{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:MN3A7F5L4SNEOIKGSLLBWJHXZJ","short_pith_number":"pith:MN3A7F5L","canonical_record":{"source":{"id":"1801.05591","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-01-17T08:43:23Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"c31c4e975bdea2edd64c344227ddc2d5b9477d9a87256c598f66bed752853bc0","abstract_canon_sha256":"93e073b69e9f5b792557b40e9066c44aea1b517d3e7d9535763d172f95361a78"},"schema_version":"1.0"},"canonical_sha256":"63760f97abe49a47214692d61b24f7ca5338dfd5d33dca0d9b9aef869daea584","source":{"kind":"arxiv","id":"1801.05591","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.05591","created_at":"2026-05-18T00:25:40Z"},{"alias_kind":"arxiv_version","alias_value":"1801.05591v1","created_at":"2026-05-18T00:25:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.05591","created_at":"2026-05-18T00:25:40Z"},{"alias_kind":"pith_short_12","alias_value":"MN3A7F5L4SNE","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"MN3A7F5L4SNEOIKG","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"MN3A7F5L","created_at":"2026-05-18T12:32:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:MN3A7F5L4SNEOIKGSLLBWJHXZJ","target":"record","payload":{"canonical_record":{"source":{"id":"1801.05591","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-01-17T08:43:23Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"c31c4e975bdea2edd64c344227ddc2d5b9477d9a87256c598f66bed752853bc0","abstract_canon_sha256":"93e073b69e9f5b792557b40e9066c44aea1b517d3e7d9535763d172f95361a78"},"schema_version":"1.0"},"canonical_sha256":"63760f97abe49a47214692d61b24f7ca5338dfd5d33dca0d9b9aef869daea584","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:40.778966Z","signature_b64":"rhU05lCbGsLigGN6rt7DqgGC+YhCdNHZiaGszgnj8bwmFtT2nBjhv4gD8zM/bS+jpQFGnjTE1AxARj8hBQiMAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"63760f97abe49a47214692d61b24f7ca5338dfd5d33dca0d9b9aef869daea584","last_reissued_at":"2026-05-18T00:25:40.778295Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:40.778295Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.05591","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":"2026-05-18T00:25:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HB8K+cIkauSOf9NOTw2hIR253WKjfpK40B4fLFadCDL76DgJpYsoNpBFtEnVcMoN9eM/XlEYrj03dl6Ub+X0Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T14:32:07.077873Z"},"content_sha256":"2681b7194d3f480097e7a370b9c4794d50795c0d0013579a9cdbc0c579fd66d7","schema_version":"1.0","event_id":"sha256:2681b7194d3f480097e7a370b9c4794d50795c0d0013579a9cdbc0c579fd66d7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:MN3A7F5L4SNEOIKGSLLBWJHXZJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Combinatorics of patience sorting monoids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"Alan J. Cain, Ant\\'onio Malheiro, F\\'abio M. Silva","submitted_at":"2018-01-17T08:43:23Z","abstract_excerpt":"This paper makes a combinatorial study of the two monoids and the two types of tableaux that arise from the two possible generalizations of the Patience Sorting algorithm from permutations (or standard words) to words. For both types of tableaux, we present Robinson--Schensted--Knuth-type correspondences (that is, bijective correspondences between word arrays and certain pairs of semistandard tableaux of the same shape), generalizing two known correspondences: a bijective correspondence between standard words and certain pairs of standard tableaux, and an injective correspondence between words"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.05591","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":"2026-05-18T00:25:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+v9QY9UHkE72++c2l3RqOzPzh53ZUU4KlAEM4ER6djcBf08L/bZTClgucglYU7EgtlPtUMXM6LHNPDArqayMCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T14:32:07.078217Z"},"content_sha256":"93aa16b46a7d687542c3c732232ab031421e84aaad890093dbde42e283fd689d","schema_version":"1.0","event_id":"sha256:93aa16b46a7d687542c3c732232ab031421e84aaad890093dbde42e283fd689d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MN3A7F5L4SNEOIKGSLLBWJHXZJ/bundle.json","state_url":"https