{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:3GNA323XSQLDKXU43OYQPNVFRE","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":"aa4cf266fe946c87d867f965aecf8c46b0a51b6c0f7051c89a26bf14ece1c654","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-07-20T15:41:53Z","title_canon_sha256":"12b107db4233c60f29513ce56cb58237a0ac8270c4419b693fb6cac1c89a7b9d"},"schema_version":"1.0","source":{"id":"1407.5303","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.5303","created_at":"2026-05-18T02:18:01Z"},{"alias_kind":"arxiv_version","alias_value":"1407.5303v5","created_at":"2026-05-18T02:18:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.5303","created_at":"2026-05-18T02:18:01Z"},{"alias_kind":"pith_short_12","alias_value":"3GNA323XSQLD","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3GNA323XSQLDKXU4","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3GNA323X","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:bc20614ae3e1ec325b0fec8b65e290dda24d2dfa20eae231c13903084089762f","target":"graph","created_at":"2026-05-18T02:18:01Z","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 Pieri rule is an important theorem which explains how the operators e_k of multiplication by elementary symmetric functions act in the basis of Schur functions s_lambda. In this paper, for any rational number m/n, we study the relationship between the rational version e_k^{m/n} of the operators (given by the elliptic Hall algebra) and the \"rational\" version s_lambda^{m/n} of the basis (given by the Maulik-Okounkov stable basis construction)","authors_text":"Andrei Negu\\c{t}","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-07-20T15:41:53Z","title":"The m/n Pieri rule"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.5303","kind":"arxiv","version":5},"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":"sha256:286ad0d9a1c8cc6d3d6a7770cb76caaceed26146e9dae62d3db51795e9392f4b","target":"record","created_at":"2026-05-18T02:18:01Z","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":"aa4cf266fe946c87d867f965aecf8c46b0a51b6c0f7051c89a26bf14ece1c654","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-07-20T15:41:53Z","title_canon_sha256":"12b107db4233c60f29513ce56cb58237a0ac8270c4419b693fb6cac1c89a7b9d"},"schema_version":"1.0","source":{"id":"1407.5303","kind":"arxiv","version":5}},"canonical_sha256":"d99a0deb779416355e9cdbb107b6a5892cae6ba0180182534998c1925ee26d29","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d99a0deb779416355e9cdbb107b6a5892cae6ba0180182534998c1925ee26d29","first_computed_at":"2026-05-18T02:18:01.327474Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:18:01.327474Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jWJ1PZ43E+1QEcopzzNqjM+vy6ldH5jgFX8q5S9XWN+J9PAnKw5FbbBZ7DbYSzkjvgADf8fkEJ1kT/QeUZhqDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:18:01.328084Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.5303","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:286ad0d9a1c8cc6d3d6a7770cb76caaceed26146e9dae62d3db51795e9392f4b","sha256:bc20614ae3e1ec325b0fec8b65e290dda24d2dfa20eae231c13903084089762f"],"state_sha256":"d64df39da0b7d32fad10a0d5e95c56c8906e8ba76c8b3a4d96816c573cec7fd2"}