{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:GOL27GWA7XOCKYSS4TG6GHXHGM","short_pith_number":"pith:GOL27GWA","canonical_record":{"source":{"id":"1612.02964","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-12-09T10:12:28Z","cross_cats_sorted":[],"title_canon_sha256":"a9189f303b7a605200720a7b9efb3ddb89c9aaae584dc9873ad34bc8300433b8","abstract_canon_sha256":"467bc5f9f917488fb533fcd12b06810389580196c4bd0a9a16613f7bf2f5861e"},"schema_version":"1.0"},"canonical_sha256":"3397af9ac0fddc256252e4cde31ee733343d198abe9a422505854058134e5db8","source":{"kind":"arxiv","id":"1612.02964","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.02964","created_at":"2026-05-18T00:54:47Z"},{"alias_kind":"arxiv_version","alias_value":"1612.02964v2","created_at":"2026-05-18T00:54:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.02964","created_at":"2026-05-18T00:54:47Z"},{"alias_kind":"pith_short_12","alias_value":"GOL27GWA7XOC","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GOL27GWA7XOCKYSS","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GOL27GWA","created_at":"2026-05-18T12:30:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:GOL27GWA7XOCKYSS4TG6GHXHGM","target":"record","payload":{"canonical_record":{"source":{"id":"1612.02964","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-12-09T10:12:28Z","cross_cats_sorted":[],"title_canon_sha256":"a9189f303b7a605200720a7b9efb3ddb89c9aaae584dc9873ad34bc8300433b8","abstract_canon_sha256":"467bc5f9f917488fb533fcd12b06810389580196c4bd0a9a16613f7bf2f5861e"},"schema_version":"1.0"},"canonical_sha256":"3397af9ac0fddc256252e4cde31ee733343d198abe9a422505854058134e5db8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:47.095865Z","signature_b64":"8LwT3T+08AAtTiQusP2fG80EPNZrUDdPP4C0ssj9za6G0JqID1dgk9zp7zXGBs2GJ1BDFgZdqr4G6qw8sCq1CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3397af9ac0fddc256252e4cde31ee733343d198abe9a422505854058134e5db8","last_reissued_at":"2026-05-18T00:54:47.095452Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:47.095452Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.02964","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:54:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kkNJ3502+Fd8Z3FHqgHefR3OfG/WM3f7b3Ijk3JaImspZMlRu0VtNN77eEsMBO+ivJ7N3D6fWVtVX94b3CNFCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T21:56:04.317379Z"},"content_sha256":"19c551ec7bc576d3090280930c20d1ba148f5f47a41f17d3bfaaadd79a40fb1e","schema_version":"1.0","event_id":"sha256:19c551ec7bc576d3090280930c20d1ba148f5f47a41f17d3bfaaadd79a40fb1e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:GOL27GWA7XOCKYSS4TG6GHXHGM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A sextuple equidistribution arising in Pattern Avoidance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dongsu Kim, Zhicong Lin","submitted_at":"2016-12-09T10:12:28Z","abstract_excerpt":"We construct an intriguing bijection between $021$-avoiding inversion sequences and $(2413,4213)$-avoiding permutations, which proves a sextuple equidistribution involving double Eulerian statistics. Two interesting applications of this result are also presented. Moreover, this result inspires us to characterize all permutation classes that avoid two patterns of length $4$ whose descent polynomial equals that of separable permutations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.02964","kind":"arxiv","version":2},"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":"2026-05-18T00:54:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GG6u3a2AYt+bToxeNLsNj9ztOKCrVd/b5chhrh/c86cnJyXr0/z9xQow0SFpYB44FL+jUFEJJv/J3rBJeIncAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T21:56:04.318043Z"},"content_sha256":"cb135e40ccf48d122f6c89db59e5c534af8d05acb1f7744bcef1f3853562632a","schema_version":"1.0","event_id":"sha256:cb135e40ccf48d122f6c89db59e5c534af8d05acb1f7744bcef1f3853562632a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GOL27GWA7XOCKYSS4TG6GHXHGM/bundle.json","state_url":"https://pith.