{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:F44HHTKBDQR4NS6PHTXIJWCSG3","short_pith_number":"pith:F44HHTKB","canonical_record":{"source":{"id":"1504.05902","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-04-22T17:47:05Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"9e2d48686b2e6ca5cc72944f0228d0b8ea9b576a4ffb2f08239c4df3f94ae62c","abstract_canon_sha256":"4eb2a078444fbeb4c1ee7d67fea3caabff9b6b22d448d762b2be4db6d9f6ab43"},"schema_version":"1.0"},"canonical_sha256":"2f3873cd411c23c6cbcf3cee84d85236d9237dcdb4e7773f98df9439157474ad","source":{"kind":"arxiv","id":"1504.05902","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.05902","created_at":"2026-05-18T02:18:04Z"},{"alias_kind":"arxiv_version","alias_value":"1504.05902v1","created_at":"2026-05-18T02:18:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.05902","created_at":"2026-05-18T02:18:04Z"},{"alias_kind":"pith_short_12","alias_value":"F44HHTKBDQR4","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"F44HHTKBDQR4NS6P","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"F44HHTKB","created_at":"2026-05-18T12:29:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:F44HHTKBDQR4NS6PHTXIJWCSG3","target":"record","payload":{"canonical_record":{"source":{"id":"1504.05902","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-04-22T17:47:05Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"9e2d48686b2e6ca5cc72944f0228d0b8ea9b576a4ffb2f08239c4df3f94ae62c","abstract_canon_sha256":"4eb2a078444fbeb4c1ee7d67fea3caabff9b6b22d448d762b2be4db6d9f6ab43"},"schema_version":"1.0"},"canonical_sha256":"2f3873cd411c23c6cbcf3cee84d85236d9237dcdb4e7773f98df9439157474ad","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:04.733336Z","signature_b64":"o+7OrdvWccWmWSr2jVQUBFfyU9s7sidS96YquQtTkFYv23zgOO9zUkAQLugjUuEkj5skeBdBTKuqSBC+25wGCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f3873cd411c23c6cbcf3cee84d85236d9237dcdb4e7773f98df9439157474ad","last_reissued_at":"2026-05-18T02:18:04.732569Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:04.732569Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.05902","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":"2026-05-18T02:18:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jZDh6WCLDBLQJT0z9MCWtewR+nb5brVH7FEtvKJgecAu91bnoYAENr5mnq+fEwvXx0bSXSes5lGfh3oy7xHkAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T14:11:34.699936Z"},"content_sha256":"570ced219be9aeeb4307930e8848d213d4b79cdd04e2728a3fb4d3f312f77362","schema_version":"1.0","event_id":"sha256:570ced219be9aeeb4307930e8848d213d4b79cdd04e2728a3fb4d3f312f77362"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:F44HHTKBDQR4NS6PHTXIJWCSG3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Onset of the Asymptotic Regime for Finite Orders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"math.CO","authors_text":"David P. Rideout, Joe Henson, Rafael D. Sorkin, Sumati Surya","submitted_at":"2015-04-22T17:47:05Z","abstract_excerpt":"We describe a Markov-Chain-Monte-Carlo algorithm which can be used to generate naturally labeled n-element posets at random with a probability distribution of one's choice. Implementing this algorithm for the uniform distribution, we explore the approach to the asymptotic regime in which almost every poset takes on the three-layer structure described by Kleitman and Rothschild (KR). By tracking the n-dependence of several order-invariants, among them the height of the poset, we observe an oscillatory behavior which is very unlike a monotonic approach to the KR regime. Only around n=40 or so do"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05902","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:18:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vc0iKcyOoFF4Lsh36WsNbrkxqAf7alZWymIyw+7Xqu1DQTrLwaJ/s15blUfg3cEhh4/ayG071ywpzPu0oQH4AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T14:11:34.700673Z"},"content_sha256":"920692003fa929990d03e0d15d92534c569090a48f8ea8db3817858c84d91d09","schema_version":"1.0","event_id":"sha256:920692003fa929990d03e0d15d92534c569090a48f8ea8db3817858c84d91d09"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F44HHTKBDQR4NS6PHTXIJWCSG3/bundle.json","state_url":"https