{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:JF7X4T4KLZC7CC3F5UINPTJNZV","short_pith_number":"pith:JF7X4T4K","canonical_record":{"source":{"id":"1707.02408","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-07-08T07:37:15Z","cross_cats_sorted":[],"title_canon_sha256":"64e78909c8c158ca592d0d95bce47f749596fbc5a9a3edd6dd60463cd7c7c1bd","abstract_canon_sha256":"68df9619ff4df6d5ecf00519ad82fb54cf17ab441d303dc989b04d9db7f6c7b7"},"schema_version":"1.0"},"canonical_sha256":"497f7e4f8a5e45f10b65ed10d7cd2dcd654ff60054a193e0b079b77217a7ca5c","source":{"kind":"arxiv","id":"1707.02408","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.02408","created_at":"2026-05-18T00:40:39Z"},{"alias_kind":"arxiv_version","alias_value":"1707.02408v1","created_at":"2026-05-18T00:40:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.02408","created_at":"2026-05-18T00:40:39Z"},{"alias_kind":"pith_short_12","alias_value":"JF7X4T4KLZC7","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"JF7X4T4KLZC7CC3F","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"JF7X4T4K","created_at":"2026-05-18T12:31:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:JF7X4T4KLZC7CC3F5UINPTJNZV","target":"record","payload":{"canonical_record":{"source":{"id":"1707.02408","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-07-08T07:37:15Z","cross_cats_sorted":[],"title_canon_sha256":"64e78909c8c158ca592d0d95bce47f749596fbc5a9a3edd6dd60463cd7c7c1bd","abstract_canon_sha256":"68df9619ff4df6d5ecf00519ad82fb54cf17ab441d303dc989b04d9db7f6c7b7"},"schema_version":"1.0"},"canonical_sha256":"497f7e4f8a5e45f10b65ed10d7cd2dcd654ff60054a193e0b079b77217a7ca5c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:39.244625Z","signature_b64":"lYyUGagdNnSsbfN9q4lYxbjMIqzfxlG495wo7Ipsh7iuGlwU/LfPrBOytDkhpjxL1RZwPy5PcJ7HEvaWIeWnBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"497f7e4f8a5e45f10b65ed10d7cd2dcd654ff60054a193e0b079b77217a7ca5c","last_reissued_at":"2026-05-18T00:40:39.243895Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:39.243895Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.02408","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":"2026-05-18T00:40:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qwKXI+ZNqejDHYY2h37uWA5C2zTYvYJEtg1ITriyUgs2m1vQp5rtiNuJjm4jKpxaWYBofTrPi2OPcXZai26cAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T05:35:39.539638Z"},"content_sha256":"0a80d3283a18ce226dc6e8b15a5fca0a79d0354e9539bf437cab2109beee0e5a","schema_version":"1.0","event_id":"sha256:0a80d3283a18ce226dc6e8b15a5fca0a79d0354e9539bf437cab2109beee0e5a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:JF7X4T4KLZC7CC3F5UINPTJNZV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bijections for inversion sequences, ascent sequences and 3-nonnesting set partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Sherry H.F. Yan","submitted_at":"2017-07-08T07:37:15Z","abstract_excerpt":"Set partitions avoiding $k$-crossing and $k$-nesting have been extensively studied from the aspects of both combinatorics and mathematical biology. By using the generating tree technique, the obstinate kernel method and Zeilberger's algorithm, Lin confirmed a conjecture due independently to the author and Martinez-Savage that asserts inversion sequences with no weakly decreasing subsequence of length 3 and enhanced 3-nonnesting partitions have the same cardinality. In this paper, we provide a bijective proof of this conjecture. Our bijection also enables us to provide a new bijective proof of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.02408","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":"2026-05-18T00:40:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rMOfdIsp8dUYMmeEZ5mgJbS520K85wZG3Gy5hPwGEhdycYMxExEvC+T72aqekC3vNpuZvdNdk16hfM+ic/ZUAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T05:35:39.539983Z"},"content_sha256":"809845923d329ce7eccafb7dc959fca2ea9cde4a973edd3f512016781cf7612f","schema_version":"1.0","event_id":"sha256:809845923d329ce7eccafb7dc959fca2ea9cde4a973edd3f512016781cf7612f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JF7X4T4KLZC7CC3F5UINPTJNZV/bundle.json","state_url":"https://pith.science