{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:6MSGGZUONG6GDJZLQDSJXSE4Y6","short_pith_number":"pith:6MSGGZUO","canonical_record":{"source":{"id":"1006.0265","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-06-01T22:58:22Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"67be9f23317e89babf5dbe13aafbd136a4f6a4d2f94e5e7b61d41fcf5a20f4fb","abstract_canon_sha256":"f1bea45433145a7298759160f28e3a583a75b14492780b7060ff07dfc1cf1e8c"},"schema_version":"1.0"},"canonical_sha256":"f32463668e69bc61a72b80e49bc89cc787955fb25f5f83862c8b959f0a35c6f7","source":{"kind":"arxiv","id":"1006.0265","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.0265","created_at":"2026-05-18T03:25:16Z"},{"alias_kind":"arxiv_version","alias_value":"1006.0265v3","created_at":"2026-05-18T03:25:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.0265","created_at":"2026-05-18T03:25:16Z"},{"alias_kind":"pith_short_12","alias_value":"6MSGGZUONG6G","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"6MSGGZUONG6GDJZL","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"6MSGGZUO","created_at":"2026-05-18T12:26:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:6MSGGZUONG6GDJZLQDSJXSE4Y6","target":"record","payload":{"canonical_record":{"source":{"id":"1006.0265","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-06-01T22:58:22Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"67be9f23317e89babf5dbe13aafbd136a4f6a4d2f94e5e7b61d41fcf5a20f4fb","abstract_canon_sha256":"f1bea45433145a7298759160f28e3a583a75b14492780b7060ff07dfc1cf1e8c"},"schema_version":"1.0"},"canonical_sha256":"f32463668e69bc61a72b80e49bc89cc787955fb25f5f83862c8b959f0a35c6f7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:25:16.487283Z","signature_b64":"L47Yh321FX1BqdF9fZ1+TdvD9zzr0yNxei7n2j8CI9I6lA04ZeWKq/OU79mtXcH2u9SAwBGzJ7s/EcYZTiTPBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f32463668e69bc61a72b80e49bc89cc787955fb25f5f83862c8b959f0a35c6f7","last_reissued_at":"2026-05-18T03:25:16.486798Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:25:16.486798Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1006.0265","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":"2026-05-18T03:25:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x019vhLv5VcQE0oyZnPT53sb2I8uKCjJzsnKv9emh432ztxFNATN6AuS+MgSv3kwtTcZ0VNNj6dqGX030OmvCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T03:51:51.092896Z"},"content_sha256":"e6cb297b15a26ce1d0350ffcd65f96c352026adfab796a4440e7c816d837f412","schema_version":"1.0","event_id":"sha256:e6cb297b15a26ce1d0350ffcd65f96c352026adfab796a4440e7c816d837f412"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:6MSGGZUONG6GDJZLQDSJXSE4Y6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"2-Nilpotent Real Section Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.AG","authors_text":"Kirsten Wickelgren","submitted_at":"2010-06-01T22:58:22Z","abstract_excerpt":"We show a 2-nilpotent section conjecture over R: for a geometrically connected curve X over R such that each irreducible component of its normalization has R-points, pi_0(X(R)) is determined by the maximal 2-nilpotent quotient of the fundamental group with its Galois action, as the kernel of an obstruction of Jordan Ellenberg. This implies that for X smooth and proper, X(R)^{+/-} is determined by the maximal 2-nilpotent quotient of Gal(C(X)) with its Gal(R)-action, where X(R)^{+/-} denotes the set of real points equipped with a real tangent direction, showing a 2-nilpotent birational real sect"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.0265","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":"2026-05-18T03:25:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jdbHn8UnZPVqhBKN0uYiIA7PTyJNa04ljOsz0SQlJoOgljMDbjIYotScCYI3VVj69uQRlswtoV14Oe3bWGo8BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T03:51:51.093517Z"},"content_sha256":"eee86412a8cd17aff5f051c840985da2a26864e21af52022102699eb1ab4b6be","schema_version":"1.0","event_id":"sha256:eee86412a8cd17aff5f051c840985da2a26864e21af52022102699eb1ab4b6be"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6MSGGZUONG6GDJZLQDSJXSE4Y6/bundle.json