{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:U467YB6NLGTKMH24BYIIO2MFQV","short_pith_number":"pith:U467YB6N","canonical_record":{"source":{"id":"1609.06458","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-09-21T08:18:08Z","cross_cats_sorted":[],"title_canon_sha256":"e91a639fd1101e401b4fabc2253790df7de9a4d6eb89590af7c14a4ddaff0480","abstract_canon_sha256":"a33910217e50ae80f4e8526792a3a19d83f819dad7f869ac4e5456b4f5886be2"},"schema_version":"1.0"},"canonical_sha256":"a73dfc07cd59a6a61f5c0e10876985856f843579f211a75b5dd55f3b16325a8f","source":{"kind":"arxiv","id":"1609.06458","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.06458","created_at":"2026-05-18T00:53:07Z"},{"alias_kind":"arxiv_version","alias_value":"1609.06458v4","created_at":"2026-05-18T00:53:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.06458","created_at":"2026-05-18T00:53:07Z"},{"alias_kind":"pith_short_12","alias_value":"U467YB6NLGTK","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"U467YB6NLGTKMH24","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"U467YB6N","created_at":"2026-05-18T12:30:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:U467YB6NLGTKMH24BYIIO2MFQV","target":"record","payload":{"canonical_record":{"source":{"id":"1609.06458","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-09-21T08:18:08Z","cross_cats_sorted":[],"title_canon_sha256":"e91a639fd1101e401b4fabc2253790df7de9a4d6eb89590af7c14a4ddaff0480","abstract_canon_sha256":"a33910217e50ae80f4e8526792a3a19d83f819dad7f869ac4e5456b4f5886be2"},"schema_version":"1.0"},"canonical_sha256":"a73dfc07cd59a6a61f5c0e10876985856f843579f211a75b5dd55f3b16325a8f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:07.427974Z","signature_b64":"GjNmSo0aSR+SO7hKwKIiEaenSA4iaV4ny35g6FudocGXU+l3Bjp0E0kLz7Bu/CmNbSJupFtlRSiUdcRTb+sGCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a73dfc07cd59a6a61f5c0e10876985856f843579f211a75b5dd55f3b16325a8f","last_reissued_at":"2026-05-18T00:53:07.427609Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:07.427609Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.06458","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:53:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N6qrt27wkFDmahDD62w3VZsvmJHC3BRFBH6zA+SKsR46uqdZSgC/cZSFbNQA+630dlm8qXaF4fBolErGKxKOCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T19:52:28.640798Z"},"content_sha256":"7b9230fece3d39d57045593404f52623e29110f354d29f92e2367c4c34b67632","schema_version":"1.0","event_id":"sha256:7b9230fece3d39d57045593404f52623e29110f354d29f92e2367c4c34b67632"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:U467YB6NLGTKMH24BYIIO2MFQV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The a-function for N=2 supersymmetric gauge theories in three dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"C. Poole, I. Jack, J. A. Gracey, Y. Schroder","submitted_at":"2016-09-21T08:18:08Z","abstract_excerpt":"Recently, the existence of a candidate a-function for renormalisable theories in three dimensions was demonstrated for a general theory at leading order and for a scalar-fermion theory at next-to-leading order. Here we extend this work by constructing the a-function at next-to-leading order for an N=2 supersymmetric Chern-Simons theory. This increase in precision for the a-function necessitated the evaluation of the underlying renormalization-group functions at four loops."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.06458","kind":"arxiv","version":4},"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":"2026-05-18T00:53:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GaVqbrETPRIOIBd3wq6wQzC/qXgfhSOx/8M822VI+J8s3kQaxvG6mMDBORPef9HazHgDPLg9pIHWfAq20qFADQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T19:52:28.641267Z"},"content_sha256":"40b367b335c1ab8cb949979cd503e4eb57a24828cdcb6927d6b4eee4d4ee9c7a","schema_version":"1.0","event_id":"sha256:40b367b335c1ab8cb949979cd503e4eb57a24828cdcb6927d6b4eee4d4ee9c7a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U467YB6NLGTKMH24BYIIO2MFQV/bundle.json","state_url":"https://