{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:GALUTNBPEVKZYKZVZ77IO6K7TK","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":"b78afa379f2d3dcdaacedeedc8cab9f7d03d49b64355b5bea598d26b5a7db8e9","cross_cats_sorted":[],"license":"","primary_cat":"hep-ph","submitted_at":"2001-06-11T04:09:22Z","title_canon_sha256":"39e3586cae1d4cbf51483ee25e75f572ca6eb4e1f7b47f5c015fece1f2592aac"},"schema_version":"1.0","source":{"id":"hep-ph/0106100","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-ph/0106100","created_at":"2026-05-18T01:06:14Z"},{"alias_kind":"arxiv_version","alias_value":"hep-ph/0106100v1","created_at":"2026-05-18T01:06:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-ph/0106100","created_at":"2026-05-18T01:06:14Z"},{"alias_kind":"pith_short_12","alias_value":"GALUTNBPEVKZ","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"GALUTNBPEVKZYKZV","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"GALUTNBP","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:b1b69768fe7374330a6cf083e759db83374bddc729d25936a3c885e5cd64a5ea","target":"graph","created_at":"2026-05-18T01:06:14Z","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":"The evolution of polarized quark distribution functions is taken into account the gluon emission and absorption, quark pair production and annihilation processes and treated by a statistical method which provides quark distribution functions at small $Q^2$. The evolution function of quark distributions is derived and solved by numerical methods. Then the $Q^2$ dependent and $\\alpha_{s}$ dependent structure functions $F_{2}(x, Q^{2})$ are obtained and the example of it, the proton structure function, is calculated, whose increase and decrease tendency with $\\alpha_{s}$ at different $x$ is consi","authors_text":"Hai Lin","cross_cats":[],"headline":"","license":"","primary_cat":"hep-ph","submitted_at":"2001-06-11T04:09:22Z","title":"A Statistical Treatment to the Evolution Equation for Quark Distributions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-ph/0106100","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:c26d63dd914eb8417cfe476a1ac9755fd9307c99b2a9834b9cb2723118cb6b9e","target":"record","created_at":"2026-05-18T01:06:14Z","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":"b78afa379f2d3dcdaacedeedc8cab9f7d03d49b64355b5bea598d26b5a7db8e9","cross_cats_sorted":[],"license":"","primary_cat":"hep-ph","submitted_at":"2001-06-11T04:09:22Z","title_canon_sha256":"39e3586cae1d4cbf51483ee25e75f572ca6eb4e1f7b47f5c015fece1f2592aac"},"schema_version":"1.0","source":{"id":"hep-ph/0106100","kind":"arxiv","version":1}},"canonical_sha256":"301749b42f25559c2b35cffe87795f9ab0f197af6c94ce01183d75de2f269dc1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"301749b42f25559c2b35cffe87795f9ab0f197af6c94ce01183d75de2f269dc1","first_computed_at":"2026-05-18T01:06:14.759128Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:06:14.759128Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8At/LMD4HTqZd6uQ2AfiDShaG765mO45pDdd1ijCBgpSw9MDcaua/w41FkLbIIomATilHPqF+hS8PzjB6Al9CA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:06:14.759711Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-ph/0106100","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c26d63dd914eb8417cfe476a1ac9755fd9307c99b2a9834b9cb2723118cb6b9e","sha256:b1b69768fe7374330a6cf083e759db83374bddc729d25936a3c885e5cd64a5ea"],"state_sha256":"1e7bf03d8482c29b2660bb54f651dc70877828b02df4b6a1fd10176197e79d7e"}