{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:FBS2IZTWMKXPPYXPPR74QHHD7X","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":"3c5e7673711de3f4683111e7c0464b32bbc2e96144d4fbb836b5a3e11caa0acb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-11-05T15:22:14Z","title_canon_sha256":"7d69338d43129458370d65c7f507aa5d1076c4d314d6659cf30cf885b17446b6"},"schema_version":"1.0","source":{"id":"1811.01787","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.01787","created_at":"2026-05-18T00:01:33Z"},{"alias_kind":"arxiv_version","alias_value":"1811.01787v1","created_at":"2026-05-18T00:01:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.01787","created_at":"2026-05-18T00:01:33Z"},{"alias_kind":"pith_short_12","alias_value":"FBS2IZTWMKXP","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"FBS2IZTWMKXPPYXP","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"FBS2IZTW","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:24ec7a3a370286753b4b49bac2956752ad28fb7abc0a2a8742f1e7875571573c","target":"graph","created_at":"2026-05-18T00:01:33Z","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(t) be a Gaussian random field R d $\\rightarrow$ R. Using the notion of (d -- 1)-integral geometric measures, we establish a relation between (a) the volume of the level set (b) the number of crossings of the restriction of the random field to a line. Using this relation we prove the equivalence between the finiteness of the expectation and the finiteness of the second spectral moment matrix. Sufficient conditions for finiteness of higher moments are also established.","authors_text":"David Ginsbourger, Diego Armentano (UDELAR), Jean-Marc Azais (IMT), Jos\\'e Rafael Leon (UDELAR)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-11-05T15:22:14Z","title":"Conditions for the finiteness of the moments of the volume of level sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.01787","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:a2757bdb46b8b470492a13e62cd2722f0329b7e9eba43e18fe0a3d3f15d50403","target":"record","created_at":"2026-05-18T00:01:33Z","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":"3c5e7673711de3f4683111e7c0464b32bbc2e96144d4fbb836b5a3e11caa0acb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-11-05T15:22:14Z","title_canon_sha256":"7d69338d43129458370d65c7f507aa5d1076c4d314d6659cf30cf885b17446b6"},"schema_version":"1.0","source":{"id":"1811.01787","kind":"arxiv","version":1}},"canonical_sha256":"2865a4667662aef7e2ef7c7fc81ce3fde0be021e9dbaeb5a43d27a3c62b89159","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2865a4667662aef7e2ef7c7fc81ce3fde0be021e9dbaeb5a43d27a3c62b89159","first_computed_at":"2026-05-18T00:01:33.260388Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:33.260388Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RvAhL6cKiPnxwKsO0QVDg5dBVzY3p7o2YGA3JxFCTlS1b35DgUNzUjud0xB/Is4B0X61e7t9rzyt6KPhbev0Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:33.260894Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.01787","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a2757bdb46b8b470492a13e62cd2722f0329b7e9eba43e18fe0a3d3f15d50403","sha256:24ec7a3a370286753b4b49bac2956752ad28fb7abc0a2a8742f1e7875571573c"],"state_sha256":"5b5ef35e84854367d23fc6a7375b9cda96de2092bd6a587ccfbcd755414df0be"}