pith.science/pith/U467YB6NLGTKMH24BYIIO2MFQV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U467YB6NLGTKMH24BYIIO2MFQV/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":"2026-05-21T19:52:28Z","links":{"resolver":"https://pith.science/pith/U467YB6NLGTKMH24BYIIO2MFQV","bundle":"https://pith.science/pith/U467YB6NLGTKMH24BYIIO2MFQV/bundle.json","state":"https://pith.science/pith/U467YB6NLGTKMH24BYIIO2MFQV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U467YB6NLGTKMH24BYIIO2MFQV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:U467YB6NLGTKMH24BYIIO2MFQV","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":"a33910217e50ae80f4e8526792a3a19d83f819dad7f869ac4e5456b4f5886be2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-09-21T08:18:08Z","title_canon_sha256":"e91a639fd1101e401b4fabc2253790df7de9a4d6eb89590af7c14a4ddaff0480"},"schema_version":"1.0","source":{"id":"1609.06458","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.06458","created_at":"2026-05-18T00:53:07Z"},{"alias_kind":"arxiv_version","alias_value":"1609.06458v4","created_at":"2026-05-18T00:53:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.06458","created_at":"2026-05-18T00:53:07Z"},{"alias_kind":"pith_short_12","alias_value":"U467YB6NLGTK","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"U467YB6NLGTKMH24","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"U467YB6N","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:40b367b335c1ab8cb949979cd503e4eb57a24828cdcb6927d6b4eee4d4ee9c7a","target":"graph","created_at":"2026-05-18T00:53:07Z","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, the existence of a candidate a-function for renormalisable theories in three dimensions was demonstrated for a general theory at leading order and for a scalar-fermion theory at next-to-leading order. Here we extend this work by constructing the a-function at next-to-leading order for an N=2 supersymmetric Chern-Simons theory. This increase in precision for the a-function necessitated the evaluation of the underlying renormalization-group functions at four loops.","authors_text":"C. Poole, I. Jack, J. A. Gracey, Y. Schroder","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-09-21T08:18:08Z","title":"The a-function for N=2 supersymmetric gauge theories in three dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.06458","kind":"arxiv","version":4},"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":"sha256:7b9230fece3d39d57045593404f52623e29110f354d29f92e2367c4c34b67632","target":"record","created_at":"2026-05-18T00:53:07Z","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":"a33910217e50ae80f4e8526792a3a19d83f819dad7f869ac4e5456b4f5886be2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-09-21T08:18:08Z","title_canon_sha256":"e91a639fd1101e401b4fabc2253790df7de9a4d6eb89590af7c14a4ddaff0480"},"schema_version":"1.0","source":{"id":"1609.06458","kind":"arxiv","version":4}},"canonical_sha256":"a73dfc07cd59a6a61f5c0e10876985856f843579f211a75b5dd55f3b16325a8f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a73dfc07cd59a6a61f5c0e10876985856f843579f211a75b5dd55f3b16325a8f","first_computed_at":"2026-05-18T00:53:07.427609Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:07.427609Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GjNmSo0aSR+SO7hKwKIiEaenSA4iaV4ny35g6FudocGXU+l3Bjp0E0kLz7Bu/CmNbSJupFtlRSiUdcRTb+sGCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:07.427974Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.06458","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7b9230fece3d39d57045593404f52623e29110f354d29f92e2367c4c34b67632","sha256:40b367b335c1ab8cb949979cd503e4eb57a24828cdcb6927d6b4eee4d4ee9c7a"],"state_sha256":"f44b970f801ed88cd1edbd0e37a162727c465dc5cab77f0714dcc30ce6948ffa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I2JaTYGYQkW/8pBZg/63jfU7KlEpk7K8Of3/Tu/srd5eZLZaZGD1n2VRqud8iXZIULrPhE7kzQpLMriezPSnBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-21T19:52:28.644323Z","bundle_sha256":"7a80f2fa7264bdd120162ccd3549844100b9e698e4fc0cc7f673e23bf2422b57"}}