{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:S2QYVJU2ZZMT4KGJKIAMOM4Y42","short_pith_number":"pith:S2QYVJU2","canonical_record":{"source":{"id":"1004.1149","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2010-04-07T18:38:02Z","cross_cats_sorted":[],"title_canon_sha256":"5e9af98a41bdebebc4812481e86bccfea70a9bfb4ad67d24501db651aa0381cf","abstract_canon_sha256":"86be080cf977c1df9ed1bbb44754bc322f9735c161f65d26a55d85cc5db4597e"},"schema_version":"1.0"},"canonical_sha256":"96a18aa69ace593e28c95200c73398e6a7a2b1691df14cf7359e97e6307ff693","source":{"kind":"arxiv","id":"1004.1149","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.1149","created_at":"2026-05-18T02:33:34Z"},{"alias_kind":"arxiv_version","alias_value":"1004.1149v1","created_at":"2026-05-18T02:33:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.1149","created_at":"2026-05-18T02:33:34Z"},{"alias_kind":"pith_short_12","alias_value":"S2QYVJU2ZZMT","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"S2QYVJU2ZZMT4KGJ","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"S2QYVJU2","created_at":"2026-05-18T12:26:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:S2QYVJU2ZZMT4KGJKIAMOM4Y42","target":"record","payload":{"canonical_record":{"source":{"id":"1004.1149","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2010-04-07T18:38:02Z","cross_cats_sorted":[],"title_canon_sha256":"5e9af98a41bdebebc4812481e86bccfea70a9bfb4ad67d24501db651aa0381cf","abstract_canon_sha256":"86be080cf977c1df9ed1bbb44754bc322f9735c161f65d26a55d85cc5db4597e"},"schema_version":"1.0"},"canonical_sha256":"96a18aa69ace593e28c95200c73398e6a7a2b1691df14cf7359e97e6307ff693","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:33:34.794959Z","signature_b64":"f9nZyFbLqvbzDXRKAjRBlh8gRiWm01t8o388NYo9Rt7Kxb6V/VrhENnlESQdpph6V1TasNkAKeJh3pnIjK26CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"96a18aa69ace593e28c95200c73398e6a7a2b1691df14cf7359e97e6307ff693","last_reissued_at":"2026-05-18T02:33:34.794550Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:33:34.794550Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1004.1149","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":"2026-05-18T02:33:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3d90rN2ksboxTnhZfa9Wc+o3dlRAvMEJMJEIwN7eDqDHnqyb+J00WaTaF6zCqLICbvqpRPw5nyLjuskv50MFDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T22:23:08.148930Z"},"content_sha256":"2227d91e29b21841b3c3fa6d42e435f96567f9a58aeec8136e502acfccda0d71","schema_version":"1.0","event_id":"sha256:2227d91e29b21841b3c3fa6d42e435f96567f9a58aeec8136e502acfccda0d71"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:S2QYVJU2ZZMT4KGJKIAMOM4Y42","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Four Loop Massless Propagators: a Numerical Evaluation of All Master Integrals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"A.V. Smirnov, M. Tentyukov","submitted_at":"2010-04-07T18:38:02Z","abstract_excerpt":"We present numerical results which are needed to evaluate all non-trivial  master integrals for four-loop massless propagators, confirming the recent analytic results of[1]and evaluating an extra order in $\\ep$ expansion for each master integral."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.1149","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":"2026-05-18T02:33:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"goivH+CKf8VZb4UZeuXNCrlqiGoK2B7cE4e++8rPmUecl77d/AQ9n716RGE4c83YmEnt5AI7v4mU7evku+HbBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T22:23:08.149529Z"},"content_sha256":"d5c61b158fa716e7c975d05c15bc89874e5ead9c6e9eba8217eb841d9f93fa9a","schema_version":"1.0","event_id":"sha256:d5c61b158fa716e7c975d05c15bc89874e5ead9c6e9eba8217eb841d9f93fa9a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S2QYVJU2ZZMT4KGJKIAMOM4Y42/bundle.json","state_url":"https