{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:IYLQGAV5PWKWNINARXEX7HOANK","short_pith_number":"pith:IYLQGAV5","canonical_record":{"source":{"id":"2407.04971","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2024-07-06T06:23:11Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"272a0c4869fa8542f1bca0d698021c453071b20edfb18ac49c8114661aeba8e6","abstract_canon_sha256":"f542f084bf8b6d81cc48d3e960a68c0aa028a82d6c84472170ae6bc8f1c98cff"},"schema_version":"1.0"},"canonical_sha256":"46170302bd7d9566a1a08dc97f9dc06abbb05937d3d583f7d7d428ee79b3435b","source":{"kind":"arxiv","id":"2407.04971","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.04971","created_at":"2026-07-05T08:40:44Z"},{"alias_kind":"arxiv_version","alias_value":"2407.04971v1","created_at":"2026-07-05T08:40:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.04971","created_at":"2026-07-05T08:40:44Z"},{"alias_kind":"pith_short_12","alias_value":"IYLQGAV5PWKW","created_at":"2026-07-05T08:40:44Z"},{"alias_kind":"pith_short_16","alias_value":"IYLQGAV5PWKWNINA","created_at":"2026-07-05T08:40:44Z"},{"alias_kind":"pith_short_8","alias_value":"IYLQGAV5","created_at":"2026-07-05T08:40:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:IYLQGAV5PWKWNINARXEX7HOANK","target":"record","payload":{"canonical_record":{"source":{"id":"2407.04971","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2024-07-06T06:23:11Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"272a0c4869fa8542f1bca0d698021c453071b20edfb18ac49c8114661aeba8e6","abstract_canon_sha256":"f542f084bf8b6d81cc48d3e960a68c0aa028a82d6c84472170ae6bc8f1c98cff"},"schema_version":"1.0"},"canonical_sha256":"46170302bd7d9566a1a08dc97f9dc06abbb05937d3d583f7d7d428ee79b3435b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:40:44.402933Z","signature_b64":"5xAM5SjHTK43/sYooUehiZAbHMnDna6U9oQQuFZ+x9eAl0Pni8sMf151cFazzNwJ4SuJFybeywtiaL5TWsxMDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46170302bd7d9566a1a08dc97f9dc06abbb05937d3d583f7d7d428ee79b3435b","last_reissued_at":"2026-07-05T08:40:44.402429Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:40:44.402429Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2407.04971","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":"2026-07-05T08:40:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xu9EaFocBKnpe2f/yAgXMNe144ZBzX1chDgY3lXPmFCKU7xM5aR9cuhPbDIYTlPG4jVJMmbrGFMtAJpOL0WpDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T09:58:17.380177Z"},"content_sha256":"0bded476857edffbaab24bc5e0a59620e059c4df82b40dd3c382c15f8a23d831","schema_version":"1.0","event_id":"sha256:0bded476857edffbaab24bc5e0a59620e059c4df82b40dd3c382c15f8a23d831"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:IYLQGAV5PWKWNINARXEX7HOANK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Counting Permutation Patterns with Multidimensional Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DS","authors_text":"Gal Beniamini, Nir Lavee","submitted_at":"2024-07-06T06:23:11Z","abstract_excerpt":"We consider the well-studied pattern counting problem: given a permutation $\\pi \\in \\mathbb{S}_n$ and an integer $k > 1$, count the number of order-isomorphic occurrences of every pattern $\\tau \\in \\mathbb{S}_k$ in $\\pi$.\n  Our first result is an $\\widetilde{\\mathcal{O}}(n^2)$-time algorithm for $k=6$ and $k=7$. The proof relies heavily on a new family of graphs that we introduce, called pattern-trees. Every such tree corresponds to an integer linear combination of permutations in $\\mathbb{S}_k$, and is associated with linear extensions of partially ordered sets. We design an evaluation algori"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.04971","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2407.04971/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":"2026-07-05T08:40:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"80cqKAY2y8EvoALOGS6D2Rzi6r9TkYD1JAAx6w9PfKV7X/B5es4IM2G1QcMzx1q8XtRyEwR4Y049r/7D6DnXCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T09:58:17.381102Z"},"content_sha256":"9d8a490669a437938fc8cb74fc1b92ad52e30fe2fd03ad34aab41a1855a7492d","schema_version":"1.0","event_id":"sha256:9d8a490669a437938fc8cb74fc1b92ad52e30fe2fd03ad34aab41a1855a7492d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IYLQGAV5PWKWNINARXEX7HOANK/bundle.json","state_url