{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:CYYSLGYRYGASHGVAOM6465G225","short_pith_number":"pith:CYYSLGYR","canonical_record":{"source":{"id":"2501.03238","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.HO","submitted_at":"2024-12-18T01:24:37Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"e69c821a7788d145aab412f7b9d01978eaec8b37930ca329f3a8f02854e64095","abstract_canon_sha256":"402c3737b4597903209647a340950a4d6685fe9623120522649499e269a157b5"},"schema_version":"1.0"},"canonical_sha256":"1631259b11c181239aa0733dcf74dad7572728121e99f9b66554ae14645b0c13","source":{"kind":"arxiv","id":"2501.03238","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.03238","created_at":"2026-07-05T09:57:51Z"},{"alias_kind":"arxiv_version","alias_value":"2501.03238v1","created_at":"2026-07-05T09:57:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.03238","created_at":"2026-07-05T09:57:51Z"},{"alias_kind":"pith_short_12","alias_value":"CYYSLGYRYGAS","created_at":"2026-07-05T09:57:51Z"},{"alias_kind":"pith_short_16","alias_value":"CYYSLGYRYGASHGVA","created_at":"2026-07-05T09:57:51Z"},{"alias_kind":"pith_short_8","alias_value":"CYYSLGYR","created_at":"2026-07-05T09:57:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:CYYSLGYRYGASHGVAOM6465G225","target":"record","payload":{"canonical_record":{"source":{"id":"2501.03238","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.HO","submitted_at":"2024-12-18T01:24:37Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"e69c821a7788d145aab412f7b9d01978eaec8b37930ca329f3a8f02854e64095","abstract_canon_sha256":"402c3737b4597903209647a340950a4d6685fe9623120522649499e269a157b5"},"schema_version":"1.0"},"canonical_sha256":"1631259b11c181239aa0733dcf74dad7572728121e99f9b66554ae14645b0c13","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:57:51.143101Z","signature_b64":"Fcyhz2Udhlg4PKzDzKiDg4LyJE0IPFYh6gtIpod9hQjoM2V5DRXlV59Zm29csppCeAegUMoGGworU+SKqHHkCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1631259b11c181239aa0733dcf74dad7572728121e99f9b66554ae14645b0c13","last_reissued_at":"2026-07-05T09:57:51.142665Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:57:51.142665Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2501.03238","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":"2026-07-05T09:57:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KyTrW3oXQXvBgU59k5sM3azjcNB0FEGBaRPXkP3SrjbR6n3vSjDMqlzXqVnr0UgeTlmHR4VIvhSPE+EBGVxkCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-24T00:08:07.027134Z"},"content_sha256":"d0caf9df86e15849f6164b1e2a25aa7dcb176c43bad290f4ab2ead0f9ab2d896","schema_version":"1.0","event_id":"sha256:d0caf9df86e15849f6164b1e2a25aa7dcb176c43bad290f4ab2ead0f9ab2d896"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:CYYSLGYRYGASHGVAOM6465G225","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Probability Puzzle","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.HO","authors_text":"Daniel Otero","submitted_at":"2024-12-18T01:24:37Z","abstract_excerpt":"In this short article, we present a solution to one of the probability puzzles that Daniel Litt, a mathematician at the University of Toronto, posted on his X account earlier this year. The main goal of this note is to show how some of the typical concepts taught in an undergraduate probability course can be used to solve these types of probability problems, which sound simple, but can be very difficult to solve."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.03238","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/2501.03238/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":"2026-07-05T09:57:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KFVUUgbxEeAlo4f1p9qzffWskF+qQP967KgwmYgEJDG/EOaK6fNMhAOGmY16BYPvd3Cvl6J48qpdZb18s+j6Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-24T00:08:07.027875Z"},"content_sha256":"6a7fcc1efa23f473b20d750661a43702abb48fc9c41b772fd3fceaf20e7904b2","schema_version":"1.0","event_id":"sha256:6a7fcc1efa23f473b20d750661a43702abb48fc9c41b772fd3fceaf20e7904b2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CYYSLGYRYGASHGVAOM6465G225/bundle.json","state_url":"https://pith.science/pith/CYYSLGYRYGASHGVAOM6465G225/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CYYSLGYRYGASHGVAOM6465G225/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":"2026-08-24T00:08:07Z","links":{"resolver":"https://pith.science/pith/CYYSLGYRYGASHGVAOM6465G225","bundle":"https://pith.science/pith/CYYSLGYRYGASHGVAOM6465G225/bundle.json","state":"https://pith.science/pith/CYYSLGYRYGASHGVAOM6465G225/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CYYSLGYRYGASHGVAOM6465G225/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:CYYSLGYRYGASHGVAOM6465G225","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":"402c3737b4597903209647a340950a4d6685fe9623120522649499e269a157b5","cross_cats_sorted":["math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.HO","submitted_at":"2024-12-18T01:24:37Z","title_canon_sha256":"e69c821a7788d145aab412f7b9d01978eaec8b37930ca329f3a8f02854e64095"},"schema_version":"1.0","source":{"id":"2501.03238","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.03238","created_at":"2026-07-05T09:57:51Z"},{"alias_kind":"arxiv_version","alias_value":"2501.03238v1","created_at":"2026-07-05T09:57:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.03238","created_at":"2026-07-05T09:57:51Z"},{"alias_kind":"pith_short_12","alias_value":"CYYSLGYRYGAS","created_at":"2026-07-05T09:57:51Z"},{"alias_kind":"pith_short_16","alias_value":"CYYSLGYRYGASHGVA","created_at":"2026-07-05T09:57:51Z"},{"alias_kind":"pith_short_8","alias_value":"CYYSLGYR","created_at":"2026-07-05T09:57:51Z"}],"graph_snapshots":[{"event_id":"sha256:6a7fcc1efa23f473b20d750661a43702abb48fc9c41b772fd3fceaf20e7904b2","target":"graph","created_at":"2026-07-05T09:57:51Z","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/2501.03238/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this short article, we present a solution to one of the probability puzzles that Daniel Litt, a mathematician at the University of Toronto, posted on his X account earlier this year. The main goal of this note is to show how some of the typical concepts taught in an undergraduate probability course can be used to solve these types of probability problems, which sound simple, but can be very difficult to solve.","authors_text":"Daniel Otero","cross_cats":["math.PR"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.HO","submitted_at":"2024-12-18T01:24:37Z","title":"A Probability Puzzle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.03238","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:d0caf9df86e15849f6164b1e2a25aa7dcb176c43bad290f4ab2ead0f9ab2d896","target":"record","created_at":"2026-07-05T09:57:51Z","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":"402c3737b4597903209647a340950a4d6685fe9623120522649499e269a157b5","cross_cats_sorted":["math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.HO","submitted_at":"2024-12-18T01:24:37Z","title_canon_sha256":"e69c821a7788d145aab412f7b9d01978eaec8b37930ca329f3a8f02854e64095"},"schema_version":"1.0","source":{"id":"2501.03238","kind":"arxiv","version":1}},"canonical_sha256":"1631259b11c181239aa0733dcf74dad7572728121e99f9b66554ae14645b0c13","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1631259b11c181239aa0733dcf74dad7572728121e99f9b66554ae14645b0c13","first_computed_at":"2026-07-05T09:57:51.142665Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:57:51.142665Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Fcyhz2Udhlg4PKzDzKiDg4LyJE0IPFYh6gtIpod9hQjoM2V5DRXlV59Zm29csppCeAegUMoGGworU+SKqHHkCA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:57:51.143101Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.03238","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d0caf9df86e15849f6164b1e2a25aa7dcb176c43bad290f4ab2ead0f9ab2d896","sha256:6a7fcc1efa23f473b20d750661a43702abb48fc9c41b772fd3fceaf20e7904b2"],"state_sha256":"f4f64eb62759bfadecbf9ed863beb585d539fb7979886b905fd66bbb12479ed1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DWgimHsL6TvLNItfZVc/eXKGIFFwPaJtTzgbFQYHwP54J3wx2M5TKtLrgPZrB8a2sgeGedONuXfTZ4lvW9PiDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-24T00:08:07.033053Z","bundle_sha256":"83390d8c131b82c65f894479ac2b3606a2ae5b038cba0caa723a1c093184fdb2"}}