{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:S5T7QHM2J2QVPF4RIBJCAEN6XJ","short_pith_number":"pith:S5T7QHM2","canonical_record":{"source":{"id":"1703.05349","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2017-03-15T18:52:31Z","cross_cats_sorted":[],"title_canon_sha256":"7ff7fd7e8b374ea9954671b3dd18930cc2c245b624c31ddfc5eb253bb010640e","abstract_canon_sha256":"2bd62f4ddf40c1836fcb1ff42fcd4293c7ac65ebe558416b059a384e8dff881d"},"schema_version":"1.0"},"canonical_sha256":"9767f81d9a4ea157979140522011beba7a20921ffb222295ab5b84e71bbaaa94","source":{"kind":"arxiv","id":"1703.05349","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.05349","created_at":"2026-05-18T00:48:34Z"},{"alias_kind":"arxiv_version","alias_value":"1703.05349v1","created_at":"2026-05-18T00:48:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.05349","created_at":"2026-05-18T00:48:34Z"},{"alias_kind":"pith_short_12","alias_value":"S5T7QHM2J2QV","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"S5T7QHM2J2QVPF4R","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"S5T7QHM2","created_at":"2026-05-18T12:31:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:S5T7QHM2J2QVPF4RIBJCAEN6XJ","target":"record","payload":{"canonical_record":{"source":{"id":"1703.05349","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2017-03-15T18:52:31Z","cross_cats_sorted":[],"title_canon_sha256":"7ff7fd7e8b374ea9954671b3dd18930cc2c245b624c31ddfc5eb253bb010640e","abstract_canon_sha256":"2bd62f4ddf40c1836fcb1ff42fcd4293c7ac65ebe558416b059a384e8dff881d"},"schema_version":"1.0"},"canonical_sha256":"9767f81d9a4ea157979140522011beba7a20921ffb222295ab5b84e71bbaaa94","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:34.533282Z","signature_b64":"kVCk1tvq8TF1IwzAJHcsw2P21ImJj/rH/N7lEy2t9jPePqXmArgn38hu9ThtdodPenyZBW+jEv9blw+Xe1neCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9767f81d9a4ea157979140522011beba7a20921ffb222295ab5b84e71bbaaa94","last_reissued_at":"2026-05-18T00:48:34.532749Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:34.532749Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.05349","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:48:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QMm3Q49Oq75oGaO7sWofzV/7LzqbEZA8HuuKfKCjDlonbs2OLuTVlFiLTpGRKV1QcZwErP03ep0gq1Rj8NgqCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T07:19:50.875376Z"},"content_sha256":"c56bd7d4d053279c428f91ebdfb327a3d88f0d5be4d39c257fd7a8901c74dfcc","schema_version":"1.0","event_id":"sha256:c56bd7d4d053279c428f91ebdfb327a3d88f0d5be4d39c257fd7a8901c74dfcc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:S5T7QHM2J2QVPF4RIBJCAEN6XJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gamma and Factorial in the Monthly","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.HO","authors_text":"Jonathan M. Borwein, Robert M. Corless","submitted_at":"2017-03-15T18:52:31Z","abstract_excerpt":"The Monthly has published roughly fifty papers on the $\\Gamma$ function or Stirling's formula. We survey those papers (discussing only our favourites in any detail) and place them in the context of the larger mathematical literature on $\\Gamma$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.05349","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:48:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mzv5nJVcs8XqBpW/Q3HXIhMc1UMksMu476mJ529HvKgmb4HqfDAfLSuWrYhkTFPJwgMpXmC6VeABUw8NJzfPBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T07:19:50.875709Z"},"content_sha256":"ae99e16c579d07e1e00c9a663ba16c83fe974f0a1c68ee762c1b1b63daf0f31e","schema_version":"1.0","event_id":"sha256:ae99e16c579d07e1e00c9a663ba16c83fe974f0a1c68ee762c1b1b63daf0f31e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S5T7QHM2J2QVPF4RIBJCAEN6XJ/bundle.json","state_url":"https://pith.science