{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:R7DV7DQ2UL42ACC2CG2PE3ORTM","short_pith_number":"pith:R7DV7DQ2","canonical_record":{"source":{"id":"1607.00236","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-07-01T13:30:59Z","cross_cats_sorted":[],"title_canon_sha256":"14ce0f9e80f6e5c68fa6563403552186a5bd979627e84c5d7698c5e58553bc0b","abstract_canon_sha256":"91470844d027150aa8222625d968d92e48220c1a7351dd8a0c99ebb980e37c6e"},"schema_version":"1.0"},"canonical_sha256":"8fc75f8e1aa2f9a0085a11b4f26dd19b188d611fa4a9c8d18d6bac4c1727c43f","source":{"kind":"arxiv","id":"1607.00236","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.00236","created_at":"2026-05-18T00:52:09Z"},{"alias_kind":"arxiv_version","alias_value":"1607.00236v3","created_at":"2026-05-18T00:52:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.00236","created_at":"2026-05-18T00:52:09Z"},{"alias_kind":"pith_short_12","alias_value":"R7DV7DQ2UL42","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"R7DV7DQ2UL42ACC2","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"R7DV7DQ2","created_at":"2026-05-18T12:30:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:R7DV7DQ2UL42ACC2CG2PE3ORTM","target":"record","payload":{"canonical_record":{"source":{"id":"1607.00236","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-07-01T13:30:59Z","cross_cats_sorted":[],"title_canon_sha256":"14ce0f9e80f6e5c68fa6563403552186a5bd979627e84c5d7698c5e58553bc0b","abstract_canon_sha256":"91470844d027150aa8222625d968d92e48220c1a7351dd8a0c99ebb980e37c6e"},"schema_version":"1.0"},"canonical_sha256":"8fc75f8e1aa2f9a0085a11b4f26dd19b188d611fa4a9c8d18d6bac4c1727c43f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:09.454337Z","signature_b64":"UG+hBaX3M+0yEPNBMOu/HWtJXCLMueGDsnEXBH5FBFk2BUlNRblvyCPGQ3pVBem8X4GufLZmZ1J0MqRZwAh9Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8fc75f8e1aa2f9a0085a11b4f26dd19b188d611fa4a9c8d18d6bac4c1727c43f","last_reissued_at":"2026-05-18T00:52:09.453701Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:09.453701Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.00236","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:52:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JOTfGG2c1cRdjx90oZGgE5gkrt39bi4BlmBHMT4B09R5JkSIOIz4B0V4giQoRgipva+idjTu03+oPhHBYcHJBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T10:33:52.999839Z"},"content_sha256":"746699285d58efdf086c188dc41bca1cab0bcdf76b72964f8f903778aa47feb7","schema_version":"1.0","event_id":"sha256:746699285d58efdf086c188dc41bca1cab0bcdf76b72964f8f903778aa47feb7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:R7DV7DQ2UL42ACC2CG2PE3ORTM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The a-function in three dimensions: beyond leading order","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"C. Poole, I. Jack","submitted_at":"2016-07-01T13:30:59Z","abstract_excerpt":"Recently, evidence was provided for the existence of an $a$-function for renormalisable quantum field theories in three dimensions. An explicit expression was given at lowest order for general theories involving scalars and fermions, and shown to be related to the beta-functions by a gradient flow equation with positive-definite metric as in four dimensions. Here, we extend this lowest-order calculation to a general abelian Chern-Simons gauge theory coupled to fermions and scalars, and derive a prediction for part of the four-loop Yukawa beta-function. We also compute the complete four-loop Yu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.00236","kind":"arxiv","version":3},"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":"2026-05-18T00:52:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SKE3FgILPVhjQ9keHwZ3HrWkO0YyAUxBB32zzb1bDUBgbDS6RM40E+5DA+nqwT0IwHd11pGutZZ3nySBijSLAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T10:33:53.000469Z"},"content_sha256":"0f643112a0f34973674f7046569032616a62b91b8ed4e13e9263239e10e17cb1","schema_version":"1.0","event_id":"sha256:0f643112a0f34973674f7046569032616a62b91b8ed4e13e9263239e10e17cb1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/R7DV7DQ2UL42ACC2CG2PE3ORTM/bundle.json","state_url":"https://pith.