{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:P55UVMKBGD2VKQCM7UAYZ5T6ZF","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":"44a4ad380a5f4ba4b8d9776d0b8c3f0885d6fda9f1f4314b58cdc261cfa5ce29","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2013-06-08T08:15:16Z","title_canon_sha256":"53a816674c7c519bfbd77fc1c3b819c11d3f7296446f8bf6198d98a75c34ff9e"},"schema_version":"1.0","source":{"id":"1306.1891","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.1891","created_at":"2026-05-18T03:20:22Z"},{"alias_kind":"arxiv_version","alias_value":"1306.1891v1","created_at":"2026-05-18T03:20:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.1891","created_at":"2026-05-18T03:20:22Z"},{"alias_kind":"pith_short_12","alias_value":"P55UVMKBGD2V","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"P55UVMKBGD2VKQCM","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"P55UVMKB","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:3d6e6667e07ffcf5da4ecd7c1048f09ed7e39f3cabbd3903789a1848b83eb649","target":"graph","created_at":"2026-05-18T03:20:22Z","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":"Momentum sum rule can be used as an inequality to estimate the lower and upper bounds of the momentum fractions of quarks and gluons in a model of proton valid in a limited \\textit{x} range. We compute such bounds in a self-similarity based model of proton structure function valid in the range $ 6.2\\times 10^{-7} \\leq x \\leq 10^{-2} $. The results conform to the asymptotic QCD expectations.","authors_text":"Akbari Jahan, D K Choudhury","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2013-06-08T08:15:16Z","title":"An Analysis of Momentum Fractions of Quarks and Gluons in a model of Proton"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.1891","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":"sha256:6ab29965ec8944d584b3c6d9d3e032de2f23de58079a8975f1ce29d5a05e9fca","target":"record","created_at":"2026-05-18T03:20:22Z","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":"44a4ad380a5f4ba4b8d9776d0b8c3f0885d6fda9f1f4314b58cdc261cfa5ce29","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2013-06-08T08:15:16Z","title_canon_sha256":"53a816674c7c519bfbd77fc1c3b819c11d3f7296446f8bf6198d98a75c34ff9e"},"schema_version":"1.0","source":{"id":"1306.1891","kind":"arxiv","version":1}},"canonical_sha256":"7f7b4ab14130f555404cfd018cf67ec978f14f8981dc17493c6ae04f263c6c29","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7f7b4ab14130f555404cfd018cf67ec978f14f8981dc17493c6ae04f263c6c29","first_computed_at":"2026-05-18T03:20:22.136461Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:20:22.136461Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+IFz9n8mCk7aJ1kBmtYBFS4TTQsBVvSXZ+wjnWTBW9Yhi4R1l8a3sL6vj/2R1zQ2ypyNusw3uupISkGLjq7aCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:20:22.137156Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.1891","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6ab29965ec8944d584b3c6d9d3e032de2f23de58079a8975f1ce29d5a05e9fca","sha256:3d6e6667e07ffcf5da4ecd7c1048f09ed7e39f3cabbd3903789a1848b83eb649"],"state_sha256":"c062cd094801848582cb9047814c1130ea1a052856c7800a2c1a87a143297152"}