T03:44:44Z","title":"Hammering Higher Order Set Theory","version":1},"reference_index":2021,"source":"pdf_text","source_observed_at":"2026-08-04T21:00:35.654361Z"},"links":{"citing_paper":"/paper/2509.08264"},"observation_digest":"sha256:96dd6658604cde4b16804539230a1ef523e5eaabbecb77d81469a8632194732e","observation_id":"926d223b-d2ca-4892-9425-c8307b2dc203","resolution":{"observed_at":"2026-08-04T21:00:36.620070Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2509.08264","last_updated":"2025-09-10T03:44:44Z","latest_version":1,"primary_category":"cs.LO","snapshot_observed_at":"2026-08-04T21:00:34.972904Z","submitted_at":"2025-09-10T03:44:44Z","title":"Hammering Higher Order Set Theory"},"reference_resolution":{"displayed":46,"state_counts":{"malformed_identifier":6,"metadata_mismatch":1,"parse_uncertain":0,"unresolved":18,"verified_exact":5,"verified_fuzzy":16},"total_outbound_references":46},"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":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+00:00","source":"retraction_watch"}],"thesis":"As of 7 August 2026, this Paper Citation Record lists 46 of 46 outbound references and 0 inbound Pith citation observations for arXiv:2509.08264."}