{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:4A3NXAFKHDTPJYYTFBDOD4OKKJ","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":"70107d0816275687a5c860857d3ee067cebf07dceb7e8bc9d06cead2000d56ac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-11-05T15:42:48Z","title_canon_sha256":"9468a62ede302f5344abd8e7550647df8b6ea1fa5bcc5d77460b69e75b302986"},"schema_version":"1.0","source":{"id":"1411.1301","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.1301","created_at":"2026-05-18T00:39:29Z"},{"alias_kind":"arxiv_version","alias_value":"1411.1301v2","created_at":"2026-05-18T00:39:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.1301","created_at":"2026-05-18T00:39:29Z"},{"alias_kind":"pith_short_12","alias_value":"4A3NXAFKHDTP","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"4A3NXAFKHDTPJYYT","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"4A3NXAFK","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:613c6c231313dd8c101a37bf1ea9881d534528ceefd5a52c0a9225f355e7f7c4","target":"graph","created_at":"2026-05-18T00:39:29Z","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":"The a-function is a proposed quantity defined for quantum field theories which has a monotonic behaviour along renormalisation group flows, being related to the beta-functions via a gradient flow equation involving a positive definite metric. We construct the a-function at four loop order for a general gauge theory with fermions and scalars, using only one and two loop beta-functions; we are then able to provide a stringent consistency check on the general three-loop gauge beta-function. In the case of an N=1 supersymmetric gauge theory, we present a general condition on the chiral field anoma","authors_text":"C. Poole, I. Jack","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-11-05T15:42:48Z","title":"The a-function for gauge theories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.1301","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":"sha256:214219be6f74cfe269da80ae9219ea3628896432e7b26854726c8765e5a69af1","target":"record","created_at":"2026-05-18T00:39:29Z","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":"70107d0816275687a5c860857d3ee067cebf07dceb7e8bc9d06cead2000d56ac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-11-05T15:42:48Z","title_canon_sha256":"9468a62ede302f5344abd8e7550647df8b6ea1fa5bcc5d77460b69e75b302986"},"schema_version":"1.0","source":{"id":"1411.1301","kind":"arxiv","version":2}},"canonical_sha256":"e036db80aa38e6f4e3132846e1f1ca527b74b6a3299a2ef86290f8212dd435a1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e036db80aa38e6f4e3132846e1f1ca527b74b6a3299a2ef86290f8212dd435a1","first_computed_at":"2026-05-18T00:39:29.309991Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:39:29.309991Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ryCw52jtOvQmimtTRcJ5R9rsoixJYw6aX/pz6Reopz+SLVGDNnnxAdru2HIYpaiISMCqgcAAG6eVwHvAv8P6DA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:39:29.310643Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.1301","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:214219be6f74cfe269da80ae9219ea3628896432e7b26854726c8765e5a69af1","sha256:613c6c231313dd8c101a37bf1ea9881d534528ceefd5a52c0a9225f355e7f7c4"],"state_sha256":"f6db6a01a7b0d6ce53d3d001261f05718460c3e2f4f7db7b3718889498133766"}