{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:24JWUIZMNTI2NWKNFV2XIZWYDK","short_pith_number":"pith:24JWUIZM","canonical_record":{"source":{"id":"math/0401385","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"2004-01-27T18:45:05Z","cross_cats_sorted":[],"title_canon_sha256":"0d1350d5dad3a34988518863677c12035d5f1ded345d23f8ac75cb12fde240f8","abstract_canon_sha256":"59c7b8677d4f702e742008dc749c72cbeef0a13df1d1bf352d0b8a84be10451e"},"schema_version":"1.0"},"canonical_sha256":"d7136a232c6cd1a6d94d2d757466d81a86613bdfc79c5d557625e5f24319514a","source":{"kind":"arxiv","id":"math/0401385","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0401385","created_at":"2026-05-18T04:03:32Z"},{"alias_kind":"arxiv_version","alias_value":"math/0401385v2","created_at":"2026-05-18T04:03:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0401385","created_at":"2026-05-18T04:03:32Z"},{"alias_kind":"pith_short_12","alias_value":"24JWUIZMNTI2","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"24JWUIZMNTI2NWKN","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"24JWUIZM","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:24JWUIZMNTI2NWKNFV2XIZWYDK","target":"record","payload":{"canonical_record":{"source":{"id":"math/0401385","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"2004-01-27T18:45:05Z","cross_cats_sorted":[],"title_canon_sha256":"0d1350d5dad3a34988518863677c12035d5f1ded345d23f8ac75cb12fde240f8","abstract_canon_sha256":"59c7b8677d4f702e742008dc749c72cbeef0a13df1d1bf352d0b8a84be10451e"},"schema_version":"1.0"},"canonical_sha256":"d7136a232c6cd1a6d94d2d757466d81a86613bdfc79c5d557625e5f24319514a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:03:32.962476Z","signature_b64":"la0HbpD9TbGsLUz+Xf6Dvq7pQAiearVpH8Dw8ARKrWaOdGca3nj561NZdf53hfqdwnACKFhdK18VyuTkPCGiDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d7136a232c6cd1a6d94d2d757466d81a86613bdfc79c5d557625e5f24319514a","last_reissued_at":"2026-05-18T04:03:32.961801Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:03:32.961801Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0401385","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:03:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+GrutEgyPxtx3h8ZtU2DV021J60b+M9qruNrTQ18ibIOV0kYcuwSwepmV0R2WHx4YRcg2H4rZj8PjvdIhnanCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T12:23:41.706432Z"},"content_sha256":"21f264f9fbf42c087009cd314b77eedb84c453930ab6b41fdd77ef6fa540c53a","schema_version":"1.0","event_id":"sha256:21f264f9fbf42c087009cd314b77eedb84c453930ab6b41fdd77ef6fa540c53a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:24JWUIZMNTI2NWKNFV2XIZWYDK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Random Bulgarian solitaire","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Serguei Popov","submitted_at":"2004-01-27T18:45:05Z","abstract_excerpt":"We consider a stochastic variant of the game of Bulgarian solitaire [M. Gardner (1983), Sci. Amer. 249, 12-21]. For the stationary measure of the random Bulgarian solitaire, we prove that most of its mass is concentrated on (roughly) triangular configurations of certain type."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0401385","kind":"arxiv","version":2},"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":"2026-05-18T04:03:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V4F/DT4HskRkEZ45z1Lvmt/dPaq+nJu80DbN4qqaAsU+/9PWCo5oxScllqGjgYZCELSynXNJH8NxSB57tdGPDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T12:23:41.707133Z"},"content_sha256":"7f5df0c37fbb59f613586d8f932fe657e10e141fb5bf2feef92b092cb6ed23fd","schema_version":"1.0","event_id":"sha256:7f5df0c37fbb59f613586d8f932fe657e10e141fb5bf2feef92b092cb6ed23fd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/24JWUIZMNTI2NWKNFV2XIZWYDK/bundle.json","state_url":"https://pith.science/pith/24JWUIZMNTI2NWKNFV2XIZWYDK