{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:5C5NH4OD7TJAUF6HQMJWL5TT56","short_pith_number":"pith:5C5NH4OD","canonical_record":{"source":{"id":"1412.1657","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-12-04T13:21:40Z","cross_cats_sorted":[],"title_canon_sha256":"5a65d5ff3fbdd23153280dfe8a0f48d72a25d1774dd15aa1dae0891c452dd5cf","abstract_canon_sha256":"38e71d992539dc8a80e5c4703e7f6c3192f77e2865d0ef0f056196360d109b80"},"schema_version":"1.0"},"canonical_sha256":"e8bad3f1c3fcd20a17c7831365f673ef8bc9c96aabe72f5fc5d2f5c0a7a94983","source":{"kind":"arxiv","id":"1412.1657","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.1657","created_at":"2026-05-18T02:27:20Z"},{"alias_kind":"arxiv_version","alias_value":"1412.1657v2","created_at":"2026-05-18T02:27:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.1657","created_at":"2026-05-18T02:27:20Z"},{"alias_kind":"pith_short_12","alias_value":"5C5NH4OD7TJA","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"5C5NH4OD7TJAUF6H","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"5C5NH4OD","created_at":"2026-05-18T12:28:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:5C5NH4OD7TJAUF6HQMJWL5TT56","target":"record","payload":{"canonical_record":{"source":{"id":"1412.1657","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-12-04T13:21:40Z","cross_cats_sorted":[],"title_canon_sha256":"5a65d5ff3fbdd23153280dfe8a0f48d72a25d1774dd15aa1dae0891c452dd5cf","abstract_canon_sha256":"38e71d992539dc8a80e5c4703e7f6c3192f77e2865d0ef0f056196360d109b80"},"schema_version":"1.0"},"canonical_sha256":"e8bad3f1c3fcd20a17c7831365f673ef8bc9c96aabe72f5fc5d2f5c0a7a94983","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:20.795762Z","signature_b64":"vjXCgnEe2bm/O0euMdYJEEc05ijWd5rxjRfAxRpYH9NYP+fhFb+LbsHGvZwJJ74xDGZ4PU1Az8twnWHFZbcZCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e8bad3f1c3fcd20a17c7831365f673ef8bc9c96aabe72f5fc5d2f5c0a7a94983","last_reissued_at":"2026-05-18T02:27:20.795106Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:20.795106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.1657","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:27:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nsCGIM1HCX95dcGW2p8Md+d+cVw0JbvE6/xXECz4Gs2DJWtCwYfbshWQk7X5UfnxMbQ5p1A/kxx8KD5Ch6ueBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T05:00:19.653106Z"},"content_sha256":"2fdc7b69872df3ee6aa0d0e7f4630382b33eddcefebb5aed2045bc3b5bb1c196","schema_version":"1.0","event_id":"sha256:2fdc7b69872df3ee6aa0d0e7f4630382b33eddcefebb5aed2045bc3b5bb1c196"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:5C5NH4OD7TJAUF6HQMJWL5TT56","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Filtrations in Dyson-Schwinger equations: next-to^{j} -leading log expansions systematically","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Dirk Kreimer, Olaf Krueger","submitted_at":"2014-12-04T13:21:40Z","abstract_excerpt":"Dyson-Schwinger equations determine the Green functions $G^r(\\alpha,L)$ in quantum field theory. Their solutions are triangular series in a coupling constant $\\alpha$ and an external scale parameter $L$ for a chosen amplitude $r$, with the order in $L$ bounded by the order in the coupling. Perturbation theory calculates the first few orders in $\\alpha$. On the other hand, Dyson--Schwinger equations determine next-to$^{\\{\\mathrm{j}\\}}$-leading log expansions, $G^r(\\alpha,L) = 1 + \\sum_{j=0}^\\infty \\sum_{\\mathcal{M}} p_j^{\\mathcal{M}}\\alpha^j \\mathcal{M}(u)$. $\\sum_{\\mathcal{M}}$ sums a finite n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.1657","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T02:27:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a9X9T9PRqA/IbtJNZDPLsZ8tGuAxkDDnK1G1i8watvEGHoisonE/4fTTs88hbAqgjRmWlCBbFmKyJ3EPuxSqBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T05:00:19.653701Z"},"content_sha256":"a75156b5292fc0107c765c703d6fe26430a099c234273b53223a9cc472285d0c","schema_version":"1.0","event_id":"sha256:a75156b5292fc0107c765c703d6fe26430a099c234273b53223a9cc472285d0c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5C5NH4OD7TJAUF6HQMJWL5TT56/bundle.json","state_url":"https://pith.science/pith/5C5NH4OD7