{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:AXITD2Y5RJSCA5OIWHUJU2FMAX","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":"5b4073f7e9dac326b3f066b25f9a13e1809b06353888b4e31f66344f251da221","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-08-26T18:39:37Z","title_canon_sha256":"4245cbb37c6d2d3c42a339e0d51f1866a76bdd55e338751f1576a5781c0853ef"},"schema_version":"1.0","source":{"id":"1708.08009","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.08009","created_at":"2026-05-18T00:36:37Z"},{"alias_kind":"arxiv_version","alias_value":"1708.08009v1","created_at":"2026-05-18T00:36:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.08009","created_at":"2026-05-18T00:36:37Z"},{"alias_kind":"pith_short_12","alias_value":"AXITD2Y5RJSC","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"AXITD2Y5RJSCA5OI","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"AXITD2Y5","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:6bea8b30cc02f04d7d2008b1c042684b6844ba8f69e514544b821dcd8308e0c9","target":"graph","created_at":"2026-05-18T00:36:37Z","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":"Let $p$ a prime number. For all $N \\in \\mathbb{N}^{\\ast}$ prime to $p$, let $k_{N}$ be a finite field of characteristic $p$ containing a primitive $N$-th root of unity. Let $X_{k_{N},N}=\\text{ }\\mathbb{P}^{1} - (\\{0,\\infty\\} \\cup \\mu_{N})\\text{ }/\\text{ }k_{N}$. This work is an explicit theory of the crystalline pro-unipotent fundamental groupoid $(\\pi_{1}^{\\un,\\crys})$ of $X_{k_{N},N}$. In the parts I to IV, we have considered each possible value of $N$ separately. The purpose of part V is to study the role of the morphisms relating $\\pi_{1}^{\\un}(\\mathbb{P}^{1} - \\{0,\\mu_{N_{1}},\\infty\\})$ a","authors_text":"David Jarossay","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-08-26T18:39:37Z","title":"An explicit theory of $\\pi_{1}^{\\un,\\crys}(\\mathbb{P}^{1} - \\{0,\\mu_{N},\\infty\\})$ - V-1 : The Frobenius extended to $\\pi_{1}^{\\un,\\DR}(\\mathbb{P}^{1} - \\{0,\\mu_{p^{\\alpha}N},\\infty\\})$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.08009","kind":"arxiv","version":1},"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:c23c34b86cb29a067e83124345b133be7737ff7adf9c3ec47fe24c62e1a88655","target":"record","created_at":"2026-05-18T00:36:37Z","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":"5b4073f7e9dac326b3f066b25f9a13e1809b06353888b4e31f66344f251da221","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-08-26T18:39:37Z","title_canon_sha256":"4245cbb37c6d2d3c42a339e0d51f1866a76bdd55e338751f1576a5781c0853ef"},"schema_version":"1.0","source":{"id":"1708.08009","kind":"arxiv","version":1}},"canonical_sha256":"05d131eb1d8a642075c8b1e89a68ac05ea0429d8d19c3ad1dbe9f3752ef30de2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"05d131eb1d8a642075c8b1e89a68ac05ea0429d8d19c3ad1dbe9f3752ef30de2","first_computed_at":"2026-05-18T00:36:37.304248Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:37.304248Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e1NN9fANZ0xoZbbv0utkgGK68X5U/XQD0KIehEqdhlY/fWoXkCbcmXT7hHDb1yJOAislcpKmNjPmbcf/3H3LDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:37.304917Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.08009","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c23c34b86cb29a067e83124345b133be7737ff7adf9c3ec47fe24c62e1a88655","sha256:6bea8b30cc02f04d7d2008b1c042684b6844ba8f69e514544b821dcd8308e0c9"],"state_sha256":"444244b896b7985da779a698efdda4c10fb15e3b6ae536b07ee15636ed75c8e2"}