{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:YX766LSVFW6W76AYRNQRMLRNER","short_pith_number":"pith:YX766LSV","schema_version":"1.0","canonical_sha256":"c5ffef2e552dbd6ff8188b61162e2d244ff6382bc55b6dc86694b2bba1ac3d5a","source":{"kind":"arxiv","id":"0910.1932","version":10},"attestation_state":"computed","paper":{"title":"On a conjecture by Pierre Cartier about a group of associators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Vincel Hoang Ngoc Minh (LIPN)","submitted_at":"2009-10-10T17:20:41Z","abstract_excerpt":"In \\cite{cartier2}, Pierre Cartier conjectured that for any non commutative formal power series $\\Phi$ on $X=\\{x_0,x_1\\}$ with coefficients in a $\\Q$-extension, $A$, subjected to some suitable conditions, there exists an unique algebra homomorphism $\\varphi$ from the $\\Q$-algebra generated by the convergent polyz\\^etas to $A$ such that $\\Phi$ is computed from $\\Phi_{KZ}$ Drinfel'd associator by applying $\\varphi$ to each coefficient. We prove $\\varphi$ exists and it is a free Lie exponential over $X$. Moreover, we give a complete description of the kernel of polyz\\^eta and draw some consequenc"},"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":"0910.1932","kind":"arxiv","version":10},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-10-10T17:20:41Z","cross_cats_sorted":[],"title_canon_sha256":"dfe483107f4656630077d89063768c2f18d01fa827a5867082490f86525f3d7c","abstract_canon_sha256":"607f37be8bdef74fafc6c9595738ef597ad856747894b12d33d760151b09b379"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:53:55.058954Z","signature_b64":"wqimbioDo45mTIT6uA+p7B4tE0G75rULkszd2FT8yR4XKuTrivwi9qqkjuD7MVMtQR3hFo88iNPzq64fMqyzAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c5ffef2e552dbd6ff8188b61162e2d244ff6382bc55b6dc86694b2bba1ac3d5a","last_reissued_at":"2026-05-18T03:53:55.058443Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:53:55.058443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On a conjecture by Pierre Cartier about a group of associators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Vincel Hoang Ngoc Minh (LIPN)","submitted_at":"2009-10-10T17:20:41Z","abstract_excerpt":"In \\cite{cartier2}, Pierre Cartier conjectured that for any non commutative formal power series $\\Phi$ on $X=\\{x_0,x_1\\}$ with coefficients in a $\\Q$-extension, $A$, subjected to some suitable conditions, there exists an unique algebra homomorphism $\\varphi$ from the $\\Q$-algebra generated by the convergent polyz\\^etas to $A$ such that $\\Phi$ is computed from $\\Phi_{KZ}$ Drinfel'd associator by applying $\\varphi$ to each coefficient. We prove $\\varphi$ exists and it is a free Lie exponential over $X$. Moreover, we give a complete description of the kernel of polyz\\^eta and draw some consequenc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.1932","kind":"arxiv","version":10},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"0910.1932","created_at":"2026-05-18T03:53:55.058544+00:00"},{"alias_kind":"arxiv_version","alias_value":"0910.1932v10","created_at":"2026-05-18T03:53:55.058544+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.1932","created_at":"2026-05-18T03:53:55.058544+00:00"},{"alias_kind":"pith_short_12","alias_value":"YX766LSVFW6W","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_16","alias_value":"YX766LSVFW6W76AY","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_8","alias_value":"YX766LSV","created_at":"2026-05-18T12:26:02.257875+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/YX766LSVFW6W76AYRNQRMLRNER","json":"https://pith.science/pith/YX766LSVFW6W76AYRNQRMLRNER.json","graph_json":"https://pith.science/api/pith-number/YX766LSVFW6W76AYRNQRMLRNER/graph.json","events_json":"https://pith.science/api/pith-number/YX766LSVFW6W76AYRNQRMLRNER/events.json","paper":"https://pith.science/paper/YX766LSV"},"agent_actions":{"view_html":"https://pith.science/pith/YX766LSVFW6W76AYRNQRMLRNER","download_json":"https://pith.science/pith/YX766LSVFW6W76AYRNQRMLRNER.json","view_paper":"https://pith.science/paper/YX766LSV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0910.1932&json=true","fetch_graph":"https://pith.science/api/pith-number/YX766LSVFW6W76AYRNQRMLRNER/graph.json","fetch_events":"https://pith.science/api/pith-number/YX766LSVFW6W76AYRNQRMLRNER/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YX766LSVFW6W76AYRNQRMLRNER/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YX766LSVFW6W76AYRNQRMLRNER/action/storage_attestation","attest_author":"https://pith.science/pith/YX766LSVFW6W76AYRNQRMLRNER/action/author_attestation","sign_citation":"https://pith.science/pith/YX766LSVFW6W76AYRNQRMLRNER/action/citation_signature","submit_replication":"https://pith.science/pith/YX766LSVFW6W76AYRNQRMLRNER/action/replication_record"}},"created_at":"2026-05-18T03:53:55.058544+00:00","updated_at":"2026-05-18T03:53:55.058544+00:00"}