://pith.science/pith/F44HHTKBDQR4NS6PHTXIJWCSG3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F44HHTKBDQR4NS6PHTXIJWCSG3/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":"2026-05-26T14:11:34Z","links":{"resolver":"https://pith.science/pith/F44HHTKBDQR4NS6PHTXIJWCSG3","bundle":"https://pith.science/pith/F44HHTKBDQR4NS6PHTXIJWCSG3/bundle.json","state":"https://pith.science/pith/F44HHTKBDQR4NS6PHTXIJWCSG3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F44HHTKBDQR4NS6PHTXIJWCSG3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:F44HHTKBDQR4NS6PHTXIJWCSG3","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":"4eb2a078444fbeb4c1ee7d67fea3caabff9b6b22d448d762b2be4db6d9f6ab43","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-04-22T17:47:05Z","title_canon_sha256":"9e2d48686b2e6ca5cc72944f0228d0b8ea9b576a4ffb2f08239c4df3f94ae62c"},"schema_version":"1.0","source":{"id":"1504.05902","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.05902","created_at":"2026-05-18T02:18:04Z"},{"alias_kind":"arxiv_version","alias_value":"1504.05902v1","created_at":"2026-05-18T02:18:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.05902","created_at":"2026-05-18T02:18:04Z"},{"alias_kind":"pith_short_12","alias_value":"F44HHTKBDQR4","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"F44HHTKBDQR4NS6P","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"F44HHTKB","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:920692003fa929990d03e0d15d92534c569090a48f8ea8db3817858c84d91d09","target":"graph","created_at":"2026-05-18T02:18:04Z","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 describe a Markov-Chain-Monte-Carlo algorithm which can be used to generate naturally labeled n-element posets at random with a probability distribution of one's choice. Implementing this algorithm for the uniform distribution, we explore the approach to the asymptotic regime in which almost every poset takes on the three-layer structure described by Kleitman and Rothschild (KR). By tracking the n-dependence of several order-invariants, among them the height of the poset, we observe an oscillatory behavior which is very unlike a monotonic approach to the KR regime. Only around n=40 or so do","authors_text":"David P. Rideout, Joe Henson, Rafael D. Sorkin, Sumati Surya","cross_cats":["gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-04-22T17:47:05Z","title":"Onset of the Asymptotic Regime for Finite Orders"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05902","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":"sha256:570ced219be9aeeb4307930e8848d213d4b79cdd04e2728a3fb4d3f312f77362","target":"record","created_at":"2026-05-18T02:18:04Z","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":"4eb2a078444fbeb4c1ee7d67fea3caabff9b6b22d448d762b2be4db6d9f6ab43","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-04-22T17:47:05Z","title_canon_sha256":"9e2d48686b2e6ca5cc72944f0228d0b8ea9b576a4ffb2f08239c4df3f94ae62c"},"schema_version":"1.0","source":{"id":"1504.05902","kind":"arxiv","version":1}},"canonical_sha256":"2f3873cd411c23c6cbcf3cee84d85236d9237dcdb4e7773f98df9439157474ad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2f3873cd411c23c6cbcf3cee84d85236d9237dcdb4e7773f98df9439157474ad","first_computed_at":"2026-05-18T02:18:04.732569Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:18:04.732569Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o+7OrdvWccWmWSr2jVQUBFfyU9s7sidS96YquQtTkFYv23zgOO9zUkAQLugjUuEkj5skeBdBTKuqSBC+25wGCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:18:04.733336Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.05902","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:570ced219be9aeeb4307930e8848d213d4b79cdd04e2728a3fb4d3f312f77362","sha256:920692003fa929990d03e0d15d92534c569090a48f8ea8db3817858c84d91d09"],"state_sha256":"c2be13dde72b6a4a00e67c674902d6f9426d186febeaae56a8f2f673e27380a1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Yb8NeZvOS8VfbctRKfkxyg6va3vPVZOkbn/FgrjL/D7433X4Npoqjn4Jpke3mhKoAaqmpX7TruBBuPoCVX5yCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T14:11:34.704271Z","bundle_sha256":"a8f7dfc8e98b5a2801bf293efcf7e0a007a874f301681d35d0bfe244c37e9ba5"}}