{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:WTIQTFAZPJSCLEQF4OFFJZAGCQ","short_pith_number":"pith:WTIQTFAZ","schema_version":"1.0","canonical_sha256":"b4d10994197a64259205e38a54e40614192197fcbc22325dd35f6567a537f878","source":{"kind":"arxiv","id":"1309.1180","version":1},"attestation_state":"computed","paper":{"title":"Orthogonal Schurs for Classical Gauge Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Pablo Diaz","submitted_at":"2013-09-04T20:16:47Z","abstract_excerpt":"Finite N physics of half-BPS operators for gauge groups SO(N) and Sp(N) has recently been studied[1, 2]. Among other things they showed that, alike U(N), Schur operators (but in the square of their eigenvalues) diagonalize the free field two-point function of half-BPS operators for SO(N) and Sp(N) gauge groups. This result was unexpected since Wick contractions behave differently. In this paper we solve the puzzle by treating all gauge groups in a unified framework and showing how orthogonality of Schur operators emerges naturally from the embedding structure of classical Lie algebras g(N) -> "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1309.1180","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-09-04T20:16:47Z","cross_cats_sorted":[],"title_canon_sha256":"58e9ca783a29b07037052a9c99e28b3c2b476c4a2cf4c4d36001dd96b201c711","abstract_canon_sha256":"dd7ce6c26134a32e93d2b9604e616c39c95409711806eeae52f816503589869c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:47:49.679583Z","signature_b64":"KXqeDIwrFA+sOOrXRVXABvxpY9DUOqXG2Rz6AavhOg4TGUK8l82odgIFLb9JFfS7YVKH7kIHPUefZRyUVg0ZBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b4d10994197a64259205e38a54e40614192197fcbc22325dd35f6567a537f878","last_reissued_at":"2026-05-18T01:47:49.679182Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:47:49.679182Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Orthogonal Schurs for Classical Gauge Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Pablo Diaz","submitted_at":"2013-09-04T20:16:47Z","abstract_excerpt":"Finite N physics of half-BPS operators for gauge groups SO(N) and Sp(N) has recently been studied[1, 2]. Among other things they showed that, alike U(N), Schur operators (but in the square of their eigenvalues) diagonalize the free field two-point function of half-BPS operators for SO(N) and Sp(N) gauge groups. This result was unexpected since Wick contractions behave differently. In this paper we solve the puzzle by treating all gauge groups in a unified framework and showing how orthogonality of Schur operators emerges naturally from the embedding structure of classical Lie algebras g(N) -> "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1180","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1309.1180","created_at":"2026-05-18T01:47:49.679246+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.1180v1","created_at":"2026-05-18T01:47:49.679246+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.1180","created_at":"2026-05-18T01:47:49.679246+00:00"},{"alias_kind":"pith_short_12","alias_value":"WTIQTFAZPJSC","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_16","alias_value":"WTIQTFAZPJSCLEQF","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_8","alias_value":"WTIQTFAZ","created_at":"2026-05-18T12:28:04.890932+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WTIQTFAZPJSCLEQF4OFFJZAGCQ","json":"https://pith.science/pith/WTIQTFAZPJSCLEQF4OFFJZAGCQ.json","graph_json":"https://pith.science/api/pith-number/WTIQTFAZPJSCLEQF4OFFJZAGCQ/graph.json","events_json":"https://pith.science/api/pith-number/WTIQTFAZPJSCLEQF4OFFJZAGCQ/events.json","paper":"https://pith.science/paper/WTIQTFAZ"},"agent_actions":{"view_html":"https://pith.science/pith/WTIQTFAZPJSCLEQF4OFFJZAGCQ","download_json":"https://pith.science/pith/WTIQTFAZPJSCLEQF4OFFJZAGCQ.json","view_paper":"https://pith.science/paper/WTIQTFAZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.1180&json=true","fetch_graph":"https://pith.science/api/pith-number/WTIQTFAZPJSCLEQF4OFFJZAGCQ/graph.json","fetch_events":"https://pith.science/api/pith-number/WTIQTFAZPJSCLEQF4OFFJZAGCQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WTIQTFAZPJSCLEQF4OFFJZAGCQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WTIQTFAZPJSCLEQF4OFFJZAGCQ/action/storage_attestation","attest_author":"https://pith.science/pith/WTIQTFAZPJSCLEQF4OFFJZAGCQ/action/author_attestation","sign_citation":"https://pith.science/pith/WTIQTFAZPJSCLEQF4OFFJZAGCQ/action/citation_signature","submit_replication":"https://pith.science/pith/WTIQTFAZPJSCLEQF4OFFJZAGCQ/action/replication_record"}},"created_at":"2026-05-18T01:47:49.679246+00:00","updated_at":"2026-05-18T01:47:49.679246+00:00"}