science/pith/R7DV7DQ2UL42ACC2CG2PE3ORTM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/R7DV7DQ2UL42ACC2CG2PE3ORTM/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":"2026-05-21T10:33:53Z","links":{"resolver":"https://pith.science/pith/R7DV7DQ2UL42ACC2CG2PE3ORTM","bundle":"https://pith.science/pith/R7DV7DQ2UL42ACC2CG2PE3ORTM/bundle.json","state":"https://pith.science/pith/R7DV7DQ2UL42ACC2CG2PE3ORTM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/R7DV7DQ2UL42ACC2CG2PE3ORTM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:R7DV7DQ2UL42ACC2CG2PE3ORTM","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":"91470844d027150aa8222625d968d92e48220c1a7351dd8a0c99ebb980e37c6e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-07-01T13:30:59Z","title_canon_sha256":"14ce0f9e80f6e5c68fa6563403552186a5bd979627e84c5d7698c5e58553bc0b"},"schema_version":"1.0","source":{"id":"1607.00236","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.00236","created_at":"2026-05-18T00:52:09Z"},{"alias_kind":"arxiv_version","alias_value":"1607.00236v3","created_at":"2026-05-18T00:52:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.00236","created_at":"2026-05-18T00:52:09Z"},{"alias_kind":"pith_short_12","alias_value":"R7DV7DQ2UL42","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"R7DV7DQ2UL42ACC2","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"R7DV7DQ2","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:0f643112a0f34973674f7046569032616a62b91b8ed4e13e9263239e10e17cb1","target":"graph","created_at":"2026-05-18T00:52:09Z","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":"Recently, evidence was provided for the existence of an $a$-function for renormalisable quantum field theories in three dimensions. An explicit expression was given at lowest order for general theories involving scalars and fermions, and shown to be related to the beta-functions by a gradient flow equation with positive-definite metric as in four dimensions. Here, we extend this lowest-order calculation to a general abelian Chern-Simons gauge theory coupled to fermions and scalars, and derive a prediction for part of the four-loop Yukawa beta-function. We also compute the complete four-loop Yu","authors_text":"C. Poole, I. Jack","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-07-01T13:30:59Z","title":"The a-function in three dimensions: beyond leading order"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.00236","kind":"arxiv","version":3},"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":"sha256:746699285d58efdf086c188dc41bca1cab0bcdf76b72964f8f903778aa47feb7","target":"record","created_at":"2026-05-18T00:52:09Z","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":"91470844d027150aa8222625d968d92e48220c1a7351dd8a0c99ebb980e37c6e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-07-01T13:30:59Z","title_canon_sha256":"14ce0f9e80f6e5c68fa6563403552186a5bd979627e84c5d7698c5e58553bc0b"},"schema_version":"1.0","source":{"id":"1607.00236","kind":"arxiv","version":3}},"canonical_sha256":"8fc75f8e1aa2f9a0085a11b4f26dd19b188d611fa4a9c8d18d6bac4c1727c43f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8fc75f8e1aa2f9a0085a11b4f26dd19b188d611fa4a9c8d18d6bac4c1727c43f","first_computed_at":"2026-05-18T00:52:09.453701Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:09.453701Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UG+hBaX3M+0yEPNBMOu/HWtJXCLMueGDsnEXBH5FBFk2BUlNRblvyCPGQ3pVBem8X4GufLZmZ1J0MqRZwAh9Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:09.454337Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.00236","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:746699285d58efdf086c188dc41bca1cab0bcdf76b72964f8f903778aa47feb7","sha256:0f643112a0f34973674f7046569032616a62b91b8ed4e13e9263239e10e17cb1"],"state_sha256":"d6a2547cb6d38384fe341f17527fc0d3672587ba20621fd6cdbf7af45b0f2722"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2Za5Q3c+yFao8A9zM9Yo6q9PyxdVh6lvkGoHnfwaOG5t5zlxKs+cq4wvXWQy5dl9Zaj7WWxAEZ7hjwp9UB43Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-21T10:33:53.003343Z","bundle_sha256":"aa01feb433a85dfd377f436aab77c0d83b75e3a14a49c0ff89b35a07dbdd9f63"}}