{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:7KOJ2MDA7PTBJXHNDWPAVZOCAC","short_pith_number":"pith:7KOJ2MDA","canonical_record":{"source":{"id":"1805.06460","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2018-05-16T18:00:02Z","cross_cats_sorted":[],"title_canon_sha256":"b593efd86a18deaff23609b92fd9294ff9006e4746c89360d8600f287c335655","abstract_canon_sha256":"4d2b238af2642b066c8b4fa611a3a4a9911f108370f515e3b41d020a19ac93f5"},"schema_version":"1.0"},"canonical_sha256":"fa9c9d3060fbe614dced1d9e0ae5c200a0bf8bc413588050bed499068ea3ecf9","source":{"kind":"arxiv","id":"1805.06460","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.06460","created_at":"2026-05-18T00:11:27Z"},{"alias_kind":"arxiv_version","alias_value":"1805.06460v2","created_at":"2026-05-18T00:11:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.06460","created_at":"2026-05-18T00:11:27Z"},{"alias_kind":"pith_short_12","alias_value":"7KOJ2MDA7PTB","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"7KOJ2MDA7PTBJXHN","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"7KOJ2MDA","created_at":"2026-05-18T12:32:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:7KOJ2MDA7PTBJXHNDWPAVZOCAC","target":"record","payload":{"canonical_record":{"source":{"id":"1805.06460","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2018-05-16T18:00:02Z","cross_cats_sorted":[],"title_canon_sha256":"b593efd86a18deaff23609b92fd9294ff9006e4746c89360d8600f287c335655","abstract_canon_sha256":"4d2b238af2642b066c8b4fa611a3a4a9911f108370f515e3b41d020a19ac93f5"},"schema_version":"1.0"},"canonical_sha256":"fa9c9d3060fbe614dced1d9e0ae5c200a0bf8bc413588050bed499068ea3ecf9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:27.929936Z","signature_b64":"dQqfdcop5oDSJWR7sXZuDF+2FYZjSyW/Gxp2Szq99TntJa4S0xLm51nLdRBW/+zPwv/ty3PuK/lLRwrUzyAxAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fa9c9d3060fbe614dced1d9e0ae5c200a0bf8bc413588050bed499068ea3ecf9","last_reissued_at":"2026-05-18T00:11:27.929464Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:27.929464Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.06460","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:11:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0FTDfXnxNzcb31FpVF2AM/0NdkLGayKo1rA7tzIHYJuxNGw0vVwhysq7f9UhCDHeBOfOMfdKoStf5tAgIm37Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T16:39:18.367090Z"},"content_sha256":"d95a77a256290afbeed42f2d93458f52c72ed1d5f156fdbbf854998db446788e","schema_version":"1.0","event_id":"sha256:d95a77a256290afbeed42f2d93458f52c72ed1d5f156fdbbf854998db446788e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:7KOJ2MDA7PTBJXHNDWPAVZOCAC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Four-loop splitting functions at small $x$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Marco Bonvini, Simone Marzani","submitted_at":"2018-05-16T18:00:02Z","abstract_excerpt":"We consider the expansion of small-$x$ resummed DGLAP splitting functions at next-to-leading logarithmic (NLL) accuracy to four-loop order, namely next-to-next-to-next-to-leading order (N$^3$LO). From this, we extract the exact LL and NLL small-$x$ contributions to the yet unknown N$^3$LO splitting functions, both in the standard $\\overline{MS}$ scheme and in the $Q_0 \\overline{MS}$ scheme usually considered in small-$x$ literature. We show that the impact of unknown subleading logarithmic contributions (NNLL and beyond) at N$^3$LO is significant, thus motivating future work towards their comp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.06460","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:11:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+GG400oLceWFMC/Ma1ROvbzNDM8iFfbO7vNYqoP3dhZ7TL3HDf+6M+OdXftOYF+J5raUVaHqA+i3WJuUUcpWAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T16:39:18.367807Z"},"content_sha256":"7c402c8316e6b0f46be9881cf2ea6a62fd06331159bdfb501d4e4704090915e7","schema_version":"1.0","event_id":"sha256:7c402c8316e6b0f46be9881cf2ea6a62fd06331159bdfb501d4e4704090915e7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7KOJ2MDA7PTBJXHNDWPAVZOCAC/bundle.json","state_url":"https://pith.science/pith/7KOJ2