{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:S6SAHK54BQC5QLDSBSX43HPPBH","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":"f3f753cab3da62d61200440c3c34e6f0cbe40bba149a66f6a34dff96aa4d8c41","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-08-18T14:32:50Z","title_canon_sha256":"7547e74a8432b984b73f622e9e494c219196bdda006f13fc590b42800372e334"},"schema_version":"1.0","source":{"id":"1008.3094","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.3094","created_at":"2026-05-18T03:13:58Z"},{"alias_kind":"arxiv_version","alias_value":"1008.3094v2","created_at":"2026-05-18T03:13:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.3094","created_at":"2026-05-18T03:13:58Z"},{"alias_kind":"pith_short_12","alias_value":"S6SAHK54BQC5","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"S6SAHK54BQC5QLDS","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"S6SAHK54","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:234fbd63c3d6720bae1a5b821e6067f39c4290413479cb434748b95578054768","target":"graph","created_at":"2026-05-18T03:13:58Z","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 use Young's raising operators to give short and uniform proofs of several well known results about Schur polynomials and symmetric functions, starting from the Jacobi-Trudi identity.","authors_text":"Harry Tamvakis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-08-18T14:32:50Z","title":"The theory of Schur polynomials revisited"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.3094","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:c20d16eca87ac1f6176cefbf599f988268304eddaf40710bd4ba8b9e6954adb6","target":"record","created_at":"2026-05-18T03:13:58Z","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":"f3f753cab3da62d61200440c3c34e6f0cbe40bba149a66f6a34dff96aa4d8c41","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-08-18T14:32:50Z","title_canon_sha256":"7547e74a8432b984b73f622e9e494c219196bdda006f13fc590b42800372e334"},"schema_version":"1.0","source":{"id":"1008.3094","kind":"arxiv","version":2}},"canonical_sha256":"97a403abbc0c05d82c720cafcd9def09c31aad5d6f8859c7e03d88c2b794fc71","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"97a403abbc0c05d82c720cafcd9def09c31aad5d6f8859c7e03d88c2b794fc71","first_computed_at":"2026-05-18T03:13:58.606102Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:13:58.606102Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3z0jQePc1m3Ou4UPoPtEmLHqH5PbBrxWSvXCEEr1hZkPDkyeqpc/utjXMvlyFr9cQ55f5nLYhNJO3+zHaBnOAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:13:58.606836Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.3094","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c20d16eca87ac1f6176cefbf599f988268304eddaf40710bd4ba8b9e6954adb6","sha256:234fbd63c3d6720bae1a5b821e6067f39c4290413479cb434748b95578054768"],"state_sha256":"477ba0894158e433d4f2e29b5c7c82474fbf14bafb6cfa34bd7f3d3775d665a3"}