{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:L7OF5PH6LI2GL4NO7EW2AB6UNX","short_pith_number":"pith:L7OF5PH6","canonical_record":{"source":{"id":"0906.3456","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-06-18T14:38:46Z","cross_cats_sorted":[],"title_canon_sha256":"13dfa382b07410cc005d7143bb232a16a7a87f891a5758cddd7b9d8d2e101134","abstract_canon_sha256":"8e4cb455f41b1dacd8e9fc203d1c3c16cf2b502b9be6309f2e57ffad2fee9451"},"schema_version":"1.0"},"canonical_sha256":"5fdc5ebcfe5a3465f1aef92da007d46dfafde1dd82c9fbb5e373f2c208ffa0db","source":{"kind":"arxiv","id":"0906.3456","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0906.3456","created_at":"2026-05-18T02:58:03Z"},{"alias_kind":"arxiv_version","alias_value":"0906.3456v1","created_at":"2026-05-18T02:58:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.3456","created_at":"2026-05-18T02:58:03Z"},{"alias_kind":"pith_short_12","alias_value":"L7OF5PH6LI2G","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"L7OF5PH6LI2GL4NO","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"L7OF5PH6","created_at":"2026-05-18T12:26:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:L7OF5PH6LI2GL4NO7EW2AB6UNX","target":"record","payload":{"canonical_record":{"source":{"id":"0906.3456","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-06-18T14:38:46Z","cross_cats_sorted":[],"title_canon_sha256":"13dfa382b07410cc005d7143bb232a16a7a87f891a5758cddd7b9d8d2e101134","abstract_canon_sha256":"8e4cb455f41b1dacd8e9fc203d1c3c16cf2b502b9be6309f2e57ffad2fee9451"},"schema_version":"1.0"},"canonical_sha256":"5fdc5ebcfe5a3465f1aef92da007d46dfafde1dd82c9fbb5e373f2c208ffa0db","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:03.084562Z","signature_b64":"aIPSrmh/f7r1KZ3/S1pumWSPIsa0mp/HMAicrjc5MZqzFF3SnCM37aiOSuw7Y9sURXrnJjSBdBf//ACDR9pYCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5fdc5ebcfe5a3465f1aef92da007d46dfafde1dd82c9fbb5e373f2c208ffa0db","last_reissued_at":"2026-05-18T02:58:03.084030Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:03.084030Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0906.3456","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:58:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O5W3WJOhg3rgNhL2O+aouJ0/Ozfie5Mq2HSiLr1AD8ogVPy+055LlnE1XpgNZ9AC8UJ0Fj7fiLMe58HwUhcDCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T10:48:52.881953Z"},"content_sha256":"3ee02b3112c98d40329f965bbf1c0764b9a5d82c7a9b06bf28bcd0e48d40ddd7","schema_version":"1.0","event_id":"sha256:3ee02b3112c98d40329f965bbf1c0764b9a5d82c7a9b06bf28bcd0e48d40ddd7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:L7OF5PH6LI2GL4NO7EW2AB6UNX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Le d\\'efaut d'approximation forte dans les groupes lin\\'eaires connexes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Cyril Demarche","submitted_at":"2009-06-18T14:38:46Z","abstract_excerpt":"Let G be a connected linear algebraic group over a number field k. We establish an exact sequence describing the closure of the group G(k) of rational points of G in the group of adelic points of G. This exact sequence describes the defect of strong approximation on G in terms of the algebraic Brauer group of G. In particular, we deduce from those results that the integral Brauer-Manin obstruction on a torsor under the group G is the only obstruction to the existence of an integral point on this torsor. We also obtain a non-abelian Poitou-Tate exact sequence for the Galois cohomology of the li"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.3456","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:58:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QvBaXGnKIlgxK6jSo6ofsTaeITWWbQKf1x+ZtJGD5LXf+dlhWvuMh7EQcC9hvmio+oyBgqQULh+hmpvOMfggCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T10:48:52.882298Z"},"content_sha256":"c78e4676ccc12636cbcf8b8435ef19fd3d776caf9a19ab241f50a9fd04145cfb","schema_version":"1.0","event_id":"sha256:c78e4676ccc12636cbcf8b8435ef19fd3d776caf9a19ab241f50a9fd04145cfb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L7OF5PH6LI2GL4NO7EW2AB6UNX/bundle.json","state_url":"https://pith.science