MDA7PTBJXHNDWPAVZOCAC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7KOJ2MDA7PTBJXHNDWPAVZOCAC/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-25T16:39:18Z","links":{"resolver":"https://pith.science/pith/7KOJ2MDA7PTBJXHNDWPAVZOCAC","bundle":"https://pith.science/pith/7KOJ2MDA7PTBJXHNDWPAVZOCAC/bundle.json","state":"https://pith.science/pith/7KOJ2MDA7PTBJXHNDWPAVZOCAC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7KOJ2MDA7PTBJXHNDWPAVZOCAC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:7KOJ2MDA7PTBJXHNDWPAVZOCAC","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":"4d2b238af2642b066c8b4fa611a3a4a9911f108370f515e3b41d020a19ac93f5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2018-05-16T18:00:02Z","title_canon_sha256":"b593efd86a18deaff23609b92fd9294ff9006e4746c89360d8600f287c335655"},"schema_version":"1.0","source":{"id":"1805.06460","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.06460","created_at":"2026-05-18T00:11:27Z"},{"alias_kind":"arxiv_version","alias_value":"1805.06460v2","created_at":"2026-05-18T00:11:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.06460","created_at":"2026-05-18T00:11:27Z"},{"alias_kind":"pith_short_12","alias_value":"7KOJ2MDA7PTB","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"7KOJ2MDA7PTBJXHN","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"7KOJ2MDA","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:7c402c8316e6b0f46be9881cf2ea6a62fd06331159bdfb501d4e4704090915e7","target":"graph","created_at":"2026-05-18T00:11:27Z","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":"We consider the expansion of small-$x$ resummed DGLAP splitting functions at next-to-leading logarithmic (NLL) accuracy to four-loop order, namely next-to-next-to-next-to-leading order (N$^3$LO). From this, we extract the exact LL and NLL small-$x$ contributions to the yet unknown N$^3$LO splitting functions, both in the standard $\\overline{MS}$ scheme and in the $Q_0 \\overline{MS}$ scheme usually considered in small-$x$ literature. We show that the impact of unknown subleading logarithmic contributions (NNLL and beyond) at N$^3$LO is significant, thus motivating future work towards their comp","authors_text":"Marco Bonvini, Simone Marzani","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2018-05-16T18:00:02Z","title":"Four-loop splitting functions at small $x$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.06460","kind":"arxiv","version":2},"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:d95a77a256290afbeed42f2d93458f52c72ed1d5f156fdbbf854998db446788e","target":"record","created_at":"2026-05-18T00:11:27Z","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":"4d2b238af2642b066c8b4fa611a3a4a9911f108370f515e3b41d020a19ac93f5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2018-05-16T18:00:02Z","title_canon_sha256":"b593efd86a18deaff23609b92fd9294ff9006e4746c89360d8600f287c335655"},"schema_version":"1.0","source":{"id":"1805.06460","kind":"arxiv","version":2}},"canonical_sha256":"fa9c9d3060fbe614dced1d9e0ae5c200a0bf8bc413588050bed499068ea3ecf9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fa9c9d3060fbe614dced1d9e0ae5c200a0bf8bc413588050bed499068ea3ecf9","first_computed_at":"2026-05-18T00:11:27.929464Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:11:27.929464Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dQqfdcop5oDSJWR7sXZuDF+2FYZjSyW/Gxp2Szq99TntJa4S0xLm51nLdRBW/+zPwv/ty3PuK/lLRwrUzyAxAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:11:27.929936Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.06460","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d95a77a256290afbeed42f2d93458f52c72ed1d5f156fdbbf854998db446788e","sha256:7c402c8316e6b0f46be9881cf2ea6a62fd06331159bdfb501d4e4704090915e7"],"state_sha256":"1a2db325a66e05a2d453be361081751fd7dc70d4003946dc7ae255b32632c176"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p8y9itJ9huvCyCPJg0MWRuB2YmDpOgoGwHlURO75chYfvH2Jy7RpehGVorRRCStc67FXqWu2DXDzuviELFHxCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T16:39:18.371491Z","bundle_sha256":"f2a78105ee88c770dd06a0f627cfe9b997b4ef8a2fd055842b442fd0ec2041a8"}}