science/pith/GOL27GWA7XOCKYSS4TG6GHXHGM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GOL27GWA7XOCKYSS4TG6GHXHGM/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":"2026-06-05T21:56:04Z","links":{"resolver":"https://pith.science/pith/GOL27GWA7XOCKYSS4TG6GHXHGM","bundle":"https://pith.science/pith/GOL27GWA7XOCKYSS4TG6GHXHGM/bundle.json","state":"https://pith.science/pith/GOL27GWA7XOCKYSS4TG6GHXHGM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GOL27GWA7XOCKYSS4TG6GHXHGM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:GOL27GWA7XOCKYSS4TG6GHXHGM","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":"467bc5f9f917488fb533fcd12b06810389580196c4bd0a9a16613f7bf2f5861e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-12-09T10:12:28Z","title_canon_sha256":"a9189f303b7a605200720a7b9efb3ddb89c9aaae584dc9873ad34bc8300433b8"},"schema_version":"1.0","source":{"id":"1612.02964","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.02964","created_at":"2026-05-18T00:54:47Z"},{"alias_kind":"arxiv_version","alias_value":"1612.02964v2","created_at":"2026-05-18T00:54:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.02964","created_at":"2026-05-18T00:54:47Z"},{"alias_kind":"pith_short_12","alias_value":"GOL27GWA7XOC","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GOL27GWA7XOCKYSS","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GOL27GWA","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:cb135e40ccf48d122f6c89db59e5c534af8d05acb1f7744bcef1f3853562632a","target":"graph","created_at":"2026-05-18T00:54:47Z","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":"We construct an intriguing bijection between $021$-avoiding inversion sequences and $(2413,4213)$-avoiding permutations, which proves a sextuple equidistribution involving double Eulerian statistics. Two interesting applications of this result are also presented. Moreover, this result inspires us to characterize all permutation classes that avoid two patterns of length $4$ whose descent polynomial equals that of separable permutations.","authors_text":"Dongsu Kim, Zhicong Lin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-12-09T10:12:28Z","title":"A sextuple equidistribution arising in Pattern Avoidance"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.02964","kind":"arxiv","version":2},"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":"sha256:19c551ec7bc576d3090280930c20d1ba148f5f47a41f17d3bfaaadd79a40fb1e","target":"record","created_at":"2026-05-18T00:54:47Z","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":"467bc5f9f917488fb533fcd12b06810389580196c4bd0a9a16613f7bf2f5861e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-12-09T10:12:28Z","title_canon_sha256":"a9189f303b7a605200720a7b9efb3ddb89c9aaae584dc9873ad34bc8300433b8"},"schema_version":"1.0","source":{"id":"1612.02964","kind":"arxiv","version":2}},"canonical_sha256":"3397af9ac0fddc256252e4cde31ee733343d198abe9a422505854058134e5db8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3397af9ac0fddc256252e4cde31ee733343d198abe9a422505854058134e5db8","first_computed_at":"2026-05-18T00:54:47.095452Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:47.095452Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8LwT3T+08AAtTiQusP2fG80EPNZrUDdPP4C0ssj9za6G0JqID1dgk9zp7zXGBs2GJ1BDFgZdqr4G6qw8sCq1CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:47.095865Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.02964","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:19c551ec7bc576d3090280930c20d1ba148f5f47a41f17d3bfaaadd79a40fb1e","sha256:cb135e40ccf48d122f6c89db59e5c534af8d05acb1f7744bcef1f3853562632a"],"state_sha256":"222ea97542ddcfa029d2f3a9e6e6c73aa55c4fff635c01fe87f11dec8c64dfc2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ww0Cze7LSIU02vM/hgl+3Tr51DG5sazswqa3Mid2cqn9wz3RPwd/S2HzrPvASKlP4aNDfzFND75Uk1CbRrN0BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T21:56:04.321737Z","bundle_sha256":"33e898568759d2c7a4368fedcf2c83ac6c6e809fa93487386e05fd59a6993c96"}}