/pith/S5T7QHM2J2QVPF4RIBJCAEN6XJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S5T7QHM2J2QVPF4RIBJCAEN6XJ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-20T07:19:50Z","links":{"resolver":"https://pith.science/pith/S5T7QHM2J2QVPF4RIBJCAEN6XJ","bundle":"https://pith.science/pith/S5T7QHM2J2QVPF4RIBJCAEN6XJ/bundle.json","state":"https://pith.science/pith/S5T7QHM2J2QVPF4RIBJCAEN6XJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S5T7QHM2J2QVPF4RIBJCAEN6XJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:S5T7QHM2J2QVPF4RIBJCAEN6XJ","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":"2bd62f4ddf40c1836fcb1ff42fcd4293c7ac65ebe558416b059a384e8dff881d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2017-03-15T18:52:31Z","title_canon_sha256":"7ff7fd7e8b374ea9954671b3dd18930cc2c245b624c31ddfc5eb253bb010640e"},"schema_version":"1.0","source":{"id":"1703.05349","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.05349","created_at":"2026-05-18T00:48:34Z"},{"alias_kind":"arxiv_version","alias_value":"1703.05349v1","created_at":"2026-05-18T00:48:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.05349","created_at":"2026-05-18T00:48:34Z"},{"alias_kind":"pith_short_12","alias_value":"S5T7QHM2J2QV","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"S5T7QHM2J2QVPF4R","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"S5T7QHM2","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:ae99e16c579d07e1e00c9a663ba16c83fe974f0a1c68ee762c1b1b63daf0f31e","target":"graph","created_at":"2026-05-18T00:48:34Z","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"},"paper":{"abstract_excerpt":"The Monthly has published roughly fifty papers on the $\\Gamma$ function or Stirling's formula. We survey those papers (discussing only our favourites in any detail) and place them in the context of the larger mathematical literature on $\\Gamma$.","authors_text":"Jonathan M. Borwein, Robert M. Corless","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2017-03-15T18:52:31Z","title":"Gamma and Factorial in the Monthly"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.05349","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:c56bd7d4d053279c428f91ebdfb327a3d88f0d5be4d39c257fd7a8901c74dfcc","target":"record","created_at":"2026-05-18T00:48:34Z","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":"2bd62f4ddf40c1836fcb1ff42fcd4293c7ac65ebe558416b059a384e8dff881d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2017-03-15T18:52:31Z","title_canon_sha256":"7ff7fd7e8b374ea9954671b3dd18930cc2c245b624c31ddfc5eb253bb010640e"},"schema_version":"1.0","source":{"id":"1703.05349","kind":"arxiv","version":1}},"canonical_sha256":"9767f81d9a4ea157979140522011beba7a20921ffb222295ab5b84e71bbaaa94","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9767f81d9a4ea157979140522011beba7a20921ffb222295ab5b84e71bbaaa94","first_computed_at":"2026-05-18T00:48:34.532749Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:34.532749Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kVCk1tvq8TF1IwzAJHcsw2P21ImJj/rH/N7lEy2t9jPePqXmArgn38hu9ThtdodPenyZBW+jEv9blw+Xe1neCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:34.533282Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.05349","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c56bd7d4d053279c428f91ebdfb327a3d88f0d5be4d39c257fd7a8901c74dfcc","sha256:ae99e16c579d07e1e00c9a663ba16c83fe974f0a1c68ee762c1b1b63daf0f31e"],"state_sha256":"b948fb0079a53cbf306916833c665f1c81ec93d98f3c4ae2143c3d3df70d553d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gujd/edsCadwEkenvcQmbyhSFjtlLxL12SiH/wW8gFp8C18Yt63OzRVAPBfzliuqu4RkpkNJF9sAAg4bkbHGBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T07:19:50.877555Z","bundle_sha256":"120c5e422eb40d3b2bb11e4fd8cceed518de432b5defd9caf5fdce90daa6abb3"}}