{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:LSHJNYVKBD6C5QJZGQRQV6PQJI","short_pith_number":"pith:LSHJNYVK","schema_version":"1.0","canonical_sha256":"5c8e96e2aa08fc2ec13934230af9f04a146f31777be25c31930a3fb5603dfb81","source":{"kind":"arxiv","id":"1212.0836","version":1},"attestation_state":"computed","paper":{"title":"An Improved Lower Bound for Stack Sorting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Luke Schaeffer","submitted_at":"2012-12-04T19:40:54Z","abstract_excerpt":"We consider the problem of sorting elements on a series of stacks, introduced by Tarjan and Knuth. We improve the asymptotic lower bound for the number of stacks necessary to sort $n$ elements to $0.561 \\log_2 n + O(1)$. This is the first significant improvement since the previous lower bound, $1/2 \\log_2 n + O(1)$, was established by Knuth in 1972."},"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":"1212.0836","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-12-04T19:40:54Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"25fb51dfae8c2e5f5f5133eb138c0aa76a6dad457667dea33c112cd9957c2b6b","abstract_canon_sha256":"bc405624cc2d5cafb139aa44d441f2a04fcf6aebd99bfc32c6cbb71248969ca0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:39:15.100900Z","signature_b64":"gHNYuYP8v69qdp6SDuSF/IPN5tfee8ayFgCXZFD6Dbt/yJ82hK/rPR5VnFwYuFRDsVVmB+YGrGz46qR7PAmIBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5c8e96e2aa08fc2ec13934230af9f04a146f31777be25c31930a3fb5603dfb81","last_reissued_at":"2026-05-18T03:39:15.100308Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:39:15.100308Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An Improved Lower Bound for Stack Sorting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Luke Schaeffer","submitted_at":"2012-12-04T19:40:54Z","abstract_excerpt":"We consider the problem of sorting elements on a series of stacks, introduced by Tarjan and Knuth. We improve the asymptotic lower bound for the number of stacks necessary to sort $n$ elements to $0.561 \\log_2 n + O(1)$. This is the first significant improvement since the previous lower bound, $1/2 \\log_2 n + O(1)$, was established by Knuth in 1972."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.0836","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":"1212.0836","created_at":"2026-05-18T03:39:15.100407+00:00"},{"alias_kind":"arxiv_version","alias_value":"1212.0836v1","created_at":"2026-05-18T03:39:15.100407+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.0836","created_at":"2026-05-18T03:39:15.100407+00:00"},{"alias_kind":"pith_short_12","alias_value":"LSHJNYVKBD6C","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_16","alias_value":"LSHJNYVKBD6C5QJZ","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_8","alias_value":"LSHJNYVK","created_at":"2026-05-18T12:27:14.488303+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/LSHJNYVKBD6C5QJZGQRQV6PQJI","json":"https://pith.science/pith/LSHJNYVKBD6C5QJZGQRQV6PQJI.json","graph_json":"https://pith.science/api/pith-number/LSHJNYVKBD6C5QJZGQRQV6PQJI/graph.json","events_json":"https://pith.science/api/pith-number/LSHJNYVKBD6C5QJZGQRQV6PQJI/events.json","paper":"https://pith.science/paper/LSHJNYVK"},"agent_actions":{"view_html":"https://pith.science/pith/LSHJNYVKBD6C5QJZGQRQV6PQJI","download_json":"https://pith.science/pith/LSHJNYVKBD6C5QJZGQRQV6PQJI.json","view_paper":"https://pith.science/paper/LSHJNYVK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1212.0836&json=true","fetch_graph":"https://pith.science/api/pith-number/LSHJNYVKBD6C5QJZGQRQV6PQJI/graph.json","fetch_events":"https://pith.science/api/pith-number/LSHJNYVKBD6C5QJZGQRQV6PQJI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LSHJNYVKBD6C5QJZGQRQV6PQJI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LSHJNYVKBD6C5QJZGQRQV6PQJI/action/storage_attestation","attest_author":"https://pith.science/pith/LSHJNYVKBD6C5QJZGQRQV6PQJI/action/author_attestation","sign_citation":"https://pith.science/pith/LSHJNYVKBD6C5QJZGQRQV6PQJI/action/citation_signature","submit_replication":"https://pith.science/pith/LSHJNYVKBD6C5QJZGQRQV6PQJI/action/replication_record"}},"created_at":"2026-05-18T03:39:15.100407+00:00","updated_at":"2026-05-18T03:39:15.100407+00:00"}