{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:FAZHLICJJP2FKIV5NMVTN3MH2R","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":"608680565bdcf88f68728f9bf17d39e292796a9d4d81e4e7e3df6341bc235375","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-02-21T18:46:31Z","title_canon_sha256":"4e8c80f02a150fabac3581bdec3e5e6db72940c8850fd27134dd0ee8aef9b8b9"},"schema_version":"1.0","source":{"id":"1702.06518","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.06518","created_at":"2026-05-18T00:25:34Z"},{"alias_kind":"arxiv_version","alias_value":"1702.06518v2","created_at":"2026-05-18T00:25:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.06518","created_at":"2026-05-18T00:25:34Z"},{"alias_kind":"pith_short_12","alias_value":"FAZHLICJJP2F","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FAZHLICJJP2FKIV5","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FAZHLICJ","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:4f96b9a0037e4dfcb00b4190ca54f24a4ecca54723282616110a79fb15c992c8","target":"graph","created_at":"2026-05-18T00:25:34Z","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 investigate the problem of the number of flats simultaneously tangent to several convex hypersurfaces in real projective space from a random point of view. More precisely, we say that smooth convex hypersurfaces $X_1, \\ldots, X_{d_{k,n}}\\subset \\mathbb{R}\\textrm{P}^n$, where $d_{k,n}=(k+1)(n-k)$, are in random position if each one of them is randomly translated by elements $g_1, \\ldots, g_{{d_{k,n}}}$ sampled independently and uniformly from the Orthogonal group; we denote by $\\tau_k(X_1, \\ldots, X_{d_{k,n}})$ the average number of $k$-dimensional projective subspaces (flats) which are simu","authors_text":"Antonio Lerario, Khazhgali Kozhasov","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-02-21T18:46:31Z","title":"On the number of flats tangent to convex hypersurfaces in random position"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.06518","kind":"arxiv","version":2},"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":"sha256:1cc4fac05cb336b05905534cae7fde2e4777406c6b83a29d5eddd96b7a7a630d","target":"record","created_at":"2026-05-18T00:25:34Z","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":"608680565bdcf88f68728f9bf17d39e292796a9d4d81e4e7e3df6341bc235375","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-02-21T18:46:31Z","title_canon_sha256":"4e8c80f02a150fabac3581bdec3e5e6db72940c8850fd27134dd0ee8aef9b8b9"},"schema_version":"1.0","source":{"id":"1702.06518","kind":"arxiv","version":2}},"canonical_sha256":"283275a0494bf45522bd6b2b36ed87d46e4197ce22556247341433ed1755fa1b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"283275a0494bf45522bd6b2b36ed87d46e4197ce22556247341433ed1755fa1b","first_computed_at":"2026-05-18T00:25:34.599770Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:34.599770Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cRXRBHtQnJsKTnAd8j4vP2HxQa2syYWFux0JV5qysnAHUlFnSMfLFWu5ZkXjeWcqoeyTUs0s0qdDCNLQ8PYzAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:34.600516Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.06518","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1cc4fac05cb336b05905534cae7fde2e4777406c6b83a29d5eddd96b7a7a630d","sha256:4f96b9a0037e4dfcb00b4190ca54f24a4ecca54723282616110a79fb15c992c8"],"state_sha256":"83f121fc65eedd2ca21af8408d431c3ac0672c89d6213f9d74f12749ae7f23c9"}