{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:6PHZ434QLUXZ3IMPH2UNR7N63A","short_pith_number":"pith:6PHZ434Q","schema_version":"1.0","canonical_sha256":"f3cf9e6f905d2f9da18f3ea8d8fdbed82b54929bd668da367e517d440d82ad6a","source":{"kind":"arxiv","id":"1301.4429","version":2},"attestation_state":"computed","paper":{"title":"Lifting Galois sections along torsors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Jakob Stix, Michel Emsalem, Niels Borne","submitted_at":"2013-01-18T16:50:07Z","abstract_excerpt":"The cuspidalization conjecture, which is a consequence of Grothendieck's section conjecture, asserts that for any smooth hyperbolic curve $X$ over a finitely generated field $k$ of characteristic $0$ and any non empty Zariski open $U \\subset X$, every section of $\\pi _1 (X, \\bar x) \\to \\mathrm{Gal}_k$ lifts to a section of $\\pi _1 (U,\\bar x) \\to \\mathrm{Gal}_k$. We consider in this article the problem of lifting Galois sections to the intermediate quotient $ \\pi_1^{cc}(U)$ introduced by Mochizuki. We show that when $k = \\mathbb Q$ and $D=X\\setminus U$ is an union of torsion sub-packets every G"},"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":"1301.4429","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-01-18T16:50:07Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"7a39ec73f79ff77925b37e57a1c497a99df9c3921303aeca42a7181bb1dabd76","abstract_canon_sha256":"6ca787df60266fc3736c90cc369a4945fdeb5a42a3274d80e22a78a5c7aae348"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:16.883025Z","signature_b64":"woaaALh8Yu9YRUbeNfOg4R8+jzu3lnEMnXkT6o3JgwDa+SWiXisICTPcuGk2wV3LdW+5NL08xfWa3cHsdMuDCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f3cf9e6f905d2f9da18f3ea8d8fdbed82b54929bd668da367e517d440d82ad6a","last_reissued_at":"2026-05-18T01:35:16.882546Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:16.882546Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lifting Galois sections along torsors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Jakob Stix, Michel Emsalem, Niels Borne","submitted_at":"2013-01-18T16:50:07Z","abstract_excerpt":"The cuspidalization conjecture, which is a consequence of Grothendieck's section conjecture, asserts that for any smooth hyperbolic curve $X$ over a finitely generated field $k$ of characteristic $0$ and any non empty Zariski open $U \\subset X$, every section of $\\pi _1 (X, \\bar x) \\to \\mathrm{Gal}_k$ lifts to a section of $\\pi _1 (U,\\bar x) \\to \\mathrm{Gal}_k$. We consider in this article the problem of lifting Galois sections to the intermediate quotient $ \\pi_1^{cc}(U)$ introduced by Mochizuki. We show that when $k = \\mathbb Q$ and $D=X\\setminus U$ is an union of torsion sub-packets every G"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.4429","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":"1301.4429","created_at":"2026-05-18T01:35:16.882616+00:00"},{"alias_kind":"arxiv_version","alias_value":"1301.4429v2","created_at":"2026-05-18T01:35:16.882616+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.4429","created_at":"2026-05-18T01:35:16.882616+00:00"},{"alias_kind":"pith_short_12","alias_value":"6PHZ434QLUXZ","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_16","alias_value":"6PHZ434QLUXZ3IMP","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_8","alias_value":"6PHZ434Q","created_at":"2026-05-18T12:27:36.564083+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/6PHZ434QLUXZ3IMPH2UNR7N63A","json":"https://pith.science/pith/6PHZ434QLUXZ3IMPH2UNR7N63A.json","graph_json":"https://pith.science/api/pith-number/6PHZ434QLUXZ3IMPH2UNR7N63A/graph.json","events_json":"https://pith.science/api/pith-number/6PHZ434QLUXZ3IMPH2UNR7N63A/events.json","paper":"https://pith.science/paper/6PHZ434Q"},"agent_actions":{"view_html":"https://pith.science/pith/6PHZ434QLUXZ3IMPH2UNR7N63A","download_json":"https://pith.science/pith/6PHZ434QLUXZ3IMPH2UNR7N63A.json","view_paper":"https://pith.science/paper/6PHZ434Q","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1301.4429&json=true","fetch_graph":"https://pith.science/api/pith-number/6PHZ434QLUXZ3IMPH2UNR7N63A/graph.json","fetch_events":"https://pith.science/api/pith-number/6PHZ434QLUXZ3IMPH2UNR7N63A/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6PHZ434QLUXZ3IMPH2UNR7N63A/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6PHZ434QLUXZ3IMPH2UNR7N63A/action/storage_attestation","attest_author":"https://pith.science/pith/6PHZ434QLUXZ3IMPH2UNR7N63A/action/author_attestation","sign_citation":"https://pith.science/pith/6PHZ434QLUXZ3IMPH2UNR7N63A/action/citation_signature","submit_replication":"https://pith.science/pith/6PHZ434QLUXZ3IMPH2UNR7N63A/action/replication_record"}},"created_at":"2026-05-18T01:35:16.882616+00:00","updated_at":"2026-05-18T01:35:16.882616+00:00"}