/pith/L7OF5PH6LI2GL4NO7EW2AB6UNX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L7OF5PH6LI2GL4NO7EW2AB6UNX/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-01T10:48:52Z","links":{"resolver":"https://pith.science/pith/L7OF5PH6LI2GL4NO7EW2AB6UNX","bundle":"https://pith.science/pith/L7OF5PH6LI2GL4NO7EW2AB6UNX/bundle.json","state":"https://pith.science/pith/L7OF5PH6LI2GL4NO7EW2AB6UNX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L7OF5PH6LI2GL4NO7EW2AB6UNX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:L7OF5PH6LI2GL4NO7EW2AB6UNX","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":"8e4cb455f41b1dacd8e9fc203d1c3c16cf2b502b9be6309f2e57ffad2fee9451","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-06-18T14:38:46Z","title_canon_sha256":"13dfa382b07410cc005d7143bb232a16a7a87f891a5758cddd7b9d8d2e101134"},"schema_version":"1.0","source":{"id":"0906.3456","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0906.3456","created_at":"2026-05-18T02:58:03Z"},{"alias_kind":"arxiv_version","alias_value":"0906.3456v1","created_at":"2026-05-18T02:58:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.3456","created_at":"2026-05-18T02:58:03Z"},{"alias_kind":"pith_short_12","alias_value":"L7OF5PH6LI2G","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"L7OF5PH6LI2GL4NO","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"L7OF5PH6","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:c78e4676ccc12636cbcf8b8435ef19fd3d776caf9a19ab241f50a9fd04145cfb","target":"graph","created_at":"2026-05-18T02:58:03Z","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 G be a connected linear algebraic group over a number field k. We establish an exact sequence describing the closure of the group G(k) of rational points of G in the group of adelic points of G. This exact sequence describes the defect of strong approximation on G in terms of the algebraic Brauer group of G. In particular, we deduce from those results that the integral Brauer-Manin obstruction on a torsor under the group G is the only obstruction to the existence of an integral point on this torsor. We also obtain a non-abelian Poitou-Tate exact sequence for the Galois cohomology of the li","authors_text":"Cyril Demarche","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-06-18T14:38:46Z","title":"Le d\\'efaut d'approximation forte dans les groupes lin\\'eaires connexes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.3456","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":"sha256:3ee02b3112c98d40329f965bbf1c0764b9a5d82c7a9b06bf28bcd0e48d40ddd7","target":"record","created_at":"2026-05-18T02:58:03Z","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":"8e4cb455f41b1dacd8e9fc203d1c3c16cf2b502b9be6309f2e57ffad2fee9451","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-06-18T14:38:46Z","title_canon_sha256":"13dfa382b07410cc005d7143bb232a16a7a87f891a5758cddd7b9d8d2e101134"},"schema_version":"1.0","source":{"id":"0906.3456","kind":"arxiv","version":1}},"canonical_sha256":"5fdc5ebcfe5a3465f1aef92da007d46dfafde1dd82c9fbb5e373f2c208ffa0db","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5fdc5ebcfe5a3465f1aef92da007d46dfafde1dd82c9fbb5e373f2c208ffa0db","first_computed_at":"2026-05-18T02:58:03.084030Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:03.084030Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aIPSrmh/f7r1KZ3/S1pumWSPIsa0mp/HMAicrjc5MZqzFF3SnCM37aiOSuw7Y9sURXrnJjSBdBf//ACDR9pYCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:03.084562Z","signed_message":"canonical_sha256_bytes"},"source_id":"0906.3456","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3ee02b3112c98d40329f965bbf1c0764b9a5d82c7a9b06bf28bcd0e48d40ddd7","sha256:c78e4676ccc12636cbcf8b8435ef19fd3d776caf9a19ab241f50a9fd04145cfb"],"state_sha256":"14f031e58f0ea27a9e188d5aa340114ddb653a5285d0395ac311260a699ab28a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W7l90yFsnNycqVxbZCRsdGt3stto2edxRMpjOg8bKdqaqNHZWtdSq2Cqi6GUGotk4iBNVdWccEZ34BOygL1ADw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T10:48:52.884412Z","bundle_sha256":"8bb6af3a1efc2d5eefa5f4d245e709670cb81dcbca3d01e2e6060be0d6a16c4e"}}