{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:X7LJCOW66S6T5TBNDUMHZWBLR3","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":"b568bf3151041594cffa734778925c6c456bd0e0ac689804abd750a251df1188","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2020-07-09T07:25:38Z","title_canon_sha256":"723a44dad16000fd58ba786a377a8230fc990be1b9d2427e30121c654640a1b2"},"schema_version":"1.0","source":{"id":"2007.04603","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2007.04603","created_at":"2026-07-05T09:30:53Z"},{"alias_kind":"arxiv_version","alias_value":"2007.04603v3","created_at":"2026-07-05T09:30:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2007.04603","created_at":"2026-07-05T09:30:53Z"},{"alias_kind":"pith_short_12","alias_value":"X7LJCOW66S6T","created_at":"2026-07-05T09:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"X7LJCOW66S6T5TBN","created_at":"2026-07-05T09:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"X7LJCOW6","created_at":"2026-07-05T09:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:62b2db93919dff9feb93045a0f439f79477989a527502c23660efd443da65868","target":"graph","created_at":"2026-07-05T09:30:53Z","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/2007.04603/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We compute the three-loop beta functions of long-range multi-scalar models with general quartic interactions. The long-range nature of the models is encoded in a kinetic term with a Laplacian to the power $0<\\zeta<1$, rendering the computation of Feynman diagrams much harder than in the usual short-range case ($\\zeta=1$). As a consequence, previous results stopped at two loops, while six-loop results are available for short-range models. We push the renormalization group analysis to three loops, in an $\\epsilon=4\\zeta-d$ expansion at fixed dimension $d<4$, extensively using the Mellin-Barnes r","authors_text":"Dario Benedetti, Kenta Suzuki, Razvan Gurau, Sabine Harribey","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2020-07-09T07:25:38Z","title":"Long-range multi-scalar models at three loops"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.04603","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:b7fdcdd8a9aa7671979501e2adaa5518de01769cc69e71490e5b3dca9af61aab","target":"record","created_at":"2026-07-05T09:30:53Z","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":"b568bf3151041594cffa734778925c6c456bd0e0ac689804abd750a251df1188","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2020-07-09T07:25:38Z","title_canon_sha256":"723a44dad16000fd58ba786a377a8230fc990be1b9d2427e30121c654640a1b2"},"schema_version":"1.0","source":{"id":"2007.04603","kind":"arxiv","version":3}},"canonical_sha256":"bfd6913adef4bd3ecc2d1d187cd82b8efd9cbf549b63bc48272d589310185d32","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bfd6913adef4bd3ecc2d1d187cd82b8efd9cbf549b63bc48272d589310185d32","first_computed_at":"2026-07-05T09:30:53.531559Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:30:53.531559Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bDz09sMmbGbtI4E1bgV3/Hmjien+KrM8co52mDlX+BgnLIQdYp2AU1OywawpWGOAPTKot6vlpT21uGxjaNkCCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:30:53.532072Z","signed_message":"canonical_sha256_bytes"},"source_id":"2007.04603","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b7fdcdd8a9aa7671979501e2adaa5518de01769cc69e71490e5b3dca9af61aab","sha256:62b2db93919dff9feb93045a0f439f79477989a527502c23660efd443da65868"],"state_sha256":"9f835d5962d0f9dc3964966a4f846315db2874c18cad8db4d963eadbad587b8e"}