{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:OKDPVGKSFO2JXI3OAMZG6CJUZU","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":"fb4fcc2244042dd1a04af5c60be3069e4ce98b150325d66cb74af383412a0962","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-10-13T16:16:03Z","title_canon_sha256":"32d710797a3488a26d3a008351e1c4256cbcfcc51b003dce7f221ba06bad007b"},"schema_version":"1.0","source":{"id":"1210.3715","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.3715","created_at":"2026-05-18T03:43:17Z"},{"alias_kind":"arxiv_version","alias_value":"1210.3715v1","created_at":"2026-05-18T03:43:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.3715","created_at":"2026-05-18T03:43:17Z"},{"alias_kind":"pith_short_12","alias_value":"OKDPVGKSFO2J","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"OKDPVGKSFO2JXI3O","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"OKDPVGKS","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:515a66cd091363062c33df426878b5e6a833418b417c9cace9045ae63c504889","target":"graph","created_at":"2026-05-18T03:43:17Z","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 that the Zariski closure of the set of hypersurfaces of degree $M$ in ${\\mathbb P}^{M}$, where $M\\geq 5$, which are either not factorial or not birationally superrigid, is of codimension at least $\\binom{M-3}{2}+1$ in the parameter space.","authors_text":"Aleksandr Pukhlikov, Thomas Eckl","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-10-13T16:16:03Z","title":"On the locus of non-rigid hypersurfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.3715","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:d2ca9d9c6ee229caa8c183ed37a7588573e76d0c944295f6cb213cd34c644bf9","target":"record","created_at":"2026-05-18T03:43:17Z","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":"fb4fcc2244042dd1a04af5c60be3069e4ce98b150325d66cb74af383412a0962","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-10-13T16:16:03Z","title_canon_sha256":"32d710797a3488a26d3a008351e1c4256cbcfcc51b003dce7f221ba06bad007b"},"schema_version":"1.0","source":{"id":"1210.3715","kind":"arxiv","version":1}},"canonical_sha256":"7286fa99522bb49ba36e03326f0934cd2ce1a137bd45992e56bb74f7f917460c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7286fa99522bb49ba36e03326f0934cd2ce1a137bd45992e56bb74f7f917460c","first_computed_at":"2026-05-18T03:43:17.297899Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:43:17.297899Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AgrTNH+oWMb0iI6GrbN3YF5Is8j9R/l8ydwBwLQGOunvBuDNmFxlWjH1xYZvaGKxTiy/jZn60ZurYo0324qzAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:43:17.298467Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.3715","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d2ca9d9c6ee229caa8c183ed37a7588573e76d0c944295f6cb213cd34c644bf9","sha256:515a66cd091363062c33df426878b5e6a833418b417c9cace9045ae63c504889"],"state_sha256":"850fbf388c13b8e60a023a66096681704eadc5c5ef942eece3be82577d254776"}