{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:JM6Y6E7ZEGFIONYSEQ6R23PMHU","short_pith_number":"pith:JM6Y6E7Z","canonical_record":{"source":{"id":"1409.5570","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-09-19T09:33:03Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"b8c3ac77a4bb42c7b4e29c13dda756d025143630b0e620a20946ebf503f29e2b","abstract_canon_sha256":"15748c8f3ce76006bc85a61a2cebe387f0d3517d51ea9d6fabfed39d043c7d62"},"schema_version":"1.0"},"canonical_sha256":"4b3d8f13f9218a873712243d1d6dec3d252e898b8f29dd4425e94c4c3e684227","source":{"kind":"arxiv","id":"1409.5570","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.5570","created_at":"2026-05-18T02:42:27Z"},{"alias_kind":"arxiv_version","alias_value":"1409.5570v1","created_at":"2026-05-18T02:42:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.5570","created_at":"2026-05-18T02:42:27Z"},{"alias_kind":"pith_short_12","alias_value":"JM6Y6E7ZEGFI","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"JM6Y6E7ZEGFIONYS","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"JM6Y6E7Z","created_at":"2026-05-18T12:28:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:JM6Y6E7ZEGFIONYSEQ6R23PMHU","target":"record","payload":{"canonical_record":{"source":{"id":"1409.5570","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-09-19T09:33:03Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"b8c3ac77a4bb42c7b4e29c13dda756d025143630b0e620a20946ebf503f29e2b","abstract_canon_sha256":"15748c8f3ce76006bc85a61a2cebe387f0d3517d51ea9d6fabfed39d043c7d62"},"schema_version":"1.0"},"canonical_sha256":"4b3d8f13f9218a873712243d1d6dec3d252e898b8f29dd4425e94c4c3e684227","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:42:27.030374Z","signature_b64":"SUFCQypFR2c4JJSMSmQJ3omGDyeHszBm/Sb6vHo4V5fWQk5hBiea9w+xI7cBLTNhe1FZm/F/QGx9I/BqoxsGDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4b3d8f13f9218a873712243d1d6dec3d252e898b8f29dd4425e94c4c3e684227","last_reissued_at":"2026-05-18T02:42:27.029429Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:42:27.029429Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.5570","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":"2026-05-18T02:42:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IX23C3X0eqN3xvOZ9bkoIDk1T8Ung0bhbku1rc5/irm+jp8BeO+ZqrwZ3ZdZhuUHXW/g5wqBM8Xjh3kIaoEtBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T01:17:23.666377Z"},"content_sha256":"ace93cd7eb072ca209d5b81f612151779cb49e93bb4eb3308f3c686621b0128e","schema_version":"1.0","event_id":"sha256:ace93cd7eb072ca209d5b81f612151779cb49e93bb4eb3308f3c686621b0128e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:JM6Y6E7ZEGFIONYSEQ6R23PMHU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Algebraic geometry informs perturbative quantum field theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"hep-th","authors_text":"David Broadhurst, Oliver Schnetz","submitted_at":"2014-09-19T09:33:03Z","abstract_excerpt":"Single-scale Feynman diagrams yield integrals that are periods, namely projective integrals of rational functions of Schwinger parameters. Algebraic geometry may therefore inform us of the types of number to which these integrals evaluate. We give examples at 3, 4 and 6 loops of massive Feynman diagrams that evaluate to Dirichlet $L$-series of modular forms and examples at 6, 7 and 8 loops of counterterms that evaluate to multiple zeta values or polylogarithms of the sixth root of unity. At 8 loops and beyond, algebraic geometry informs us that polylogs are insufficient for the evaluation of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.5570","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":"2026-05-18T02:42:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rAioByT3m5652/QBPRfnnITzpH7YFFkBJY7Rp3BvkkfQ+zeK3dz8/j+QYH3iAF/VuDgcSC3TBIDeNf6W45C3CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T01:17:23.666735Z"},"content_sha256":"03ce575a4f2c3c82d128968d12542a02bf810514a72b49daa61d0c920e2d4b73","schema_version":"1.0","event_id":"sha256:03ce575a4f2c3c82d128968d12542a02bf810514a72b49daa61d0c920e2d4b73"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JM6Y6E7ZEGFIONYSEQ6R23PMHU/bundle.json","