{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:HHEA4QIP6XDKL5T7BP5O6RY5GJ","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":"7e66a949ba6ba1ddf78312259ab5fa43270f8efc48c3a87afd36b813ad6e8686","cross_cats_sorted":["hep-th","nucl-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2009-05-25T13:40:55Z","title_canon_sha256":"168d881d97ad98aee7e7c00051e76c093462383b1ad1356d57e70639644eae65"},"schema_version":"1.0","source":{"id":"0905.3922","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0905.3922","created_at":"2026-05-18T03:40:03Z"},{"alias_kind":"arxiv_version","alias_value":"0905.3922v3","created_at":"2026-05-18T03:40:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.3922","created_at":"2026-05-18T03:40:03Z"},{"alias_kind":"pith_short_12","alias_value":"HHEA4QIP6XDK","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"HHEA4QIP6XDKL5T7","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"HHEA4QIP","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:a5957fd5d879262ed54acda5630be2c28e6ebe59b19b028c2d45501f12701eed","target":"graph","created_at":"2026-05-18T03:40:03Z","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 $Q^2$ evolution of fragmentation function in non-equilibrium QCD by using DGLAP evolution equation may be necessary to study hadron formation from quark-gluon plasma at RHIC and LHC. In this paper we study splitting functions in non-equilibrium QCD by using Schwinger-Keldysh closed-time path integral formalism. For quarks and gluons with arbitrary non-equilibrium distribution functions $f_q({\\vec p})$ and $f_g({\\vec p})$, we derive expressions for quark and gluon splitting functions in non-equilibrium QCD at leading order in $\\alpha_s$. We make a comparison of these splitting functions wit","authors_text":"Gouranga C. Nayak","cross_cats":["hep-th","nucl-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2009-05-25T13:40:55Z","title":"Altarelli-Parisi Equation in Non-Equilibrium QCD"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.3922","kind":"arxiv","version":3},"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:c23ea9326d53e106479fe8a73cd048adc4d3a5b2c903313f2347dd6f20d2cd28","target":"record","created_at":"2026-05-18T03:40:03Z","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":"7e66a949ba6ba1ddf78312259ab5fa43270f8efc48c3a87afd36b813ad6e8686","cross_cats_sorted":["hep-th","nucl-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2009-05-25T13:40:55Z","title_canon_sha256":"168d881d97ad98aee7e7c00051e76c093462383b1ad1356d57e70639644eae65"},"schema_version":"1.0","source":{"id":"0905.3922","kind":"arxiv","version":3}},"canonical_sha256":"39c80e410ff5c6a5f67f0bfaef471d3249656db956fa3e218daaae9c4a4c0b39","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"39c80e410ff5c6a5f67f0bfaef471d3249656db956fa3e218daaae9c4a4c0b39","first_computed_at":"2026-05-18T03:40:03.833688Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:40:03.833688Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YfvtaIiFNiT9a9+V2WrZyFv5Fq4qVICS5rsJ4HSAYBCiFceiwDaPV597P4tcY8GnRcZoKySQE0d/Tqa7TtohDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:40:03.834190Z","signed_message":"canonical_sha256_bytes"},"source_id":"0905.3922","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c23ea9326d53e106479fe8a73cd048adc4d3a5b2c903313f2347dd6f20d2cd28","sha256:a5957fd5d879262ed54acda5630be2c28e6ebe59b19b028c2d45501f12701eed"],"state_sha256":"43253bf96233475f2d59a5d9f33cdaee7484efdf3f87197e703888eafce930d4"}