{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:OB7UUE7VBIWNXODVAYPROAFDLB","short_pith_number":"pith:OB7UUE7V","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"},"canonical_sha256":"707f4a13f50a2cdbb875061f1700a35875ab1d227dd042d0bf1a9a7d0ecc2f51","source":{"kind":"arxiv","id":"1510.07663","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.07663","created_at":"2026-05-18T01:25:31Z"},{"alias_kind":"arxiv_version","alias_value":"1510.07663v1","created_at":"2026-05-18T01:25:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.07663","created_at":"2026-05-18T01:25:31Z"},{"alias_kind":"pith_short_12","alias_value":"OB7UUE7VBIWN","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OB7UUE7VBIWNXODV","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OB7UUE7V","created_at":"2026-05-18T12:29:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:OB7UUE7VBIWNXODVAYPROAFDLB","target":"record","payload":{"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"},"canonical_sha256":"707f4a13f50a2cdbb875061f1700a35875ab1d227dd042d0bf1a9a7d0ecc2f51","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"},"source_kind":"arxiv","source_id":"1510.07663","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:25:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tFqDrV6Evatz/nfSiIs1gbhc0QR3OM0+fs3CKd1f+xGUkXsgTyZQfHVnCXTi/KGNdFdPDhbBCReZqvkdCB9XCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T05:02:33.143028Z"},"content_sha256":"9d903ad2f18682437c412f51365e3e4e749f1e8c009f9ddea99c6873168749cc","schema_version":"1.0","event_id":"sha256:9d903ad2f18682437c412f51365e3e4e749f1e8c009f9ddea99c6873168749cc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:OB7UUE7VBIWNXODVAYPROAFDLB","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:25:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"THhEn5Dvzr4e+lBajfc6F6PnS1JHG9zV1L7JdctCUgo3skPcJ/UvicgpQXR8Ny7dVdpcIr6g4rutZBjpOWzhCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T05:02:33.143803Z"},"content_sha256":"73836590d6fe26c4ca7fb5130077349f3ea21fca2d74c4274ca1bf6fd5cda9bf","schema_version":"1.0","event_id":"sha256:73836590d6fe26c4ca7fb5130077349f3ea21fca2d74c4274ca1bf6fd5cda9bf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OB7UUE7VBIWNXODVAYPROAFDLB/bundle.json","state_url":"https://pith.science/pith/OB7UUE7VBIWNXODVAYPROAFDLB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OB7UUE7VBIWNXODVAYPROAFDLB/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-20T05:02:33Z","links":{"resolver":"https://pith.science/pith/OB7UUE7VBIWNXODVAYPROAFDLB","bundle":"https://pith.science/pith/OB7UUE7VBIWNXODVAYPROAFDLB/bundle.json","state":"https://pith.science/pith/OB7UUE7VBIWNXODVAYPROAFDLB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OB7UUE7VBIWNXODVAYPROAFDLB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:OB7UUE7VBIWNXODVAYPROAFDLB","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":"64c707ceb5c725ffbe6d54f3c54cc2a87fe17db791f9c47ceb81f5f916da237f","cross_cats_sorted":["hep-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-10-26T20:27:28Z","title_canon_sha256":"335652b1197ad21e35e570a003e03af77aa4ab19695d9427112a95a05e462524"},"schema_version":"1.0","source":{"id":"1510.07663","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.07663","created_at":"2026-05-18T01:25:31Z"},{"alias_kind":"arxiv_version","alias_value":"1510.07663v1","created_at":"2026-05-18T01:25:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.07663","created_at":"2026-05-18T01:25:31Z"},{"alias_kind":"pith_short_12","alias_value":"OB7UUE7VBIWN","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OB7UUE7VBIWNXODV","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OB7UUE7V","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:73836590d6fe26c4ca7fb5130077349f3ea21fca2d74c4274ca1bf6fd5cda9bf","target":"graph","created_at":"2026-05-18T01:25:31Z","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 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","authors_text":"Robert Shrock, Yan-Liang Shi","cross_cats":["hep-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-10-26T20:27:28Z","title":"$A_k \\bar F$ Chiral Gauge Theories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.07663","kind":"arxiv","version":1},"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":"sha256:9d903ad2f18682437c412f51365e3e4e749f1e8c009f9ddea99c6873168749cc","target":"record","created_at":"2026-05-18T01:25:31Z","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":"64c707ceb5c725ffbe6d54f3c54cc2a87fe17db791f9c47ceb81f5f916da237f","cross_cats_sorted":["hep-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-10-26T20:27:28Z","title_canon_sha256":"335652b1197ad21e35e570a003e03af77aa4ab19695d9427112a95a05e462524"},"schema_version":"1.0","source":{"id":"1510.07663","kind":"arxiv","version":1}},"canonical_sha256":"707f4a13f50a2cdbb875061f1700a35875ab1d227dd042d0bf1a9a7d0ecc2f51","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"707f4a13f50a2cdbb875061f1700a35875ab1d227dd042d0bf1a9a7d0ecc2f51","first_computed_at":"2026-05-18T01:25:31.132959Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:25:31.132959Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xFP9rI+njaW2/hLHJ5TcMWGWYWHOilqFNaFnyWbNy9peFVATaOEQH3goZ0q4KTgeYrd5LdT3utGHY1qTc/E6AA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:25:31.133382Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.07663","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d903ad2f18682437c412f51365e3e4e749f1e8c009f9ddea99c6873168749cc","sha256:73836590d6fe26c4ca7fb5130077349f3ea21fca2d74c4274ca1bf6fd5cda9bf"],"state_sha256":"58bc5759f476e27473a10fe036a02644259e671bc6fd958c2db1aef177c5c576"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bB8/xtxU8KTf/WQd0eAM79RGJZ2czyx7CTxcB7D+uW0VxiDoMKekyQq7R/he/1hK05nqI9TEv/LF9+c72BB6CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-20T05:02:33.148896Z","bundle_sha256":"79fecfbe56c607ede0c59b23d8798360f38957121196cde6fb9e38caa1255758"}}