{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:MYEMZZXTDXHZXINWXG2XLXS7WQ","short_pith_number":"pith:MYEMZZXT","canonical_record":{"source":{"id":"1511.01770","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-11-05T15:08:59Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"5acfcab4d800a0140c73f148a3e8bda4c30757fbb3904d3b71de8a3d34e2799e","abstract_canon_sha256":"08042c5903e6e43a01894598a9e03f5c687588c4cb1aa220d68fbf075414f3fb"},"schema_version":"1.0"},"canonical_sha256":"6608cce6f31dcf9ba1b6b9b575de5fb427ab5d671340ff27bdaf62e0dc60303b","source":{"kind":"arxiv","id":"1511.01770","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.01770","created_at":"2026-05-18T01:27:39Z"},{"alias_kind":"arxiv_version","alias_value":"1511.01770v1","created_at":"2026-05-18T01:27:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.01770","created_at":"2026-05-18T01:27:39Z"},{"alias_kind":"pith_short_12","alias_value":"MYEMZZXTDXHZ","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MYEMZZXTDXHZXINW","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MYEMZZXT","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:MYEMZZXTDXHZXINWXG2XLXS7WQ","target":"record","payload":{"canonical_record":{"source":{"id":"1511.01770","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-11-05T15:08:59Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"5acfcab4d800a0140c73f148a3e8bda4c30757fbb3904d3b71de8a3d34e2799e","abstract_canon_sha256":"08042c5903e6e43a01894598a9e03f5c687588c4cb1aa220d68fbf075414f3fb"},"schema_version":"1.0"},"canonical_sha256":"6608cce6f31dcf9ba1b6b9b575de5fb427ab5d671340ff27bdaf62e0dc60303b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:39.846903Z","signature_b64":"N3SXZNufvz4f5I55ukvrTFjg4nXb7oTsMPGUZoEljna72nSOt8/9DkYxhZlTZoBELekSfj8B+EwLnwlFEHpSAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6608cce6f31dcf9ba1b6b9b575de5fb427ab5d671340ff27bdaf62e0dc60303b","last_reissued_at":"2026-05-18T01:27:39.846435Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:39.846435Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.01770","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":"2026-05-18T01:27:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ASZxkIzQxpNnZQoGw8UrJVZ8c0D3Yy4r3iYYrOGEd6NaqrIur4Y1zOb/h7rvALLrz5X8MEHbRnvQCDKrxZxsBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T15:39:45.982436Z"},"content_sha256":"c3d81942ccd5eeaa047ea70bdd2365445d6fe60c20798e7fac4f2721af5a3787","schema_version":"1.0","event_id":"sha256:c3d81942ccd5eeaa047ea70bdd2365445d6fe60c20798e7fac4f2721af5a3787"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:MYEMZZXTDXHZXINWXG2XLXS7WQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Pattern matching in $(213,231)$-avoiding permutations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DS","authors_text":"Both Emerite Neou, Romeo Rizzi, St\\'ephane Vialette","submitted_at":"2015-11-05T15:08:59Z","abstract_excerpt":"Given permutations $\\sigma \\in S_k$ and $\\pi \\in S_n$ with $k<n$, the \\emph{pattern matching} problem is to decide whether $\\pi$ matches $\\sigma$ as an order-isomorphic subsequence. We give a linear-time algorithm in case both $\\pi$ and $\\sigma$ avoid the two size-$3$ permutations $213$ and $231$. For the special case where only $\\sigma$ avoids $213$ and $231$, we present a $O(max(kn^2,n^2\\log(\\log(n)))$ time algorithm. We extend our research to bivincular patterns that avoid $213$ and $231$ and present a $O(kn^4)$ time algorithm. Finally we look at the related problem of the longest subsequen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.01770","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":"2026-05-18T01:27:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RnFIbP7H9TlvqvtnkZkxeJE7ELkgU0uaE/C0xXbJZkNZoJLROmd9jl2BzKJ3jQcYas5F43gx6BRqbUaB7HgOAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T15:39:45.982793Z"},"content_sha256":"4084ea94e7624d2293b069717dab76afe839ad27d1e34e48dd9cb0e865e93aad","schema_version":"1.0","event_id":"sha256:4084ea94e7624d2293b069717dab76afe839ad27d1e34e48dd9cb0e865e93aad"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MYEMZZXTDXHZXINWXG2XLXS7WQ/bundle.json","state_url":"https