{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:HOFA5IYT6TWMI4BMQDCDUFNMAR","short_pith_number":"pith:HOFA5IYT","schema_version":"1.0","canonical_sha256":"3b8a0ea313f4ecc4702c80c43a15ac046a430f6faece7fde6accc499117f61e1","source":{"kind":"arxiv","id":"1703.07102","version":1},"attestation_state":"computed","paper":{"title":"An exponential limit shape of random $q$-proportion Bulgarian solitaire","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Kimmo Eriksson, Markus Jonsson abd Jonas Sj\\\"ostrand","submitted_at":"2017-03-21T09:25:36Z","abstract_excerpt":"We introduce \\emph{$p_n$-random $q_n$-proportion Bulgarian solitaire} ($0<p_n,q_n\\le 1$), played on $n$ cards distributed in piles. In each pile, a number of cards equal to the proportion $q_n$ of the pile size rounded upward to the nearest integer are candidates to be picked. Each candidate card is picked with probability $p_n$, independently of other candidate cards. This generalizes Popov's random Bulgarian solitaire, in which there is a single candidate card in each pile. Popov showed that a triangular limit shape is obtained for a fixed $p$ as $n$ tends to infinity. Here we let both $p_n$"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1703.07102","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-03-21T09:25:36Z","cross_cats_sorted":[],"title_canon_sha256":"185ea9824b2c98f88c6c333c04fca7c7c17a9c68a0fcd6dd976a0fff3c818115","abstract_canon_sha256":"ec404ae82d8907291a62e09714cf502ec59f459cff12758656c45084cdddce76"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:11.330266Z","signature_b64":"ynD7z9XvnExuWgsAz9Cpk0kBcpknPJcMNoRPraqzJnkA6A6lxWUaZZclvVD7jT6x1HCsxLjCuwsQ7zATId3YAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b8a0ea313f4ecc4702c80c43a15ac046a430f6faece7fde6accc499117f61e1","last_reissued_at":"2026-05-18T00:48:11.329637Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:11.329637Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An exponential limit shape of random $q$-proportion Bulgarian solitaire","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Kimmo Eriksson, Markus Jonsson abd Jonas Sj\\\"ostrand","submitted_at":"2017-03-21T09:25:36Z","abstract_excerpt":"We introduce \\emph{$p_n$-random $q_n$-proportion Bulgarian solitaire} ($0<p_n,q_n\\le 1$), played on $n$ cards distributed in piles. In each pile, a number of cards equal to the proportion $q_n$ of the pile size rounded upward to the nearest integer are candidates to be picked. Each candidate card is picked with probability $p_n$, independently of other candidate cards. This generalizes Popov's random Bulgarian solitaire, in which there is a single candidate card in each pile. Popov showed that a triangular limit shape is obtained for a fixed $p$ as $n$ tends to infinity. Here we let both $p_n$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.07102","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1703.07102","created_at":"2026-05-18T00:48:11.329730+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.07102v1","created_at":"2026-05-18T00:48:11.329730+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.07102","created_at":"2026-05-18T00:48:11.329730+00:00"},{"alias_kind":"pith_short_12","alias_value":"HOFA5IYT6TWM","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_16","alias_value":"HOFA5IYT6TWMI4BM","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_8","alias_value":"HOFA5IYT","created_at":"2026-05-18T12:31:18.294218+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HOFA5IYT6TWMI4BMQDCDUFNMAR","json":"https://pith.science/pith/HOFA5IYT6TWMI4BMQDCDUFNMAR.json","graph_json":"https://pith.science/api/pith-number/HOFA5IYT6TWMI4BMQDCDUFNMAR/graph.json","events_json":"https://pith.science/api/pith-number/HOFA5IYT6TWMI4BMQDCDUFNMAR/events.json","paper":"https://pith.science/paper/HOFA5IYT"},"agent_actions":{"view_html":"https://pith.science/pith/HOFA5IYT6TWMI4BMQDCDUFNMAR","download_json":"https://pith.science/pith/HOFA5IYT6TWMI4BMQDCDUFNMAR.json","view_paper":"https://pith.science/paper/HOFA5IYT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.07102&json=true","fetch_graph":"https://pith.science/api/pith-number/HOFA5IYT6TWMI4BMQDCDUFNMAR/graph.json","fetch_events":"https://pith.science/api/pith-number/HOFA5IYT6TWMI4BMQDCDUFNMAR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HOFA5IYT6TWMI4BMQDCDUFNMAR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HOFA5IYT6TWMI4BMQDCDUFNMAR/action/storage_attestation","attest_author":"https://pith.science/pith/HOFA5IYT6TWMI4BMQDCDUFNMAR/action/author_attestation","sign_citation":"https://pith.science/pith/HOFA5IYT6TWMI4BMQDCDUFNMAR/action/citation_signature","submit_replication":"https://pith.science/pith/HOFA5IYT6TWMI4BMQDCDUFNMAR/action/replication_record"}},"created_at":"2026-05-18T00:48:11.329730+00:00","updated_at":"2026-05-18T00:48:11.329730+00:00"}