{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2003:LIGKRXYMV4JDCQ3HFAFMLRTZJZ","short_pith_number":"pith:LIGKRXYM","canonical_record":{"source":{"id":"hep-ph/0307101","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-ph","submitted_at":"2003-07-08T18:47:05Z","cross_cats_sorted":[],"title_canon_sha256":"8e52c0571c1047b357070be855ecdb13c86cb5e8ca2f46d869a59a90c6764eb7","abstract_canon_sha256":"8faa70497b70d8f5eb32a7c9e25b1bd62d3d7fb12d135e596c5d5d49324f1e02"},"schema_version":"1.0"},"canonical_sha256":"5a0ca8df0caf12314367280ac5c6794e6775eda7e2a5237dbddb599aaa59c234","source":{"kind":"arxiv","id":"hep-ph/0307101","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-ph/0307101","created_at":"2026-05-18T02:36:30Z"},{"alias_kind":"arxiv_version","alias_value":"hep-ph/0307101v1","created_at":"2026-05-18T02:36:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-ph/0307101","created_at":"2026-05-18T02:36:30Z"},{"alias_kind":"pith_short_12","alias_value":"LIGKRXYMV4JD","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"LIGKRXYMV4JDCQ3H","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"LIGKRXYM","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2003:LIGKRXYMV4JDCQ3HFAFMLRTZJZ","target":"record","payload":{"canonical_record":{"source":{"id":"hep-ph/0307101","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-ph","submitted_at":"2003-07-08T18:47:05Z","cross_cats_sorted":[],"title_canon_sha256":"8e52c0571c1047b357070be855ecdb13c86cb5e8ca2f46d869a59a90c6764eb7","abstract_canon_sha256":"8faa70497b70d8f5eb32a7c9e25b1bd62d3d7fb12d135e596c5d5d49324f1e02"},"schema_version":"1.0"},"canonical_sha256":"5a0ca8df0caf12314367280ac5c6794e6775eda7e2a5237dbddb599aaa59c234","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:36:30.612751Z","signature_b64":"74yp5z6BSq+2JYmCJe8kJRR2zkCosmyX8W8FdGUQ2e5bW8bF6wLOTLJRXXHyYHVZVtLhDzDanClw/aYufcN5BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5a0ca8df0caf12314367280ac5c6794e6775eda7e2a5237dbddb599aaa59c234","last_reissued_at":"2026-05-18T02:36:30.612354Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:36:30.612354Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"hep-ph/0307101","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":"2026-05-18T02:36:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mL+4j/KfatmR674jDqG7yRsBwgJ9UDV8b4sbpksganZTTVlU13w+PJtlxZWH3hnvnI3FZo6NiBerIWug3Jv3BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T14:41:51.718264Z"},"content_sha256":"8732bdb1902cfa5f2f8a29bcb072e75172eac196aef15d7201718bd6b2046dcc","schema_version":"1.0","event_id":"sha256:8732bdb1902cfa5f2f8a29bcb072e75172eac196aef15d7201718bd6b2046dcc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2003:LIGKRXYMV4JDCQ3HFAFMLRTZJZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Evaluation of two-loop self-energy basis integrals using differential equations","license":"","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Stephen P. Martin","submitted_at":"2003-07-08T18:47:05Z","abstract_excerpt":"I study the Feynman integrals needed to compute two-loop self-energy functions for general masses and external momenta. A convenient basis for these functions consists of the four integrals obtained at the end of Tarasov's recurrence relation algorithm. The basis functions are modified here to include one-loop and two-loop counterterms to render them finite; this simplifies the presentation of results in practical applications. I find the derivatives of these basis functions with respect to all squared-mass arguments, the renormalization scale, and the external momentum invariant, and express "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-ph/0307101","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":"2026-05-18T02:36:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H2nPdQhsqrCMyLqtOziokThRzNzAdn/12rCUhB7HiThbgiVHjHrR3h6CVjohv2ecW3l0aRcyzNuYa+T2Hs1aAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T14:41:51.718734Z"},"content_sha256":"a04df9c66eee5f8ca5e6d082039cf488111cc95927824acd2208122e7211c830","schema_version":"1.0","event_id":"sha256:a04df9c66eee5f8ca5e6d082039cf488111cc95927824acd2208122e7211c830"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LIGKRXYMV4JDCQ3HFAFMLRTZJZ/bundle.json","state_url":"https://pith.science