{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:O77SEMMXV5VOQ35XJW54KRMIKG","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":"e8acf414c81ae745ee83fb6a5ad9946a1fe9e6125033d3f7de332928eacdcc07","cross_cats_sorted":["math-ph","math.GT","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-09-01T08:30:42Z","title_canon_sha256":"aa0caf519076aafdbcbb69910f26767087a1891ab6b62a1dab737e774ffa8063"},"schema_version":"1.0","source":{"id":"1609.00143","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.00143","created_at":"2026-05-18T00:32:03Z"},{"alias_kind":"arxiv_version","alias_value":"1609.00143v2","created_at":"2026-05-18T00:32:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.00143","created_at":"2026-05-18T00:32:03Z"},{"alias_kind":"pith_short_12","alias_value":"O77SEMMXV5VO","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"O77SEMMXV5VOQ35X","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"O77SEMMX","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:d58257a26006632a70b4c56857e15ce4ef6f60cd01160a0e4fe8a614bd30d7e9","target":"graph","created_at":"2026-05-18T00:32:03Z","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 rewrite the recently proposed differential expansion formula for HOMFLY polynomials of the knot $4_1$ in arbitrary rectangular representation $R=[r^s]$ as a sum over all Young sub-diagrams $\\lambda$ of $R$ with extraordinary simple coefficients $D_{\\lambda^{tr}}(r)\\cdot D_\\lambda(s)$ in front of the $Z$-factors. Somewhat miraculously, these coefficients are made from quantum dimensions of symmetric representations of the groups $SL(r)$ and $SL(s)$ and restrict summation to diagrams with no more than $s$ rows and $r$ columns. They possess a natural $\\beta$-deformation to Macdonald dimensions","authors_text":"A. Morozov, Ya. Kononov","cross_cats":["math-ph","math.GT","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-09-01T08:30:42Z","title":"Rectangular superpolynomials for the figure-eight knot"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.00143","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":"sha256:479c18b5a2e2e1ca9e81d21ab081e14d478db2c414661123ae1aa8130b17b8d3","target":"record","created_at":"2026-05-18T00:32:03Z","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":"e8acf414c81ae745ee83fb6a5ad9946a1fe9e6125033d3f7de332928eacdcc07","cross_cats_sorted":["math-ph","math.GT","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-09-01T08:30:42Z","title_canon_sha256":"aa0caf519076aafdbcbb69910f26767087a1891ab6b62a1dab737e774ffa8063"},"schema_version":"1.0","source":{"id":"1609.00143","kind":"arxiv","version":2}},"canonical_sha256":"77ff223197af6ae86fb74dbbc54588519afe041e8f7db935e359b2e555fbd74b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"77ff223197af6ae86fb74dbbc54588519afe041e8f7db935e359b2e555fbd74b","first_computed_at":"2026-05-18T00:32:03.045236Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:32:03.045236Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MvWNSlRVI/cEIDi4pQGGIjrXvM4bcJsOD/KeDNH2iRExARG+sr3APksezQUfn0PBuuxpmkWwCsV14AsSdHCfAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:32:03.045906Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.00143","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:479c18b5a2e2e1ca9e81d21ab081e14d478db2c414661123ae1aa8130b17b8d3","sha256:d58257a26006632a70b4c56857e15ce4ef6f60cd01160a0e4fe8a614bd30d7e9"],"state_sha256":"6ed0d8bb136f8a7563766e10bcc65e66c3d8ab722d5b2f14e7da9c30cc9b0285"}