{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:EB6B3CHHSUYKXAEF2J5KLV55YC","short_pith_number":"pith:EB6B3CHH","schema_version":"1.0","canonical_sha256":"207c1d88e79530ab8085d27aa5d7bdc09373d69f363fb90813f60e0cc6eb3221","source":{"kind":"arxiv","id":"hep-ph/0607185","version":1},"attestation_state":"computed","paper":{"title":"Master Integrals for Massless Three-Loop Form Factors: One-Loop and Two-Loop Insertions","license":"","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"C. Studerus, G. Heinrich, T. Gehrmann, T. Huber","submitted_at":"2006-07-17T10:24:31Z","abstract_excerpt":"The three-loop form factors in massless QCD can be expressed as a linear combination of master integrals. Besides a number of master integrals which factorise into products of one-loop and two-loop integrals, one finds 16 genuine three-loop integrals. Of these, six have the form of a bubble insertion inside a one-loop or two-loop vertex integral. We compute all master integrals with these insertion topologies."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"hep-ph/0607185","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-ph","submitted_at":"2006-07-17T10:24:31Z","cross_cats_sorted":[],"title_canon_sha256":"42e297af3903213e06acf0d25ee55c62e101db7b8a5becdd60670718ceef55de","abstract_canon_sha256":"1b13b6117f2d7ca40372df14c0042d2e38c28a8d605a22be7630acb5e8030eed"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T17:24:39.684909Z","signature_b64":"bjQXI2XNnsYKiYGM4jow+HsUQ3J5DhtiIPAng9G38dTuCnhKZOfaJ42IGqzqQqSuk2COnen1IOKbs6UTsmUNAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"207c1d88e79530ab8085d27aa5d7bdc09373d69f363fb90813f60e0cc6eb3221","last_reissued_at":"2026-07-04T17:24:39.684440Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T17:24:39.684440Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Master Integrals for Massless Three-Loop Form Factors: One-Loop and Two-Loop Insertions","license":"","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"C. Studerus, G. Heinrich, T. Gehrmann, T. Huber","submitted_at":"2006-07-17T10:24:31Z","abstract_excerpt":"The three-loop form factors in massless QCD can be expressed as a linear combination of master integrals. Besides a number of master integrals which factorise into products of one-loop and two-loop integrals, one finds 16 genuine three-loop integrals. Of these, six have the form of a bubble insertion inside a one-loop or two-loop vertex integral. We compute all master integrals with these insertion topologies."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-ph/0607185","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/hep-ph/0607185/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"hep-ph/0607185","created_at":"2026-07-04T17:24:39.684511+00:00"},{"alias_kind":"arxiv_version","alias_value":"hep-ph/0607185v1","created_at":"2026-07-04T17:24:39.684511+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-ph/0607185","created_at":"2026-07-04T17:24:39.684511+00:00"},{"alias_kind":"pith_short_12","alias_value":"EB6B3CHHSUYK","created_at":"2026-07-04T17:24:39.684511+00:00"},{"alias_kind":"pith_short_16","alias_value":"EB6B3CHHSUYKXAEF","created_at":"2026-07-04T17:24:39.684511+00:00"},{"alias_kind":"pith_short_8","alias_value":"EB6B3CHH","created_at":"2026-07-04T17:24:39.684511+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2505.22595","citing_title":"Off-shell form factor: factorization is violated","ref_index":74,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/EB6B3CHHSUYKXAEF2J5KLV55YC","json":"https://pith.science/pith/EB6B3CHHSUYKXAEF2J5KLV55YC.json","graph_json":"https://pith.science/api/pith-number/EB6B3CHHSUYKXAEF2J5KLV55YC/graph.json","events_json":"https://pith.science/api/pith-number/EB6B3CHHSUYKXAEF2J5KLV55YC/events.json","paper":"https://pith.science/paper/EB6B3CHH"},"agent_actions":{"view_html":"https://pith.science/pith/EB6B3CHHSUYKXAEF2J5KLV55YC","download_json":"https://pith.science/pith/EB6B3CHHSUYKXAEF2J5KLV55YC.json","view_paper":"https://pith.science/paper/EB6B3CHH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=hep-ph/0607185&json=true","fetch_graph":"https://pith.science/api/pith-number/EB6B3CHHSUYKXAEF2J5KLV55YC/graph.json","fetch_events":"https://pith.science/api/pith-number/EB6B3CHHSUYKXAEF2J5KLV55YC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EB6B3CHHSUYKXAEF2J5KLV55YC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EB6B3CHHSUYKXAEF2J5KLV55YC/action/storage_attestation","attest_author":"https://pith.science/pith/EB6B3CHHSUYKXAEF2J5KLV55YC/action/author_attestation","sign_citation":"https://pith.science/pith/EB6B3CHHSUYKXAEF2J5KLV55YC/action/citation_signature","submit_replication":"https://pith.science/pith/EB6B3CHHSUYKXAEF2J5KLV55YC/action/replication_record"}},"created_at":"2026-07-04T17:24:39.684511+00:00","updated_at":"2026-07-04T17:24:39.684511+00:00"}