/pith/LIGKRXYMV4JDCQ3HFAFMLRTZJZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LIGKRXYMV4JDCQ3HFAFMLRTZJZ/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":"2026-08-08T14:41:51Z","links":{"resolver":"https://pith.science/pith/LIGKRXYMV4JDCQ3HFAFMLRTZJZ","bundle":"https://pith.science/pith/LIGKRXYMV4JDCQ3HFAFMLRTZJZ/bundle.json","state":"https://pith.science/pith/LIGKRXYMV4JDCQ3HFAFMLRTZJZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LIGKRXYMV4JDCQ3HFAFMLRTZJZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:LIGKRXYMV4JDCQ3HFAFMLRTZJZ","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":"8faa70497b70d8f5eb32a7c9e25b1bd62d3d7fb12d135e596c5d5d49324f1e02","cross_cats_sorted":[],"license":"","primary_cat":"hep-ph","submitted_at":"2003-07-08T18:47:05Z","title_canon_sha256":"8e52c0571c1047b357070be855ecdb13c86cb5e8ca2f46d869a59a90c6764eb7"},"schema_version":"1.0","source":{"id":"hep-ph/0307101","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-ph/0307101","created_at":"2026-05-18T02:36:30Z"},{"alias_kind":"arxiv_version","alias_value":"hep-ph/0307101v1","created_at":"2026-05-18T02:36:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-ph/0307101","created_at":"2026-05-18T02:36:30Z"},{"alias_kind":"pith_short_12","alias_value":"LIGKRXYMV4JD","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"LIGKRXYMV4JDCQ3H","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"LIGKRXYM","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:a04df9c66eee5f8ca5e6d082039cf488111cc95927824acd2208122e7211c830","target":"graph","created_at":"2026-05-18T02:36:30Z","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":"I study the Feynman integrals needed to compute two-loop self-energy functions for general masses and external momenta. A convenient basis for these functions consists of the four integrals obtained at the end of Tarasov's recurrence relation algorithm. The basis functions are modified here to include one-loop and two-loop counterterms to render them finite; this simplifies the presentation of results in practical applications. I find the derivatives of these basis functions with respect to all squared-mass arguments, the renormalization scale, and the external momentum invariant, and express ","authors_text":"Stephen P. Martin","cross_cats":[],"headline":"","license":"","primary_cat":"hep-ph","submitted_at":"2003-07-08T18:47:05Z","title":"Evaluation of two-loop self-energy basis integrals using differential equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-ph/0307101","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":"sha256:8732bdb1902cfa5f2f8a29bcb072e75172eac196aef15d7201718bd6b2046dcc","target":"record","created_at":"2026-05-18T02:36:30Z","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":"8faa70497b70d8f5eb32a7c9e25b1bd62d3d7fb12d135e596c5d5d49324f1e02","cross_cats_sorted":[],"license":"","primary_cat":"hep-ph","submitted_at":"2003-07-08T18:47:05Z","title_canon_sha256":"8e52c0571c1047b357070be855ecdb13c86cb5e8ca2f46d869a59a90c6764eb7"},"schema_version":"1.0","source":{"id":"hep-ph/0307101","kind":"arxiv","version":1}},"canonical_sha256":"5a0ca8df0caf12314367280ac5c6794e6775eda7e2a5237dbddb599aaa59c234","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5a0ca8df0caf12314367280ac5c6794e6775eda7e2a5237dbddb599aaa59c234","first_computed_at":"2026-05-18T02:36:30.612354Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:36:30.612354Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"74yp5z6BSq+2JYmCJe8kJRR2zkCosmyX8W8FdGUQ2e5bW8bF6wLOTLJRXXHyYHVZVtLhDzDanClw/aYufcN5BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:36:30.612751Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-ph/0307101","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8732bdb1902cfa5f2f8a29bcb072e75172eac196aef15d7201718bd6b2046dcc","sha256:a04df9c66eee5f8ca5e6d082039cf488111cc95927824acd2208122e7211c830"],"state_sha256":"eb33ee2b228b4844007805b6078eadadaa1c020c7894893fa827cc2ab21eefda"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LzaRHIBgkpZXon20ebxgo5Gd8a+Ok6MgXWcbLecf6Ge1pndFRCn3orybvb8ZbDhWDGKlgM/LmIYABWmAykYjDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T14:41:51.723532Z","bundle_sha256":"85c473e87f4de778e8d741619d2e7ef346e3a8d37aaf060500d4ac3614379a56"}}