://pith.science/pith/MN3A7F5L4SNEOIKGSLLBWJHXZJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MN3A7F5L4SNEOIKGSLLBWJHXZJ/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":"2026-06-23T14:32:07Z","links":{"resolver":"https://pith.science/pith/MN3A7F5L4SNEOIKGSLLBWJHXZJ","bundle":"https://pith.science/pith/MN3A7F5L4SNEOIKGSLLBWJHXZJ/bundle.json","state":"https://pith.science/pith/MN3A7F5L4SNEOIKGSLLBWJHXZJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MN3A7F5L4SNEOIKGSLLBWJHXZJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:MN3A7F5L4SNEOIKGSLLBWJHXZJ","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":"93e073b69e9f5b792557b40e9066c44aea1b517d3e7d9535763d172f95361a78","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-01-17T08:43:23Z","title_canon_sha256":"c31c4e975bdea2edd64c344227ddc2d5b9477d9a87256c598f66bed752853bc0"},"schema_version":"1.0","source":{"id":"1801.05591","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.05591","created_at":"2026-05-18T00:25:40Z"},{"alias_kind":"arxiv_version","alias_value":"1801.05591v1","created_at":"2026-05-18T00:25:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.05591","created_at":"2026-05-18T00:25:40Z"},{"alias_kind":"pith_short_12","alias_value":"MN3A7F5L4SNE","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"MN3A7F5L4SNEOIKG","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"MN3A7F5L","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:93aa16b46a7d687542c3c732232ab031421e84aaad890093dbde42e283fd689d","target":"graph","created_at":"2026-05-18T00:25:40Z","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":"This paper makes a combinatorial study of the two monoids and the two types of tableaux that arise from the two possible generalizations of the Patience Sorting algorithm from permutations (or standard words) to words. For both types of tableaux, we present Robinson--Schensted--Knuth-type correspondences (that is, bijective correspondences between word arrays and certain pairs of semistandard tableaux of the same shape), generalizing two known correspondences: a bijective correspondence between standard words and certain pairs of standard tableaux, and an injective correspondence between words","authors_text":"Alan J. Cain, Ant\\'onio Malheiro, F\\'abio M. Silva","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-01-17T08:43:23Z","title":"Combinatorics of patience sorting monoids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.05591","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":"sha256:2681b7194d3f480097e7a370b9c4794d50795c0d0013579a9cdbc0c579fd66d7","target":"record","created_at":"2026-05-18T00:25:40Z","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":"93e073b69e9f5b792557b40e9066c44aea1b517d3e7d9535763d172f95361a78","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-01-17T08:43:23Z","title_canon_sha256":"c31c4e975bdea2edd64c344227ddc2d5b9477d9a87256c598f66bed752853bc0"},"schema_version":"1.0","source":{"id":"1801.05591","kind":"arxiv","version":1}},"canonical_sha256":"63760f97abe49a47214692d61b24f7ca5338dfd5d33dca0d9b9aef869daea584","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"63760f97abe49a47214692d61b24f7ca5338dfd5d33dca0d9b9aef869daea584","first_computed_at":"2026-05-18T00:25:40.778295Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:40.778295Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rhU05lCbGsLigGN6rt7DqgGC+YhCdNHZiaGszgnj8bwmFtT2nBjhv4gD8zM/bS+jpQFGnjTE1AxARj8hBQiMAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:40.778966Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.05591","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2681b7194d3f480097e7a370b9c4794d50795c0d0013579a9cdbc0c579fd66d7","sha256:93aa16b46a7d687542c3c732232ab031421e84aaad890093dbde42e283fd689d"],"state_sha256":"368ec48fa5a5bb310a9d66a9df6070f57d2b363156040667e90d94b0caf34c72"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HZxG1iE3egqt0EKzOLleQvbEoqCnwF7gaI021wuoOMLe/CD8s73aKxWAiGEgGchcqCQaSwa8Xi9fmGEh+9lLDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T14:32:07.080178Z","bundle_sha256":"a304ab2821e25d78ceeebe6e1bcf64a9ba91f5be79744ae0812d95449f614425"}}