{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:OYMSZJBRDWXGO7GNY6YKWQGCT3","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"1387793d68bd75f814f78da70adf06f0025378818a081b290705b1a10cdef938","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.HO","submitted_at":"2020-12-22T13:01:48Z","title_canon_sha256":"7f8312ebbe3bd4584875329829c098fb6a482df5b99573a293c8d5ae5a42a197"},"schema_version":"1.0","source":{"id":"2012.12692","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2012.12692","created_at":"2026-07-05T02:01:40Z"},{"alias_kind":"arxiv_version","alias_value":"2012.12692v1","created_at":"2026-07-05T02:01:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2012.12692","created_at":"2026-07-05T02:01:40Z"},{"alias_kind":"pith_short_12","alias_value":"OYMSZJBRDWXG","created_at":"2026-07-05T02:01:40Z"},{"alias_kind":"pith_short_16","alias_value":"OYMSZJBRDWXGO7GN","created_at":"2026-07-05T02:01:40Z"},{"alias_kind":"pith_short_8","alias_value":"OYMSZJBR","created_at":"2026-07-05T02:01:40Z"}],"graph_snapshots":[{"event_id":"sha256:39eb72e4987f69d27ceb26dd7aa53316138e73fed919ca83d56e08696850b3ed","target":"graph","created_at":"2026-07-05T02:01:40Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2012.12692/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Several continued fraction expansions for $e$ have been produced by an automated conjecture generator (ACG) called \\emph{The Ramanujan Machine}. Some of these were already known, some have recently been proved and some remain unproven. While an ACG can produce interesting putative results, it gives very limited insight into their significance. In this paper, we derive an elegant continued fraction expansion, equivalent to a result from the Ramanujan Machine, using the sequence of ratios of factorials to subfactorials or derangement numbers.","authors_text":"Peter Lynch","cross_cats":["math.CO"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.HO","submitted_at":"2020-12-22T13:01:48Z","title":"Derangements and Continued Fractions for $e$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.12692","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c9f8093b256837128824be4843133e0eb70e15a918e2bef6573b2ab23af9c628","target":"record","created_at":"2026-07-05T02:01:40Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"1387793d68bd75f814f78da70adf06f0025378818a081b290705b1a10cdef938","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.HO","submitted_at":"2020-12-22T13:01:48Z","title_canon_sha256":"7f8312ebbe3bd4584875329829c098fb6a482df5b99573a293c8d5ae5a42a197"},"schema_version":"1.0","source":{"id":"2012.12692","kind":"arxiv","version":1}},"canonical_sha256":"76192ca4311dae677ccdc7b0ab40c29ef4be4c30a8ce6422c7454b7465ac9fd4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"76192ca4311dae677ccdc7b0ab40c29ef4be4c30a8ce6422c7454b7465ac9fd4","first_computed_at":"2026-07-05T02:01:40.337517Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:01:40.337517Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3Q9LiNAiJGVU3vvmsltthCZyQFWOxF01mfAI3gLmbhmp8Ux5hORPqQ6l6Ks+hm/76Y67T+hSgPM8zfEff6OvDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T02:01:40.337992Z","signed_message":"canonical_sha256_bytes"},"source_id":"2012.12692","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c9f8093b256837128824be4843133e0eb70e15a918e2bef6573b2ab23af9c628","sha256:39eb72e4987f69d27ceb26dd7aa53316138e73fed919ca83d56e08696850b3ed"],"state_sha256":"7d3292af05ea74ca7208dfccb7aa4a1d87e1447f9bef0ca8e30826b084fd4ae6"}