{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2000:6RI7YAJBUJIN7FT54G3QDDLJGC","short_pith_number":"pith:6RI7YAJB","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"},"canonical_sha256":"f451fc0121a250df967de1b7018d6930a798085bf8bbddf86a11379bae732bb1","source":{"kind":"arxiv","id":"hep-th/0012146","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0012146","created_at":"2026-07-04T16:21:08Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0012146v1","created_at":"2026-07-04T16:21:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0012146","created_at":"2026-07-04T16:21:08Z"},{"alias_kind":"pith_short_12","alias_value":"6RI7YAJBUJIN","created_at":"2026-07-04T16:21:08Z"},{"alias_kind":"pith_short_16","alias_value":"6RI7YAJBUJIN7FT5","created_at":"2026-07-04T16:21:08Z"},{"alias_kind":"pith_short_8","alias_value":"6RI7YAJB","created_at":"2026-07-04T16:21:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2000:6RI7YAJBUJIN7FT54G3QDDLJGC","target":"record","payload":{"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"},"canonical_sha256":"f451fc0121a250df967de1b7018d6930a798085bf8bbddf86a11379bae732bb1","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"},"source_kind":"arxiv","source_id":"hep-th/0012146","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T16:21:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aJfO+v58WQcdWSOPV2GrI4+Z4MDUri9Zx//yG3yUrzXMbzFUh3i380l8EI9OVYCRRN5dFmWs0ikO0L0DvdNKBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T18:13:51.097577Z"},"content_sha256":"1cf36e5742ce0554a759b6f9ebcc8c7f12011b915ea5a9ffd00b3567ee7ac60c","schema_version":"1.0","event_id":"sha256:1cf36e5742ce0554a759b6f9ebcc8c7f12011b915ea5a9ffd00b3567ee7ac60c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2000:6RI7YAJBUJIN7FT54G3QDDLJGC","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T16:21:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ParlYm+6Z6VoExwdDMIzghoYnXt/yPXMe4IbA36no/uMMFVSvh9vqqtyedHDrLUrS2NkHGggOwxgv0gvaOEFBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T18:13:51.098087Z"},"content_sha256":"65d195a360cf0f77ca1a006e1efffac86f3885d16b10581186665e38b3dc6f9b","schema_version":"1.0","event_id":"sha256:65d195a360cf0f77ca1a006e1efffac86f3885d16b10581186665e38b3dc6f9b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6RI7YAJBUJIN7FT54G3QDDLJGC/bundle.json","state_url":"https://pith.science/pith/6RI7YAJBUJIN7FT54G3QDDLJGC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6RI7YAJBUJIN7FT54G3QDDLJGC/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-17T18:13:51Z","links":{"resolver":"https://pith.science/pith/6RI7YAJBUJIN7FT54G3QDDLJGC","bundle":"https://pith.science/pith/6RI7YAJBUJIN7FT54G3QDDLJGC/bundle.json","state":"https://pith.science/pith/6RI7YAJBUJIN7FT54G3QDDLJGC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6RI7YAJBUJIN7FT54G3QDDLJGC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:6RI7YAJBUJIN7FT54G3QDDLJGC","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":"d9be564871b2809b4f0379627724204d9a62fc45cc270c43f76d29f57b6736e8","cross_cats_sorted":["hep-ph","math.QA"],"license":"","primary_cat":"hep-th","submitted_at":"2000-12-17T16:20:00Z","title_canon_sha256":"af2e861d7a47526a8849b5e7d6bf424043717e74922686848825c76c3f40c10a"},"schema_version":"1.0","source":{"id":"hep-th/0012146","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0012146","created_at":"2026-07-04T16:21:08Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0012146v1","created_at":"2026-07-04T16:21:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0012146","created_at":"2026-07-04T16:21:08Z"},{"alias_kind":"pith_short_12","alias_value":"6RI7YAJBUJIN","created_at":"2026-07-04T16:21:08Z"},{"alias_kind":"pith_short_16","alias_value":"6RI7YAJBUJIN7FT5","created_at":"2026-07-04T16:21:08Z"},{"alias_kind":"pith_short_8","alias_value":"6RI7YAJB","created_at":"2026-07-04T16:21:08Z"}],"graph_snapshots":[{"event_id":"sha256:65d195a360cf0f77ca1a006e1efffac86f3885d16b10581186665e38b3dc6f9b","target":"graph","created_at":"2026-07-04T16:21:08Z","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-th/0012146/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"D.J.Broadhurst, D.Kreimer","cross_cats":["hep-ph","math.QA"],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"2000-12-17T16:20:00Z","title":"Exact solutions of Dyson-Schwinger equations for iterated one-loop integrals and propagator-coupling duality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0012146","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":"sha256:1cf36e5742ce0554a759b6f9ebcc8c7f12011b915ea5a9ffd00b3567ee7ac60c","target":"record","created_at":"2026-07-04T16:21:08Z","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":"d9be564871b2809b4f0379627724204d9a62fc45cc270c43f76d29f57b6736e8","cross_cats_sorted":["hep-ph","math.QA"],"license":"","primary_cat":"hep-th","submitted_at":"2000-12-17T16:20:00Z","title_canon_sha256":"af2e861d7a47526a8849b5e7d6bf424043717e74922686848825c76c3f40c10a"},"schema_version":"1.0","source":{"id":"hep-th/0012146","kind":"arxiv","version":1}},"canonical_sha256":"f451fc0121a250df967de1b7018d6930a798085bf8bbddf86a11379bae732bb1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f451fc0121a250df967de1b7018d6930a798085bf8bbddf86a11379bae732bb1","first_computed_at":"2026-07-04T16:21:08.860603Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:21:08.860603Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QgucFh2Kod5qD06ThUlnOnQK+HMPS+uUlPnGutHiQYQOEX2h7ZZ/N89brKa1vhc83z2rPFfkCl2VLWCu9vMoBA==","signature_status":"signed_v1","signed_at":"2026-07-04T16:21:08.861044Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/0012146","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1cf36e5742ce0554a759b6f9ebcc8c7f12011b915ea5a9ffd00b3567ee7ac60c","sha256:65d195a360cf0f77ca1a006e1efffac86f3885d16b10581186665e38b3dc6f9b"],"state_sha256":"ec214002e737f7ec7257efc78a9df0f4ee4f7da46e3df6408f2a70a6d6755704"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CbrnUQ1JhpHH+rSQ5RY0zeF01jZ24XYJWks8orf7uNm7NR2aZXw+WZhZdpjqFajlKak9ksM0DGicr9PMQwzWCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T18:13:51.103252Z","bundle_sha256":"a8206e7434cdc32731714a7fadd12dfd9ce5f462d175f6355c16fb5b449df4b2"}}