{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:KXSZVTTZYKBEEW4Y362AUUUXYD","short_pith_number":"pith:KXSZVTTZ","canonical_record":{"source":{"id":"1101.0069","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2010-12-30T11:30:53Z","cross_cats_sorted":[],"title_canon_sha256":"44f02c6179bf516d18594690e102f764fdbe56d38e7485b65d0a6da967eb157d","abstract_canon_sha256":"e05f07f22b786c1f4436b2181b81e9af26a47ba4a1c82cbe7276db50142d454e"},"schema_version":"1.0"},"canonical_sha256":"55e59ace79c282425b98dfb40a5297c0f030a31c5252f963747b8b99992f4101","source":{"kind":"arxiv","id":"1101.0069","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.0069","created_at":"2026-05-18T02:53:17Z"},{"alias_kind":"arxiv_version","alias_value":"1101.0069v1","created_at":"2026-05-18T02:53:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.0069","created_at":"2026-05-18T02:53:17Z"},{"alias_kind":"pith_short_12","alias_value":"KXSZVTTZYKBE","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"KXSZVTTZYKBEEW4Y","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"KXSZVTTZ","created_at":"2026-05-18T12:26:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:KXSZVTTZYKBEEW4Y362AUUUXYD","target":"record","payload":{"canonical_record":{"source":{"id":"1101.0069","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2010-12-30T11:30:53Z","cross_cats_sorted":[],"title_canon_sha256":"44f02c6179bf516d18594690e102f764fdbe56d38e7485b65d0a6da967eb157d","abstract_canon_sha256":"e05f07f22b786c1f4436b2181b81e9af26a47ba4a1c82cbe7276db50142d454e"},"schema_version":"1.0"},"canonical_sha256":"55e59ace79c282425b98dfb40a5297c0f030a31c5252f963747b8b99992f4101","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:53:17.837086Z","signature_b64":"rGPrYOqMLb0q8JCdaJaWuEeeOs2Cl6EJO/3WrG9gmY9eZvT1CR0yyf8IDxWH7rKPHh/cWj9KTX7fftUBzu9JBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"55e59ace79c282425b98dfb40a5297c0f030a31c5252f963747b8b99992f4101","last_reissued_at":"2026-05-18T02:53:17.836414Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:53:17.836414Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1101.0069","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":"2026-05-18T02:53:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XRmKdXAT2ixQxYwZi4nDYcl8MA5RXb6HWqoFvEp6MbCwILF0WASuYieyr1v/+gwsjxZ5HNl+yU/sYai90f04BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T17:53:00.772744Z"},"content_sha256":"5fcace92cbd8eeca374514bfa2be0a2c8cb493ed965d4c3335bc6b2819944255","schema_version":"1.0","event_id":"sha256:5fcace92cbd8eeca374514bfa2be0a2c8cb493ed965d4c3335bc6b2819944255"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:KXSZVTTZYKBEEW4Y362AUUUXYD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fractal Inspired Models of Quark and Gluon Distributions and Longitudinal Structure Function FL(x, Q2) at small x","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Akbari Jahan, D. K. Choudhury","submitted_at":"2010-12-30T11:30:53Z","abstract_excerpt":"In recent years, Fractal Inspired Models of quark and gluon densities at small x have been proposed. In this paper, we investigate longitudinal structure function F-L (x, Q2) within this approach. We make predictions using the QCD based approximate relation between the longitudinal structure function and the gluon density. As the Altarelli-Martinelli equation for the longitudinal structure function cannot be applied to Model I due to the presence of a singularity in the Bjorken x-space we consider Model II only. The qualitative feature of the prediction of Model II is found to be compatible wi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.0069","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":""},"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":"2026-05-18T02:53:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bXjai8tXDRD2xuyARM0erFk2gmyEQkJV7iwjX4LPY9CFPc8NGEhLsB9nuN7mGuFEPTkCFpkAFYPEh4jzJnmqCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T17:53:00.773339Z"},"content_sha256":"64dd30560165789589cf3ade16b9dc7ccab8dba4ac2e9b5d395af193d45074d4","schema_version":"1.0","event_id":"sha256:64dd30560165789589cf3ade16b9dc7ccab8dba4ac2e9b5d395af193d45074d4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KXSZVTTZYKBEEW4Y362AUUUXYD/