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We denote these as $A_k \\, \\bar F$ theories. We take $N \\ge 2k+1$ so that $n_{\\bar F} \\ge 1$. The $A_2 \\, \\bar F$ theories form an infinite family with $N \\ge 5$, but we show that the $A_3 \\, \\bar F$ and $A_4 \\,\\bar F$ theories"},"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":"1510.07663","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-10-26T20:27:28Z","cross_cats_sorted":["hep-ph"],"title_canon_sha256":"335652b1197ad21e35e570a003e03af77aa4ab19695d9427112a95a05e462524","abstract_canon_sha256":"64c707ceb5c725ffbe6d54f3c54cc2a87fe17db791f9c47ceb81f5f916da237f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:25:31.133382Z","signature_b64":"xFP9rI+njaW2/hLHJ5TcMWGWYWHOilqFNaFnyWbNy9peFVATaOEQH3goZ0q4KTgeYrd5LdT3utGHY1qTc/E6AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"707f4a13f50a2cdbb875061f1700a35875ab1d227dd042d0bf1a9a7d0ecc2f51","last_reissued_at":"2026-05-18T01:25:31.132959Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:25:31.132959Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$A_k \\bar F$ Chiral Gauge Theories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ph"],"primary_cat":"hep-th","authors_text":"Robert Shrock, Yan-Liang Shi","submitted_at":"2015-10-26T20:27:28Z","abstract_excerpt":"We study asymptotically free chiral gauge theories with an SU($N$) gauge group and chiral fermions transforming according to the antisymmetric rank-$k$ tensor representation, $A_k \\equiv [k]_N$, and the requisite number, $n_{\\bar F}$, of copies of fermions in the conjugate fundamental representation, $\\bar F \\equiv \\overline{[1]}_N$, to render the theories anomaly-free. We denote these as $A_k \\, \\bar F$ theories. We take $N \\ge 2k+1$ so that $n_{\\bar F} \\ge 1$. The $A_2 \\, \\bar F$ theories form an infinite family with $N \\ge 5$, but we show that the $A_3 \\, \\bar F$ and $A_4 \\,\\bar F$ theories"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.07663","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":"1510.07663","created_at":"2026-05-18T01:25:31.133026+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.07663v1","created_at":"2026-05-18T01:25:31.133026+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.07663","created_at":"2026-05-18T01:25:31.133026+00:00"},{"alias_kind":"pith_short_12","alias_value":"OB7UUE7VBIWN","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_16","alias_value":"OB7UUE7VBIWNXODV","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_8","alias_value":"OB7UUE7V","created_at":"2026-05-18T12:29:34.919912+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.10416","citing_title":"Infrared spectra of some strongly--coupled chiral gauge theories","ref_index":12,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OB7UUE7VBIWNXODVAYPROAFDLB","json":"https://pith.science/pith/OB7UUE7VBIWNXODVAYPROAFDLB.json","graph_json":"https://pith.science/api/pith-number/OB7UUE7VBIWNXODVAYPROAFDLB/graph.json","events_json":"https://pith.science/api/pith-number/OB7UUE7VBIWNXODVAYPROAFDLB/events.json","paper":"https://pith.science/paper/OB7UUE7V"},"agent_actions":{"view_html":"https://pith.science/pith/OB7UUE7VBIWNXODVAYPROAFDLB","download_json":"https://pith.science/pith/OB7UUE7VBIWNXODVAYPROAFDLB.json","view_paper":"https://pith.science/paper/OB7UUE7V","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.07663&json=true","fetch_graph":"https://pith.science/api/pith-number/OB7UUE7VBIWNXODVAYPROAFDLB/graph.json","fetch_events":"https://pith.science/api/pith-number/OB7UUE7VBIWNXODVAYPROAFDLB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OB7UUE7VBIWNXODVAYPROAFDLB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OB7UUE7VBIWNXODVAYPROAFDLB/action/storage_attestation","attest_author":"https://pith.science/pith/OB7UUE7VBIWNXODVAYPROAFDLB/action/author_attestation","sign_citation":"https://pith.science/pith/OB7UUE7VBIWNXODVAYPROAFDLB/action/citation_signature","submit_replication":"https://pith.science/pith/OB7UUE7VBIWNXODVAYPROAFDLB/action/replication_record"}},"created_at":"2026-05-18T01:25:31.133026+00:00","updated_at":"2026-05-18T01:25:31.133026+00:00"}