{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:E5XPT4GXQOUTMRCGZ6LI7IETHK","short_pith_number":"pith:E5XPT4GX","schema_version":"1.0","canonical_sha256":"276ef9f0d783a9364446cf968fa0933a8351e63078489bd178206f200ad89c32","source":{"kind":"arxiv","id":"2508.00195","version":1},"attestation_state":"computed","paper":{"title":"Analytic Solution for the Helicity Evolution Equations at Small $x$ and Large $N_c\\&N_f$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nucl-th"],"primary_cat":"hep-ph","authors_text":"Jeremy Borden, Yuri V. Kovchegov","submitted_at":"2025-07-31T22:28:37Z","abstract_excerpt":"We construct an exact analytic solution of the revised small-$x$ helicity evolution equations, where the contributions of the quark-to-gluon and gluon-to-quark transition operators were newly included. These evolution equations are written in the large-$N_c\\&N_f$ limit and are double-logarithmic, resumming powers of $\\alpha_s\\ln^2(1/x)$. Here $N_c$ and $N_f$ are the numbers of quark colors and flavors, while $\\alpha_s$ is the strong coupling constant and $x$ is the Bjorken-$x$ variable. Using our solution, we obtain analytic expressions for the flavor singlet quark and gluon helicity parton di"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2508.00195","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2025-07-31T22:28:37Z","cross_cats_sorted":["nucl-th"],"title_canon_sha256":"f8c34a7104a7839f16147ea9140f31361bee1cec7de68b60015aa2c9ca6826e3","abstract_canon_sha256":"3e6be339515f04905fa8b80231801f2f271c7c5abdb734546e2a1c77299258ee"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:46:50.986783Z","signature_b64":"+/AUp9uoSgcNJcBC1mh5cMNBa3WT+o2aNtHls3dCp+nfwPpC0CRJCgLxsuP9aCISxx20KxekACReCUXDIUHmDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"276ef9f0d783a9364446cf968fa0933a8351e63078489bd178206f200ad89c32","last_reissued_at":"2026-07-05T11:46:50.986289Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:46:50.986289Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Analytic Solution for the Helicity Evolution Equations at Small $x$ and Large $N_c\\&N_f$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nucl-th"],"primary_cat":"hep-ph","authors_text":"Jeremy Borden, Yuri V. Kovchegov","submitted_at":"2025-07-31T22:28:37Z","abstract_excerpt":"We construct an exact analytic solution of the revised small-$x$ helicity evolution equations, where the contributions of the quark-to-gluon and gluon-to-quark transition operators were newly included. These evolution equations are written in the large-$N_c\\&N_f$ limit and are double-logarithmic, resumming powers of $\\alpha_s\\ln^2(1/x)$. Here $N_c$ and $N_f$ are the numbers of quark colors and flavors, while $\\alpha_s$ is the strong coupling constant and $x$ is the Bjorken-$x$ variable. Using our solution, we obtain analytic expressions for the flavor singlet quark and gluon helicity parton di"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.00195","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/2508.00195/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2508.00195","created_at":"2026-07-05T11:46:50.986359+00:00"},{"alias_kind":"arxiv_version","alias_value":"2508.00195v1","created_at":"2026-07-05T11:46:50.986359+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.00195","created_at":"2026-07-05T11:46:50.986359+00:00"},{"alias_kind":"pith_short_12","alias_value":"E5XPT4GXQOUT","created_at":"2026-07-05T11:46:50.986359+00:00"},{"alias_kind":"pith_short_16","alias_value":"E5XPT4GXQOUTMRCG","created_at":"2026-07-05T11:46:50.986359+00:00"},{"alias_kind":"pith_short_8","alias_value":"E5XPT4GX","created_at":"2026-07-05T11:46:50.986359+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2607.00439","citing_title":"Sub-eikonal stress and model dependence of the small-$x$ gluon D-term","ref_index":103,"is_internal_anchor":false},{"citing_arxiv_id":"2604.24629","citing_title":"On the Two $R$-Factors in the Small-$x$ Shockwave Formalism","ref_index":169,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/E5XPT4GXQOUTMRCGZ6LI7IETHK","json":"https://pith.science/pith/E5XPT4GXQOUTMRCGZ6LI7IETHK.json","graph_json":"https://pith.science/api/pith-number/E5XPT4GXQOUTMRCGZ6LI7IETHK/graph.json","events_json":"https://pith.science/api/pith-number/E5XPT4GXQOUTMRCGZ6LI7IETHK/events.json","paper":"https://pith.science/paper/E5XPT4GX"},"agent_actions":{"view_html":"https://pith.science/pith/E5XPT4GXQOUTMRCGZ6LI7IETHK","download_json":"https://pith.science/pith/E5XPT4GXQOUTMRCGZ6LI7IETHK.json","view_paper":"https://pith.science/paper/E5XPT4GX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2508.00195&json=true","fetch_graph":"https://pith.science/api/pith-number/E5XPT4GXQOUTMRCGZ6LI7IETHK/graph.json","fetch_events":"https://pith.science/api/pith-number/E5XPT4GXQOUTMRCGZ6LI7IETHK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/E5XPT4GXQOUTMRCGZ6LI7IETHK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/E5XPT4GXQOUTMRCGZ6LI7IETHK/action/storage_attestation","attest_author":"https://pith.science/pith/E5XPT4GXQOUTMRCGZ6LI7IETHK/action/author_attestation","sign_citation":"https://pith.science/pith/E5XPT4GXQOUTMRCGZ6LI7IETHK/action/citation_signature","submit_replication":"https://pith.science/pith/E5XPT4GXQOUTMRCGZ6LI7IETHK/action/replication_record"}},"created_at":"2026-07-05T11:46:50.986359+00:00","updated_at":"2026-07-05T11:46:50.986359+00:00"}