{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:W4P2W2WW4O4X62QXTTZHNNSM6I","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":"a4d4da5d754f0f9c3051864768555cb04da76ae1886989b595fd8e54b87274b7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-05-18T15:22:59Z","title_canon_sha256":"7baacd72c5ec92cf2d1bc529d7800d8dd8f05da4e8e55695556c139bbb293d85"},"schema_version":"1.0","source":{"id":"1005.3228","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.3228","created_at":"2026-05-18T04:04:31Z"},{"alias_kind":"arxiv_version","alias_value":"1005.3228v1","created_at":"2026-05-18T04:04:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.3228","created_at":"2026-05-18T04:04:31Z"},{"alias_kind":"pith_short_12","alias_value":"W4P2W2WW4O4X","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"W4P2W2WW4O4X62QX","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"W4P2W2WW","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:dc6431b2f883003050e3d8c19e73eb43213c8e62f1e854ac99eabe1f5fdb9dfe","target":"graph","created_at":"2026-05-18T04:04:31Z","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":"Given a positive real Hermitian holomorphic line bundle L over a smooth real projective manifold X, the space of real holomorphic sections of the bundle L^d inherits for every positive integer d a L^2 scalar product which induces a Gaussian measure. When X is a curve or a surface, we estimate the volume of the cone of real sections whose vanishing locus contains many real components. In particular, the volume of the cone of maximal real sections decreases exponentially as d grows to infinity.","authors_text":"Damien Gayet (ICJ), Jean-Yves Welschinger (ICJ)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-05-18T15:22:59Z","title":"Exponential rarefaction of real curves with many components"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.3228","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:b369b3bf755827b3ffc3de400f46571cca03923532f1b11f347ec0ffeccda586","target":"record","created_at":"2026-05-18T04:04:31Z","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":"a4d4da5d754f0f9c3051864768555cb04da76ae1886989b595fd8e54b87274b7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-05-18T15:22:59Z","title_canon_sha256":"7baacd72c5ec92cf2d1bc529d7800d8dd8f05da4e8e55695556c139bbb293d85"},"schema_version":"1.0","source":{"id":"1005.3228","kind":"arxiv","version":1}},"canonical_sha256":"b71fab6ad6e3b97f6a179cf276b64cf2273b0c28fd5a91e87ad119a2d099e000","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b71fab6ad6e3b97f6a179cf276b64cf2273b0c28fd5a91e87ad119a2d099e000","first_computed_at":"2026-05-18T04:04:31.303028Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:04:31.303028Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oIUWSDHnefHWNJgDRLi0Kf45vFeiHbIGbzwWdpa2qFNPnSYy1oTCagRTj9eKGugKc8oenymOOtQhTg2ivUM5Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:04:31.303726Z","signed_message":"canonical_sha256_bytes"},"source_id":"1005.3228","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b369b3bf755827b3ffc3de400f46571cca03923532f1b11f347ec0ffeccda586","sha256:dc6431b2f883003050e3d8c19e73eb43213c8e62f1e854ac99eabe1f5fdb9dfe"],"state_sha256":"a8db8abdeab3620b058e9fc346e8d35d5834056dfb1c1d260c72dec64ddeede7"}