{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:BYDMOSLS3GACSP2EJE2R5YP32M","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":"0a6c0057defcd03b55d900378710497d8528e18551a444e8fd9801a3f8316164","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2020-08-10T12:50:58Z","title_canon_sha256":"3155cdf87287fb576c3750a5e0501e70ef81ccb1ce24221cccc4853ffd168e41"},"schema_version":"1.0","source":{"id":"2008.04077","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2008.04077","created_at":"2026-07-05T01:51:20Z"},{"alias_kind":"arxiv_version","alias_value":"2008.04077v4","created_at":"2026-07-05T01:51:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2008.04077","created_at":"2026-07-05T01:51:20Z"},{"alias_kind":"pith_short_12","alias_value":"BYDMOSLS3GAC","created_at":"2026-07-05T01:51:20Z"},{"alias_kind":"pith_short_16","alias_value":"BYDMOSLS3GACSP2E","created_at":"2026-07-05T01:51:20Z"},{"alias_kind":"pith_short_8","alias_value":"BYDMOSLS","created_at":"2026-07-05T01:51:20Z"}],"graph_snapshots":[{"event_id":"sha256:33168f875267d4646b39668f6c665307d6a28e59166fd3881fec747a03ecf86b","target":"graph","created_at":"2026-07-05T01:51:20Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2008.04077/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We adopt a combination of analytical and numerical methods to study the renormalization group flow of the most general field theory with quartic interaction in $d=4-\\epsilon$ with $N=3$ and $N=4$ scalars. For $N=3$, we find that it admits only three nondecomposable critical points: the Wilson-Fisher with $O(3)$ symmetry, the cubic with $H_3=(\\mathbb{Z}_2)^3\\rtimes S_3$ symmetry, and the biconical with $O(2)\\times \\mathbb{Z}_2$. For $N=4$, our analysis reveals the existence of new nontrivial solutions with discrete symmetries and with up to three distinct field anomalous dimensions.","authors_text":"Alessandro Codello, Gian Paolo Vacca, Mahmoud Safari, Omar Zanusso","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2020-08-10T12:50:58Z","title":"On critical models with $N\\leq 4$ scalars in $d=4-\\epsilon$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.04077","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":"sha256:74c14e18e6756996bae8e818d6f9035eb321ca27aebe4d6abad04eaa57003ca3","target":"record","created_at":"2026-07-05T01:51:20Z","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":"0a6c0057defcd03b55d900378710497d8528e18551a444e8fd9801a3f8316164","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2020-08-10T12:50:58Z","title_canon_sha256":"3155cdf87287fb576c3750a5e0501e70ef81ccb1ce24221cccc4853ffd168e41"},"schema_version":"1.0","source":{"id":"2008.04077","kind":"arxiv","version":4}},"canonical_sha256":"0e06c74972d980293f4449351ee1fbd32e0651914411659728f4d6539e6e692b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0e06c74972d980293f4449351ee1fbd32e0651914411659728f4d6539e6e692b","first_computed_at":"2026-07-05T01:51:20.980661Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:51:20.980661Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6N+q7J0335ft5vmxzdUYqIQy0xE72OhPRbMCQmL/PztuJHcpswB6w0oVQt2zG3dfdpwUouajh8dbo6pTqmhXDA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:51:20.981068Z","signed_message":"canonical_sha256_bytes"},"source_id":"2008.04077","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:74c14e18e6756996bae8e818d6f9035eb321ca27aebe4d6abad04eaa57003ca3","sha256:33168f875267d4646b39668f6c665307d6a28e59166fd3881fec747a03ecf86b"],"state_sha256":"4892cc27e32e88df371af644a3c3e846b6346733acebe56ec8172f03cbfd068a"}