{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ELJ4VEEAOWYFEJ2XD5QZPFKR4Y","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":"0659afed98596626c19a85a7173fa8db5729c21e39289f4f18370240148f5fda","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-05-08T13:33:02Z","title_canon_sha256":"f5740290e8d791b4561ede0081ac6919c4e74b12f56242e88d2b1ee9df8eaa8e"},"schema_version":"1.0","source":{"id":"1205.1694","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.1694","created_at":"2026-05-18T03:56:09Z"},{"alias_kind":"arxiv_version","alias_value":"1205.1694v1","created_at":"2026-05-18T03:56:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.1694","created_at":"2026-05-18T03:56:09Z"},{"alias_kind":"pith_short_12","alias_value":"ELJ4VEEAOWYF","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"ELJ4VEEAOWYFEJ2X","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"ELJ4VEEA","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:5e84b06442ce2040004e06e5f7bbb08e1091a98b603d2e2f8d2e9a2e6b944bcd","target":"graph","created_at":"2026-05-18T03:56:09Z","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":"We introduce the parameterized generic Galois group of a q-difference module, that is a differential group in the sense of Kolchin. It is associated to the smallest differential tannakian category generated by the q-difference module, equipped with the forgetful functor. Our previous results on the Grothendieck conjecture for q-difference equations lead to an adelic description of the parameterized generic Galois group, in the spirit of the Grothendieck-Katz's conjecture on p-curvatures. Using this description, we show that the Malgrange-Granier D-groupoid of a nonlinear q-difference system co","authors_text":"Charlotte Hardouin, Lucia Di Vizio","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-05-08T13:33:02Z","title":"Parameterized generic Galois groups for q-difference equations, followed by the appendix \"The Galois D-groupoid of a q-difference system\" by Anne Granier"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1694","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:b5d32f91517287c27c54a7d55db187a4db20ac78656d37f94f6b6015e90e9515","target":"record","created_at":"2026-05-18T03:56:09Z","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":"0659afed98596626c19a85a7173fa8db5729c21e39289f4f18370240148f5fda","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-05-08T13:33:02Z","title_canon_sha256":"f5740290e8d791b4561ede0081ac6919c4e74b12f56242e88d2b1ee9df8eaa8e"},"schema_version":"1.0","source":{"id":"1205.1694","kind":"arxiv","version":1}},"canonical_sha256":"22d3ca908075b05227571f61979551e612c6e56d4cc0a1465dc42216a400f6a7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"22d3ca908075b05227571f61979551e612c6e56d4cc0a1465dc42216a400f6a7","first_computed_at":"2026-05-18T03:56:09.374942Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:56:09.374942Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cVDRwSqEmikCmmPo3PWDWWnclQ02z75OtR31sZY6fAkqYQMBo1pPtujoaca7pa7jOjHGn4g+SgkiaXl4l5BQDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:56:09.375765Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.1694","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b5d32f91517287c27c54a7d55db187a4db20ac78656d37f94f6b6015e90e9515","sha256:5e84b06442ce2040004e06e5f7bbb08e1091a98b603d2e2f8d2e9a2e6b944bcd"],"state_sha256":"f742cd54d9310f9fe64062d4f4da760a30d7c3d4a803c5fe408cf1ee6e80194c"}