{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:RQZWQNWNJ2YEUAI2SSIAS3PQW2","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":"d2f4a9d3e30dd9aa215f240b75a4b7889b965f612fd8d205cf3b495b29e66414","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-ph","submitted_at":"2026-07-20T18:00:01Z","title_canon_sha256":"a873ba0b93be5994f911ab5f2b1331aff7bee99186d71ab230e42d7d54decf87"},"schema_version":"1.0","source":{"id":"2607.18377","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.18377","created_at":"2026-07-22T00:22:44Z"},{"alias_kind":"arxiv_version","alias_value":"2607.18377v1","created_at":"2026-07-22T00:22:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.18377","created_at":"2026-07-22T00:22:44Z"},{"alias_kind":"pith_short_12","alias_value":"RQZWQNWNJ2YE","created_at":"2026-07-22T00:22:44Z"},{"alias_kind":"pith_short_16","alias_value":"RQZWQNWNJ2YEUAI2","created_at":"2026-07-22T00:22:44Z"},{"alias_kind":"pith_short_8","alias_value":"RQZWQNWN","created_at":"2026-07-22T00:22:44Z"}],"graph_snapshots":[{"event_id":"sha256:dfca9b655086b8495ef05b741043c541a3b15ef190bf59be0347d6280bbd9775","target":"graph","created_at":"2026-07-22T00:22:44Z","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/2607.18377/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In strongly ordered collinear limits, triple-collinear $1\\to 3$ splitting functions factorize into products of $1\\to 2$ splitting functions. Here, we investigate whether, and under which conditions, this factorization persists in a finite QCD medium. To this end, we reformulate the opacity expansion as a medium-modification of the compact Catani-Grazzini representation of collinear $1\\to n$ splitting functions. We compute the fully differential medium-modified triple-collinear $q\\to q c\\bar{c}$ splitting function to first order in opacity and leading order in $N_c$, and show that it can be exp","authors_text":"Shahin Iqbal, Urs Achim Wiedemann","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-ph","submitted_at":"2026-07-20T18:00:01Z","title":"Factorization of the triple-collinear $q \\to qc\\bar{c}$ splitting function at first order in opacity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.18377","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:d264fa8a09405d886f5a2440e3bde85d028682c573f4d89641fb5fb1c4b9b1d2","target":"record","created_at":"2026-07-22T00:22:44Z","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":"d2f4a9d3e30dd9aa215f240b75a4b7889b965f612fd8d205cf3b495b29e66414","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-ph","submitted_at":"2026-07-20T18:00:01Z","title_canon_sha256":"a873ba0b93be5994f911ab5f2b1331aff7bee99186d71ab230e42d7d54decf87"},"schema_version":"1.0","source":{"id":"2607.18377","kind":"arxiv","version":1}},"canonical_sha256":"8c336836cd4eb04a011a9490096df0b6ba90fd808f324b6089554126cf231a2e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8c336836cd4eb04a011a9490096df0b6ba90fd808f324b6089554126cf231a2e","first_computed_at":"2026-07-22T00:22:44.260238Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-22T00:22:44.260238Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kAKgZl0R/08ZBEbGDvCycRhV6z+W0WyuvMr8Nls5LARjurAMgSqZbaaIfJby406Dm4/PjMf1K+yd/Yvpd7u8Bw==","signature_status":"signed_v1","signed_at":"2026-07-22T00:22:44.261072Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.18377","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d264fa8a09405d886f5a2440e3bde85d028682c573f4d89641fb5fb1c4b9b1d2","sha256:dfca9b655086b8495ef05b741043c541a3b15ef190bf59be0347d6280bbd9775"],"state_sha256":"322f202b21281d633e4eb11b22e0c14d7e78933a14a228c48824a2441da6f0a9"}