{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:4WYSTBIEZZFQH6CU5JHJPR4PR3","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":"79087363dd4cbda05a28c95a13958781db2327585c3fdd18263fb8781f3a83c1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-01-08T00:31:53Z","title_canon_sha256":"a9d312ea85e5bf95c468a4818cd6a783e879be13699c7d1a083de6c5b712490b"},"schema_version":"1.0","source":{"id":"2501.04200","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.04200","created_at":"2026-07-05T09:58:31Z"},{"alias_kind":"arxiv_version","alias_value":"2501.04200v1","created_at":"2026-07-05T09:58:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.04200","created_at":"2026-07-05T09:58:31Z"},{"alias_kind":"pith_short_12","alias_value":"4WYSTBIEZZFQ","created_at":"2026-07-05T09:58:31Z"},{"alias_kind":"pith_short_16","alias_value":"4WYSTBIEZZFQH6CU","created_at":"2026-07-05T09:58:31Z"},{"alias_kind":"pith_short_8","alias_value":"4WYSTBIE","created_at":"2026-07-05T09:58:31Z"}],"graph_snapshots":[{"event_id":"sha256:f0fdb96377de092b1e9c9f5598477d657f23fe8b0dd51de62f33fa7c1d6ba951","target":"graph","created_at":"2026-07-05T09:58:31Z","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/2501.04200/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For closed $k$-Schur Katalan functions $\\fg{\\lambda}{k}$ with $k$ a positive integer and $\\lambda$ a $k$-bounded partition, Blasiak, Morse and Seelinger proposed the alternating dual Pieri rule conjecture and the $k$-branching conjecture. In the present paper, we positively prove the first one for large enough $k$ and for strictly decreasing partitions $\\lambda$ respectively, as well as the second one for strictly decreasing partitions $\\lambda$.","authors_text":"Xing Gao, Yaozhou Fang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-01-08T00:31:53Z","title":"Alternating dual Pieri rule conjecture and $k$-branching conjecture of closed $k$-Schur Katalan functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.04200","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:eb272239f891380cdff7db8dc556af7c300d9ce584d2243d8feb580061e89462","target":"record","created_at":"2026-07-05T09:58:31Z","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":"79087363dd4cbda05a28c95a13958781db2327585c3fdd18263fb8781f3a83c1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-01-08T00:31:53Z","title_canon_sha256":"a9d312ea85e5bf95c468a4818cd6a783e879be13699c7d1a083de6c5b712490b"},"schema_version":"1.0","source":{"id":"2501.04200","kind":"arxiv","version":1}},"canonical_sha256":"e5b1298504ce4b03f854ea4e97c78f8ec4f8a2e78e9d96eee9618b4807db9452","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e5b1298504ce4b03f854ea4e97c78f8ec4f8a2e78e9d96eee9618b4807db9452","first_computed_at":"2026-07-05T09:58:31.563852Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:58:31.563852Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i074yUiWM/IgREDPH8a2D/Phk3M7PaVuDkQ04LnbJ3IZXk8XKiYWU/UlhD3HlimupWej2Vg6vw5c1aNa5Fg5DQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:58:31.564195Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.04200","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eb272239f891380cdff7db8dc556af7c300d9ce584d2243d8feb580061e89462","sha256:f0fdb96377de092b1e9c9f5598477d657f23fe8b0dd51de62f33fa7c1d6ba951"],"state_sha256":"3e05bfe017b2ac8e1b00ccbd597a7b0b645d7aaddf3eb56fbc814e4f5987e4d0"}