{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:SM3SZV5UOD7GCBSPSYZUFZLRGK","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":"35155e004c30dc93088fe009d97bd54758de9554101b70845cb3e18834888053","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2024-07-01T14:16:55Z","title_canon_sha256":"6213bf5c47e41ea8b2c693309c2cbd8f44122894c2f1126dacc28056b4aa4472"},"schema_version":"1.0","source":{"id":"2407.01309","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.01309","created_at":"2026-07-05T10:20:13Z"},{"alias_kind":"arxiv_version","alias_value":"2407.01309v3","created_at":"2026-07-05T10:20:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.01309","created_at":"2026-07-05T10:20:13Z"},{"alias_kind":"pith_short_12","alias_value":"SM3SZV5UOD7G","created_at":"2026-07-05T10:20:13Z"},{"alias_kind":"pith_short_16","alias_value":"SM3SZV5UOD7GCBSP","created_at":"2026-07-05T10:20:13Z"},{"alias_kind":"pith_short_8","alias_value":"SM3SZV5U","created_at":"2026-07-05T10:20:13Z"}],"graph_snapshots":[{"event_id":"sha256:520594f7709c2679e3df776c8e996e580edc466a94b3f790d0e2094856f5e786","target":"graph","created_at":"2026-07-05T10:20:13Z","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/2407.01309/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The differential equations of the Wilson renormalization group are a powerful tool to study the Schwinger functions of Euclidean quantum field theory. In particular renormalization theory can be based entirely on inductively bounding their perturbatively expanded solutions. Recently the solutions of these equations for scalar field theory have been analysed rigorously without recourse to perturbation theory, at the cost of restricting to the mean-field approximation. In particular it was shown there that one-component $\\varphi^4_4$-theory is trivial if the bare coupling constant of the UV regu","authors_text":"Christoph Kopper, Pierre Wang","cross_cats":["math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2024-07-01T14:16:55Z","title":"Triviality proof for mean-field $\\varphi_4^4$-theories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.01309","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":"sha256:69370be142b1e5234bff316741247a96d9b0fb2d831e97aa0a6e3fe2b04ff25b","target":"record","created_at":"2026-07-05T10:20:13Z","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":"35155e004c30dc93088fe009d97bd54758de9554101b70845cb3e18834888053","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2024-07-01T14:16:55Z","title_canon_sha256":"6213bf5c47e41ea8b2c693309c2cbd8f44122894c2f1126dacc28056b4aa4472"},"schema_version":"1.0","source":{"id":"2407.01309","kind":"arxiv","version":3}},"canonical_sha256":"93372cd7b470fe61064f963342e571328eeb4f7f8c8fc5d728c58ea30f33a004","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"93372cd7b470fe61064f963342e571328eeb4f7f8c8fc5d728c58ea30f33a004","first_computed_at":"2026-07-05T10:20:13.411768Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:20:13.411768Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZmaxAxrLjb6dnBVu7G4R1sbzxrDVW/Yok42Gp16tYU1mZ/a5twQmxRG4CJ94mudSXHV8USnBPzg2h8NtvK1gBw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:20:13.412226Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.01309","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:69370be142b1e5234bff316741247a96d9b0fb2d831e97aa0a6e3fe2b04ff25b","sha256:520594f7709c2679e3df776c8e996e580edc466a94b3f790d0e2094856f5e786"],"state_sha256":"7c4e389a4ee2cfc76ed08cded5941e34add6e2f77a9192b70d854558bbe2d87d"}