{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:EBZSNYOBY6XVMUVUB7GZA4G2E5","short_pith_number":"pith:EBZSNYOB","schema_version":"1.0","canonical_sha256":"207326e1c1c7af5652b40fcd9070da2756af97f2fa0decc83598e05f74864a71","source":{"kind":"arxiv","id":"2607.28163","version":1},"attestation_state":"computed","paper":{"title":"Double shuffle relations imply the infinitesimal hexagon equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Muze Ren","submitted_at":"2026-07-30T13:03:56Z","abstract_excerpt":"Double shuffle Lie algebra $\\mathfrak{dmr}_0$ was introduced by G.~Racinet in the algebraic study of the multiple zeta values. In this note, we prove that for any $\\psi\\in \\mathfrak{dmr}_0$, it satisfies the infinitesimal hexagon equation $[\\psi(x,y),x]+[\\psi(-x-y,y),-x-y]=0$. The proof is through the comparison of two different Hopf algebras."},"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":"2607.28163","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2026-07-30T13:03:56Z","cross_cats_sorted":[],"title_canon_sha256":"81193295b66219ba10d9c9886cc60fe0cb62c212c66aefc5a43dbaef6584b94d","abstract_canon_sha256":"504dd35c2e19d78aca2035f83b1565680e3d8e88f1983063669acc564b824e7c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"207326e1c1c7af5652b40fcd9070da2756af97f2fa0decc83598e05f74864a71","last_reissued_at":"2026-07-31T01:36:06.148912Z","signature_status":"unsigned_v0","first_computed_at":"2026-07-31T01:36:06.148912Z"},"graph_snapshot":{"paper":{"title":"Double shuffle relations imply the infinitesimal hexagon equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Muze Ren","submitted_at":"2026-07-30T13:03:56Z","abstract_excerpt":"Double shuffle Lie algebra $\\mathfrak{dmr}_0$ was introduced by G.~Racinet in the algebraic study of the multiple zeta values. In this note, we prove that for any $\\psi\\in \\mathfrak{dmr}_0$, it satisfies the infinitesimal hexagon equation $[\\psi(x,y),x]+[\\psi(-x-y,y),-x-y]=0$. The proof is through the comparison of two different Hopf algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.28163","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/2607.28163/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":"2607.28163","created_at":"2026-07-31T01:36:06.152067+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.28163v1","created_at":"2026-07-31T01:36:06.152067+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.28163","created_at":"2026-07-31T01:36:06.152067+00:00"},{"alias_kind":"pith_short_12","alias_value":"EBZSNYOBY6XV","created_at":"2026-07-31T01:36:06.152067+00:00"},{"alias_kind":"pith_short_16","alias_value":"EBZSNYOBY6XVMUVU","created_at":"2026-07-31T01:36:06.152067+00:00"},{"alias_kind":"pith_short_8","alias_value":"EBZSNYOB","created_at":"2026-07-31T01:36:06.152067+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/EBZSNYOBY6XVMUVUB7GZA4G2E5","json":"https://pith.science/pith/EBZSNYOBY6XVMUVUB7GZA4G2E5.json","graph_json":"https://pith.science/api/pith-number/EBZSNYOBY6XVMUVUB7GZA4G2E5/graph.json","events_json":"https://pith.science/api/pith-number/EBZSNYOBY6XVMUVUB7GZA4G2E5/events.json","paper":"https://pith.science/paper/EBZSNYOB"},"agent_actions":{"view_html":"https://pith.science/pith/EBZSNYOBY6XVMUVUB7GZA4G2E5","download_json":"https://pith.science/pith/EBZSNYOBY6XVMUVUB7GZA4G2E5.json","view_paper":"https://pith.science/paper/EBZSNYOB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.28163&json=true","fetch_graph":"https://pith.science/api/pith-number/EBZSNYOBY6XVMUVUB7GZA4G2E5/graph.json","fetch_events":"https://pith.science/api/pith-number/EBZSNYOBY6XVMUVUB7GZA4G2E5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EBZSNYOBY6XVMUVUB7GZA4G2E5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EBZSNYOBY6XVMUVUB7GZA4G2E5/action/storage_attestation","attest_author":"https://pith.science/pith/EBZSNYOBY6XVMUVUB7GZA4G2E5/action/author_attestation","sign_citation":"https://pith.science/pith/EBZSNYOBY6XVMUVUB7GZA4G2E5/action/citation_signature","submit_replication":"https://pith.science/pith/EBZSNYOBY6XVMUVUB7GZA4G2E5/action/replication_record"}},"created_at":"2026-07-31T01:36:06.152067+00:00","updated_at":"2026-07-31T01:36:06.152067+00:00"}