{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:FAEGZGV7K7PD4OH26XY2MPWB65","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":"af5fff98a662466f3aa9b0785ae99f38c7ba2a62b0dff4e6fe99838265657bb7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-07-19T17:26:26Z","title_canon_sha256":"57e05c764fc64dbd9f7404f7ad9bd1b2c398c41fdfc795e82e66643140812fd7"},"schema_version":"1.0","source":{"id":"1307.5287","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.5287","created_at":"2026-05-18T02:51:34Z"},{"alias_kind":"arxiv_version","alias_value":"1307.5287v2","created_at":"2026-05-18T02:51:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.5287","created_at":"2026-05-18T02:51:34Z"},{"alias_kind":"pith_short_12","alias_value":"FAEGZGV7K7PD","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"FAEGZGV7K7PD4OH2","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"FAEGZGV7","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:246e14295bc9486644360ed4b61dc94e16f1e11cfe102984d6289cc0d8bf2eba","target":"graph","created_at":"2026-05-18T02:51:34Z","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":"Let X be a smooth complex projective manifold of dimension n equipped with an ample line bundle L and a rank k holomorphic vector bundle E. We assume that 0< k <=n, that X, E and L are defined over the reals and denote by RX the real locus of X. Then, we estimate from above and below the expected Betti numbers of the vanishing loci in RX of holomorphic real sections of E tensored with L^d, where d is a large enough integer. Moreover, given any closed connected codimension k submanifold S of R^n with trivial normal bundle, we prove that a real section of E tensored with L^d has a positive proba","authors_text":"Damien Gayet (IF), Jean-Yves Welschinger (ICJ)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-07-19T17:26:26Z","title":"Expected topology of random real algebraic submanifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.5287","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":"sha256:90d01ffdbdc04a2cc220c202b53842d9776d29eea5988d894ed6389b547ce0be","target":"record","created_at":"2026-05-18T02:51:34Z","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":"af5fff98a662466f3aa9b0785ae99f38c7ba2a62b0dff4e6fe99838265657bb7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-07-19T17:26:26Z","title_canon_sha256":"57e05c764fc64dbd9f7404f7ad9bd1b2c398c41fdfc795e82e66643140812fd7"},"schema_version":"1.0","source":{"id":"1307.5287","kind":"arxiv","version":2}},"canonical_sha256":"28086c9abf57de3e38faf5f1a63ec1f7656743b72fb3ed430433da5317f24df2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"28086c9abf57de3e38faf5f1a63ec1f7656743b72fb3ed430433da5317f24df2","first_computed_at":"2026-05-18T02:51:34.129266Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:51:34.129266Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MpoTYgWQNL6hvRtp7WqsprenGANEpiCViL4yH1SqnAbGJ/RAwIztPRyiFmV8kHWu7s17GdCpZa7mQEeoqFVfBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:51:34.129805Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.5287","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:90d01ffdbdc04a2cc220c202b53842d9776d29eea5988d894ed6389b547ce0be","sha256:246e14295bc9486644360ed4b61dc94e16f1e11cfe102984d6289cc0d8bf2eba"],"state_sha256":"2c8f3b6cffbbb28dcdae7d2b5570dbb0e4bdbc5af05682dc0cf3b8cc8f670540"}