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/24JWUIZMNTI2NWKNFV2XIZWYDK/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":"2026-06-06T12:23:41Z","links":{"resolver":"https://pith.science/pith/24JWUIZMNTI2NWKNFV2XIZWYDK","bundle":"https://pith.science/pith/24JWUIZMNTI2NWKNFV2XIZWYDK/bundle.json","state":"https://pith.science/pith/24JWUIZMNTI2NWKNFV2XIZWYDK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/24JWUIZMNTI2NWKNFV2XIZWYDK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:24JWUIZMNTI2NWKNFV2XIZWYDK","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":"59c7b8677d4f702e742008dc749c72cbeef0a13df1d1bf352d0b8a84be10451e","cross_cats_sorted":[],"license":"","primary_cat":"math.PR","submitted_at":"2004-01-27T18:45:05Z","title_canon_sha256":"0d1350d5dad3a34988518863677c12035d5f1ded345d23f8ac75cb12fde240f8"},"schema_version":"1.0","source":{"id":"math/0401385","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0401385","created_at":"2026-05-18T04:03:32Z"},{"alias_kind":"arxiv_version","alias_value":"math/0401385v2","created_at":"2026-05-18T04:03:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0401385","created_at":"2026-05-18T04:03:32Z"},{"alias_kind":"pith_short_12","alias_value":"24JWUIZMNTI2","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"24JWUIZMNTI2NWKN","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"24JWUIZM","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:7f5df0c37fbb59f613586d8f932fe657e10e141fb5bf2feef92b092cb6ed23fd","target":"graph","created_at":"2026-05-18T04:03:32Z","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":"We consider a stochastic variant of the game of Bulgarian solitaire [M. Gardner (1983), Sci. Amer. 249, 12-21]. For the stationary measure of the random Bulgarian solitaire, we prove that most of its mass is concentrated on (roughly) triangular configurations of certain type.","authors_text":"Serguei Popov","cross_cats":[],"headline":"","license":"","primary_cat":"math.PR","submitted_at":"2004-01-27T18:45:05Z","title":"Random Bulgarian solitaire"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0401385","kind":"arxiv","version":2},"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":"sha256:21f264f9fbf42c087009cd314b77eedb84c453930ab6b41fdd77ef6fa540c53a","target":"record","created_at":"2026-05-18T04:03:32Z","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":"59c7b8677d4f702e742008dc749c72cbeef0a13df1d1bf352d0b8a84be10451e","cross_cats_sorted":[],"license":"","primary_cat":"math.PR","submitted_at":"2004-01-27T18:45:05Z","title_canon_sha256":"0d1350d5dad3a34988518863677c12035d5f1ded345d23f8ac75cb12fde240f8"},"schema_version":"1.0","source":{"id":"math/0401385","kind":"arxiv","version":2}},"canonical_sha256":"d7136a232c6cd1a6d94d2d757466d81a86613bdfc79c5d557625e5f24319514a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d7136a232c6cd1a6d94d2d757466d81a86613bdfc79c5d557625e5f24319514a","first_computed_at":"2026-05-18T04:03:32.961801Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:03:32.961801Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"la0HbpD9TbGsLUz+Xf6Dvq7pQAiearVpH8Dw8ARKrWaOdGca3nj561NZdf53hfqdwnACKFhdK18VyuTkPCGiDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:03:32.962476Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0401385","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:21f264f9fbf42c087009cd314b77eedb84c453930ab6b41fdd77ef6fa540c53a","sha256:7f5df0c37fbb59f613586d8f932fe657e10e141fb5bf2feef92b092cb6ed23fd"],"state_sha256":"e564711cf23c66956c609da0a4f31aaccf3359ff2752b722fc330cc4a7fdee4f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/4cKxXTc/Yx8b3QcUPFBqwmQFlXkBuU7zKZ8ipjp9lb43MF2OmL0nqG8ePiO2DtPiqc6r71IgxFGrwLRnlyvAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T12:23:41.711517Z","bundle_sha256":"e78057252215f01896589a6bc24df6b1ee449e7d7ec9b18031413d6fa64dd420"}}