{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1994:BIJTBM6HAJ76IUNTVRMJICHB7D","short_pith_number":"pith:BIJTBM6H","schema_version":"1.0","canonical_sha256":"0a1330b3c7027fe451b3ac589408e1f8ee7110d0b970801eb5e1ce7cef497d2a","source":{"kind":"arxiv","id":"hep-ph/9405320","version":3},"attestation_state":"computed","paper":{"title":"Double Asymptotic Scaling at HERA","license":"","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"R. D. Ball, S. Forte","submitted_at":"1994-05-18T15:52:52Z","abstract_excerpt":"Perturbative QCD predicts that at sufficiently large $Q^2$ and small $x$ nucleon structure functions should exhibit scaling in the two variables $\\sqrt{\\ln\\smallfrac{1}{x}\\ln\\ln Q^2}$ and $\\sqrt{\\ln\\smallfrac{1}{x}\\big/\\ln\\ln Q^2}$, provided only that the small-$x$ behaviour of the input to the perturbative QCD evolution is sufficiently soft. We derive these asymptotic results by writing the gluonic Altarelli--Parisi equation at small $x$ as a two--dimensional wave equation, which propagates the gluon distribution from its boundaries into the asymptotic region. We then show that the existing e"},"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":"hep-ph/9405320","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"hep-ph","submitted_at":"1994-05-18T15:52:52Z","cross_cats_sorted":[],"title_canon_sha256":"bf862ee94fcb2c6a8911d9c195ff1aa9e62a3136651bc4af5a583e31ac204411","abstract_canon_sha256":"a11455a8a118829487aedf7d1e1824df44ba941921adb19387c2dd2e9296abaa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:37:13.277018Z","signature_b64":"RDMI5dcJaBmWIxZoa1ZLOXhFNSRbsf6yB673NmT2ccVefaprwghy01YFfKLplZVco98eXklb/OpPtzBimPWPCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0a1330b3c7027fe451b3ac589408e1f8ee7110d0b970801eb5e1ce7cef497d2a","last_reissued_at":"2026-05-18T02:37:13.276590Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:37:13.276590Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Double Asymptotic Scaling at HERA","license":"","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"R. D. Ball, S. Forte","submitted_at":"1994-05-18T15:52:52Z","abstract_excerpt":"Perturbative QCD predicts that at sufficiently large $Q^2$ and small $x$ nucleon structure functions should exhibit scaling in the two variables $\\sqrt{\\ln\\smallfrac{1}{x}\\ln\\ln Q^2}$ and $\\sqrt{\\ln\\smallfrac{1}{x}\\big/\\ln\\ln Q^2}$, provided only that the small-$x$ behaviour of the input to the perturbative QCD evolution is sufficiently soft. We derive these asymptotic results by writing the gluonic Altarelli--Parisi equation at small $x$ as a two--dimensional wave equation, which propagates the gluon distribution from its boundaries into the asymptotic region. We then show that the existing e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-ph/9405320","kind":"arxiv","version":3},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"hep-ph/9405320","created_at":"2026-05-18T02:37:13.276655+00:00"},{"alias_kind":"arxiv_version","alias_value":"hep-ph/9405320v3","created_at":"2026-05-18T02:37:13.276655+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-ph/9405320","created_at":"2026-05-18T02:37:13.276655+00:00"},{"alias_kind":"pith_short_12","alias_value":"BIJTBM6HAJ76","created_at":"2026-05-18T12:25:47.102015+00:00"},{"alias_kind":"pith_short_16","alias_value":"BIJTBM6HAJ76IUNT","created_at":"2026-05-18T12:25:47.102015+00:00"},{"alias_kind":"pith_short_8","alias_value":"BIJTBM6H","created_at":"2026-05-18T12:25:47.102015+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":2,"sample":[{"citing_arxiv_id":"2308.00025","citing_title":"On the positivity of MSbar parton distributions","ref_index":18,"is_internal_anchor":true},{"citing_arxiv_id":"2605.16019","citing_title":"Inclusive charm and bottom quark pair production cross sections at hadron colliders at next-to-next-to-leading-order accuracy","ref_index":84,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BIJTBM6HAJ76IUNTVRMJICHB7D","json":"https://pith.science/pith/BIJTBM6HAJ76IUNTVRMJICHB7D.json","graph_json":"https://pith.science/api/pith-number/BIJTBM6HAJ76IUNTVRMJICHB7D/graph.json","events_json":"https://pith.science/api/pith-number/BIJTBM6HAJ76IUNTVRMJICHB7D/events.json","paper":"https://pith.science/paper/BIJTBM6H"},"agent_actions":{"view_html":"https://pith.science/pith/BIJTBM6HAJ76IUNTVRMJICHB7D","download_json":"https://pith.science/pith/BIJTBM6HAJ76IUNTVRMJICHB7D.json","view_paper":"https://pith.science/paper/BIJTBM6H","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=hep-ph/9405320&json=true","fetch_graph":"https://pith.science/api/pith-number/BIJTBM6HAJ76IUNTVRMJICHB7D/graph.json","fetch_events":"https://pith.science/api/pith-number/BIJTBM6HAJ76IUNTVRMJICHB7D/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BIJTBM6HAJ76IUNTVRMJICHB7D/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BIJTBM6HAJ76IUNTVRMJICHB7D/action/storage_attestation","attest_author":"https://pith.science/pith/BIJTBM6HAJ76IUNTVRMJICHB7D/action/author_attestation","sign_citation":"https://pith.science/pith/BIJTBM6HAJ76IUNTVRMJICHB7D/action/citation_signature","submit_replication":"https://pith.science/pith/BIJTBM6HAJ76IUNTVRMJICHB7D/action/replication_record"}},"created_at":"2026-05-18T02:37:13.276655+00:00","updated_at":"2026-05-18T02:37:13.276655+00:00"}