{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:4X6FCYQDPM4YDA35BJG6LYFP6V","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":"89fbad5c1d955990c781e0af298a0e6ab391c27a83f3e4cc53d1b78cac799064","cross_cats_sorted":["math.AP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-04-21T14:22:09Z","title_canon_sha256":"2e453bde41a8bcf22644a4dbd076c106b694db63ce64c696ebdd4aed28b18981"},"schema_version":"1.0","source":{"id":"1404.5206","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.5206","created_at":"2026-05-18T01:22:48Z"},{"alias_kind":"arxiv_version","alias_value":"1404.5206v3","created_at":"2026-05-18T01:22:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.5206","created_at":"2026-05-18T01:22:48Z"},{"alias_kind":"pith_short_12","alias_value":"4X6FCYQDPM4Y","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"4X6FCYQDPM4YDA35","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"4X6FCYQD","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:4e99db5e7428e470e7c308250ed5bd65f49bf4fd0acafc5d90c490a47563bb67","target":"graph","created_at":"2026-05-18T01:22:48Z","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 prove that the Euler form of a metric connection on real oriented vector bundle $E$ over a compact oriented manifold $M$ can be identified, as a current, with the expectation of the random current defined by the zero-locus of a certain random section of the bundle. We also explain how to reconstruct probabilistically the metric and the connection on $E$ from the statistics of random sections of $E$.","authors_text":"Liviu I. Nicolaescu, Nikhil Savale","cross_cats":["math.AP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-04-21T14:22:09Z","title":"The Gauss-Bonnet-Chern theorem: a probabilistic perspective"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5206","kind":"arxiv","version":3},"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:cff6668219707d9ec026cf1098002d61ec0af4159c67a7d738d58cfe071e05c3","target":"record","created_at":"2026-05-18T01:22:48Z","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":"89fbad5c1d955990c781e0af298a0e6ab391c27a83f3e4cc53d1b78cac799064","cross_cats_sorted":["math.AP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-04-21T14:22:09Z","title_canon_sha256":"2e453bde41a8bcf22644a4dbd076c106b694db63ce64c696ebdd4aed28b18981"},"schema_version":"1.0","source":{"id":"1404.5206","kind":"arxiv","version":3}},"canonical_sha256":"e5fc5162037b3981837d0a4de5e0aff5552c51596d0ef46a28629b514876ba0e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e5fc5162037b3981837d0a4de5e0aff5552c51596d0ef46a28629b514876ba0e","first_computed_at":"2026-05-18T01:22:48.926820Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:48.926820Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lKSnAcrAlCQcu9m5L1bJIhptXvvouQmHdk7pbfjXLzSo0AXfeneCKluIDnjYgdy2I5M6FNYdHgBgwkjH8lqBBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:48.927446Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.5206","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cff6668219707d9ec026cf1098002d61ec0af4159c67a7d738d58cfe071e05c3","sha256:4e99db5e7428e470e7c308250ed5bd65f49bf4fd0acafc5d90c490a47563bb67"],"state_sha256":"75fd7c6fc5270a3cc2c18c570018b2e2a3a720b62968e74facb92b5471fa9018"}