://pith.science/pith/S2QYVJU2ZZMT4KGJKIAMOM4Y42/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S2QYVJU2ZZMT4KGJKIAMOM4Y42/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":"2026-06-04T22:23:08Z","links":{"resolver":"https://pith.science/pith/S2QYVJU2ZZMT4KGJKIAMOM4Y42","bundle":"https://pith.science/pith/S2QYVJU2ZZMT4KGJKIAMOM4Y42/bundle.json","state":"https://pith.science/pith/S2QYVJU2ZZMT4KGJKIAMOM4Y42/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S2QYVJU2ZZMT4KGJKIAMOM4Y42/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:S2QYVJU2ZZMT4KGJKIAMOM4Y42","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":"86be080cf977c1df9ed1bbb44754bc322f9735c161f65d26a55d85cc5db4597e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2010-04-07T18:38:02Z","title_canon_sha256":"5e9af98a41bdebebc4812481e86bccfea70a9bfb4ad67d24501db651aa0381cf"},"schema_version":"1.0","source":{"id":"1004.1149","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.1149","created_at":"2026-05-18T02:33:34Z"},{"alias_kind":"arxiv_version","alias_value":"1004.1149v1","created_at":"2026-05-18T02:33:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.1149","created_at":"2026-05-18T02:33:34Z"},{"alias_kind":"pith_short_12","alias_value":"S2QYVJU2ZZMT","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"S2QYVJU2ZZMT4KGJ","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"S2QYVJU2","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:d5c61b158fa716e7c975d05c15bc89874e5ead9c6e9eba8217eb841d9f93fa9a","target":"graph","created_at":"2026-05-18T02:33:34Z","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":"We present numerical results which are needed to evaluate all non-trivial  master integrals for four-loop massless propagators, confirming the recent analytic results of[1]and evaluating an extra order in $\\ep$ expansion for each master integral.","authors_text":"A.V. Smirnov, M. Tentyukov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2010-04-07T18:38:02Z","title":"Four Loop Massless Propagators: a Numerical Evaluation of All Master Integrals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.1149","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":"sha256:2227d91e29b21841b3c3fa6d42e435f96567f9a58aeec8136e502acfccda0d71","target":"record","created_at":"2026-05-18T02:33:34Z","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":"86be080cf977c1df9ed1bbb44754bc322f9735c161f65d26a55d85cc5db4597e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2010-04-07T18:38:02Z","title_canon_sha256":"5e9af98a41bdebebc4812481e86bccfea70a9bfb4ad67d24501db651aa0381cf"},"schema_version":"1.0","source":{"id":"1004.1149","kind":"arxiv","version":1}},"canonical_sha256":"96a18aa69ace593e28c95200c73398e6a7a2b1691df14cf7359e97e6307ff693","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"96a18aa69ace593e28c95200c73398e6a7a2b1691df14cf7359e97e6307ff693","first_computed_at":"2026-05-18T02:33:34.794550Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:33:34.794550Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f9nZyFbLqvbzDXRKAjRBlh8gRiWm01t8o388NYo9Rt7Kxb6V/VrhENnlESQdpph6V1TasNkAKeJh3pnIjK26CA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:33:34.794959Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.1149","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2227d91e29b21841b3c3fa6d42e435f96567f9a58aeec8136e502acfccda0d71","sha256:d5c61b158fa716e7c975d05c15bc89874e5ead9c6e9eba8217eb841d9f93fa9a"],"state_sha256":"1947fcebecc77e6a97a501029c4ed72080771dc394926c4e62bde0fdab4a2a3b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NMDFyz2kFtWnbK+0RxiwgypAzARoTKUYWzeIZd/JOxOjf0BC5XxB0o/nOHIp6j/+HixYZdha/XmFy2rNTeXDBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T22:23:08.152865Z","bundle_sha256":"04928959012c87166eeaab8090012b26e47bcfbff1d584bfecf2f7db5919dd3b"}}