{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:PNZ4DZVQKLMTWC7BEWUEFV3EAV","short_pith_number":"pith:PNZ4DZVQ","canonical_record":{"source":{"id":"1903.11624","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2019-03-27T18:05:32Z","cross_cats_sorted":["hep-th","nucl-th"],"title_canon_sha256":"cc4fd1cf99e3053d148b72d519d954bed7176334355421c087b1fb43f5c9697a","abstract_canon_sha256":"0e014b75e5e4adf1575663a38e8b10ec41065c746a1a8e83b1e867f227ce43c2"},"schema_version":"1.0"},"canonical_sha256":"7b73c1e6b052d93b0be125a842d76405631cabf8c852e83e3932d70bf2d9e87b","source":{"kind":"arxiv","id":"1903.11624","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.11624","created_at":"2026-07-05T00:05:07Z"},{"alias_kind":"arxiv_version","alias_value":"1903.11624v2","created_at":"2026-07-05T00:05:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.11624","created_at":"2026-07-05T00:05:07Z"},{"alias_kind":"pith_short_12","alias_value":"PNZ4DZVQKLMT","created_at":"2026-07-05T00:05:07Z"},{"alias_kind":"pith_short_16","alias_value":"PNZ4DZVQKLMTWC7B","created_at":"2026-07-05T00:05:07Z"},{"alias_kind":"pith_short_8","alias_value":"PNZ4DZVQ","created_at":"2026-07-05T00:05:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:PNZ4DZVQKLMTWC7BEWUEFV3EAV","target":"record","payload":{"canonical_record":{"source":{"id":"1903.11624","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2019-03-27T18:05:32Z","cross_cats_sorted":["hep-th","nucl-th"],"title_canon_sha256":"cc4fd1cf99e3053d148b72d519d954bed7176334355421c087b1fb43f5c9697a","abstract_canon_sha256":"0e014b75e5e4adf1575663a38e8b10ec41065c746a1a8e83b1e867f227ce43c2"},"schema_version":"1.0"},"canonical_sha256":"7b73c1e6b052d93b0be125a842d76405631cabf8c852e83e3932d70bf2d9e87b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:05:07.759526Z","signature_b64":"rp84TF4ZnRs1rn4OFUpdl5eK1tQXyVygePW9imFK4ac304NmkmXgJbyeWl4LxRxBA4kzIrLxmYqBij4+VdFSBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7b73c1e6b052d93b0be125a842d76405631cabf8c852e83e3932d70bf2d9e87b","last_reissued_at":"2026-07-05T00:05:07.758999Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:05:07.758999Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.11624","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":"2026-07-05T00:05:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"21YqenOsr/Th+7Ek31kYXFJ4p005OYO/abd7tgW5YQnKMUoRu9DhKDDNQ6k5RZ7fzlvuawRzkgX+UT3PuE0BBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T05:01:09.848667Z"},"content_sha256":"449d96f06e7e9f239255ad4159be0d82678f113e624e8438187bac9c8c6388ae","schema_version":"1.0","event_id":"sha256:449d96f06e7e9f239255ad4159be0d82678f113e624e8438187bac9c8c6388ae"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:PNZ4DZVQKLMTWC7BEWUEFV3EAV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Structure functions at small x from world-lines. I: Unpolarized distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","nucl-th"],"primary_cat":"hep-ph","authors_text":"Andrey Tarasov, Raju Venugopalan","submitted_at":"2019-03-27T18:05:32Z","abstract_excerpt":"The world-line representation of quantum field theory is a powerful framework for the computation of perturbative multi-leg Feynman amplitudes. In particular, in gauge theories, it provides an efficient way, via point particle Grassmann functional integrals, to compute spinor and color traces in these amplitudes. Further, semi-classical approximations to quantum mechanical world-line trajectories provide useful intuition in a wide range of dynamical problems. We develop here the world-line approach to compute deeply inelastic structure functions in the small x Regge limit of QCD. In particular"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.11624","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1903.11624/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":"2026-07-05T00:05:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d32MM1U/CG0RgcIOTC5yBLU6q1H5mzIAZIb2nneT4zOcIGcfM+QaiZ7M6VvDLzXMpHEQXtdDu/zm6Stn/hZhAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T05:01:09.849236Z"},"content_sha256":"b47a3391a1ad5d5c4e16c2ba95d8bf387ca7c611cccac10750d11fe735b812f3","schema_version":"1.0","event_id":"sha256:b47a3391a1ad5d5c4e16c2ba95d8bf387ca7c611cccac10750d11fe735b812f3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PNZ4DZVQKLMTWC7BEWUEFV3EAV/bundle.json","state_url":"https://pith.science/pith/PNZ4