TJAUF6HQMJWL5TT56/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5C5NH4OD7TJAUF6HQMJWL5TT56/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":"2026-06-01T05:00:19Z","links":{"resolver":"https://pith.science/pith/5C5NH4OD7TJAUF6HQMJWL5TT56","bundle":"https://pith.science/pith/5C5NH4OD7TJAUF6HQMJWL5TT56/bundle.json","state":"https://pith.science/pith/5C5NH4OD7TJAUF6HQMJWL5TT56/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5C5NH4OD7TJAUF6HQMJWL5TT56/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:5C5NH4OD7TJAUF6HQMJWL5TT56","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":"38e71d992539dc8a80e5c4703e7f6c3192f77e2865d0ef0f056196360d109b80","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-12-04T13:21:40Z","title_canon_sha256":"5a65d5ff3fbdd23153280dfe8a0f48d72a25d1774dd15aa1dae0891c452dd5cf"},"schema_version":"1.0","source":{"id":"1412.1657","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.1657","created_at":"2026-05-18T02:27:20Z"},{"alias_kind":"arxiv_version","alias_value":"1412.1657v2","created_at":"2026-05-18T02:27:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.1657","created_at":"2026-05-18T02:27:20Z"},{"alias_kind":"pith_short_12","alias_value":"5C5NH4OD7TJA","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"5C5NH4OD7TJAUF6H","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"5C5NH4OD","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:a75156b5292fc0107c765c703d6fe26430a099c234273b53223a9cc472285d0c","target":"graph","created_at":"2026-05-18T02:27:20Z","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"},"paper":{"abstract_excerpt":"Dyson-Schwinger equations determine the Green functions $G^r(\\alpha,L)$ in quantum field theory. Their solutions are triangular series in a coupling constant $\\alpha$ and an external scale parameter $L$ for a chosen amplitude $r$, with the order in $L$ bounded by the order in the coupling. Perturbation theory calculates the first few orders in $\\alpha$. On the other hand, Dyson--Schwinger equations determine next-to$^{\\{\\mathrm{j}\\}}$-leading log expansions, $G^r(\\alpha,L) = 1 + \\sum_{j=0}^\\infty \\sum_{\\mathcal{M}} p_j^{\\mathcal{M}}\\alpha^j \\mathcal{M}(u)$. $\\sum_{\\mathcal{M}}$ sums a finite n","authors_text":"Dirk Kreimer, Olaf Krueger","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-12-04T13:21:40Z","title":"Filtrations in Dyson-Schwinger equations: next-to^{j} -leading log expansions systematically"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.1657","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":"sha256:2fdc7b69872df3ee6aa0d0e7f4630382b33eddcefebb5aed2045bc3b5bb1c196","target":"record","created_at":"2026-05-18T02:27:20Z","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":"38e71d992539dc8a80e5c4703e7f6c3192f77e2865d0ef0f056196360d109b80","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-12-04T13:21:40Z","title_canon_sha256":"5a65d5ff3fbdd23153280dfe8a0f48d72a25d1774dd15aa1dae0891c452dd5cf"},"schema_version":"1.0","source":{"id":"1412.1657","kind":"arxiv","version":2}},"canonical_sha256":"e8bad3f1c3fcd20a17c7831365f673ef8bc9c96aabe72f5fc5d2f5c0a7a94983","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e8bad3f1c3fcd20a17c7831365f673ef8bc9c96aabe72f5fc5d2f5c0a7a94983","first_computed_at":"2026-05-18T02:27:20.795106Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:20.795106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vjXCgnEe2bm/O0euMdYJEEc05ijWd5rxjRfAxRpYH9NYP+fhFb+LbsHGvZwJJ74xDGZ4PU1Az8twnWHFZbcZCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:20.795762Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.1657","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2fdc7b69872df3ee6aa0d0e7f4630382b33eddcefebb5aed2045bc3b5bb1c196","sha256:a75156b5292fc0107c765c703d6fe26430a099c234273b53223a9cc472285d0c"],"state_sha256":"ef8dfbdeed74abb8bf4837307695c98cdb8c056aea79281d46d99e6bfaead5bc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/kezFMOFtwy5B9e91VbTUmQUNQVWqU4QeGNc5qCf6KRjAkA1llKGWhileCajrketdebvuXqqgiCmznIF9dFuCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T05:00:19.656583Z","bundle_sha256":"47a5837aeb639414a73c830e6f3697bd5a6076507a50a53a2fd9090ae0bea5b0"}}