{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:T24ER4KKX3K37O6YK2HDPNZ2QH","short_pith_number":"pith:T24ER4KK","canonical_record":{"source":{"id":"2007.13015","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-07-25T21:43:32Z","cross_cats_sorted":[],"title_canon_sha256":"cc74f36c4cf97a26aca5caf68eb6a09d489c8cac42a7e914741d6465b21d59f2","abstract_canon_sha256":"aa1486be34538c6e236ac1fe8d53c3b4af5b6357c9db765f37880c5ce9c69d62"},"schema_version":"1.0"},"canonical_sha256":"9eb848f14abed5bfbbd8568e37b73a81c1787723c8be6de5b5f5686c1eee135f","source":{"kind":"arxiv","id":"2007.13015","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2007.13015","created_at":"2026-07-05T01:22:05Z"},{"alias_kind":"arxiv_version","alias_value":"2007.13015v1","created_at":"2026-07-05T01:22:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2007.13015","created_at":"2026-07-05T01:22:05Z"},{"alias_kind":"pith_short_12","alias_value":"T24ER4KKX3K3","created_at":"2026-07-05T01:22:05Z"},{"alias_kind":"pith_short_16","alias_value":"T24ER4KKX3K37O6Y","created_at":"2026-07-05T01:22:05Z"},{"alias_kind":"pith_short_8","alias_value":"T24ER4KK","created_at":"2026-07-05T01:22:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:T24ER4KKX3K37O6YK2HDPNZ2QH","target":"record","payload":{"canonical_record":{"source":{"id":"2007.13015","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-07-25T21:43:32Z","cross_cats_sorted":[],"title_canon_sha256":"cc74f36c4cf97a26aca5caf68eb6a09d489c8cac42a7e914741d6465b21d59f2","abstract_canon_sha256":"aa1486be34538c6e236ac1fe8d53c3b4af5b6357c9db765f37880c5ce9c69d62"},"schema_version":"1.0"},"canonical_sha256":"9eb848f14abed5bfbbd8568e37b73a81c1787723c8be6de5b5f5686c1eee135f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:22:05.853454Z","signature_b64":"j00TS8uaO+2ZGkZHxSeolI95TNXHrLgRpy7LQDUOektzuCeBBuGz0a9kBOx48XXnMxB8xotpnxd3bu2QXDFfCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9eb848f14abed5bfbbd8568e37b73a81c1787723c8be6de5b5f5686c1eee135f","last_reissued_at":"2026-07-05T01:22:05.853021Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:22:05.853021Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2007.13015","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":"2026-07-05T01:22:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JuOyVtMDuw4lTFoJEj9K6A4mh/0BMfuTR9jIYP8OgvfUVQ8H0GT2S9+2MUKZBWInjkVfsGnV57a8fVWfPJAfAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T00:31:01.074294Z"},"content_sha256":"e7fb2243a01d3670285cd6f198b58b754d871c3bde125c6ea0eef642ffb73cb6","schema_version":"1.0","event_id":"sha256:e7fb2243a01d3670285cd6f198b58b754d871c3bde125c6ea0eef642ffb73cb6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:T24ER4KKX3K37O6YK2HDPNZ2QH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Equidistributions of mesh patterns of length two and Kitaev and Zhang's conjectures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bin Han, Jiang Zeng","submitted_at":"2020-07-25T21:43:32Z","abstract_excerpt":"A systematic study of avoidance of mesh patterns of length 2 was conducted by Hilmarsson et al. in 2015. In a recent paper Kitaev and Zhang examined the distribution of the aforementioned patterns. The aim of this paper is to prove more equidistributions of mesh pattern and confirm Kitaev and Zhang's four conjectures by constructing two involutions on permutations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.13015","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/2007.13015/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":"2026-07-05T01:22:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2wIz8KS77HZyVFdWf43WAO3u0//006gK5m7BX7kF2QLEnCJFD3Bg3wGFpjQN5TYYaXh38/mB6jGiY+Jgr2pFCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T00:31:01.074943Z"},"content_sha256":"e85bb800286a4b8e2723faeb58b8ec3648a6567c63c6fa05e0599adb8b032eba","schema_version":"1.0","event_id":"sha256:e85bb800286a4b8e2723faeb58b8ec3648a6567c63c6fa05e0599adb8b032eba"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T24ER4KKX3K37O6YK2HDPNZ2QH/bundle.json","state_url":"https://pith.science