{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:C3RHJHOSCESZF6KUSH5JWCZKYB","short_pith_number":"pith:C3RHJHOS","schema_version":"1.0","canonical_sha256":"16e2749dd2112592f95491fa9b0b2ac040cad71fdbfb491645367dee547924eb","source":{"kind":"arxiv","id":"1603.05155","version":1},"attestation_state":"computed","paper":{"title":"Periods of the motivic fundamental groupoid of $\\boldsymbol{\\mathbb{P}^{1} \\diagdown \\lbrace 0, \\mu_{N}, \\infty \\rbrace}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Claire Glanois","submitted_at":"2016-03-16T15:59:24Z","abstract_excerpt":"In this thesis, following F. Brown's point of view, we look at the Hopf algebra structure of motivic cyclotomic multiple zeta values, which are motivic periods of the fundamental groupoid of $\\mathbb{P}^{1} \\diagdown \\lbrace 0, \\mu_{N}, \\infty \\rbrace $. By application of a surjective \\textit{period} map (which, under Grothendieck's period conjecture, is an isomorphism), we deduce results (such as generating families, identities, etc.) on cyclotomic multiple zeta values, which are complex numbers. The coaction of this Hopf algebra (explicitly given by a combinatorial formula from A. Goncharov "},"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":"1603.05155","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-03-16T15:59:24Z","cross_cats_sorted":[],"title_canon_sha256":"a1d0325a17daee1e1c8e9cc43e36bdb11bd2d6bb6c57412d837e94ca85e630a5","abstract_canon_sha256":"95693cad8c08f7bd41b17ea1b1fbe7c06040e495b4c751e1cf1456355f3e6989"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:57.950723Z","signature_b64":"kOzv+fshEHLTUXp2xFTK0eoQltJR1U/ueH3YQe73j2dgNhVaNUkdfViSV63JMxD0nDWbdUsV8aDOoWtVR0mMDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"16e2749dd2112592f95491fa9b0b2ac040cad71fdbfb491645367dee547924eb","last_reissued_at":"2026-05-18T01:18:57.950358Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:57.950358Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Periods of the motivic fundamental groupoid of $\\boldsymbol{\\mathbb{P}^{1} \\diagdown \\lbrace 0, \\mu_{N}, \\infty \\rbrace}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Claire Glanois","submitted_at":"2016-03-16T15:59:24Z","abstract_excerpt":"In this thesis, following F. Brown's point of view, we look at the Hopf algebra structure of motivic cyclotomic multiple zeta values, which are motivic periods of the fundamental groupoid of $\\mathbb{P}^{1} \\diagdown \\lbrace 0, \\mu_{N}, \\infty \\rbrace $. By application of a surjective \\textit{period} map (which, under Grothendieck's period conjecture, is an isomorphism), we deduce results (such as generating families, identities, etc.) on cyclotomic multiple zeta values, which are complex numbers. The coaction of this Hopf algebra (explicitly given by a combinatorial formula from A. Goncharov "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05155","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":""},"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":"1603.05155","created_at":"2026-05-18T01:18:57.950424+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.05155v1","created_at":"2026-05-18T01:18:57.950424+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.05155","created_at":"2026-05-18T01:18:57.950424+00:00"},{"alias_kind":"pith_short_12","alias_value":"C3RHJHOSCESZ","created_at":"2026-05-18T12:30:09.641336+00:00"},{"alias_kind":"pith_short_16","alias_value":"C3RHJHOSCESZF6KU","created_at":"2026-05-18T12:30:09.641336+00:00"},{"alias_kind":"pith_short_8","alias_value":"C3RHJHOS","created_at":"2026-05-18T12:30:09.641336+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.10262","citing_title":"An explicit Galois descent for multiple $t$-values of maximal height","ref_index":19,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/C3RHJHOSCESZF6KUSH5JWCZKYB","json":"https://pith.science/pith/C3RHJHOSCESZF6KUSH5JWCZKYB.json","graph_json":"https://pith.science/api/pith-number/C3RHJHOSCESZF6KUSH5JWCZKYB/graph.json","events_json":"https://pith.science/api/pith-number/C3RHJHOSCESZF6KUSH5JWCZKYB/events.json","paper":"https://pith.science/paper/C3RHJHOS"},"agent_actions":{"view_html":"https://pith.science/pith/C3RHJHOSCESZF6KUSH5JWCZKYB","download_json":"https://pith.science/pith/C3RHJHOSCESZF6KUSH5JWCZKYB.json","view_paper":"https://pith.science/paper/C3RHJHOS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.05155&json=true","fetch_graph":"https://pith.science/api/pith-number/C3RHJHOSCESZF6KUSH5JWCZKYB/graph.json","fetch_events":"https://pith.science/api/pith-number/C3RHJHOSCESZF6KUSH5JWCZKYB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/C3RHJHOSCESZF6KUSH5JWCZKYB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/C3RHJHOSCESZF6KUSH5JWCZKYB/action/storage_attestation","attest_author":"https://pith.science/pith/C3RHJHOSCESZF6KUSH5JWCZKYB/action/author_attestation","sign_citation":"https://pith.science/pith/C3RHJHOSCESZF6KUSH5JWCZKYB/action/citation_signature","submit_replication":"https://pith.science/pith/C3RHJHOSCESZF6KUSH5JWCZKYB/action/replication_record"}},"created_at":"2026-05-18T01:18:57.950424+00:00","updated_at":"2026-05-18T01:18:57.950424+00:00"}