{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:QI5H3ACHPCMRGR27WZTGTI6VUW","short_pith_number":"pith:QI5H3ACH","canonical_record":{"source":{"id":"1903.09672","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-03-22T18:38:47Z","cross_cats_sorted":["hep-lat","hep-ph"],"title_canon_sha256":"ede1d2a0ed5cda9fc81667b19bcce15af709e4ba09e0f0aef634063e7e19fecb","abstract_canon_sha256":"3068aa9bfd84f8321ad4c571946e26b534ea77d53055ddcbac897eb23c840424"},"schema_version":"1.0"},"canonical_sha256":"823a7d8047789913475fb66669a3d5a5b2ca4df3f2639aa6238e9af3b78e773e","source":{"kind":"arxiv","id":"1903.09672","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.09672","created_at":"2026-05-17T23:42:02Z"},{"alias_kind":"arxiv_version","alias_value":"1903.09672v1","created_at":"2026-05-17T23:42:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.09672","created_at":"2026-05-17T23:42:02Z"},{"alias_kind":"pith_short_12","alias_value":"QI5H3ACHPCMR","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"QI5H3ACHPCMRGR27","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"QI5H3ACH","created_at":"2026-05-18T12:33:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:QI5H3ACHPCMRGR27WZTGTI6VUW","target":"record","payload":{"canonical_record":{"source":{"id":"1903.09672","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-03-22T18:38:47Z","cross_cats_sorted":["hep-lat","hep-ph"],"title_canon_sha256":"ede1d2a0ed5cda9fc81667b19bcce15af709e4ba09e0f0aef634063e7e19fecb","abstract_canon_sha256":"3068aa9bfd84f8321ad4c571946e26b534ea77d53055ddcbac897eb23c840424"},"schema_version":"1.0"},"canonical_sha256":"823a7d8047789913475fb66669a3d5a5b2ca4df3f2639aa6238e9af3b78e773e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:02.387702Z","signature_b64":"rU7GDpYaOMJ4O9q7lgtbqX3bnkJTunZR4OO3/EREWP8WXsAuUa7olpPkAZYKABimAp+M6fA5u48aCcjNOMc7Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"823a7d8047789913475fb66669a3d5a5b2ca4df3f2639aa6238e9af3b78e773e","last_reissued_at":"2026-05-17T23:42:02.386984Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:02.386984Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.09672","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":"2026-05-17T23:42:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SflENGBCvIHnh5iU0hk7TspEl0e/v7zJu/7FfuU26KSRfQ9Q1xJ89PwR9x9DeJnheLU9IcFNlw8YCOHzBUZXBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T09:41:16.288153Z"},"content_sha256":"ced976c8912a9439a74a3dcc5405bbf44f8e2489d4a1731bde401f5ffb92e534","schema_version":"1.0","event_id":"sha256:ced976c8912a9439a74a3dcc5405bbf44f8e2489d4a1731bde401f5ffb92e534"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:QI5H3ACHPCMRGR27WZTGTI6VUW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Large-$N_c$ and Large-$N_F$ Limits of SU($N_c$) Gauge Theories with Fermions in Different Representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-lat","hep-ph"],"primary_cat":"hep-th","authors_text":"Robert Shrock, Sudhakantha Girmohanta, Thomas A. Ryttov","submitted_at":"2019-03-22T18:38:47Z","abstract_excerpt":"We present calculations of certain limits of scheme-independent series expansions for the anomalous dimensions of gauge-invariant fermion bilinear operators and for the derivative of the beta function at an infrared fixed point in SU($N_c$) gauge theories with fermions transforming according to two different representations. We first study a theory with $N_f$ fermions in the fundamental representation and $N_{f'}$ fermions in the adjoint or symmetric or antisymmetric rank-2 tensor representation, in the limit $N_c \\to \\infty$, $N_f \\to \\infty$ with $N_f/N_c$ fixed and finite. We then study the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.09672","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":"2026-05-17T23:42:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kflMXldf53zyyV/mM4xETyd86O0zs4bDW3VXBULQjTR2gxhMpv8s/Hscewx4v0V0xI0GQI6vnudLT6HgmCktAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T09:41:16.288770Z"},"content_sha256":"cb95342aa2c0eb73909662a4030d07200890e545f2144ad44be812eabfc8fee5","schema_version":"1.0","event_id":"sha256:cb95342aa2c0eb73909662a4030d07200890e545f2144ad44be812eabfc8fee5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QI5H3ACHPCMRGR27WZTGTI6VUW/bundle.json","state_url":"https://