/pith/T24ER4KKX3K37O6YK2HDPNZ2QH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T24ER4KKX3K37O6YK2HDPNZ2QH/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":"2026-08-11T00:31:01Z","links":{"resolver":"https://pith.science/pith/T24ER4KKX3K37O6YK2HDPNZ2QH","bundle":"https://pith.science/pith/T24ER4KKX3K37O6YK2HDPNZ2QH/bundle.json","state":"https://pith.science/pith/T24ER4KKX3K37O6YK2HDPNZ2QH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T24ER4KKX3K37O6YK2HDPNZ2QH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:T24ER4KKX3K37O6YK2HDPNZ2QH","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":"aa1486be34538c6e236ac1fe8d53c3b4af5b6357c9db765f37880c5ce9c69d62","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-07-25T21:43:32Z","title_canon_sha256":"cc74f36c4cf97a26aca5caf68eb6a09d489c8cac42a7e914741d6465b21d59f2"},"schema_version":"1.0","source":{"id":"2007.13015","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2007.13015","created_at":"2026-07-05T01:22:05Z"},{"alias_kind":"arxiv_version","alias_value":"2007.13015v1","created_at":"2026-07-05T01:22:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2007.13015","created_at":"2026-07-05T01:22:05Z"},{"alias_kind":"pith_short_12","alias_value":"T24ER4KKX3K3","created_at":"2026-07-05T01:22:05Z"},{"alias_kind":"pith_short_16","alias_value":"T24ER4KKX3K37O6Y","created_at":"2026-07-05T01:22:05Z"},{"alias_kind":"pith_short_8","alias_value":"T24ER4KK","created_at":"2026-07-05T01:22:05Z"}],"graph_snapshots":[{"event_id":"sha256:e85bb800286a4b8e2723faeb58b8ec3648a6567c63c6fa05e0599adb8b032eba","target":"graph","created_at":"2026-07-05T01:22:05Z","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/2007.13015/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A systematic study of avoidance of mesh patterns of length 2 was conducted by Hilmarsson et al. in 2015. In a recent paper Kitaev and Zhang examined the distribution of the aforementioned patterns. The aim of this paper is to prove more equidistributions of mesh pattern and confirm Kitaev and Zhang's four conjectures by constructing two involutions on permutations.","authors_text":"Bin Han, Jiang Zeng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-07-25T21:43:32Z","title":"Equidistributions of mesh patterns of length two and Kitaev and Zhang's conjectures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.13015","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:e7fb2243a01d3670285cd6f198b58b754d871c3bde125c6ea0eef642ffb73cb6","target":"record","created_at":"2026-07-05T01:22:05Z","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":"aa1486be34538c6e236ac1fe8d53c3b4af5b6357c9db765f37880c5ce9c69d62","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-07-25T21:43:32Z","title_canon_sha256":"cc74f36c4cf97a26aca5caf68eb6a09d489c8cac42a7e914741d6465b21d59f2"},"schema_version":"1.0","source":{"id":"2007.13015","kind":"arxiv","version":1}},"canonical_sha256":"9eb848f14abed5bfbbd8568e37b73a81c1787723c8be6de5b5f5686c1eee135f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9eb848f14abed5bfbbd8568e37b73a81c1787723c8be6de5b5f5686c1eee135f","first_computed_at":"2026-07-05T01:22:05.853021Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:22:05.853021Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j00TS8uaO+2ZGkZHxSeolI95TNXHrLgRpy7LQDUOektzuCeBBuGz0a9kBOx48XXnMxB8xotpnxd3bu2QXDFfCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T01:22:05.853454Z","signed_message":"canonical_sha256_bytes"},"source_id":"2007.13015","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e7fb2243a01d3670285cd6f198b58b754d871c3bde125c6ea0eef642ffb73cb6","sha256:e85bb800286a4b8e2723faeb58b8ec3648a6567c63c6fa05e0599adb8b032eba"],"state_sha256":"971dfe46f4e77ca293d50746f9ddf43f2eb34efee2918f8e273948bb6ea6b792"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Sttd0be7El8z5EEdnYm0YcGpXoXsKlejYjdRxSrOAgUhUdK+PQ4qDhuZWHdTRhq1j8OeFAizMGU3v9avLHeXBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T00:31:01.080615Z","bundle_sha256":"66e37babb8f824b55f9cff2c166ef905d406fc2213e7f6a379045154bc4dbe14"}}