{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:IDXUE5ZKOVGUSSO4EU5S6MPNFN","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":"54ae94b6e82fc08786dc3c75a4d719dd5143b03bd5323a9fa049506e936dadd4","cross_cats_sorted":["hep-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-03-22T10:34:32Z","title_canon_sha256":"e8172073a59eef4c0a265e5d8b017ee485d5626aac0b9f121df976a3417b432e"},"schema_version":"1.0","source":{"id":"1603.06726","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.06726","created_at":"2026-05-18T01:10:24Z"},{"alias_kind":"arxiv_version","alias_value":"1603.06726v1","created_at":"2026-05-18T01:10:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.06726","created_at":"2026-05-18T01:10:24Z"},{"alias_kind":"pith_short_12","alias_value":"IDXUE5ZKOVGU","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"IDXUE5ZKOVGUSSO4","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"IDXUE5ZK","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:7fe2dd28e8d3eb51f698b117237da1822f7b925b43a1c5ad080809bd13a31a24","target":"graph","created_at":"2026-05-18T01:10:24Z","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 apply pseudo-spectral methods to integrate functional flow equations with high accuracy, extending earlier work on functional fixed point equations \\cite{Borchardt:2015rxa}. The advantages of our method are illustrated with the help of two classes of models: first, to make contact with literature, we investigate flows of the O$(N)$-model in 3 dimensions, for $N=1, 4$ and in the large $N$ limit. For the case of a fractal dimension, $d=2.4$, and $N=1$, we follow the flow along a separatrix from a multicritical fixed point to the Wilson-Fisher fixed point over almost 13 orders of magnitude. As","authors_text":"Benjamin Knorr, Julia Borchardt","cross_cats":["hep-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-03-22T10:34:32Z","title":"Solving functional flow equations with pseudo-spectral methods"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.06726","kind":"arxiv","version":1},"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":"sha256:581c3e56923cd5590c0cfab4f8356592101ad8efe591f2ca16cbe7406ca84301","target":"record","created_at":"2026-05-18T01:10:24Z","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":"54ae94b6e82fc08786dc3c75a4d719dd5143b03bd5323a9fa049506e936dadd4","cross_cats_sorted":["hep-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-03-22T10:34:32Z","title_canon_sha256":"e8172073a59eef4c0a265e5d8b017ee485d5626aac0b9f121df976a3417b432e"},"schema_version":"1.0","source":{"id":"1603.06726","kind":"arxiv","version":1}},"canonical_sha256":"40ef42772a754d4949dc253b2f31ed2b55d8e503027effc0637cb1cba3d9803c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"40ef42772a754d4949dc253b2f31ed2b55d8e503027effc0637cb1cba3d9803c","first_computed_at":"2026-05-18T01:10:24.539817Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:24.539817Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rVzl4wRl91W2tEFT8EJ6qmRwEZaO1rRqlIsHSfUL8U5H5lnZYLkBZYg069wLUVFvU9oeOmQa5xapO8FFvpdiDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:24.540233Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.06726","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:581c3e56923cd5590c0cfab4f8356592101ad8efe591f2ca16cbe7406ca84301","sha256:7fe2dd28e8d3eb51f698b117237da1822f7b925b43a1c5ad080809bd13a31a24"],"state_sha256":"a665c09dc84b97f44ede4f379f2307898b5564f3275182edb58f51267afcd559"}