{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:5AONWHTGUMHFR2BRJXYFH42DT2","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":"f7ed8722ef27d7af486953ff178755fade6fb176e15e019385ad5b6a244209b6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-01-14T16:56:50Z","title_canon_sha256":"fc45e58c46b59a3c4ea3e33e41aea0bbb3af5a766748488b6eb12f4d718d8fbd"},"schema_version":"1.0","source":{"id":"1501.03408","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.03408","created_at":"2026-05-18T01:20:47Z"},{"alias_kind":"arxiv_version","alias_value":"1501.03408v3","created_at":"2026-05-18T01:20:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.03408","created_at":"2026-05-18T01:20:47Z"},{"alias_kind":"pith_short_12","alias_value":"5AONWHTGUMHF","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"5AONWHTGUMHFR2BR","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"5AONWHTG","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:451642af84af0dccebebc4573905a6591edb1d61b3489ce8b70a1b3bf46cf2bd","target":"graph","created_at":"2026-05-18T01:20:47Z","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 study the multiple Eisenstein series introduced by Gangl, Kaneko and Zagier. We give a proof of (restricted) finite double shuffle relations for multiple Eisenstein series by developing an explicit connection between the Fourier expansion of multiple Eisenstein series and the Goncharov coproduct on Hopf algebras of iterated integrals.","authors_text":"Henrik Bachmann, Koji Tasaka","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-01-14T16:56:50Z","title":"The double shuffle relations for multiple Eisenstein series"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.03408","kind":"arxiv","version":3},"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:f1ab8c9e653dffc68d12d7cc5f638a12a6a8cbd85182376d34358e7f218b4928","target":"record","created_at":"2026-05-18T01:20:47Z","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":"f7ed8722ef27d7af486953ff178755fade6fb176e15e019385ad5b6a244209b6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-01-14T16:56:50Z","title_canon_sha256":"fc45e58c46b59a3c4ea3e33e41aea0bbb3af5a766748488b6eb12f4d718d8fbd"},"schema_version":"1.0","source":{"id":"1501.03408","kind":"arxiv","version":3}},"canonical_sha256":"e81cdb1e66a30e58e8314df053f3439e81e74e49fb206948384b27173e9a7e65","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e81cdb1e66a30e58e8314df053f3439e81e74e49fb206948384b27173e9a7e65","first_computed_at":"2026-05-18T01:20:47.145135Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:47.145135Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uZ4lfifVpNc25HV13FTNnb5MQpFvxKgLeXPaxWiUPmUmGrATG36moyB9+1LJGdpx5ek3bE1Mdtzy15t2sesSDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:47.145590Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.03408","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f1ab8c9e653dffc68d12d7cc5f638a12a6a8cbd85182376d34358e7f218b4928","sha256:451642af84af0dccebebc4573905a6591edb1d61b3489ce8b70a1b3bf46cf2bd"],"state_sha256":"aded058134fb6a127664516a3bf51e981166eae11ae01dd60bd5b16ced4e0a04"}