{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:2WPSZNP5OLIPFMOP2ATVSXY2BP","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":"5f2ee366e01f302d523f5bf2c4a88684c623b5eb5f1476742c003a6792b68a11","cross_cats_sorted":["hep-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-02-21T21:00:01Z","title_canon_sha256":"9a5ef1743d7908e0fca04601b793de6c2528b73eff871ba7626af3278b253924"},"schema_version":"1.0","source":{"id":"1202.4757","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.4757","created_at":"2026-05-18T01:33:24Z"},{"alias_kind":"arxiv_version","alias_value":"1202.4757v3","created_at":"2026-05-18T01:33:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.4757","created_at":"2026-05-18T01:33:24Z"},{"alias_kind":"pith_short_12","alias_value":"2WPSZNP5OLIP","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"2WPSZNP5OLIPFMOP","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"2WPSZNP5","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:7bab349d085dc8259232b4b8731401a86a2382b6769a0fc88b7140985c6d7a9f","target":"graph","created_at":"2026-05-18T01:33:24Z","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":"We carry out a three-loop computation that establishes the existence of scale without conformal invariance in dimensional regularization with the MS scheme in d=4-epsilon spacetime dimensions. We also comment on the effects of scheme changes in theories with many couplings, as well as in theories that live on non-conformal scale-invariant renormalization group trajectories. Stability properties of such trajectories are analyzed, revealing both attractive and repulsive directions in a specific example. We explain how our results are in accord with those of Jack & Osborn on a c-theorem in d=4 (a","authors_text":"Andreas Stergiou, Benjam\\'in Grinstein, Jean-Fran\\c{c}ois Fortin","cross_cats":["hep-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-02-21T21:00:01Z","title":"Scale without Conformal Invariance at Three Loops"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.4757","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":"sha256:63c9b590d451b9b908af462f0063b24d6038b8f12a1ed9fa04bd62c4f9d05a89","target":"record","created_at":"2026-05-18T01:33:24Z","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":"5f2ee366e01f302d523f5bf2c4a88684c623b5eb5f1476742c003a6792b68a11","cross_cats_sorted":["hep-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-02-21T21:00:01Z","title_canon_sha256":"9a5ef1743d7908e0fca04601b793de6c2528b73eff871ba7626af3278b253924"},"schema_version":"1.0","source":{"id":"1202.4757","kind":"arxiv","version":3}},"canonical_sha256":"d59f2cb5fd72d0f2b1cfd027595f1a0be651de79ceb862a4290e271c0d1c077d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d59f2cb5fd72d0f2b1cfd027595f1a0be651de79ceb862a4290e271c0d1c077d","first_computed_at":"2026-05-18T01:33:24.722054Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:24.722054Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UnUqZiWADohdsrpMCUczQ1yM6OIqLI8EQqAUaMvwFbfjb+OdL/d4ISU+jEytC3MwPraxafqnL0yqWLUNsl+MBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:24.722975Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.4757","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:63c9b590d451b9b908af462f0063b24d6038b8f12a1ed9fa04bd62c4f9d05a89","sha256:7bab349d085dc8259232b4b8731401a86a2382b6769a0fc88b7140985c6d7a9f"],"state_sha256":"05ab940a33ef495ba3ff29511b45a9d07369ece68a988b54c23ea628f1e6f279"}