","state_url":"https://pith.science/pith/6MSGGZUONG6GDJZLQDSJXSE4Y6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6MSGGZUONG6GDJZLQDSJXSE4Y6/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":"2026-06-09T03:51:51Z","links":{"resolver":"https://pith.science/pith/6MSGGZUONG6GDJZLQDSJXSE4Y6","bundle":"https://pith.science/pith/6MSGGZUONG6GDJZLQDSJXSE4Y6/bundle.json","state":"https://pith.science/pith/6MSGGZUONG6GDJZLQDSJXSE4Y6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6MSGGZUONG6GDJZLQDSJXSE4Y6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:6MSGGZUONG6GDJZLQDSJXSE4Y6","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":"f1bea45433145a7298759160f28e3a583a75b14492780b7060ff07dfc1cf1e8c","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-06-01T22:58:22Z","title_canon_sha256":"67be9f23317e89babf5dbe13aafbd136a4f6a4d2f94e5e7b61d41fcf5a20f4fb"},"schema_version":"1.0","source":{"id":"1006.0265","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.0265","created_at":"2026-05-18T03:25:16Z"},{"alias_kind":"arxiv_version","alias_value":"1006.0265v3","created_at":"2026-05-18T03:25:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.0265","created_at":"2026-05-18T03:25:16Z"},{"alias_kind":"pith_short_12","alias_value":"6MSGGZUONG6G","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"6MSGGZUONG6GDJZL","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"6MSGGZUO","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:eee86412a8cd17aff5f051c840985da2a26864e21af52022102699eb1ab4b6be","target":"graph","created_at":"2026-05-18T03:25:16Z","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 show a 2-nilpotent section conjecture over R: for a geometrically connected curve X over R such that each irreducible component of its normalization has R-points, pi_0(X(R)) is determined by the maximal 2-nilpotent quotient of the fundamental group with its Galois action, as the kernel of an obstruction of Jordan Ellenberg. This implies that for X smooth and proper, X(R)^{+/-} is determined by the maximal 2-nilpotent quotient of Gal(C(X)) with its Gal(R)-action, where X(R)^{+/-} denotes the set of real points equipped with a real tangent direction, showing a 2-nilpotent birational real sect","authors_text":"Kirsten Wickelgren","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-06-01T22:58:22Z","title":"2-Nilpotent Real Section Conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.0265","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:e6cb297b15a26ce1d0350ffcd65f96c352026adfab796a4440e7c816d837f412","target":"record","created_at":"2026-05-18T03:25:16Z","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":"f1bea45433145a7298759160f28e3a583a75b14492780b7060ff07dfc1cf1e8c","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-06-01T22:58:22Z","title_canon_sha256":"67be9f23317e89babf5dbe13aafbd136a4f6a4d2f94e5e7b61d41fcf5a20f4fb"},"schema_version":"1.0","source":{"id":"1006.0265","kind":"arxiv","version":3}},"canonical_sha256":"f32463668e69bc61a72b80e49bc89cc787955fb25f5f83862c8b959f0a35c6f7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f32463668e69bc61a72b80e49bc89cc787955fb25f5f83862c8b959f0a35c6f7","first_computed_at":"2026-05-18T03:25:16.486798Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:25:16.486798Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"L47Yh321FX1BqdF9fZ1+TdvD9zzr0yNxei7n2j8CI9I6lA04ZeWKq/OU79mtXcH2u9SAwBGzJ7s/EcYZTiTPBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:25:16.487283Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.0265","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e6cb297b15a26ce1d0350ffcd65f96c352026adfab796a4440e7c816d837f412","sha256:eee86412a8cd17aff5f051c840985da2a26864e21af52022102699eb1ab4b6be"],"state_sha256":"6d027d624245bacc648a89237df5d8bb61c890aceccaeea76f04a2b020e057ab"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G20Ffq1/18q9WZ3onjbvHodLNyu0cEgpp0wOvGxaUdm3EVlZxfmYN9NHvNRNRmVPXiMgHWDb62PWttJswGAiBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T03:51:51.097059Z","bundle_sha256":"5ef17988854975a1e0dd3fdd12862bd01f16ba0e64ed47a54a0a3eba79254eca"}}