pith.science/pith/QI5H3ACHPCMRGR27WZTGTI6VUW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QI5H3ACHPCMRGR27WZTGTI6VUW/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":"2026-05-27T09:41:16Z","links":{"resolver":"https://pith.science/pith/QI5H3ACHPCMRGR27WZTGTI6VUW","bundle":"https://pith.science/pith/QI5H3ACHPCMRGR27WZTGTI6VUW/bundle.json","state":"https://pith.science/pith/QI5H3ACHPCMRGR27WZTGTI6VUW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QI5H3ACHPCMRGR27WZTGTI6VUW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:QI5H3ACHPCMRGR27WZTGTI6VUW","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":"3068aa9bfd84f8321ad4c571946e26b534ea77d53055ddcbac897eb23c840424","cross_cats_sorted":["hep-lat","hep-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-03-22T18:38:47Z","title_canon_sha256":"ede1d2a0ed5cda9fc81667b19bcce15af709e4ba09e0f0aef634063e7e19fecb"},"schema_version":"1.0","source":{"id":"1903.09672","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.09672","created_at":"2026-05-17T23:42:02Z"},{"alias_kind":"arxiv_version","alias_value":"1903.09672v1","created_at":"2026-05-17T23:42:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.09672","created_at":"2026-05-17T23:42:02Z"},{"alias_kind":"pith_short_12","alias_value":"QI5H3ACHPCMR","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"QI5H3ACHPCMRGR27","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"QI5H3ACH","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:cb95342aa2c0eb73909662a4030d07200890e545f2144ad44be812eabfc8fee5","target":"graph","created_at":"2026-05-17T23:42:02Z","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 present calculations of certain limits of scheme-independent series expansions for the anomalous dimensions of gauge-invariant fermion bilinear operators and for the derivative of the beta function at an infrared fixed point in SU($N_c$) gauge theories with fermions transforming according to two different representations. We first study a theory with $N_f$ fermions in the fundamental representation and $N_{f'}$ fermions in the adjoint or symmetric or antisymmetric rank-2 tensor representation, in the limit $N_c \\to \\infty$, $N_f \\to \\infty$ with $N_f/N_c$ fixed and finite. We then study the","authors_text":"Robert Shrock, Sudhakantha Girmohanta, Thomas A. Ryttov","cross_cats":["hep-lat","hep-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-03-22T18:38:47Z","title":"Large-$N_c$ and Large-$N_F$ Limits of SU($N_c$) Gauge Theories with Fermions in Different Representations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.09672","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:ced976c8912a9439a74a3dcc5405bbf44f8e2489d4a1731bde401f5ffb92e534","target":"record","created_at":"2026-05-17T23:42:02Z","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":"3068aa9bfd84f8321ad4c571946e26b534ea77d53055ddcbac897eb23c840424","cross_cats_sorted":["hep-lat","hep-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-03-22T18:38:47Z","title_canon_sha256":"ede1d2a0ed5cda9fc81667b19bcce15af709e4ba09e0f0aef634063e7e19fecb"},"schema_version":"1.0","source":{"id":"1903.09672","kind":"arxiv","version":1}},"canonical_sha256":"823a7d8047789913475fb66669a3d5a5b2ca4df3f2639aa6238e9af3b78e773e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"823a7d8047789913475fb66669a3d5a5b2ca4df3f2639aa6238e9af3b78e773e","first_computed_at":"2026-05-17T23:42:02.386984Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:02.386984Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rU7GDpYaOMJ4O9q7lgtbqX3bnkJTunZR4OO3/EREWP8WXsAuUa7olpPkAZYKABimAp+M6fA5u48aCcjNOMc7Aw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:02.387702Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.09672","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ced976c8912a9439a74a3dcc5405bbf44f8e2489d4a1731bde401f5ffb92e534","sha256:cb95342aa2c0eb73909662a4030d07200890e545f2144ad44be812eabfc8fee5"],"state_sha256":"fc4afd906ea7866737e5a41792bacfd4e4d699e487096435cd77484d85959988"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HTKPppcXFSawg18ItY6im+8vu+OpTDFRCd5vY+5mdLVq8kevY9PnHbCvvI+uKedv5OCK/HdS+XWCrTrYVD47AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T09:41:16.292099Z","bundle_sha256":"f9fcd8a54df46fdb56504358f2106e72e5f53c5c9382a09b02a7f911f369fe5b"}}