bundle.json","state_url":"https://pith.science/pith/KXSZVTTZYKBEEW4Y362AUUUXYD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KXSZVTTZYKBEEW4Y362AUUUXYD/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":"2026-06-05T17:53:00Z","links":{"resolver":"https://pith.science/pith/KXSZVTTZYKBEEW4Y362AUUUXYD","bundle":"https://pith.science/pith/KXSZVTTZYKBEEW4Y362AUUUXYD/bundle.json","state":"https://pith.science/pith/KXSZVTTZYKBEEW4Y362AUUUXYD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KXSZVTTZYKBEEW4Y362AUUUXYD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:KXSZVTTZYKBEEW4Y362AUUUXYD","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":"e05f07f22b786c1f4436b2181b81e9af26a47ba4a1c82cbe7276db50142d454e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2010-12-30T11:30:53Z","title_canon_sha256":"44f02c6179bf516d18594690e102f764fdbe56d38e7485b65d0a6da967eb157d"},"schema_version":"1.0","source":{"id":"1101.0069","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.0069","created_at":"2026-05-18T02:53:17Z"},{"alias_kind":"arxiv_version","alias_value":"1101.0069v1","created_at":"2026-05-18T02:53:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.0069","created_at":"2026-05-18T02:53:17Z"},{"alias_kind":"pith_short_12","alias_value":"KXSZVTTZYKBE","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"KXSZVTTZYKBEEW4Y","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"KXSZVTTZ","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:64dd30560165789589cf3ade16b9dc7ccab8dba4ac2e9b5d395af193d45074d4","target":"graph","created_at":"2026-05-18T02:53:17Z","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":"In recent years, Fractal Inspired Models of quark and gluon densities at small x have been proposed. In this paper, we investigate longitudinal structure function F-L (x, Q2) within this approach. We make predictions using the QCD based approximate relation between the longitudinal structure function and the gluon density. As the Altarelli-Martinelli equation for the longitudinal structure function cannot be applied to Model I due to the presence of a singularity in the Bjorken x-space we consider Model II only. The qualitative feature of the prediction of Model II is found to be compatible wi","authors_text":"Akbari Jahan, D. K. Choudhury","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2010-12-30T11:30:53Z","title":"Fractal Inspired Models of Quark and Gluon Distributions and Longitudinal Structure Function FL(x, Q2) at small x"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.0069","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":"sha256:5fcace92cbd8eeca374514bfa2be0a2c8cb493ed965d4c3335bc6b2819944255","target":"record","created_at":"2026-05-18T02:53:17Z","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":"e05f07f22b786c1f4436b2181b81e9af26a47ba4a1c82cbe7276db50142d454e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2010-12-30T11:30:53Z","title_canon_sha256":"44f02c6179bf516d18594690e102f764fdbe56d38e7485b65d0a6da967eb157d"},"schema_version":"1.0","source":{"id":"1101.0069","kind":"arxiv","version":1}},"canonical_sha256":"55e59ace79c282425b98dfb40a5297c0f030a31c5252f963747b8b99992f4101","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"55e59ace79c282425b98dfb40a5297c0f030a31c5252f963747b8b99992f4101","first_computed_at":"2026-05-18T02:53:17.836414Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:53:17.836414Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rGPrYOqMLb0q8JCdaJaWuEeeOs2Cl6EJO/3WrG9gmY9eZvT1CR0yyf8IDxWH7rKPHh/cWj9KTX7fftUBzu9JBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:53:17.837086Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.0069","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5fcace92cbd8eeca374514bfa2be0a2c8cb493ed965d4c3335bc6b2819944255","sha256:64dd30560165789589cf3ade16b9dc7ccab8dba4ac2e9b5d395af193d45074d4"],"state_sha256":"46deb5217e0d092c4d59a56bdf7feca6d9965e0ed996019db077fec225e8370f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Tej/FTlxSDJ/F18osZhOKhqZ2goyOM9GmsD6qylupHYwK2uwjt8R7lUc9O1qchcSRGkIa/dabuT4+YR8YHEgBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T17:53:00.776452Z","bundle_sha256":"5505fd895467dc21f571818ec6be6e514ed33404e082877a25636abae82ac43d"}}