{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:QK663U62UMHRRO4BWX762BFAHE","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":"4efcd06d7d0e3c5a73b455a6080f90c3ca86f4b9f37622c3d23e50c724b94e22","cross_cats_sorted":["math-ph","math.KT","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-09-18T21:47:18Z","title_canon_sha256":"a91f8332cd52ca90ddccb75443a903e73185f3b2f51c36e0e6611ba3dd8782dd"},"schema_version":"1.0","source":{"id":"1609.05557","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.05557","created_at":"2026-05-18T01:04:26Z"},{"alias_kind":"arxiv_version","alias_value":"1609.05557v1","created_at":"2026-05-18T01:04:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.05557","created_at":"2026-05-18T01:04:26Z"},{"alias_kind":"pith_short_12","alias_value":"QK663U62UMHR","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"QK663U62UMHRRO4B","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"QK663U62","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:c4b23786c51e4869b05f0144d2351df39724f4e3c949fb1cc38e97c9bb127078","target":"graph","created_at":"2026-05-18T01:04:26Z","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":"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. 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).","authors_text":"Herbert Gangl","cross_cats":["math-ph","math.KT","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-09-18T21:47:18Z","title":"Multiple polylogarithms in weight 4"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.05557","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:e0bb065cfe6f4da2afb4e4aa1d762770531f7413cbce97e6027b0e2835fbc593","target":"record","created_at":"2026-05-18T01:04:26Z","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":"4efcd06d7d0e3c5a73b455a6080f90c3ca86f4b9f37622c3d23e50c724b94e22","cross_cats_sorted":["math-ph","math.KT","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-09-18T21:47:18Z","title_canon_sha256":"a91f8332cd52ca90ddccb75443a903e73185f3b2f51c36e0e6611ba3dd8782dd"},"schema_version":"1.0","source":{"id":"1609.05557","kind":"arxiv","version":1}},"canonical_sha256":"82bdedd3daa30f18bb81b5ffed04a039311d5f35fefda0b75646b9f3199d9946","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"82bdedd3daa30f18bb81b5ffed04a039311d5f35fefda0b75646b9f3199d9946","first_computed_at":"2026-05-18T01:04:26.073618Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:26.073618Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IgBLapINQLpRuECdix+hAtrA8iKGHFD2jGO25gGWm2CaBvAz0D8hkDvscQ9M+O62ERy8pH0M6852JLmqoKIRDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:26.074395Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.05557","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e0bb065cfe6f4da2afb4e4aa1d762770531f7413cbce97e6027b0e2835fbc593","sha256:c4b23786c51e4869b05f0144d2351df39724f4e3c949fb1cc38e97c9bb127078"],"state_sha256":"9ee48a0e69e2c41b46de120ae9c82e55c5766f2d306cdacd1d79cfd3797b1377"}