{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1999:4FSLS3MMAY5Q54ZJ743WDSDXHV","short_pith_number":"pith:4FSLS3MM","schema_version":"1.0","canonical_sha256":"e164b96d8c063b0ef329ff3761c8773d7de4baa4f49a9c62545575255aad77ec","source":{"kind":"arxiv","id":"hep-ph/9905237","version":1},"attestation_state":"computed","paper":{"title":"Harmonic Polylogarithms","license":"","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"E. Remiddi, J. A. M. Vermaseren","submitted_at":"1999-05-04T13:03:18Z","abstract_excerpt":"The harmonic polylogarithms (hpl's) are introduced. They are a generalization of Nielsen's polylogarithms, satisfying a product algebra (the product of two hpl's is in turn a combination of hpl's) and forming a set closed under the transformation of the arguments x=1/z and x=(1-t)/(1+t). The coefficients of their expansions and their Mellin transforms are harmonic sums."},"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/9905237","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-ph","submitted_at":"1999-05-04T13:03:18Z","cross_cats_sorted":[],"title_canon_sha256":"ade822ef4a47d3c3c77fb1c5d525ce76e2a4a30e5fcc7dcd1fff957bc03c64b4","abstract_canon_sha256":"fee4a25dd65a25dda169bd3d0b3bc75715b936a43c68e71ced3701405818a53a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:14:16.298137Z","signature_b64":"fjQMbbX7XMiMtVdRBbMcjgJ/PK90j/pWKRsLz9Qb526gCWaf6XWiY7vTVb7k2C872pRBkfdzFEkLAjnHWZ5UCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e164b96d8c063b0ef329ff3761c8773d7de4baa4f49a9c62545575255aad77ec","last_reissued_at":"2026-07-04T16:14:16.297740Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:14:16.297740Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Harmonic Polylogarithms","license":"","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"E. Remiddi, J. A. M. Vermaseren","submitted_at":"1999-05-04T13:03:18Z","abstract_excerpt":"The harmonic polylogarithms (hpl's) are introduced. They are a generalization of Nielsen's polylogarithms, satisfying a product algebra (the product of two hpl's is in turn a combination of hpl's) and forming a set closed under the transformation of the arguments x=1/z and x=(1-t)/(1+t). The coefficients of their expansions and their Mellin transforms are harmonic sums."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-ph/9905237","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/hep-ph/9905237/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"hep-ph/9905237","created_at":"2026-07-04T16:14:16.297798+00:00"},{"alias_kind":"arxiv_version","alias_value":"hep-ph/9905237v1","created_at":"2026-07-04T16:14:16.297798+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-ph/9905237","created_at":"2026-07-04T16:14:16.297798+00:00"},{"alias_kind":"pith_short_12","alias_value":"4FSLS3MMAY5Q","created_at":"2026-07-04T16:14:16.297798+00:00"},{"alias_kind":"pith_short_16","alias_value":"4FSLS3MMAY5Q54ZJ","created_at":"2026-07-04T16:14:16.297798+00:00"},{"alias_kind":"pith_short_8","alias_value":"4FSLS3MM","created_at":"2026-07-04T16:14:16.297798+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":22,"internal_anchor_count":18,"sample":[{"citing_arxiv_id":"2606.21702","citing_title":"Analytic results for heavy-quark contributions to charged-current DIS at NNLO","ref_index":90,"is_internal_anchor":true},{"citing_arxiv_id":"2606.13627","citing_title":"A Graphical Coaction for FRW Integrals from Partial/Relative Twisted (Co)homology","ref_index":30,"is_internal_anchor":true},{"citing_arxiv_id":"2606.12584","citing_title":"The $\\mu$-extension of iterated integrals and nested sums","ref_index":60,"is_internal_anchor":true},{"citing_arxiv_id":"2606.02744","citing_title":"IterInt: Evaluating iterated integrals via differential equations","ref_index":12,"is_internal_anchor":true},{"citing_arxiv_id":"2606.28239","citing_title":"Gravitational Compton scattering at the fourth post-Minkowskian order","ref_index":103,"is_internal_anchor":true},{"citing_arxiv_id":"2606.30708","citing_title":"LinApart3: efficient algorithm for multivariate partial fraction decomposition with linear