DZVQKLMTWC7BEWUEFV3EAV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PNZ4DZVQKLMTWC7BEWUEFV3EAV/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":"2026-08-18T05:01:09Z","links":{"resolver":"https://pith.science/pith/PNZ4DZVQKLMTWC7BEWUEFV3EAV","bundle":"https://pith.science/pith/PNZ4DZVQKLMTWC7BEWUEFV3EAV/bundle.json","state":"https://pith.science/pith/PNZ4DZVQKLMTWC7BEWUEFV3EAV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PNZ4DZVQKLMTWC7BEWUEFV3EAV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:PNZ4DZVQKLMTWC7BEWUEFV3EAV","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":"0e014b75e5e4adf1575663a38e8b10ec41065c746a1a8e83b1e867f227ce43c2","cross_cats_sorted":["hep-th","nucl-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2019-03-27T18:05:32Z","title_canon_sha256":"cc4fd1cf99e3053d148b72d519d954bed7176334355421c087b1fb43f5c9697a"},"schema_version":"1.0","source":{"id":"1903.11624","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.11624","created_at":"2026-07-05T00:05:07Z"},{"alias_kind":"arxiv_version","alias_value":"1903.11624v2","created_at":"2026-07-05T00:05:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.11624","created_at":"2026-07-05T00:05:07Z"},{"alias_kind":"pith_short_12","alias_value":"PNZ4DZVQKLMT","created_at":"2026-07-05T00:05:07Z"},{"alias_kind":"pith_short_16","alias_value":"PNZ4DZVQKLMTWC7B","created_at":"2026-07-05T00:05:07Z"},{"alias_kind":"pith_short_8","alias_value":"PNZ4DZVQ","created_at":"2026-07-05T00:05:07Z"}],"graph_snapshots":[{"event_id":"sha256:b47a3391a1ad5d5c4e16c2ba95d8bf387ca7c611cccac10750d11fe735b812f3","target":"graph","created_at":"2026-07-05T00:05:07Z","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/1903.11624/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The world-line representation of quantum field theory is a powerful framework for the computation of perturbative multi-leg Feynman amplitudes. In particular, in gauge theories, it provides an efficient way, via point particle Grassmann functional integrals, to compute spinor and color traces in these amplitudes. Further, semi-classical approximations to quantum mechanical world-line trajectories provide useful intuition in a wide range of dynamical problems. We develop here the world-line approach to compute deeply inelastic structure functions in the small x Regge limit of QCD. In particular","authors_text":"Andrey Tarasov, Raju Venugopalan","cross_cats":["hep-th","nucl-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2019-03-27T18:05:32Z","title":"Structure functions at small x from world-lines. I: Unpolarized distributions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.11624","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":"sha256:449d96f06e7e9f239255ad4159be0d82678f113e624e8438187bac9c8c6388ae","target":"record","created_at":"2026-07-05T00:05:07Z","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":"0e014b75e5e4adf1575663a38e8b10ec41065c746a1a8e83b1e867f227ce43c2","cross_cats_sorted":["hep-th","nucl-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2019-03-27T18:05:32Z","title_canon_sha256":"cc4fd1cf99e3053d148b72d519d954bed7176334355421c087b1fb43f5c9697a"},"schema_version":"1.0","source":{"id":"1903.11624","kind":"arxiv","version":2}},"canonical_sha256":"7b73c1e6b052d93b0be125a842d76405631cabf8c852e83e3932d70bf2d9e87b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7b73c1e6b052d93b0be125a842d76405631cabf8c852e83e3932d70bf2d9e87b","first_computed_at":"2026-07-05T00:05:07.758999Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:05:07.758999Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rp84TF4ZnRs1rn4OFUpdl5eK1tQXyVygePW9imFK4ac304NmkmXgJbyeWl4LxRxBA4kzIrLxmYqBij4+VdFSBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T00:05:07.759526Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.11624","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:449d96f06e7e9f239255ad4159be0d82678f113e624e8438187bac9c8c6388ae","sha256:b47a3391a1ad5d5c4e16c2ba95d8bf387ca7c611cccac10750d11fe735b812f3"],"state_sha256":"cb5162f23ddc23438399a1186854e7f7a375361596632421b9749ff221ca668e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m42qHFg4KLXvF0uIhlQmw1J5MYCX1TyFFd8WW+IXQQea3iZR//st3ypOQOXv0fFz7g+YzqNHXpmx4DXyjpvrCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T05:01:09.854672Z","bundle_sha256":"0e82d378de8788c61f772c32d873742f41db0091999ab81ac3dc08126baf7cfb"}}