{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:SWVFOB3TX3NOSBLYKIWZHS3SPC","short_pith_number":"pith:SWVFOB3T","schema_version":"1.0","canonical_sha256":"95aa570773bedae90578522d93cb727897cf4295399db438874df5dcfcb6d737","source":{"kind":"arxiv","id":"2010.16222","version":3},"attestation_state":"computed","paper":{"title":"Bounds on multiscalar CFTs in the epsilon expansion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"hep-th","authors_text":"Chiara Toldo, Matthijs Hogervorst","submitted_at":"2020-10-30T12:28:14Z","abstract_excerpt":"We study fixed points with N scalar fields in $4 - \\varepsilon$ dimensions to leading order in $\\varepsilon$ using a bottom-up approach. We do so by analyzing O(N) invariants of the quartic coupling $\\lambda_{ijkl}$ that describes such CFTs. In particular, we show that $\\lambda_{iijj}$ and $\\lambda_{ijkl}^2$ are restricted to a specific domain, refining a result by Rychkov and Stergiou. We also study averages of one-loop anomalous dimensions of composite operators without gradients. In many cases, we are able to show that the O(N) fixed point maximizes such averages. In the final part of this "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2010.16222","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2020-10-30T12:28:14Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"a0eedcbe6710c2421254802e65ea3a4a5369a86cab9485ece2fb3944802799e1","abstract_canon_sha256":"367db1078b65dd4cef9d3f1626c6630f050f4c26cd87b10b82383e7e12e99aa7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:35:20.520098Z","signature_b64":"LD99a3SqkCk8oiyOWLMM7SImUnKdYcUkBPsB7qfM0BnoDQGVSWDUoQLJhHhKeSzHbFqN2WYqKQh9+dZ5QLHPDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"95aa570773bedae90578522d93cb727897cf4295399db438874df5dcfcb6d737","last_reissued_at":"2026-07-05T02:35:20.519640Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:35:20.519640Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bounds on multiscalar CFTs in the epsilon expansion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"hep-th","authors_text":"Chiara Toldo, Matthijs Hogervorst","submitted_at":"2020-10-30T12:28:14Z","abstract_excerpt":"We study fixed points with N scalar fields in $4 - \\varepsilon$ dimensions to leading order in $\\varepsilon$ using a bottom-up approach. We do so by analyzing O(N) invariants of the quartic coupling $\\lambda_{ijkl}$ that describes such CFTs. In particular, we show that $\\lambda_{iijj}$ and $\\lambda_{ijkl}^2$ are restricted to a specific domain, refining a result by Rychkov and Stergiou. We also study averages of one-loop anomalous dimensions of composite operators without gradients. In many cases, we are able to show that the O(N) fixed point maximizes such averages. In the final part of this "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.16222","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2010.16222/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2010.16222","created_at":"2026-07-05T02:35:20.519705+00:00"},{"alias_kind":"arxiv_version","alias_value":"2010.16222v3","created_at":"2026-07-05T02:35:20.519705+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2010.16222","created_at":"2026-07-05T02:35:20.519705+00:00"},{"alias_kind":"pith_short_12","alias_value":"SWVFOB3TX3NO","created_at":"2026-07-05T02:35:20.519705+00:00"},{"alias_kind":"pith_short_16","alias_value":"SWVFOB3TX3NOSBLY","created_at":"2026-07-05T02:35:20.519705+00:00"},{"alias_kind":"pith_short_8","alias_value":"SWVFOB3T","created_at":"2026-07-05T02:35:20.519705+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2502.06940","citing_title":"Gradient Flows and the Curvature of Theory Space","ref_index":33,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SWVFOB3TX3NOSBLYKIWZHS3SPC","json":"https://pith.science/pith/SWVFOB3TX3NOSBLYKIWZHS3SPC.json","graph_json":"https://pith.science/api/pith-number/SWVFOB3TX3NOSBLYKIWZHS3SPC/graph.json","events_json":"https://pith.science/api/pith-number/SWVFOB3TX3NOSBLYKIWZHS3SPC/events.json","paper":"https://pith.science/paper/SWVFOB3T"},"agent_actions":{"view_html":"https://pith.science/pith/SWVFOB3TX3NOSBLYKIWZHS3SPC","download_json":"https://pith.science/pith/SWVFOB3TX3NOSBLYKIWZHS3SPC.json","view_paper":"https://pith.science/paper/SWVFOB3T","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2010.16222&json=true","fetch_graph":"https://pith.science/api/pith-number/SWVFOB3TX3NOSBLYKIWZHS3SPC/graph.json","fetch_events":"https://pith.science/api/pith-number/SWVFOB3TX3NOSBLYKIWZHS3SPC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SWVFOB3TX3NOSBLYKIWZHS3SPC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SWVFOB3TX3NOSBLYKIWZHS3SPC/action/storage_attestation","attest_author":"https://pith.science/pith/SWVFOB3TX3NOSBLYKIWZHS3SPC/action/author_attestation","sign_citation":"https://pith.science/pith/SWVFOB3TX3NOSBLYKIWZHS3SPC/action/citation_signature","submit_replication":"https://pith.science/pith/SWVFOB3TX3NOSBLYKIWZHS3SPC/action/replication_record"}},"created_at":"2026-07-05T02:35:20.519705+00:00","updated_at":"2026-07-05T02:35:20.519705+00:00"}