{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:QXZRXHLYIGJYAVKRC7RMURJQPY","short_pith_number":"pith:QXZRXHLY","canonical_record":{"source":{"id":"1903.04113","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-03-11T03:32:01Z","cross_cats_sorted":[],"title_canon_sha256":"6140fc959ac5ec43ca9d735d723232de3653fb47ccbdcfd18d668347c3d4124d","abstract_canon_sha256":"3332f21497975f606281776696de11ca80742cfac4acf94c871c43fe8bca8592"},"schema_version":"1.0"},"canonical_sha256":"85f31b9d78419380555117e2ca45307e2bb9c34300bc0bf096bb3e37506e57bb","source":{"kind":"arxiv","id":"1903.04113","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.04113","created_at":"2026-07-05T00:35:00Z"},{"alias_kind":"arxiv_version","alias_value":"1903.04113v4","created_at":"2026-07-05T00:35:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.04113","created_at":"2026-07-05T00:35:00Z"},{"alias_kind":"pith_short_12","alias_value":"QXZRXHLYIGJY","created_at":"2026-07-05T00:35:00Z"},{"alias_kind":"pith_short_16","alias_value":"QXZRXHLYIGJYAVKR","created_at":"2026-07-05T00:35:00Z"},{"alias_kind":"pith_short_8","alias_value":"QXZRXHLY","created_at":"2026-07-05T00:35:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:QXZRXHLYIGJYAVKRC7RMURJQPY","target":"record","payload":{"canonical_record":{"source":{"id":"1903.04113","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-03-11T03:32:01Z","cross_cats_sorted":[],"title_canon_sha256":"6140fc959ac5ec43ca9d735d723232de3653fb47ccbdcfd18d668347c3d4124d","abstract_canon_sha256":"3332f21497975f606281776696de11ca80742cfac4acf94c871c43fe8bca8592"},"schema_version":"1.0"},"canonical_sha256":"85f31b9d78419380555117e2ca45307e2bb9c34300bc0bf096bb3e37506e57bb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:35:00.122755Z","signature_b64":"1OXQZT3N3pBvI+CDyoU9ym3guKF8rLWS6qLguloCeBDfULYJy9ediI1siPSm4xqEPLGenA8gVdt95qPZvkqgAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"85f31b9d78419380555117e2ca45307e2bb9c34300bc0bf096bb3e37506e57bb","last_reissued_at":"2026-07-05T00:35:00.122356Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:35:00.122356Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.04113","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:35:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nDmh1yIFkffTvJzGMU4VimPvBmTkNMypyHQhIGJECdJ0IhUhK42PjDCBP4d49tApExJRhGJMrnQdPqdAJiwdAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T17:28:52.973595Z"},"content_sha256":"6ff749083c11cf9953ca65b0ca052b3b9821aa1b131d72f9afd327aa9054a9b3","schema_version":"1.0","event_id":"sha256:6ff749083c11cf9953ca65b0ca052b3b9821aa1b131d72f9afd327aa9054a9b3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:QXZRXHLYIGJYAVKRC7RMURJQPY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stack words and a bound for 3-stack sortable permutations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Miklos Bona","submitted_at":"2019-03-11T03:32:01Z","abstract_excerpt":"We use stack words to find a new, simple proof for the best known upper bound for the number of 3-stack sortable permutations of a given length. This is the first time that stack words are used to obtain such a result."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.04113","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1903.04113/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T00:35:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dsGviBnvGnAH9qCFYYgAeyMztMWX3OSR45JHgmmtwVKIbYgYhGOvMCubatt+ZfR8+0yM0Db8bcggJC+IzoKOBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T17:28:52.974246Z"},"content_sha256":"9f174360d37d481d3c63e4da317aaf088aef35697956c8295d02335ba1d35cf3","schema_version":"1.0","event_id":"sha256:9f174360d37d481d3c63e4da317aaf088aef35697956c8295d02335ba1d35cf3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QXZRXHLYIGJYAVKRC7RMURJQPY/bundle.json","state_url":"https://pith.science/pith/QXZRXHLYIGJYAVKRC7RMURJQPY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QXZRXHLYIGJYAVKRC7RMURJQPY/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":"2026-08-16T17:28:52Z","links":{"resolver":"https://pith.science/pith/QXZRXHLYIGJYAVKRC7RMURJQPY","bundle":"https://pith.science/pith/QXZRXHLYIGJYAVKRC7RMURJQPY/bundle.json","state":"https://pith.science/pith/QXZRXHLYIGJYAVKRC7RMURJQPY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QXZRXHLYIGJYAVKRC7RMURJQPY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:QXZRXHLYIGJYAVKRC7RMURJQPY","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":"3332f21497975f606281776696de11ca80742cfac4acf94c871c43fe8bca8592","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-03-11T03:32:01Z","title_canon_sha256":"6140fc959ac5ec43ca9d735d723232de3653fb47ccbdcfd18d668347c3d4124d"},"schema_version":"1.0","source":{"id":"1903.04113","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.04113","created_at":"2026-07-05T00:35:00Z"},{"alias_kind":"arxiv_version","alias_value":"1903.04113v4","created_at":"2026-07-05T00:35:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.04113","created_at":"2026-07-05T00:35:00Z"},{"alias_kind":"pith_short_12","alias_value":"QXZRXHLYIGJY","created_at":"2026-07-05T00:35:00Z"},{"alias_kind":"pith_short_16","alias_value":"QXZRXHLYIGJYAVKR","created_at":"2026-07-05T00:35:00Z"},{"alias_kind":"pith_short_8","alias_value":"QXZRXHLY","created_at":"2026-07-05T00:35:00Z"}],"graph_snapshots":[{"event_id":"sha256:9f174360d37d481d3c63e4da317aaf088aef35697956c8295d02335ba1d35cf3","target":"graph","created_at":"2026-07-05T00:35:00Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1903.04113/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We use stack words to find a new, simple proof for the best known upper bound for the number of 3-stack sortable permutations of a given length. This is the first time that stack words are used to obtain such a result.","authors_text":"Miklos Bona","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-03-11T03:32:01Z","title":"Stack words and a bound for 3-stack sortable permutations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.04113","kind":"arxiv","version":4},"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":"sha256:6ff749083c11cf9953ca65b0ca052b3b9821aa1b131d72f9afd327aa9054a9b3","target":"record","created_at":"2026-07-05T00:35:00Z","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":"3332f21497975f606281776696de11ca80742cfac4acf94c871c43fe8bca8592","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-03-11T03:32:01Z","title_canon_sha256":"6140fc959ac5ec43ca9d735d723232de3653fb47ccbdcfd18d668347c3d4124d"},"schema_version":"1.0","source":{"id":"1903.04113","kind":"arxiv","version":4}},"canonical_sha256":"85f31b9d78419380555117e2ca45307e2bb9c34300bc0bf096bb3e37506e57bb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"85f31b9d78419380555117e2ca45307e2bb9c34300bc0bf096bb3e37506e57bb","first_computed_at":"2026-07-05T00:35:00.122356Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:35:00.122356Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1OXQZT3N3pBvI+CDyoU9ym3guKF8rLWS6qLguloCeBDfULYJy9ediI1siPSm4xqEPLGenA8gVdt95qPZvkqgAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T00:35:00.122755Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.04113","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6ff749083c11cf9953ca65b0ca052b3b9821aa1b131d72f9afd327aa9054a9b3","sha256:9f174360d37d481d3c63e4da317aaf088aef35697956c8295d02335ba1d35cf3"],"state_sha256":"219a3f2ad1d5e8a3ad07fa68f58ce44e6bc0878b9f2c3173eb2ea555ad91ed88"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MDTEs9F3r4iSAVHtYcF4F1v3bKB+C3VJrqIOIS5cO1TBdy/WEf1tSxzs/NcRJJKP9CBf9tJc7LW/5Xjjo+UtCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T17:28:52.982622Z","bundle_sha256":"d03b3faf61c75c1b5066e8f6282d463f277ee069cf9815ff9e8fb4c855a4ff95"}}