state_url":"https://pith.science/pith/JM6Y6E7ZEGFIONYSEQ6R23PMHU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JM6Y6E7ZEGFIONYSEQ6R23PMHU/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":"2026-06-21T01:17:23Z","links":{"resolver":"https://pith.science/pith/JM6Y6E7ZEGFIONYSEQ6R23PMHU","bundle":"https://pith.science/pith/JM6Y6E7ZEGFIONYSEQ6R23PMHU/bundle.json","state":"https://pith.science/pith/JM6Y6E7ZEGFIONYSEQ6R23PMHU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JM6Y6E7ZEGFIONYSEQ6R23PMHU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:JM6Y6E7ZEGFIONYSEQ6R23PMHU","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":"15748c8f3ce76006bc85a61a2cebe387f0d3517d51ea9d6fabfed39d043c7d62","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-09-19T09:33:03Z","title_canon_sha256":"b8c3ac77a4bb42c7b4e29c13dda756d025143630b0e620a20946ebf503f29e2b"},"schema_version":"1.0","source":{"id":"1409.5570","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.5570","created_at":"2026-05-18T02:42:27Z"},{"alias_kind":"arxiv_version","alias_value":"1409.5570v1","created_at":"2026-05-18T02:42:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.5570","created_at":"2026-05-18T02:42:27Z"},{"alias_kind":"pith_short_12","alias_value":"JM6Y6E7ZEGFI","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"JM6Y6E7ZEGFIONYS","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"JM6Y6E7Z","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:03ce575a4f2c3c82d128968d12542a02bf810514a72b49daa61d0c920e2d4b73","target":"graph","created_at":"2026-05-18T02:42:27Z","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":"Single-scale Feynman diagrams yield integrals that are periods, namely projective integrals of rational functions of Schwinger parameters. Algebraic geometry may therefore inform us of the types of number to which these integrals evaluate. We give examples at 3, 4 and 6 loops of massive Feynman diagrams that evaluate to Dirichlet $L$-series of modular forms and examples at 6, 7 and 8 loops of counterterms that evaluate to multiple zeta values or polylogarithms of the sixth root of unity. At 8 loops and beyond, algebraic geometry informs us that polylogs are insufficient for the evaluation of t","authors_text":"David Broadhurst, Oliver Schnetz","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-09-19T09:33:03Z","title":"Algebraic geometry informs perturbative quantum field theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.5570","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:ace93cd7eb072ca209d5b81f612151779cb49e93bb4eb3308f3c686621b0128e","target":"record","created_at":"2026-05-18T02:42:27Z","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":"15748c8f3ce76006bc85a61a2cebe387f0d3517d51ea9d6fabfed39d043c7d62","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-09-19T09:33:03Z","title_canon_sha256":"b8c3ac77a4bb42c7b4e29c13dda756d025143630b0e620a20946ebf503f29e2b"},"schema_version":"1.0","source":{"id":"1409.5570","kind":"arxiv","version":1}},"canonical_sha256":"4b3d8f13f9218a873712243d1d6dec3d252e898b8f29dd4425e94c4c3e684227","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b3d8f13f9218a873712243d1d6dec3d252e898b8f29dd4425e94c4c3e684227","first_computed_at":"2026-05-18T02:42:27.029429Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:42:27.029429Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SUFCQypFR2c4JJSMSmQJ3omGDyeHszBm/Sb6vHo4V5fWQk5hBiea9w+xI7cBLTNhe1FZm/F/QGx9I/BqoxsGDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:42:27.030374Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.5570","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ace93cd7eb072ca209d5b81f612151779cb49e93bb4eb3308f3c686621b0128e","sha256:03ce575a4f2c3c82d128968d12542a02bf810514a72b49daa61d0c920e2d4b73"],"state_sha256":"7b321b66c1ff111e08d48fbe9bb15fbe4a5e963edfa9b3c8f8dc9735274fb7ab"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6OaYqFntuLpJQALU/iljux7b/JUUiy9hNeX/c6Ozp+Fj/WokYYk8+VhJWP2pw6mM1clfYI4Ps/DRQvXnVHXCCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T01:17:23.668714Z","bundle_sha256":"0fd6a7f3f53c6bfa33c70651082b1c3612c89b5dca26439d23c967f579f6a4ea"}}