{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2000:6RI7YAJBUJIN7FT54G3QDDLJGC","short_pith_number":"pith:6RI7YAJB","schema_version":"1.0","canonical_sha256":"f451fc0121a250df967de1b7018d6930a798085bf8bbddf86a11379bae732bb1","source":{"kind":"arxiv","id":"hep-th/0012146","version":1},"attestation_state":"computed","paper":{"title":"Exact solutions of Dyson-Schwinger equations for iterated one-loop integrals and propagator-coupling duality","license":"","headline":"","cross_cats":["hep-ph","math.QA"],"primary_cat":"hep-th","authors_text":"D.J.Broadhurst, D.Kreimer","submitted_at":"2000-12-17T16:20:00Z","abstract_excerpt":"The Hopf algebra of undecorated rooted trees has tamed the combinatorics of perturbative contributions, to anomalous dimensions in Yukawa theory and scalar $\\phi^3$ theory, from all nestings and chainings of a primitive self-energy subdivergence. Here we formulate the nonperturbative problems which these resummations approximate. For Yukawa theory, at spacetime dimension $d=4$, we obtain an integrodifferential Dyson-Schwinger equation and solve it parametrically in terms of the complementary error function. For the scalar theory, at $d=6$, the nonperturbative problem is more severe; we transfo"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"hep-th/0012146","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2000-12-17T16:20:00Z","cross_cats_sorted":["hep-ph","math.QA"],"title_canon_sha256":"af2e861d7a47526a8849b5e7d6bf424043717e74922686848825c76c3f40c10a","abstract_canon_sha256":"d9be564871b2809b4f0379627724204d9a62fc45cc270c43f76d29f57b6736e8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:21:08.861044Z","signature_b64":"QgucFh2Kod5qD06ThUlnOnQK+HMPS+uUlPnGutHiQYQOEX2h7ZZ/N89brKa1vhc83z2rPFfkCl2VLWCu9vMoBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f451fc0121a250df967de1b7018d6930a798085bf8bbddf86a11379bae732bb1","last_reissued_at":"2026-07-04T16:21:08.860603Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:21:08.860603Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exact solutions of Dyson-Schwinger equations for iterated one-loop integrals and propagator-coupling duality","license":"","headline":"","cross_cats":["hep-ph","math.QA"],"primary_cat":"hep-th","authors_text":"D.J.Broadhurst, D.Kreimer","submitted_at":"2000-12-17T16:20:00Z","abstract_excerpt":"The Hopf algebra of undecorated rooted trees has tamed the combinatorics of perturbative contributions, to anomalous dimensions in Yukawa theory and scalar $\\phi^3$ theory, from all nestings and chainings of a primitive self-energy subdivergence. Here we formulate the nonperturbative problems which these resummations approximate. For Yukawa theory, at spacetime dimension $d=4$, we obtain an integrodifferential Dyson-Schwinger equation and solve it parametrically in terms of the complementary error function. For the scalar theory, at $d=6$, the nonperturbative problem is more severe; we transfo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0012146","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/hep-th/0012146/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0012146","created_at":"2026-07-04T16:21:08.860662+00:00"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0012146v1","created_at":"2026-07-04T16:21:08.860662+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0012146","created_at":"2026-07-04T16:21:08.860662+00:00"},{"alias_kind":"pith_short_12","alias_value":"6RI7YAJBUJIN","created_at":"2026-07-04T16:21:08.860662+00:00"},{"alias_kind":"pith_short_16","alias_value":"6RI7YAJBUJIN7FT5","created_at":"2026-07-04T16:21:08.860662+00:00"},{"alias_kind":"pith_short_8","alias_value":"6RI7YAJB","created_at":"2026-07-04T16:21:08.860662+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2501.12350","citing_title":"The algebraic structure of Dyson--Schwinger equations with multiple insertion places","ref_index":9,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6RI7YAJBUJIN7FT54G3QDDLJGC","json":"https://pith.science/pith/6RI7YAJBUJIN7FT54G3QDDLJGC.json","graph_json":"https://pith.science/api/pith-number/6RI7YAJBUJIN7FT54G3QDDLJGC/graph.json","events_json":"https://pith.science/api/pith-number/6RI7YAJBUJIN7FT54G3QDDLJGC/events.json","paper":"https://pith.science/paper/6RI7YAJB"},"agent_actions":{"view_html":"https://pith.science/pith/6RI7YAJBUJIN7FT54G3QDDLJGC","download_json":"https://pith.science/pith/6RI7YAJBUJIN7FT54G3QDDLJGC.json","view_paper":"https://pith.science/paper/6RI7YAJB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=hep-th/0012146&json=true","fetch_graph":"https://pith.science/api/pith-number/6RI7YAJBUJIN7FT54G3QDDLJGC/graph.json","fetch_events":"https://pith.science/api/pith-number/6RI7YAJBUJIN7FT54G3QDDLJGC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6RI7YAJBUJIN7FT54G3QDDLJGC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6RI7YAJBUJIN7FT54G3QDDLJGC/action/storage_attestation","attest_author":"https://pith.science/pith/6RI7YAJBUJIN7FT54G3QDDLJGC/action/author_attestation","sign_citation":"https://pith.science/pith/6RI7YAJBUJIN7FT54G3QDDLJGC/action/citation_signature","submit_replication":"https://pith.science/pith/6RI7YAJBUJIN7FT54G3QDDLJGC/action/replication_record"}},"created_at":"2026-07-04T16:21:08.860662+00:00","updated_at":"2026-07-04T16:21:08.860662+00:00"}