{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:S2I45UDFSIQVBESZOFO3WMYYWC","short_pith_number":"pith:S2I45UDF","canonical_record":{"source":{"id":"1604.08027","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-04-27T11:58:08Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"fa34633263f0ebaee1e6fa09ebbc946227c9b8dae89a6dc5485897ae1972cd0b","abstract_canon_sha256":"94ec6ea0b97cb7080a9b337714738d85c58afcf9aaadda41b9ae1d32cfebcb44"},"schema_version":"1.0"},"canonical_sha256":"9691ced0659221509259715dbb3318b0861a056b2b897b8f0efd5dd0684577cb","source":{"kind":"arxiv","id":"1604.08027","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.08027","created_at":"2026-05-18T01:16:08Z"},{"alias_kind":"arxiv_version","alias_value":"1604.08027v1","created_at":"2026-05-18T01:16:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.08027","created_at":"2026-05-18T01:16:08Z"},{"alias_kind":"pith_short_12","alias_value":"S2I45UDFSIQV","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"S2I45UDFSIQVBESZ","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"S2I45UDF","created_at":"2026-05-18T12:30:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:S2I45UDFSIQVBESZOFO3WMYYWC","target":"record","payload":{"canonical_record":{"source":{"id":"1604.08027","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-04-27T11:58:08Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"fa34633263f0ebaee1e6fa09ebbc946227c9b8dae89a6dc5485897ae1972cd0b","abstract_canon_sha256":"94ec6ea0b97cb7080a9b337714738d85c58afcf9aaadda41b9ae1d32cfebcb44"},"schema_version":"1.0"},"canonical_sha256":"9691ced0659221509259715dbb3318b0861a056b2b897b8f0efd5dd0684577cb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:08.348842Z","signature_b64":"B9qwZrGYxWC/GK1mWzS6qN7fubOXwQBeBUFbxcicRn8VI+uHd5YzGnFNfSWPNFh8+z4o/7CHyuGMPWsQkOBhBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9691ced0659221509259715dbb3318b0861a056b2b897b8f0efd5dd0684577cb","last_reissued_at":"2026-05-18T01:16:08.348136Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:08.348136Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.08027","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":"2026-05-18T01:16:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MKVCi9jxXCs+26hk/MDbFQVyM1S0zZrK5E9LJhOQiazG2eTupi2t9tzwDS4ExhXQNUzzAuoZadbCiUOgqgESDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T06:01:14.944481Z"},"content_sha256":"92a3262a20da13e658f584f4ea3a8cb2288f656463d7f7fd906d0e83c1627774","schema_version":"1.0","event_id":"sha256:92a3262a20da13e658f584f4ea3a8cb2288f656463d7f7fd906d0e83c1627774"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:S2I45UDFSIQVBESZOFO3WMYYWC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Massless scalar Feynman diagrams: five loops and beyond","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"hep-th","authors_text":"David J. Broadhurst","submitted_at":"2016-04-27T11:58:08Z","abstract_excerpt":"Several powerful techniques for evaluating massless scalar Feynman diagrams are developed, viz: the solution of recurrence relations to evaluate diagrams with arbitrary numbers of loops in $n=4-2\\omega$ dimensions; the discovery and use of symmetry properties to restrict and compute Taylor series in $\\omega$; the reduction of triple sums over Chebyshev polynomials to products of Riemann zeta functions; the exploitation of conformal invariance to avoid four-dimensional Racah coefficients. As an example of the power of these techniques we evaluate all of the 216 diagrams, with 5 loops or less, w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.08027","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":""},"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":"2026-05-18T01:16:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z9GoQ2RHvZtyxfPlCU40F7jhRHllQr3u22NuHaILnIDJSS15pXeWY6FkCYPWi/Y849BkzizpNizXYS/0nrlJBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T06:01:14.944984Z"},"content_sha256":"ce478d05a5a95635b8addf90073d7cd6546d717f45ae42e8b0fb3b7dddce8e72","schema_version":"1.0","event_id":"sha256:ce478d05a5a95635b8addf90073d7cd6546d717f45ae42e8b0fb3b7dddce8e72"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S2I45UDFSIQVBESZOFO3WMYYWC/bundle.json","state_url":"https://pith.science/pith/S2I45UDFSIQVBESZOFO3WMYYWC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S2I45UDFSIQVBESZOFO3WMYYWC/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":"2026-05-22T06:01:14Z","links":{"resolver":"https://pith.science/pith/S2I45UDFSIQVBESZOFO3WMYYWC","bundle":"https://pith.science/pith/S2I45UDFSIQVBESZOFO3WMYYWC/bundle.json","state":"https://pith.science/pith/S2I45UDFSIQVBESZOFO3WMYYWC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S2I45UDFSIQVBESZOFO3WMYYWC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:S2I45UDFSIQVBESZOFO3WMYYWC","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":"94ec6ea0b97cb7080a9b337714738d85c58afcf9aaadda41b9ae1d32cfebcb44","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-04-27T11:58:08Z","title_canon_sha256":"fa34633263f0ebaee1e6fa09ebbc946227c9b8dae89a6dc5485897ae1972cd0b"},"schema_version":"1.0","source":{"id":"1604.08027","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.08027","created_at":"2026-05-18T01:16:08Z"},{"alias_kind":"arxiv_version","alias_value":"1604.08027v1","created_at":"2026-05-18T01:16:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.08027","created_at":"2026-05-18T01:16:08Z"},{"alias_kind":"pith_short_12","alias_value":"S2I45UDFSIQV","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"S2I45UDFSIQVBESZ","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"S2I45UDF","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:ce478d05a5a95635b8addf90073d7cd6546d717f45ae42e8b0fb3b7dddce8e72","target":"graph","created_at":"2026-05-18T01:16:08Z","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"},"paper":{"abstract_excerpt":"Several powerful techniques for evaluating massless scalar Feynman diagrams are developed, viz: the solution of recurrence relations to evaluate diagrams with arbitrary numbers of loops in $n=4-2\\omega$ dimensions; the discovery and use of symmetry properties to restrict and compute Taylor series in $\\omega$; the reduction of triple sums over Chebyshev polynomials to products of Riemann zeta functions; the exploitation of conformal invariance to avoid four-dimensional Racah coefficients. As an example of the power of these techniques we evaluate all of the 216 diagrams, with 5 loops or less, w","authors_text":"David J. Broadhurst","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-04-27T11:58:08Z","title":"Massless scalar Feynman diagrams: five loops and beyond"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.08027","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":"sha256:92a3262a20da13e658f584f4ea3a8cb2288f656463d7f7fd906d0e83c1627774","target":"record","created_at":"2026-05-18T01:16:08Z","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":"94ec6ea0b97cb7080a9b337714738d85c58afcf9aaadda41b9ae1d32cfebcb44","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-04-27T11:58:08Z","title_canon_sha256":"fa34633263f0ebaee1e6fa09ebbc946227c9b8dae89a6dc5485897ae1972cd0b"},"schema_version":"1.0","source":{"id":"1604.08027","kind":"arxiv","version":1}},"canonical_sha256":"9691ced0659221509259715dbb3318b0861a056b2b897b8f0efd5dd0684577cb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9691ced0659221509259715dbb3318b0861a056b2b897b8f0efd5dd0684577cb","first_computed_at":"2026-05-18T01:16:08.348136Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:08.348136Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B9qwZrGYxWC/GK1mWzS6qN7fubOXwQBeBUFbxcicRn8VI+uHd5YzGnFNfSWPNFh8+z4o/7CHyuGMPWsQkOBhBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:08.348842Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.08027","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:92a3262a20da13e658f584f4ea3a8cb2288f656463d7f7fd906d0e83c1627774","sha256:ce478d05a5a95635b8addf90073d7cd6546d717f45ae42e8b0fb3b7dddce8e72"],"state_sha256":"8586fd737fbb74e83a6147a67bd6d8f4978c28d81041a394b680075f9259fc5e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sa6YSn+Rjgb4l5VVWDmXjQz9bthBFj0frmxpsMsZJQ3LqSQ151it+zFmnhiCrYQjhi7kEXh5Ru/wdKTIzSh7Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T06:01:14.948353Z","bundle_sha256":"dd2f10041ebf32969619d0c8cccca9d443dea9af8b29c6379947ffd52c301ff2"}}