{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:BO73ZGLQ7PBCHKBM74QOWRFTKV","short_pith_number":"pith:BO73ZGLQ","canonical_record":{"source":{"id":"2606.19298","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-17T17:23:31Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"275ea08df56b23cb4094a085a6c6cc1051e6928660a68cf6405725952cd47109","abstract_canon_sha256":"63aae97d16febba80be9f0f39d44970a2cde5201708585fd1b721c4f70313874"},"schema_version":"1.0"},"canonical_sha256":"0bbfbc9970fbc223a82cff20eb44b3557e3328d7a0f151d19ac3d93ae060c412","source":{"kind":"arxiv","id":"2606.19298","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.19298","created_at":"2026-06-19T16:12:10Z"},{"alias_kind":"arxiv_version","alias_value":"2606.19298v1","created_at":"2026-06-19T16:12:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.19298","created_at":"2026-06-19T16:12:10Z"},{"alias_kind":"pith_short_12","alias_value":"BO73ZGLQ7PBC","created_at":"2026-06-19T16:12:10Z"},{"alias_kind":"pith_short_16","alias_value":"BO73ZGLQ7PBCHKBM","created_at":"2026-06-19T16:12:10Z"},{"alias_kind":"pith_short_8","alias_value":"BO73ZGLQ","created_at":"2026-06-19T16:12:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:BO73ZGLQ7PBCHKBM74QOWRFTKV","target":"record","payload":{"canonical_record":{"source":{"id":"2606.19298","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-17T17:23:31Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"275ea08df56b23cb4094a085a6c6cc1051e6928660a68cf6405725952cd47109","abstract_canon_sha256":"63aae97d16febba80be9f0f39d44970a2cde5201708585fd1b721c4f70313874"},"schema_version":"1.0"},"canonical_sha256":"0bbfbc9970fbc223a82cff20eb44b3557e3328d7a0f151d19ac3d93ae060c412","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:12:10.060764Z","signature_b64":"7oqGW6LIhQRILYohOf8m4zRw3SqfBVU7rYv5XJWiyY6/bGrL1+qHyzA3B1mJPLvxbdwD8VUSi33lAs7r+fyhBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0bbfbc9970fbc223a82cff20eb44b3557e3328d7a0f151d19ac3d93ae060c412","last_reissued_at":"2026-06-19T16:12:10.060425Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:12:10.060425Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.19298","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":"2026-06-19T16:12:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OToQwvdsvWg6+KCX8tTQJz69iO8oVbBn2j4fl2Jb/Ss780slP23RpaSMlGHtgLx2m3HAilOVjkRaYVdM3PrKAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T05:09:50.583676Z"},"content_sha256":"9c8ed5f729959e3b512ec9ca33e96ef8acf9bb2ddbc747c89eadf60045d23709","schema_version":"1.0","event_id":"sha256:9c8ed5f729959e3b512ec9ca33e96ef8acf9bb2ddbc747c89eadf60045d23709"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:BO73ZGLQ7PBCHKBM74QOWRFTKV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Secretary Problem Thresholds and Convergents of $1/e$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.PR","authors_text":"Ra\\'ul S\\'anchez Gal\\'an","submitted_at":"2026-06-17T17:23:31Z","abstract_excerpt":"We prove that if $p/q$ is a continued fraction convergent of $1/e$ with $q\\geq 3$, then, for the secretary problem with $q$ applicants, the optimal number of initially rejected applicants is $p$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.19298","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.19298/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-19T16:12:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QGb0VTZBkXvgl8HCtNCf06VG36WJy8UkLOn9dEtqy/8zTltdo12VD8jIzctOb46PP8dkKp0fmCXxcBkSWJoMDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T05:09:50.584045Z"},"content_sha256":"801bd3be364fc704db37e208a54b7cadeeaef36943bc049be88eb47b615f8a9c","schema_version":"1.0","event_id":"sha256:801bd3be364fc704db37e208a54b7cadeeaef36943bc049be88eb47b615f8a9c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BO73ZGLQ7PBCHKBM74QOWRFTKV/bundle.json","state_url":"https://