{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:73CAOZX3LYSOICLE4XG3TBSA2J","short_pith_number":"pith:73CAOZX3","canonical_record":{"source":{"id":"1301.1046","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-01-06T19:56:58Z","cross_cats_sorted":["math.AT","math.GR"],"title_canon_sha256":"d34c2bc2f3fbc83606f3c149a269ad10f5e2c78cda89dbdee9d1bb4af5c12be9","abstract_canon_sha256":"d6634d8c61b4769b610fdde289e3e96f6cc716231ae4eb062b46f38abc851e1c"},"schema_version":"1.0"},"canonical_sha256":"fec40766fb5e24e40964e5cdb98640d27ef0f4d4234c9ed220cbd091d8cc48fe","source":{"kind":"arxiv","id":"1301.1046","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.1046","created_at":"2026-05-18T02:20:29Z"},{"alias_kind":"arxiv_version","alias_value":"1301.1046v3","created_at":"2026-05-18T02:20:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.1046","created_at":"2026-05-18T02:20:29Z"},{"alias_kind":"pith_short_12","alias_value":"73CAOZX3LYSO","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"73CAOZX3LYSOICLE","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"73CAOZX3","created_at":"2026-05-18T12:27:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:73CAOZX3LYSOICLE4XG3TBSA2J","target":"record","payload":{"canonical_record":{"source":{"id":"1301.1046","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-01-06T19:56:58Z","cross_cats_sorted":["math.AT","math.GR"],"title_canon_sha256":"d34c2bc2f3fbc83606f3c149a269ad10f5e2c78cda89dbdee9d1bb4af5c12be9","abstract_canon_sha256":"d6634d8c61b4769b610fdde289e3e96f6cc716231ae4eb062b46f38abc851e1c"},"schema_version":"1.0"},"canonical_sha256":"fec40766fb5e24e40964e5cdb98640d27ef0f4d4234c9ed220cbd091d8cc48fe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:20:29.149052Z","signature_b64":"nFWuzibtn12GtmrsUjbDYhrjXlVnkhREbvL3+LQhvsU7bIA0eGk4V7vNC8Lea9pj0BgZZ510MiYlV3HVEQ6BDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fec40766fb5e24e40964e5cdb98640d27ef0f4d4234c9ed220cbd091d8cc48fe","last_reissued_at":"2026-05-18T02:20:29.148600Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:20:29.148600Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.1046","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:20:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GoRB8ESCX5qmjpgBzBVhGKWoKlxguH8l4pAbNpcqRLeLkXEf3U86W0TpnuczMWxo90d4WohztiKJXb5cmP89Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T18:39:12.982934Z"},"content_sha256":"fe5f0e1feb528fe4d1ba435958784cdeea803ba88e1b14009d52aa799c0b41e7","schema_version":"1.0","event_id":"sha256:fe5f0e1feb528fe4d1ba435958784cdeea803ba88e1b14009d52aa799c0b41e7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:73CAOZX3LYSOICLE4XG3TBSA2J","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Le groupe fondamental d'un espace homog\\`ene d'un groupe alg\\'ebrique lin\\'eaire","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.GR"],"primary_cat":"math.AG","authors_text":"Cyril Demarche, Mikhail Borovoi","submitted_at":"2013-01-06T19:56:58Z","abstract_excerpt":"Soit X un espace homog\\`ene d'un groupe alg\\'ebrique lin\\'eaire connexe G sur C. Soit x un C-point de X. On d\\'esigne par H le stabilisateur de x dans G. On montre qu'on peut d\\'efinir alg\\'ebriquement le groupe fondamental topologique \\pi_1(X(C),x), si ce groupe fondamental topologique est ab\\'elien. Si Pic(G)=0 et H est connexe ou ab\\'elien, on calcule \\pi_1(X(C),x) en termes des groupes de caract\\`eres de G et H. En outre, si G et X sont d\\'efinis sur un corps alg\\'ebriquement clos de caract\\'eristique p quelconque, on calcule la partie premi\\`ere \\`a p du groupe fondamental \\'etale de X en"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1046","kind":"arxiv","version":3},"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":"2026-05-18T02:20:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6Qetl5/Be2hAYiHKIdYjf4+5xfW9j431Cju3TCGL4TI73XwBOiHjOSK26zqjH/s0OMxboUgFUQ4aFND3mtHzDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T18:39:12.983284Z"},"content_sha256":"3c3e3020528f1e8ac29728c2ecb344bf2bfd1d596d3b3b9020378120b92c3732","schema_version":"1.0","event_id":"sha256:3c3e3020528f1e8ac29728c2ecb344bf2bfd1d596d3b3b9020378120b92c3732"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/73CAOZX3LYSOICLE4XG3TBSA2J/bundle.json","state_url":"https://pith.science/pith/73CAOZX3LYSOICLE4XG3TBSA2J/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/73CAOZX3LYSOICLE4XG3TBSA2J/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":"2026-06-03T18:39:12Z","links":{"resolver":"https://pith.science/pith/73CAOZX3LYSOICLE4XG3TBSA2J","bundle":"https://pith.science/pith/73CAOZX3LYSOICLE4XG3TBSA2J/bundle.json","state":"https://pith.science/pith/73CAOZX3LYSOICLE4XG3TBSA2J/state.json","well_known_bundle":"https://pith.science/.well-known/pith/73CAOZX3LYSOICLE4XG3TBSA2J/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:73CAOZX3LYSOICLE4XG3TBSA2J","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":"d6634d8c61b4769b610fdde289e3e96f6cc716231ae4eb062b46f38abc851e1c","cross_cats_sorted":["math.AT","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-01-06T19:56:58Z","title_canon_sha256":"d34c2bc2f3fbc83606f3c149a269ad10f5e2c78cda89dbdee9d1bb4af5c12be9"},"schema_version":"1.0","source":{"id":"1301.1046","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.1046","created_at":"2026-05-18T02:20:29Z"},{"alias_kind":"arxiv_version","alias_value":"1301.1046v3","created_at":"2026-05-18T02:20:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.1046","created_at":"2026-05-18T02:20:29Z"},{"alias_kind":"pith_short_12","alias_value":"73CAOZX3LYSO","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"73CAOZX3LYSOICLE","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"73CAOZX3","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:3c3e3020528f1e8ac29728c2ecb344bf2bfd1d596d3b3b9020378120b92c3732","target":"graph","created_at":"2026-05-18T02:20:29Z","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":"Soit X un espace homog\\`ene d'un groupe alg\\'ebrique lin\\'eaire connexe G sur C. Soit x un C-point de X. On d\\'esigne par H le stabilisateur de x dans G. On montre qu'on peut d\\'efinir alg\\'ebriquement le groupe fondamental topologique \\pi_1(X(C),x), si ce groupe fondamental topologique est ab\\'elien. Si Pic(G)=0 et H est connexe ou ab\\'elien, on calcule \\pi_1(X(C),x) en termes des groupes de caract\\`eres de G et H. En outre, si G et X sont d\\'efinis sur un corps alg\\'ebriquement clos de caract\\'eristique p quelconque, on calcule la partie premi\\`ere \\`a p du groupe fondamental \\'etale de X en","authors_text":"Cyril Demarche, Mikhail Borovoi","cross_cats":["math.AT","math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-01-06T19:56:58Z","title":"Le groupe fondamental d'un espace homog\\`ene d'un groupe alg\\'ebrique lin\\'eaire"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1046","kind":"arxiv","version":3},"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:fe5f0e1feb528fe4d1ba435958784cdeea803ba88e1b14009d52aa799c0b41e7","target":"record","created_at":"2026-05-18T02:20:29Z","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":"d6634d8c61b4769b610fdde289e3e96f6cc716231ae4eb062b46f38abc851e1c","cross_cats_sorted":["math.AT","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-01-06T19:56:58Z","title_canon_sha256":"d34c2bc2f3fbc83606f3c149a269ad10f5e2c78cda89dbdee9d1bb4af5c12be9"},"schema_version":"1.0","source":{"id":"1301.1046","kind":"arxiv","version":3}},"canonical_sha256":"fec40766fb5e24e40964e5cdb98640d27ef0f4d4234c9ed220cbd091d8cc48fe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fec40766fb5e24e40964e5cdb98640d27ef0f4d4234c9ed220cbd091d8cc48fe","first_computed_at":"2026-05-18T02:20:29.148600Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:20:29.148600Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nFWuzibtn12GtmrsUjbDYhrjXlVnkhREbvL3+LQhvsU7bIA0eGk4V7vNC8Lea9pj0BgZZ510MiYlV3HVEQ6BDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:20:29.149052Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.1046","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fe5f0e1feb528fe4d1ba435958784cdeea803ba88e1b14009d52aa799c0b41e7","sha256:3c3e3020528f1e8ac29728c2ecb344bf2bfd1d596d3b3b9020378120b92c3732"],"state_sha256":"f423225be81bbc312b0c805c0478ba6df054b1fdb1c2456481960673d1819914"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+ZqOvRLu3co2DDsRo4klj8ZRirFO5XrG/diJd9YtysLsXYi+EdEs6rI0z6oYCIKk63IOtCTOqcxmkzlxgKaeAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T18:39:12.985325Z","bundle_sha256":"64d1c34855628bf3665100af8748ccd4a9e4048d4a1e74405280e3c330bfe0a6"}}