{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:E5XPT4GXQOUTMRCGZ6LI7IETHK","short_pith_number":"pith:E5XPT4GX","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"},"canonical_sha256":"276ef9f0d783a9364446cf968fa0933a8351e63078489bd178206f200ad89c32","source":{"kind":"arxiv","id":"2508.00195","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.00195","created_at":"2026-07-05T11:46:50Z"},{"alias_kind":"arxiv_version","alias_value":"2508.00195v1","created_at":"2026-07-05T11:46:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.00195","created_at":"2026-07-05T11:46:50Z"},{"alias_kind":"pith_short_12","alias_value":"E5XPT4GXQOUT","created_at":"2026-07-05T11:46:50Z"},{"alias_kind":"pith_short_16","alias_value":"E5XPT4GXQOUTMRCG","created_at":"2026-07-05T11:46:50Z"},{"alias_kind":"pith_short_8","alias_value":"E5XPT4GX","created_at":"2026-07-05T11:46:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:E5XPT4GXQOUTMRCGZ6LI7IETHK","target":"record","payload":{"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"},"canonical_sha256":"276ef9f0d783a9364446cf968fa0933a8351e63078489bd178206f200ad89c32","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"},"source_kind":"arxiv","source_id":"2508.00195","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:46:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GYwOpK3KfFKxwOPUSwk0s+mVQjZelaViZmTxRZDkbbvWVl7VAwiuMlP+kaaPOSEbN6vTVCq7CLVWReEMwkCwDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T19:05:36.196661Z"},"content_sha256":"f81004064417528aaf19dc8ee52cfcbf91969fd1e5255149c71e1f54590e7be8","schema_version":"1.0","event_id":"sha256:f81004064417528aaf19dc8ee52cfcbf91969fd1e5255149c71e1f54590e7be8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:E5XPT4GXQOUTMRCGZ6LI7IETHK","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:46:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kAIx+M1jNUuFG4k9scI4x658tG6Gwc9zwPbDM6rrsB44E9GothjPArtzqtx/GHx27+6DwpzQ1BG14+Tnx4sqBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T19:05:36.197715Z"},"content_sha256":"9a83113f63e90df06039805bde6dd3a94be0bf654101eaf0bbe48639e243c070","schema_version":"1.0","event_id":"sha256:9a83113f63e90df06039805bde6dd3a94be0bf654101eaf0bbe48639e243c070"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E5XPT4GXQOUTMRCGZ6LI7IETHK/bundle.json","state_url":"https://pith.science/pith/E5XPT4GXQOUTMRCGZ6LI7IETHK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E5XPT4GXQOUTMRCGZ6LI7IETHK/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":"2026-08-04T19:05:36Z","links":{"resolver":"https://pith.science/pith/E5XPT4GXQOUTMRCGZ6LI7IETHK","bundle":"https://pith.science/pith/E5XPT4GXQOUTMRCGZ6LI7IETHK/bundle.json","state":"https://pith.science/pith/E5XPT4GXQOUTMRCGZ6LI7IETHK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E5XPT4GXQOUTMRCGZ6LI7IETHK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:E5XPT4GXQOUTMRCGZ6LI7IETHK","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":"3e6be339515f04905fa8b80231801f2f271c7c5abdb734546e2a1c77299258ee","cross_cats_sorted":["nucl-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2025-07-31T22:28:37Z","title_canon_sha256":"f8c34a7104a7839f16147ea9140f31361bee1cec7de68b60015aa2c9ca6826e3"},"schema_version":"1.0","source":{"id":"2508.00195","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.00195","created_at":"2026-07-05T11:46:50Z"},{"alias_kind":"arxiv_version","alias_value":"2508.00195v1","created_at":"2026-07-05T11:46:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.00195","created_at":"2026-07-05T11:46:50Z"},{"alias_kind":"pith_short_12","alias_value":"E5XPT4GXQOUT","created_at":"2026-07-05T11:46:50Z"},{"alias_kind":"pith_short_16","alias_value":"E5XPT4GXQOUTMRCG","created_at":"2026-07-05T11:46:50Z"},{"alias_kind":"pith_short_8","alias_value":"E5XPT4GX","created_at":"2026-07-05T11:46:50Z"}],"graph_snapshots":[{"event_id":"sha256:9a83113f63e90df06039805bde6dd3a94be0bf654101eaf0bbe48639e243c070","target":"graph","created_at":"2026-07-05T11:46:50Z","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/2508.00195/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Jeremy Borden, Yuri V. Kovchegov","cross_cats":["nucl-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2025-07-31T22:28:37Z","title":"Analytic Solution for the Helicity Evolution Equations at Small $x$ and Large $N_c\\&N_f$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.00195","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:f81004064417528aaf19dc8ee52cfcbf91969fd1e5255149c71e1f54590e7be8","target":"record","created_at":"2026-07-05T11:46:50Z","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":"3e6be339515f04905fa8b80231801f2f271c7c5abdb734546e2a1c77299258ee","cross_cats_sorted":["nucl-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2025-07-31T22:28:37Z","title_canon_sha256":"f8c34a7104a7839f16147ea9140f31361bee1cec7de68b60015aa2c9ca6826e3"},"schema_version":"1.0","source":{"id":"2508.00195","kind":"arxiv","version":1}},"canonical_sha256":"276ef9f0d783a9364446cf968fa0933a8351e63078489bd178206f200ad89c32","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"276ef9f0d783a9364446cf968fa0933a8351e63078489bd178206f200ad89c32","first_computed_at":"2026-07-05T11:46:50.986289Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:46:50.986289Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+/AUp9uoSgcNJcBC1mh5cMNBa3WT+o2aNtHls3dCp+nfwPpC0CRJCgLxsuP9aCISxx20KxekACReCUXDIUHmDw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:46:50.986783Z","signed_message":"canonical_sha256_bytes"},"source_id":"2508.00195","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f81004064417528aaf19dc8ee52cfcbf91969fd1e5255149c71e1f54590e7be8","sha256:9a83113f63e90df06039805bde6dd3a94be0bf654101eaf0bbe48639e243c070"],"state_sha256":"1aba743f05cdf5602f5a5cf8c886e87203fa741569dc646c496194094e7e4f3b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"herFS4DXVre7s3SXijwy5kQGUGAfPJJTmm5J5CQP7vElfnud6IYjsx0rH7iQQUvi0ShBjfCdLem8exHZwKsUDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T19:05:36.207635Z","bundle_sha256":"7cb2c9ae196002364fbb519f62139aae9b6da33d6a61020297675edb0e3e94b8"}}