/pith/JF7X4T4KLZC7CC3F5UINPTJNZV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JF7X4T4KLZC7CC3F5UINPTJNZV/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":"2026-06-20T05:35:39Z","links":{"resolver":"https://pith.science/pith/JF7X4T4KLZC7CC3F5UINPTJNZV","bundle":"https://pith.science/pith/JF7X4T4KLZC7CC3F5UINPTJNZV/bundle.json","state":"https://pith.science/pith/JF7X4T4KLZC7CC3F5UINPTJNZV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JF7X4T4KLZC7CC3F5UINPTJNZV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:JF7X4T4KLZC7CC3F5UINPTJNZV","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":"68df9619ff4df6d5ecf00519ad82fb54cf17ab441d303dc989b04d9db7f6c7b7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-07-08T07:37:15Z","title_canon_sha256":"64e78909c8c158ca592d0d95bce47f749596fbc5a9a3edd6dd60463cd7c7c1bd"},"schema_version":"1.0","source":{"id":"1707.02408","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.02408","created_at":"2026-05-18T00:40:39Z"},{"alias_kind":"arxiv_version","alias_value":"1707.02408v1","created_at":"2026-05-18T00:40:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.02408","created_at":"2026-05-18T00:40:39Z"},{"alias_kind":"pith_short_12","alias_value":"JF7X4T4KLZC7","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"JF7X4T4KLZC7CC3F","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"JF7X4T4K","created_at":"2026-05-18T12:31:24Z"}],"graph_snapshots":[{"event_id":"sha256:809845923d329ce7eccafb7dc959fca2ea9cde4a973edd3f512016781cf7612f","target":"graph","created_at":"2026-05-18T00:40:39Z","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":"Set partitions avoiding $k$-crossing and $k$-nesting have been extensively studied from the aspects of both combinatorics and mathematical biology. By using the generating tree technique, the obstinate kernel method and Zeilberger's algorithm, Lin confirmed a conjecture due independently to the author and Martinez-Savage that asserts inversion sequences with no weakly decreasing subsequence of length 3 and enhanced 3-nonnesting partitions have the same cardinality. In this paper, we provide a bijective proof of this conjecture. Our bijection also enables us to provide a new bijective proof of ","authors_text":"Sherry H.F. Yan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-07-08T07:37:15Z","title":"Bijections for inversion sequences, ascent sequences and 3-nonnesting set partitions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.02408","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":"sha256:0a80d3283a18ce226dc6e8b15a5fca0a79d0354e9539bf437cab2109beee0e5a","target":"record","created_at":"2026-05-18T00:40:39Z","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":"68df9619ff4df6d5ecf00519ad82fb54cf17ab441d303dc989b04d9db7f6c7b7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-07-08T07:37:15Z","title_canon_sha256":"64e78909c8c158ca592d0d95bce47f749596fbc5a9a3edd6dd60463cd7c7c1bd"},"schema_version":"1.0","source":{"id":"1707.02408","kind":"arxiv","version":1}},"canonical_sha256":"497f7e4f8a5e45f10b65ed10d7cd2dcd654ff60054a193e0b079b77217a7ca5c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"497f7e4f8a5e45f10b65ed10d7cd2dcd654ff60054a193e0b079b77217a7ca5c","first_computed_at":"2026-05-18T00:40:39.243895Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:39.243895Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lYyUGagdNnSsbfN9q4lYxbjMIqzfxlG495wo7Ipsh7iuGlwU/LfPrBOytDkhpjxL1RZwPy5PcJ7HEvaWIeWnBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:39.244625Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.02408","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0a80d3283a18ce226dc6e8b15a5fca0a79d0354e9539bf437cab2109beee0e5a","sha256:809845923d329ce7eccafb7dc959fca2ea9cde4a973edd3f512016781cf7612f"],"state_sha256":"76d978cdd63d36301908579a76712cae8a354cf0e5993b97942a805fce605005"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N0cH6VWaWvUjoF2svPGW/gvLTzynCwWWWJTYTgvNit4f2bsgijHCzdTsP6XzAj2ohjvX0mYJdlU/sllTUNgqCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T05:35:39.541874Z","bundle_sha256":"3536a6953ce51b033b1ded9414326341938d1fa06e6fcdd15f71e6b732187f29"}}