{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:SFZ3OGBFSIQI2PFNDDTRJLZJX2","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":"66d13a4f6e926af67687a1f90b49c4415048e636da6148fa332d00e70d7c33f3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-10-09T19:50:33Z","title_canon_sha256":"38151c0132d5669bccd98f43fe40a148704c67bad4f42e188c28526619748b70"},"schema_version":"1.0","source":{"id":"1210.2705","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.2705","created_at":"2026-05-18T03:43:40Z"},{"alias_kind":"arxiv_version","alias_value":"1210.2705v1","created_at":"2026-05-18T03:43:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.2705","created_at":"2026-05-18T03:43:40Z"},{"alias_kind":"pith_short_12","alias_value":"SFZ3OGBFSIQI","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"SFZ3OGBFSIQI2PFN","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"SFZ3OGBF","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:05e8efd959bbf8088602f24463da059f94a51c6fc741974b8a020dcaa285b2ab","target":"graph","created_at":"2026-05-18T03:43:40Z","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":"The shuffle conjecture expresses a relationship between parking functions, diagonal harmonics, and the Bergeron-Garsia $\\nabla$ operator. Recent conjectures about a family of modified Hall-Littlewood operators made by Haglund, Morse, and Zabrocki sharpen the shuffle conjecture and suggest a variety of combinatorial properties of parking functions. In particular, their conjectures combined with previously established commutativity laws of the Hall-Littlewood operators, suggest the existence of certain bijections relating parking functions with different diagonal compositions. In this paper we f","authors_text":"Angela Hicks","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-10-09T19:50:33Z","title":"A Parking Function Bijection supporting the Haglund-Morse-Zabrocki Conjectures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.2705","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:accc6a86dd43f084b43f5d6a7e41392e25d3563ec3bdaca49f4a6f7e183439c0","target":"record","created_at":"2026-05-18T03:43:40Z","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":"66d13a4f6e926af67687a1f90b49c4415048e636da6148fa332d00e70d7c33f3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-10-09T19:50:33Z","title_canon_sha256":"38151c0132d5669bccd98f43fe40a148704c67bad4f42e188c28526619748b70"},"schema_version":"1.0","source":{"id":"1210.2705","kind":"arxiv","version":1}},"canonical_sha256":"9173b7182592208d3cad18e714af29bea294f0629f4d9c38cdd8fe13c2907443","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9173b7182592208d3cad18e714af29bea294f0629f4d9c38cdd8fe13c2907443","first_computed_at":"2026-05-18T03:43:40.827740Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:43:40.827740Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4WB3A72gHZP85jo18vnCnu4HT0uGPhKg7imwzKlmH8aQz6Eh4o5V4t2trs/HPiDQzdrh9HuDDJg17ScvjqdQCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:43:40.828304Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.2705","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:accc6a86dd43f084b43f5d6a7e41392e25d3563ec3bdaca49f4a6f7e183439c0","sha256:05e8efd959bbf8088602f24463da059f94a51c6fc741974b8a020dcaa285b2ab"],"state_sha256":"34d1f9559b5c708ca54db9c5a54ee58dd9e233473db43a19f928e52466ff5870"}