{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1999:Q4KMUNH727EKG6X7PPCMLJJUCM","short_pith_number":"pith:Q4KMUNH7","canonical_record":{"source":{"id":"hep-ph/9912355","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-ph","submitted_at":"1999-12-15T14:37:37Z","cross_cats_sorted":[],"title_canon_sha256":"24c537f1dcf7f07a0fa1c4a21182a51471f6f3e9d2bb63028647d0cfe94a9e46","abstract_canon_sha256":"02d32bc6445acb8678d3f6f3cab8ff67a649d552b7e610a662c66f1e09e97696"},"schema_version":"1.0"},"canonical_sha256":"8714ca34ffd7c8a37aff7bc4c5a534133fe0f45d37b4ab2493233e64d167a681","source":{"kind":"arxiv","id":"hep-ph/9912355","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-ph/9912355","created_at":"2026-07-04T16:14:35Z"},{"alias_kind":"arxiv_version","alias_value":"hep-ph/9912355v1","created_at":"2026-07-04T16:14:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-ph/9912355","created_at":"2026-07-04T16:14:35Z"},{"alias_kind":"pith_short_12","alias_value":"Q4KMUNH727EK","created_at":"2026-07-04T16:14:35Z"},{"alias_kind":"pith_short_16","alias_value":"Q4KMUNH727EKG6X7","created_at":"2026-07-04T16:14:35Z"},{"alias_kind":"pith_short_8","alias_value":"Q4KMUNH7","created_at":"2026-07-04T16:14:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1999:Q4KMUNH727EKG6X7PPCMLJJUCM","target":"record","payload":{"canonical_record":{"source":{"id":"hep-ph/9912355","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-ph","submitted_at":"1999-12-15T14:37:37Z","cross_cats_sorted":[],"title_canon_sha256":"24c537f1dcf7f07a0fa1c4a21182a51471f6f3e9d2bb63028647d0cfe94a9e46","abstract_canon_sha256":"02d32bc6445acb8678d3f6f3cab8ff67a649d552b7e610a662c66f1e09e97696"},"schema_version":"1.0"},"canonical_sha256":"8714ca34ffd7c8a37aff7bc4c5a534133fe0f45d37b4ab2493233e64d167a681","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:14:35.809569Z","signature_b64":"rLVq0IqwPO4IIDTiFwwuLjvaBuF0gpxK+REdVeVse4us/pMEx/pPMBGD9kljyXOHFreWVkn8+KqbM9EdQ+hrAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8714ca34ffd7c8a37aff7bc4c5a534133fe0f45d37b4ab2493233e64d167a681","last_reissued_at":"2026-07-04T16:14:35.809006Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:14:35.809006Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"hep-ph/9912355","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":"2026-07-04T16:14:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gCBry/kCVhg2sBYa15naRn52OYF8Wb9qwYLb3JFdmG72Ae0zy41wurmq8LjY7Y6ioYzTLibSFdARAI4ryJWgCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T16:06:45.843659Z"},"content_sha256":"b53dac16c3549a1297b95a3d478efa7e7a54879442afcb0bfc7037306126d0d5","schema_version":"1.0","event_id":"sha256:b53dac16c3549a1297b95a3d478efa7e7a54879442afcb0bfc7037306126d0d5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1999:Q4KMUNH727EKG6X7PPCMLJJUCM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Deep Inelastic Structure Functions at two Loops","license":"","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"J.A.M. Vermaseren, S. Moch","submitted_at":"1999-12-15T14:37:37Z","abstract_excerpt":"We present the analytic calculation of the Mellin moments of the structure functions F_2, F_3 and F_L in perturbative QCD up to second order corrections and in leading twist approximation. We calculate the 2-loop contributions to the anomalous dimensions of the singlet and non-singlet operator matrix elements and the 2-loop coefficient functions of F_2, F_3 and F_L. We perform the inverse Mellin transformation analytically and find our results in agreement with earlier calculations in the literature by Zijlstra and van Neerven."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-ph/9912355","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/9912355/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T16:14:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UZA34nF623gTreVplhsSQgJ4kW+5qmp+5AMUzgdeQXmehbQgkKWiOvhU3o96VxyeyIAzLVEOcdBMZWi6p7igBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T16:06:45.844373Z"},"content_sha256":"775fee82eee52a6ffc70b5b0ef6ed500765e89dab513b4182141b90c621ab637","schema_version":"1.0","event_id":"sha256:775fee82eee52a6ffc70b5b0ef6ed500765e89dab513b4182141b90c621ab637"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q4KMUNH727EKG6X7PPCMLJJUCM/bundle.json","state_url":"https://pith.science/pith