denominators","ref_index":6,"is_internal_anchor":true},{"citing_arxiv_id":"2605.10284","citing_title":"Four-loop anomalous dimension of flavor non-singlet quark operator of twist two and Lorentz spin N for general gauge group: transcendental part","ref_index":69,"is_internal_anchor":true},{"citing_arxiv_id":"2605.28926","citing_title":"Multi-Loop Negative Geometries","ref_index":116,"is_internal_anchor":true},{"citing_arxiv_id":"2606.22380","citing_title":"Eight loop form factors, amplitudes and patterns in planar $\\mathcal{N}=4$ super-Yang-Mills theory","ref_index":34,"is_internal_anchor":true},{"citing_arxiv_id":"1912.02303","citing_title":"Analytical solution to DGLAP integro-differential equation via complex maps in domains of contour integrals","ref_index":23,"is_internal_anchor":true},{"citing_arxiv_id":"2503.02096","citing_title":"Deriving motivic coactions and single-valued maps at genus zero from zeta generators","ref_index":3,"is_internal_anchor":true},{"citing_arxiv_id":"2505.09808","citing_title":"Leading singularities and chambers of Correlahedron","ref_index":39,"is_internal_anchor":true},{"citing_arxiv_id":"2411.11846","citing_title":"Emergence of Calabi-Yau manifolds in high-precision black hole scattering","ref_index":83,"is_internal_anchor":true},{"citing_arxiv_id":"2508.02800","citing_title":"Towards Motivic Coactions at Genus One from Zeta Generators","ref_index":145,"is_internal_anchor":true},{"citing_arxiv_id":"2512.14295","citing_title":"Conformal moments of the two-loop coefficient functions in DVCS","ref_index":40,"is_internal_anchor":true},{"citing_arxiv_id":"2512.23699","citing_title":"Twisted de Rham theory for string double copy in AdS","ref_index":31,"is_internal_anchor":true},{"citing_arxiv_id":"2601.06245","citing_title":"Threshold resummation of Semi-Inclusive Deep-Inelastic Scattering","ref_index":27,"is_internal_anchor":true},{"citing_arxiv_id":"2603.15751","citing_title":"The photon-energy spectrum in $B\\to X_s\\gamma$ to N$^3$LO: light-fermion and large-$N_{\\rm c}$ corrections","ref_index":79,"is_internal_anchor":true},{"citing_arxiv_id":"2605.03889","citing_title":"Properties and implications of the four-loop non-singlet splitting functions in QCD","ref_index":23,"is_internal_anchor":false},{"citing_arxiv_id":"2605.10284","citing_title":"Four-loop anomalous dimension of flavor non-singlet quark operator of twist two and Lorentz spin N for general gauge group: transcendental part","ref_index":69,"is_internal_anchor":false},{"citing_arxiv_id":"2604.25270","citing_title":"Integrand Analysis, Leading Singularities and Canonical Bases beyond Polylogarithms","ref_index":5,"is_internal_anchor":false},{"citing_arxiv_id":"2604.08332","citing_title":"Discrete symmetries of Feynman integrals","ref_index":54,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4FSLS3MMAY5Q54ZJ743WDSDXHV","json":"https://pith.science/pith/4FSLS3MMAY5Q54ZJ743WDSDXHV.json","graph_json":"https://pith.science/api/pith-number/4FSLS3MMAY5Q54ZJ743WDSDXHV/graph.json","events_json":"https://pith.science/api/pith-number/4FSLS3MMAY5Q54ZJ743WDSDXHV/events.json","paper":"https://pith.science/paper/4FSLS3MM"},"agent_actions":{"view_html":"https://pith.science/pith/4FSLS3MMAY5Q54ZJ743WDSDXHV","download_json":"https://pith.science/pith/4FSLS3MMAY5Q54ZJ743WDSDXHV.json","view_paper":"https://pith.science/paper/4FSLS3MM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=hep-ph/9905237&json=true","fetch_graph":"https://pith.science/api/pith-number/4FSLS3MMAY5Q54ZJ743WDSDXHV/graph.json","fetch_events":"https://pith.science/api/pith-number/4FSLS3MMAY5Q54ZJ743WDSDXHV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4FSLS3MMAY5Q54ZJ743WDSDXHV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4FSLS3MMAY5Q54ZJ743WDSDXHV/action/storage_attestation","attest_author":"https://pith.science/pith/4FSLS3MMAY5Q54ZJ743WDSDXHV/action/author_attestation","sign_citation":"https://pith.science/pith/4FSLS3MMAY5Q54ZJ743WDSDXHV/action/citation_signature","submit_replication":"https://pith.science/pith/4FSLS3MMAY5Q54ZJ743WDSDXHV/action/replication_record"}},"created_at":"2026-07-04T16:14:16.297798+00:00","updated_at":"2026-07-04T16:14:16.297798+00:00"}