{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:XELNWWVUWDV3VO76KZHFM5VUZV","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":"72596d3c6ff5378b30505663f8322adcbaa14798551e2b2683ce06aa8dab2ef6","cross_cats_sorted":["hep-th","math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-03-29T20:33:05Z","title_canon_sha256":"65a010efadd77aff2acce790b05ceb0eeb266759b5f580e714a9eb57dc620264"},"schema_version":"1.0","source":{"id":"1304.0020","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.0020","created_at":"2026-05-17T23:41:13Z"},{"alias_kind":"arxiv_version","alias_value":"1304.0020v5","created_at":"2026-05-17T23:41:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.0020","created_at":"2026-05-17T23:41:13Z"},{"alias_kind":"pith_short_12","alias_value":"XELNWWVUWDV3","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XELNWWVUWDV3VO76","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XELNWWVU","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:f0ec018968aaf539d8e260616923472748a04a075decfab8fcc742c1fb9fe76b","target":"graph","created_at":"2026-05-17T23:41:13Z","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":"An element [\\Phi] of the Grassmannian of n-dimensional subspaces of the Hardy space H^2, extended over the field C(x_1,..., x_n), may be associated to any polynomial basis {\\phi} for C(x). The Pl\\\"ucker coordinates S^\\phi_{\\lambda,n}(x_1,..., x_n) of \\Phi, labelled by partitions \\lambda, provide an analog of Jacobi's bi-alternant formula, defining a generalization of Schur polynomials. Applying the recursion relations satisfied by the polynomial system to the analog of the complete symmetric functions generates a doubly infinite matrix of symmetric polynomials that determine an element [H] of ","authors_text":"Eunghyun Lee, J. Harnad","cross_cats":["hep-th","math.MP","nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-03-29T20:33:05Z","title":"Symmetric polynomials, generalized Jacobi-Trudi identities and \\tau-functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0020","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":"sha256:066afb5caabb3b2c52fd3c8f08a9b5c9868289f72fba067568f625ab68cd1997","target":"record","created_at":"2026-05-17T23:41:13Z","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":"72596d3c6ff5378b30505663f8322adcbaa14798551e2b2683ce06aa8dab2ef6","cross_cats_sorted":["hep-th","math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-03-29T20:33:05Z","title_canon_sha256":"65a010efadd77aff2acce790b05ceb0eeb266759b5f580e714a9eb57dc620264"},"schema_version":"1.0","source":{"id":"1304.0020","kind":"arxiv","version":5}},"canonical_sha256":"b916db5ab4b0ebbabbfe564e5676b4cd7c926b49d4dbd5798b74b0663a003e9b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b916db5ab4b0ebbabbfe564e5676b4cd7c926b49d4dbd5798b74b0663a003e9b","first_computed_at":"2026-05-17T23:41:13.792309Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:13.792309Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KnkpTtzV8yT2tdAN+R/HXctOu7B+AGS+s3gIAsu/I2gLKm7Yxq/5sMKR0rMs7C1keBdxqvb4GJCiqxXkrHN/Cg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:13.793064Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.0020","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:066afb5caabb3b2c52fd3c8f08a9b5c9868289f72fba067568f625ab68cd1997","sha256:f0ec018968aaf539d8e260616923472748a04a075decfab8fcc742c1fb9fe76b"],"state_sha256":"8ffee93d4d96879c72275522acbf1b571f59e53ab8744b80898800da394c732e"}