{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:TJ4ATQNYFS3YQHIDQZARDK5QGY","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":"4a3ffba822688ff2302f4d06599dd04d0270db6b8828d2abb9f20a7fdd9a652d","cross_cats_sorted":[],"license":"","primary_cat":"hep-ph","submitted_at":"2000-06-14T13:41:10Z","title_canon_sha256":"30f884d0669b5411e3e81f125fcffd88ac7adf80066ecb811dca5ac5f6b9b101"},"schema_version":"1.0","source":{"id":"hep-ph/0006154","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-ph/0006154","created_at":"2026-07-04T16:20:11Z"},{"alias_kind":"arxiv_version","alias_value":"hep-ph/0006154v1","created_at":"2026-07-04T16:20:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-ph/0006154","created_at":"2026-07-04T16:20:11Z"},{"alias_kind":"pith_short_12","alias_value":"TJ4ATQNYFS3Y","created_at":"2026-07-04T16:20:11Z"},{"alias_kind":"pith_short_16","alias_value":"TJ4ATQNYFS3YQHID","created_at":"2026-07-04T16:20:11Z"},{"alias_kind":"pith_short_8","alias_value":"TJ4ATQNY","created_at":"2026-07-04T16:20:11Z"}],"graph_snapshots":[{"event_id":"sha256:8e8c11b87d2dd18e73940ffe8993185d7bf6091e3ed987fa3fec978c8cd8d141","target":"graph","created_at":"2026-07-04T16:20:11Z","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/0006154/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the next-to-next-to-leading order (NNLO) evolution of flavour singlet parton densities and structure functions in massless perturbative QCD. Present information on the corresponding three-loop splitting functions is used to derive parametrizations of these quantities, including Bjorken-x dependent estimates of their residual uncertainties. Compact expressions are also provided for the exactly known, but in part rather lengthy two-loop singlet coefficient functions. The size of the NNLO corrections and their effect on the stability under variations of the renormalization and mass-facto","authors_text":"A. Vogt (Leiden University), W.L. van Neerven","cross_cats":[],"headline":"","license":"","primary_cat":"hep-ph","submitted_at":"2000-06-14T13:41:10Z","title":"NNLO evolution of deep-inelastic structure functions: the singlet case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-ph/0006154","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":"sha256:8b823267b4f89d0ff25c599ee2c833f70cc1ea0e5b9979b299e16361303a91a3","target":"record","created_at":"2026-07-04T16:20:11Z","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":"4a3ffba822688ff2302f4d06599dd04d0270db6b8828d2abb9f20a7fdd9a652d","cross_cats_sorted":[],"license":"","primary_cat":"hep-ph","submitted_at":"2000-06-14T13:41:10Z","title_canon_sha256":"30f884d0669b5411e3e81f125fcffd88ac7adf80066ecb811dca5ac5f6b9b101"},"schema_version":"1.0","source":{"id":"hep-ph/0006154","kind":"arxiv","version":1}},"canonical_sha256":"9a7809c1b82cb7881d03864111abb03604855352c97b06c88138dd94822710e4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9a7809c1b82cb7881d03864111abb03604855352c97b06c88138dd94822710e4","first_computed_at":"2026-07-04T16:20:11.751952Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:20:11.751952Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u/uBavR8j+EylEeZGO3vbN1M1j3SqjKRCOzs9OEiRjULkr3yMhBvnz/Jsew7Wcjs672V0NLfdcbBY4SxMpwoBw==","signature_status":"signed_v1","signed_at":"2026-07-04T16:20:11.752360Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-ph/0006154","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8b823267b4f89d0ff25c599ee2c833f70cc1ea0e5b9979b299e16361303a91a3","sha256:8e8c11b87d2dd18e73940ffe8993185d7bf6091e3ed987fa3fec978c8cd8d141"],"state_sha256":"56f7a06fd78292d03824ca557d9c20fa229447f53ba50b4df71cce14bf201062"}