{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:FVKE6HZQCWMET7KFH3XREBQDZC","short_pith_number":"pith:FVKE6HZQ","schema_version":"1.0","canonical_sha256":"2d544f1f30159849fd453eef120603c8b0d8f6aae5d6b0a7291e50cdaddab1f1","source":{"kind":"arxiv","id":"1601.01159","version":2},"attestation_state":"computed","paper":{"title":"An explicit theory of $\\pi_{1}^\\mathrm{un,crys}(\\mathbb{P}^{1} - \\{0,\\mu_{N},\\infty\\})$ - II-3 : Sequences of multiple harmonic sums viewed as periods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"David Jarossay","submitted_at":"2016-01-06T12:38:39Z","abstract_excerpt":"Let $X=\\text{ }\\mathbb{P}^{1} - (\\{0,\\infty\\} \\cup \\mu_{N})\\text{ }/\\text{ }W(\\mathbb{F}_{q})$, with $N \\in \\mathbb{N}^{\\ast}$ and $\\mathbb{F}_{q}$ of characteristic $p$ prime to $N$ and containing a primitive $N$-th root of unity. We establish an explicit theory of the crystalline Frobenius of the pro-unipotent fundamental groupoid of $X$. In part I, we have computed explicitly the Frobenius action. In part II, we use this computation to understand explicitly the algebraic relations of cyclotomic $p$-adic multiple zeta values. We have used the ideas and the vocabulary of the Galois theory of "},"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":"1601.01159","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-01-06T12:38:39Z","cross_cats_sorted":[],"title_canon_sha256":"30e72b207daec69c62a3a95b7cf33364f7af478f7a6650f9040b4c21ecbb2c4b","abstract_canon_sha256":"8f961620c0fb1c1078e67a43f75710e94be9bd08875daae0dc25085336698298"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:01:09.534924Z","signature_b64":"eFvjnvT6WseBClXp40EF+5Irp8arbrn/P724PBdIgau+OP9ET9m8KvtrGTmYwWFMYMUThSexoOVKOiEIOfWfDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2d544f1f30159849fd453eef120603c8b0d8f6aae5d6b0a7291e50cdaddab1f1","last_reissued_at":"2026-05-18T01:01:09.534275Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:01:09.534275Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An explicit theory of $\\pi_{1}^\\mathrm{un,crys}(\\mathbb{P}^{1} - \\{0,\\mu_{N},\\infty\\})$ - II-3 : Sequences of multiple harmonic sums viewed as periods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"David Jarossay","submitted_at":"2016-01-06T12:38:39Z","abstract_excerpt":"Let $X=\\text{ }\\mathbb{P}^{1} - (\\{0,\\infty\\} \\cup \\mu_{N})\\text{ }/\\text{ }W(\\mathbb{F}_{q})$, with $N \\in \\mathbb{N}^{\\ast}$ and $\\mathbb{F}_{q}$ of characteristic $p$ prime to $N$ and containing a primitive $N$-th root of unity. We establish an explicit theory of the crystalline Frobenius of the pro-unipotent fundamental groupoid of $X$. In part I, we have computed explicitly the Frobenius action. In part II, we use this computation to understand explicitly the algebraic relations of cyclotomic $p$-adic multiple zeta values. We have used the ideas and the vocabulary of the Galois theory of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.01159","kind":"arxiv","version":2},"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":"1601.01159","created_at":"2026-05-18T01:01:09.534390+00:00"},{"alias_kind":"arxiv_version","alias_value":"1601.01159v2","created_at":"2026-05-18T01:01:09.534390+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.01159","created_at":"2026-05-18T01:01:09.534390+00:00"},{"alias_kind":"pith_short_12","alias_value":"FVKE6HZQCWME","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_16","alias_value":"FVKE6HZQCWMET7KF","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_8","alias_value":"FVKE6HZQ","created_at":"2026-05-18T12:30:15.759754+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.01410","citing_title":"On generic double shuffle relations, localized multiple polylogarithms and algebraic functions","ref_index":12,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FVKE6HZQCWMET7KFH3XREBQDZC","json":"https://pith.science/pith/FVKE6HZQCWMET7KFH3XREBQDZC.json","graph_json":"https://pith.science/api/pith-number/FVKE6HZQCWMET7KFH3XREBQDZC/graph.json","events_json":"https://pith.science/api/pith-number/FVKE6HZQCWMET7KFH3XREBQDZC/events.json","paper":"https://pith.science/paper/FVKE6HZQ"},"agent_actions":{"view_html":"https://pith.science/pith/FVKE6HZQCWMET7KFH3XREBQDZC","download_json":"https://pith.science/pith/FVKE6HZQCWMET7KFH3XREBQDZC.json","view_paper":"https://pith.science/paper/FVKE6HZQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1601.01159&json=true","fetch_graph":"https://pith.science/api/pith-number/FVKE6HZQCWMET7KFH3XREBQDZC/graph.json","fetch_events":"https://pith.science/api/pith-number/FVKE6HZQCWMET7KFH3XREBQDZC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FVKE6HZQCWMET7KFH3XREBQDZC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FVKE6HZQCWMET7KFH3XREBQDZC/action/storage_attestation","attest_author":"https://pith.science/pith/FVKE6HZQCWMET7KFH3XREBQDZC/action/author_attestation","sign_citation":"https://pith.science/pith/FVKE6HZQCWMET7KFH3XREBQDZC/action/citation_signature","submit_replication":"https://pith.science/pith/FVKE6HZQCWMET7KFH3XREBQDZC/action/replication_record"}},"created_at":"2026-05-18T01:01:09.534390+00:00","updated_at":"2026-05-18T01:01:09.534390+00:00"}