://pith.science/pith/MYEMZZXTDXHZXINWXG2XLXS7WQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MYEMZZXTDXHZXINWXG2XLXS7WQ/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":"2026-06-04T15:39:45Z","links":{"resolver":"https://pith.science/pith/MYEMZZXTDXHZXINWXG2XLXS7WQ","bundle":"https://pith.science/pith/MYEMZZXTDXHZXINWXG2XLXS7WQ/bundle.json","state":"https://pith.science/pith/MYEMZZXTDXHZXINWXG2XLXS7WQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MYEMZZXTDXHZXINWXG2XLXS7WQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:MYEMZZXTDXHZXINWXG2XLXS7WQ","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":"08042c5903e6e43a01894598a9e03f5c687588c4cb1aa220d68fbf075414f3fb","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-11-05T15:08:59Z","title_canon_sha256":"5acfcab4d800a0140c73f148a3e8bda4c30757fbb3904d3b71de8a3d34e2799e"},"schema_version":"1.0","source":{"id":"1511.01770","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.01770","created_at":"2026-05-18T01:27:39Z"},{"alias_kind":"arxiv_version","alias_value":"1511.01770v1","created_at":"2026-05-18T01:27:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.01770","created_at":"2026-05-18T01:27:39Z"},{"alias_kind":"pith_short_12","alias_value":"MYEMZZXTDXHZ","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MYEMZZXTDXHZXINW","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MYEMZZXT","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:4084ea94e7624d2293b069717dab76afe839ad27d1e34e48dd9cb0e865e93aad","target":"graph","created_at":"2026-05-18T01:27:39Z","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":"Given permutations $\\sigma \\in S_k$ and $\\pi \\in S_n$ with $k<n$, the \\emph{pattern matching} problem is to decide whether $\\pi$ matches $\\sigma$ as an order-isomorphic subsequence. We give a linear-time algorithm in case both $\\pi$ and $\\sigma$ avoid the two size-$3$ permutations $213$ and $231$. For the special case where only $\\sigma$ avoids $213$ and $231$, we present a $O(max(kn^2,n^2\\log(\\log(n)))$ time algorithm. We extend our research to bivincular patterns that avoid $213$ and $231$ and present a $O(kn^4)$ time algorithm. Finally we look at the related problem of the longest subsequen","authors_text":"Both Emerite Neou, Romeo Rizzi, St\\'ephane Vialette","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-11-05T15:08:59Z","title":"Pattern matching in $(213,231)$-avoiding permutations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.01770","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:c3d81942ccd5eeaa047ea70bdd2365445d6fe60c20798e7fac4f2721af5a3787","target":"record","created_at":"2026-05-18T01:27:39Z","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":"08042c5903e6e43a01894598a9e03f5c687588c4cb1aa220d68fbf075414f3fb","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-11-05T15:08:59Z","title_canon_sha256":"5acfcab4d800a0140c73f148a3e8bda4c30757fbb3904d3b71de8a3d34e2799e"},"schema_version":"1.0","source":{"id":"1511.01770","kind":"arxiv","version":1}},"canonical_sha256":"6608cce6f31dcf9ba1b6b9b575de5fb427ab5d671340ff27bdaf62e0dc60303b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6608cce6f31dcf9ba1b6b9b575de5fb427ab5d671340ff27bdaf62e0dc60303b","first_computed_at":"2026-05-18T01:27:39.846435Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:27:39.846435Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N3SXZNufvz4f5I55ukvrTFjg4nXb7oTsMPGUZoEljna72nSOt8/9DkYxhZlTZoBELekSfj8B+EwLnwlFEHpSAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:27:39.846903Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.01770","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c3d81942ccd5eeaa047ea70bdd2365445d6fe60c20798e7fac4f2721af5a3787","sha256:4084ea94e7624d2293b069717dab76afe839ad27d1e34e48dd9cb0e865e93aad"],"state_sha256":"85291bdb9b1fdb719d57de0ac88943c6831d7072239e7c8b95a34489d2519848"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9NEiYIb/0H4B6b+9i5EUr4xwLGEjSw1Z0M4I9IjGiCuMhsdZk4WY28sxgZ6Vnxm/8SHjZHr6aIhDEZPvffkBBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T15:39:45.984782Z","bundle_sha256":"8d1db10843c2c2335eeb8fab307797bf099fdd7754d6d06713fb993a6f6b7b6d"}}