":"https://pith.science/pith/IYLQGAV5PWKWNINARXEX7HOANK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IYLQGAV5PWKWNINARXEX7HOANK/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":"2026-08-08T09:58:17Z","links":{"resolver":"https://pith.science/pith/IYLQGAV5PWKWNINARXEX7HOANK","bundle":"https://pith.science/pith/IYLQGAV5PWKWNINARXEX7HOANK/bundle.json","state":"https://pith.science/pith/IYLQGAV5PWKWNINARXEX7HOANK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IYLQGAV5PWKWNINARXEX7HOANK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:IYLQGAV5PWKWNINARXEX7HOANK","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":"f542f084bf8b6d81cc48d3e960a68c0aa028a82d6c84472170ae6bc8f1c98cff","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2024-07-06T06:23:11Z","title_canon_sha256":"272a0c4869fa8542f1bca0d698021c453071b20edfb18ac49c8114661aeba8e6"},"schema_version":"1.0","source":{"id":"2407.04971","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.04971","created_at":"2026-07-05T08:40:44Z"},{"alias_kind":"arxiv_version","alias_value":"2407.04971v1","created_at":"2026-07-05T08:40:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.04971","created_at":"2026-07-05T08:40:44Z"},{"alias_kind":"pith_short_12","alias_value":"IYLQGAV5PWKW","created_at":"2026-07-05T08:40:44Z"},{"alias_kind":"pith_short_16","alias_value":"IYLQGAV5PWKWNINA","created_at":"2026-07-05T08:40:44Z"},{"alias_kind":"pith_short_8","alias_value":"IYLQGAV5","created_at":"2026-07-05T08:40:44Z"}],"graph_snapshots":[{"event_id":"sha256:9d8a490669a437938fc8cb74fc1b92ad52e30fe2fd03ad34aab41a1855a7492d","target":"graph","created_at":"2026-07-05T08:40:44Z","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/2407.04971/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the well-studied pattern counting problem: given a permutation $\\pi \\in \\mathbb{S}_n$ and an integer $k > 1$, count the number of order-isomorphic occurrences of every pattern $\\tau \\in \\mathbb{S}_k$ in $\\pi$.\n  Our first result is an $\\widetilde{\\mathcal{O}}(n^2)$-time algorithm for $k=6$ and $k=7$. The proof relies heavily on a new family of graphs that we introduce, called pattern-trees. Every such tree corresponds to an integer linear combination of permutations in $\\mathbb{S}_k$, and is associated with linear extensions of partially ordered sets. We design an evaluation algori","authors_text":"Gal Beniamini, Nir Lavee","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2024-07-06T06:23:11Z","title":"Counting Permutation Patterns with Multidimensional Trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.04971","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":"sha256:0bded476857edffbaab24bc5e0a59620e059c4df82b40dd3c382c15f8a23d831","target":"record","created_at":"2026-07-05T08:40:44Z","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":"f542f084bf8b6d81cc48d3e960a68c0aa028a82d6c84472170ae6bc8f1c98cff","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2024-07-06T06:23:11Z","title_canon_sha256":"272a0c4869fa8542f1bca0d698021c453071b20edfb18ac49c8114661aeba8e6"},"schema_version":"1.0","source":{"id":"2407.04971","kind":"arxiv","version":1}},"canonical_sha256":"46170302bd7d9566a1a08dc97f9dc06abbb05937d3d583f7d7d428ee79b3435b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"46170302bd7d9566a1a08dc97f9dc06abbb05937d3d583f7d7d428ee79b3435b","first_computed_at":"2026-07-05T08:40:44.402429Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:40:44.402429Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5xAM5SjHTK43/sYooUehiZAbHMnDna6U9oQQuFZ+x9eAl0Pni8sMf151cFazzNwJ4SuJFybeywtiaL5TWsxMDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:40:44.402933Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.04971","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0bded476857edffbaab24bc5e0a59620e059c4df82b40dd3c382c15f8a23d831","sha256:9d8a490669a437938fc8cb74fc1b92ad52e30fe2fd03ad34aab41a1855a7492d"],"state_sha256":"a65126bd497aafbd078f1929edb0d6a01a18a43d32948475ab8ff4e7d41e57fa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hsVCO88wh3mZDIJsq+teHepUG6J0WqJsc55QaPaYqsQWLfwR7S4Ro8FC8Xc7rrfyVc9Q3MFA7PXDfcM/pL/3Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T09:58:17.391561Z","bundle_sha256":"b0b8ae6f56c0eb6c36e15a75c0552ce69128e2d309f1a280dc38fab2b06ae25b"}}