/Q4KMUNH727EKG6X7PPCMLJJUCM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q4KMUNH727EKG6X7PPCMLJJUCM/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":"2026-08-04T16:06:45Z","links":{"resolver":"https://pith.science/pith/Q4KMUNH727EKG6X7PPCMLJJUCM","bundle":"https://pith.science/pith/Q4KMUNH727EKG6X7PPCMLJJUCM/bundle.json","state":"https://pith.science/pith/Q4KMUNH727EKG6X7PPCMLJJUCM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q4KMUNH727EKG6X7PPCMLJJUCM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1999:Q4KMUNH727EKG6X7PPCMLJJUCM","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":"02d32bc6445acb8678d3f6f3cab8ff67a649d552b7e610a662c66f1e09e97696","cross_cats_sorted":[],"license":"","primary_cat":"hep-ph","submitted_at":"1999-12-15T14:37:37Z","title_canon_sha256":"24c537f1dcf7f07a0fa1c4a21182a51471f6f3e9d2bb63028647d0cfe94a9e46"},"schema_version":"1.0","source":{"id":"hep-ph/9912355","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-ph/9912355","created_at":"2026-07-04T16:14:35Z"},{"alias_kind":"arxiv_version","alias_value":"hep-ph/9912355v1","created_at":"2026-07-04T16:14:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-ph/9912355","created_at":"2026-07-04T16:14:35Z"},{"alias_kind":"pith_short_12","alias_value":"Q4KMUNH727EK","created_at":"2026-07-04T16:14:35Z"},{"alias_kind":"pith_short_16","alias_value":"Q4KMUNH727EKG6X7","created_at":"2026-07-04T16:14:35Z"},{"alias_kind":"pith_short_8","alias_value":"Q4KMUNH7","created_at":"2026-07-04T16:14:35Z"}],"graph_snapshots":[{"event_id":"sha256:775fee82eee52a6ffc70b5b0ef6ed500765e89dab513b4182141b90c621ab637","target":"graph","created_at":"2026-07-04T16:14:35Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/hep-ph/9912355/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present the analytic calculation of the Mellin moments of the structure functions F_2, F_3 and F_L in perturbative QCD up to second order corrections and in leading twist approximation. We calculate the 2-loop contributions to the anomalous dimensions of the singlet and non-singlet operator matrix elements and the 2-loop coefficient functions of F_2, F_3 and F_L. We perform the inverse Mellin transformation analytically and find our results in agreement with earlier calculations in the literature by Zijlstra and van Neerven.","authors_text":"J.A.M. Vermaseren, S. Moch","cross_cats":[],"headline":"","license":"","primary_cat":"hep-ph","submitted_at":"1999-12-15T14:37:37Z","title":"Deep Inelastic Structure Functions at two Loops"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-ph/9912355","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:b53dac16c3549a1297b95a3d478efa7e7a54879442afcb0bfc7037306126d0d5","target":"record","created_at":"2026-07-04T16:14:35Z","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":"02d32bc6445acb8678d3f6f3cab8ff67a649d552b7e610a662c66f1e09e97696","cross_cats_sorted":[],"license":"","primary_cat":"hep-ph","submitted_at":"1999-12-15T14:37:37Z","title_canon_sha256":"24c537f1dcf7f07a0fa1c4a21182a51471f6f3e9d2bb63028647d0cfe94a9e46"},"schema_version":"1.0","source":{"id":"hep-ph/9912355","kind":"arxiv","version":1}},"canonical_sha256":"8714ca34ffd7c8a37aff7bc4c5a534133fe0f45d37b4ab2493233e64d167a681","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8714ca34ffd7c8a37aff7bc4c5a534133fe0f45d37b4ab2493233e64d167a681","first_computed_at":"2026-07-04T16:14:35.809006Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:14:35.809006Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rLVq0IqwPO4IIDTiFwwuLjvaBuF0gpxK+REdVeVse4us/pMEx/pPMBGD9kljyXOHFreWVkn8+KqbM9EdQ+hrAQ==","signature_status":"signed_v1","signed_at":"2026-07-04T16:14:35.809569Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-ph/9912355","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b53dac16c3549a1297b95a3d478efa7e7a54879442afcb0bfc7037306126d0d5","sha256:775fee82eee52a6ffc70b5b0ef6ed500765e89dab513b4182141b90c621ab637"],"state_sha256":"0158f2b7bfbf6d684f218a35525c7bd36c638d574d00c964e32ed75549b0ceba"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PqAMW/3Y/cfnJQ6NlRcyJTWkm6mhq953OEnlqRNStxrAhm7yQCim4535Fzw+FBiCSGP0r5cpr0ElMiaMhrsUBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T16:06:45.856486Z","bundle_sha256":"c95d4249dd18906d67146ddf9080866b1f8956335dcf494882a067f47441c389"}}