{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1993:BEM3C77RVZTDOO7FW3HSHMDB62","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":"13759896afbfa1c9d5c05fdcf60edfc274a074ece69a195d71f9ebc951ec6a3b","cross_cats_sorted":["hep-th"],"license":"","primary_cat":"hep-ph","submitted_at":"1993-08-11T16:50:14Z","title_canon_sha256":"b02e44d0f62aa1dbb5817a340b531c5d079b0ce30960c9594e78ee61c7309c3a"},"schema_version":"1.0","source":{"id":"hep-ph/9308260","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-ph/9308260","created_at":"2026-07-04T15:27:20Z"},{"alias_kind":"arxiv_version","alias_value":"hep-ph/9308260v2","created_at":"2026-07-04T15:27:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-ph/9308260","created_at":"2026-07-04T15:27:20Z"},{"alias_kind":"pith_short_12","alias_value":"BEM3C77RVZTD","created_at":"2026-07-04T15:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"BEM3C77RVZTDOO7F","created_at":"2026-07-04T15:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"BEM3C77R","created_at":"2026-07-04T15:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:5bf561efa4d1e0e7acfabbdeedc25baced1d8274d440638437c5a50a2bad2ebe","target":"graph","created_at":"2026-07-04T15:27:20Z","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/hep-ph/9308260/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We discuss the exact renormalization group or flow equation for the effective action and its decomposition into one particle irreducible N point functions. With the help of a truncated flow equation for the four point function we study the bound state problem for scalar fields. A combination of analytic and numerical methods is proposed, which is applied to the Wick-Cutkosky model and a QCD-motivated interaction. We present results for the bound state masses and the Bethe-Salpeter wave function. (Figs. 1-4 attached as separate uuencoded post-script files.)","authors_text":"Ulrich Ellwanger","cross_cats":["hep-th"],"headline":"","license":"","primary_cat":"hep-ph","submitted_at":"1993-08-11T16:50:14Z","title":"Flow Equations for N Point Functions and Bound States"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-ph/9308260","kind":"arxiv","version":2},"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":"sha256:5c2a729837081563759966c940eb4e3af1bc0714a6330a5481b65590392fec7f","target":"record","created_at":"2026-07-04T15:27:20Z","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":"13759896afbfa1c9d5c05fdcf60edfc274a074ece69a195d71f9ebc951ec6a3b","cross_cats_sorted":["hep-th"],"license":"","primary_cat":"hep-ph","submitted_at":"1993-08-11T16:50:14Z","title_canon_sha256":"b02e44d0f62aa1dbb5817a340b531c5d079b0ce30960c9594e78ee61c7309c3a"},"schema_version":"1.0","source":{"id":"hep-ph/9308260","kind":"arxiv","version":2}},"canonical_sha256":"0919b17ff1ae66373be5b6cf23b061f6b9aeaf2e4157ccfcad1bbce67ef708d3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0919b17ff1ae66373be5b6cf23b061f6b9aeaf2e4157ccfcad1bbce67ef708d3","first_computed_at":"2026-07-04T15:27:20.536267Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:27:20.536267Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2A9MyQzv4OgqgrGYq1oAyDjFgIann78TIRs7cqwNx96+DxnJlZb8f47ESGYXZ8hyDLOk/Ge5W6WzJySESXD4Cg==","signature_status":"signed_v1","signed_at":"2026-07-04T15:27:20.536675Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-ph/9308260","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5c2a729837081563759966c940eb4e3af1bc0714a6330a5481b65590392fec7f","sha256:5bf561efa4d1e0e7acfabbdeedc25baced1d8274d440638437c5a50a2bad2ebe"],"state_sha256":"1da99cb02b7e64235482602784f7c8cd72a9c4eeff9d83d8ff047f1a845c2c86"}