{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:SSZJ3U62AI2SXZFLUC2RCH4LV4","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":"57cd29fd00ff09df98b3b8de10ae527c74c9cc203a59a84a92ed3408b9436fa1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-10-05T13:30:19Z","title_canon_sha256":"c713ddc73d3de1545b8d4e32cb9673fb27bdd71f720e2dc6797f5fd98999c0c8"},"schema_version":"1.0","source":{"id":"1610.01409","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.01409","created_at":"2026-05-18T01:03:10Z"},{"alias_kind":"arxiv_version","alias_value":"1610.01409v1","created_at":"2026-05-18T01:03:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.01409","created_at":"2026-05-18T01:03:10Z"},{"alias_kind":"pith_short_12","alias_value":"SSZJ3U62AI2S","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SSZJ3U62AI2SXZFL","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SSZJ3U62","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:70ce72867abea46fca893a68b91a82194e412035ebea7d48072afdb226d7b96e","target":"graph","created_at":"2026-05-18T01:03:10Z","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 construct algebraic families of exotic affine 3-spheres, that is, smooth affine threefolds diffeomorphic to a non-degenerate smooth complex affine quadric of dimension 3 but non algebraically isomorphic to it. We show in particular that for every smooth topologically contractible affine surface S with trivial automorphism group, there exists a canonical smooth family of pairwise non isomorphic exotic affine 3-spheres parametrized by the closed points of S.","authors_text":"Adrien Dubouloz (IMB)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-10-05T13:30:19Z","title":"Families of exotic affine 3-spheres"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.01409","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":"sha256:8eb041253b62e15850504d63c971cbffb189d4d84d9965b4a2f8e4243ae283ce","target":"record","created_at":"2026-05-18T01:03:10Z","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":"57cd29fd00ff09df98b3b8de10ae527c74c9cc203a59a84a92ed3408b9436fa1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-10-05T13:30:19Z","title_canon_sha256":"c713ddc73d3de1545b8d4e32cb9673fb27bdd71f720e2dc6797f5fd98999c0c8"},"schema_version":"1.0","source":{"id":"1610.01409","kind":"arxiv","version":1}},"canonical_sha256":"94b29dd3da02352be4aba0b5111f8baf2821e1c136b4872b5208594748c02a98","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"94b29dd3da02352be4aba0b5111f8baf2821e1c136b4872b5208594748c02a98","first_computed_at":"2026-05-18T01:03:10.922390Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:10.922390Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uHEwasFQsJaKsXoYrr5V+XqNAyl0xKcSub9ljf2In+LcreVLrJCw6HGgO61k/iwFfH5bSlVLRzEvHwU7OuTQAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:10.923162Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.01409","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8eb041253b62e15850504d63c971cbffb189d4d84d9965b4a2f8e4243ae283ce","sha256:70ce72867abea46fca893a68b91a82194e412035ebea7d48072afdb226d7b96e"],"state_sha256":"b46c777b5390786a527c117d4d8625e62a61b8b6a29b71db72edea490a426f1b"}