pith.science/pith/BO73ZGLQ7PBCHKBM74QOWRFTKV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BO73ZGLQ7PBCHKBM74QOWRFTKV/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":"2026-06-25T05:09:50Z","links":{"resolver":"https://pith.science/pith/BO73ZGLQ7PBCHKBM74QOWRFTKV","bundle":"https://pith.science/pith/BO73ZGLQ7PBCHKBM74QOWRFTKV/bundle.json","state":"https://pith.science/pith/BO73ZGLQ7PBCHKBM74QOWRFTKV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BO73ZGLQ7PBCHKBM74QOWRFTKV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:BO73ZGLQ7PBCHKBM74QOWRFTKV","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":"63aae97d16febba80be9f0f39d44970a2cde5201708585fd1b721c4f70313874","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-17T17:23:31Z","title_canon_sha256":"275ea08df56b23cb4094a085a6c6cc1051e6928660a68cf6405725952cd47109"},"schema_version":"1.0","source":{"id":"2606.19298","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.19298","created_at":"2026-06-19T16:12:10Z"},{"alias_kind":"arxiv_version","alias_value":"2606.19298v1","created_at":"2026-06-19T16:12:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.19298","created_at":"2026-06-19T16:12:10Z"},{"alias_kind":"pith_short_12","alias_value":"BO73ZGLQ7PBC","created_at":"2026-06-19T16:12:10Z"},{"alias_kind":"pith_short_16","alias_value":"BO73ZGLQ7PBCHKBM","created_at":"2026-06-19T16:12:10Z"},{"alias_kind":"pith_short_8","alias_value":"BO73ZGLQ","created_at":"2026-06-19T16:12:10Z"}],"graph_snapshots":[{"event_id":"sha256:801bd3be364fc704db37e208a54b7cadeeaef36943bc049be88eb47b615f8a9c","target":"graph","created_at":"2026-06-19T16:12:10Z","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/2606.19298/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that if $p/q$ is a continued fraction convergent of $1/e$ with $q\\geq 3$, then, for the secretary problem with $q$ applicants, the optimal number of initially rejected applicants is $p$.","authors_text":"Ra\\'ul S\\'anchez Gal\\'an","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-17T17:23:31Z","title":"Secretary Problem Thresholds and Convergents of $1/e$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.19298","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":"sha256:9c8ed5f729959e3b512ec9ca33e96ef8acf9bb2ddbc747c89eadf60045d23709","target":"record","created_at":"2026-06-19T16:12:10Z","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":"63aae97d16febba80be9f0f39d44970a2cde5201708585fd1b721c4f70313874","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-17T17:23:31Z","title_canon_sha256":"275ea08df56b23cb4094a085a6c6cc1051e6928660a68cf6405725952cd47109"},"schema_version":"1.0","source":{"id":"2606.19298","kind":"arxiv","version":1}},"canonical_sha256":"0bbfbc9970fbc223a82cff20eb44b3557e3328d7a0f151d19ac3d93ae060c412","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0bbfbc9970fbc223a82cff20eb44b3557e3328d7a0f151d19ac3d93ae060c412","first_computed_at":"2026-06-19T16:12:10.060425Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:12:10.060425Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7oqGW6LIhQRILYohOf8m4zRw3SqfBVU7rYv5XJWiyY6/bGrL1+qHyzA3B1mJPLvxbdwD8VUSi33lAs7r+fyhBg==","signature_status":"signed_v1","signed_at":"2026-06-19T16:12:10.060764Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.19298","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9c8ed5f729959e3b512ec9ca33e96ef8acf9bb2ddbc747c89eadf60045d23709","sha256:801bd3be364fc704db37e208a54b7cadeeaef36943bc049be88eb47b615f8a9c"],"state_sha256":"7603dbc328cd2a78603952a9a2acd651da9656ae24304d97bb0d9c7b3f83672e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6A6YGWpRMbpd2eX2QAj9Ka+E7OaWwDNmqfNU8JvxzBWObZziCD3pNqdutYQ0kUwTy/Ev+l9Vj+C8CCpLXMCoCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T05:09:50.587604Z","bundle_sha256":"6a84131f9bde43c3e2f78690577c03078851931c60231b6cc22e5443d67e79a9"}}