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In the process, we prove a statement conjectured by Goncharov which can be rephrased as writing the sum of iterated integrals I_{3,1}(V(x,y),z), where V(x,y) denotes a formal version of the five term relation for the dilogarithm, in terms of Li_4-terms (we need 122 such)."},"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":"1609.05557","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-09-18T21:47:18Z","cross_cats_sorted":["math-ph","math.KT","math.MP"],"title_canon_sha256":"a91f8332cd52ca90ddccb75443a903e73185f3b2f51c36e0e6611ba3dd8782dd","abstract_canon_sha256":"4efcd06d7d0e3c5a73b455a6080f90c3ca86f4b9f37622c3d23e50c724b94e22"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:26.074395Z","signature_b64":"IgBLapINQLpRuECdix+hAtrA8iKGHFD2jGO25gGWm2CaBvAz0D8hkDvscQ9M+O62ERy8pH0M6852JLmqoKIRDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"82bdedd3daa30f18bb81b5ffed04a039311d5f35fefda0b75646b9f3199d9946","last_reissued_at":"2026-05-18T01:04:26.073618Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:26.073618Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multiple polylogarithms in weight 4","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.KT","math.MP"],"primary_cat":"math.NT","authors_text":"Herbert Gangl","submitted_at":"2016-09-18T21:47:18Z","abstract_excerpt":"We clarify the relationship between different multiple polylogarithms in weight~4 by writing suitable linear combinations of a given type of iterated integral I_{n_1,...,n_d}(z_1,...,z_d), in depth d>1 and weight \\sum_i n_i=4 in terms of the classical tetralogarithm Li_4. 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