{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:Y6ADJVB55FNVJCXO4IOBUQABMG","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":"4f1f6f75a9de4aadf67b20d1dabebc03799216f62b6c0b84165b448c7341ad00","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-02-21T15:40:51Z","title_canon_sha256":"9ac8e52baf363e7f25f315d26eb447365535624579b123c9e2b8ae62630a3000"},"schema_version":"1.0","source":{"id":"1702.06444","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.06444","created_at":"2026-05-18T00:50:14Z"},{"alias_kind":"arxiv_version","alias_value":"1702.06444v1","created_at":"2026-05-18T00:50:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.06444","created_at":"2026-05-18T00:50:14Z"},{"alias_kind":"pith_short_12","alias_value":"Y6ADJVB55FNV","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"Y6ADJVB55FNVJCXO","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"Y6ADJVB5","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:b7d09b9b11736a559d03d70f2498f350595cd5642c1b5c954f05db37cc3b0b08","target":"graph","created_at":"2026-05-18T00:50:14Z","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 study the minimum number of heaps required to sort a random sequence using a generalization of Istrate and Bonchis's algorithm (2015). In a previous paper, the authors proved that the expected number of heaps grows logarithmically. In this note, we improve on the previous result by establishing the almost-sure and L 1 convergence.","authors_text":"Anne-Laure Basdevant (MODAL'X), Arvind Singh (LM-Orsay)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-02-21T15:40:51Z","title":"Almost-sure asymptotic for the number of heaps inside a random sequence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.06444","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":"sha256:539e563cc7c0afc30444bdb1472e5de8c9057b51b59cfdc0ecf7bb3c30156ac2","target":"record","created_at":"2026-05-18T00:50:14Z","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":"4f1f6f75a9de4aadf67b20d1dabebc03799216f62b6c0b84165b448c7341ad00","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-02-21T15:40:51Z","title_canon_sha256":"9ac8e52baf363e7f25f315d26eb447365535624579b123c9e2b8ae62630a3000"},"schema_version":"1.0","source":{"id":"1702.06444","kind":"arxiv","version":1}},"canonical_sha256":"c78034d43de95b548aeee21c1a4001618832dc60e9e2d2fbdf98b4d5b16f7720","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c78034d43de95b548aeee21c1a4001618832dc60e9e2d2fbdf98b4d5b16f7720","first_computed_at":"2026-05-18T00:50:14.124128Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:14.124128Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"42MzRUsThR3+KTwX+AWzusl/v88YnXu4AIoqd1VxlBt0vgSr0vhhIGwLid/48LJXvHN1x7dEcEQzY/sMPpe8DA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:14.124701Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.06444","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:539e563cc7c0afc30444bdb1472e5de8c9057b51b59cfdc0ecf7bb3c30156ac2","sha256:b7d09b9b11736a559d03d70f2498f350595cd5642c1b5c954f05db37cc3b0b08"],"state_sha256":"e3131c2af88863545beb84d01f8361caa8795a6f2c67c01b87eb4a3dd5a3fa64"}