{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:QYFXKGBHGXQU45TFKNBXVGY3U4","short_pith_number":"pith:QYFXKGBH","canonical_record":{"source":{"id":"1703.10192","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2017-03-29T18:34:48Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"dbe7025b557c09324ae8ce616493fc1cc4704432eea626ddf26d104e6dc562b4","abstract_canon_sha256":"d4ef74ad6d4333f03f47f27fc653baa48e7000221a8447dd493542815319cd1f"},"schema_version":"1.0"},"canonical_sha256":"860b75182735e14e766553437a9b1ba70d8f5f56b89f0a0e05d1ca0f2ce2f7f1","source":{"kind":"arxiv","id":"1703.10192","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.10192","created_at":"2026-05-18T00:18:37Z"},{"alias_kind":"arxiv_version","alias_value":"1703.10192v3","created_at":"2026-05-18T00:18:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.10192","created_at":"2026-05-18T00:18:37Z"},{"alias_kind":"pith_short_12","alias_value":"QYFXKGBHGXQU","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"QYFXKGBHGXQU45TF","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"QYFXKGBH","created_at":"2026-05-18T12:31:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:QYFXKGBHGXQU45TFKNBXVGY3U4","target":"record","payload":{"canonical_record":{"source":{"id":"1703.10192","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2017-03-29T18:34:48Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"dbe7025b557c09324ae8ce616493fc1cc4704432eea626ddf26d104e6dc562b4","abstract_canon_sha256":"d4ef74ad6d4333f03f47f27fc653baa48e7000221a8447dd493542815319cd1f"},"schema_version":"1.0"},"canonical_sha256":"860b75182735e14e766553437a9b1ba70d8f5f56b89f0a0e05d1ca0f2ce2f7f1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:37.119279Z","signature_b64":"lVXsfbkfZAkkOxiUPlWsWjYz5cxpOvCpqg/zHMvOVrwv5GNpqWLx7of5wnF5svmkaNFmxLfoLoOBIGyMt76gBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"860b75182735e14e766553437a9b1ba70d8f5f56b89f0a0e05d1ca0f2ce2f7f1","last_reissued_at":"2026-05-18T00:18:37.118658Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:37.118658Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.10192","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:18:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EoGFJf2432ni0ZXRdu4seFQxyklUl1D2Xt2alt/hRU3F6SyitYBDVaPedCQB+1KndDOTP+gNrqIyWsncp6a/CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T13:31:16.281027Z"},"content_sha256":"17eec27f174b54d97d900608c9041d774969a4530dfff703f21622f1cff45572","schema_version":"1.0","event_id":"sha256:17eec27f174b54d97d900608c9041d774969a4530dfff703f21622f1cff45572"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:QYFXKGBHGXQU45TFKNBXVGY3U4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Estimation of the average number of continuous crossings for non-stationary non-diffusion processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"stat.ME","authors_text":"Alexandre Genadot, Romain Aza\\\"is","submitted_at":"2017-03-29T18:34:48Z","abstract_excerpt":"Assume that you observe trajectories of a non-diffusive non-stationary process and that you are interested in the average number of times where the process crosses some threshold (in dimension $d=1$) or hypersurface (in dimension $d\\geq2$). Of course, you can actually estimate this quantity by its empirical version counting the number of observed crossings. But is there a better way? In this paper, for a wide class of piecewise smooth processes, we propose estimators of the average number of continuous crossings of an hypersurface based on Kac-Rice formulae. We revisit these formulae in the un"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.10192","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:18:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XU+fuOyEZr9EbK/9vZOqpmEbJFoLoYqyB+nLi5SsAPkzupyEWoXeNAVXI7O7rDrBSxGW/XlrYVOKf0M9XtQ+DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T13:31:16.281394Z"},"content_sha256":"4ab4451a688a29d4a7bc3df32f999dbe8607ffc482aed5df1e40ced0bcf945fa","schema_version":"1.0","event_id":"sha256:4ab4451a688a29d4a7bc3df32f999dbe8607ffc482aed5df1e40ced0bcf945fa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QYFXKGBHGXQU45TFKNBXVGY3U4/bundle.json","state_url":"https://pith.science/pith/QYFXKGBHGXQU45TFKNBXVGY3U4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QYFXKGBHGXQU45TFKNBXVGY3U4/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-25T13:31:16Z","links":{"resolver":"https://pith.science/pith/QYFXKGBHGXQU45TFKNBXVGY3U4","bundle":"https://pith.science/pith/QYFXKGBHGXQU45TFKNBXVGY3U4/bundle.json","state":"https://pith.science/pith/QYFXKGBHGXQU45TFKNBXVGY3U4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QYFXKGBHGXQU45TFKNBXVGY3U4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:QYFXKGBHGXQU45TFKNBXVGY3U4","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":"d4ef74ad6d4333f03f47f27fc653baa48e7000221a8447dd493542815319cd1f","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2017-03-29T18:34:48Z","title_canon_sha256":"dbe7025b557c09324ae8ce616493fc1cc4704432eea626ddf26d104e6dc562b4"},"schema_version":"1.0","source":{"id":"1703.10192","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.10192","created_at":"2026-05-18T00:18:37Z"},{"alias_kind":"arxiv_version","alias_value":"1703.10192v3","created_at":"2026-05-18T00:18:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.10192","created_at":"2026-05-18T00:18:37Z"},{"alias_kind":"pith_short_12","alias_value":"QYFXKGBHGXQU","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"QYFXKGBHGXQU45TF","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"QYFXKGBH","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:4ab4451a688a29d4a7bc3df32f999dbe8607ffc482aed5df1e40ced0bcf945fa","target":"graph","created_at":"2026-05-18T00:18:37Z","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":"Assume that you observe trajectories of a non-diffusive non-stationary process and that you are interested in the average number of times where the process crosses some threshold (in dimension $d=1$) or hypersurface (in dimension $d\\geq2$). Of course, you can actually estimate this quantity by its empirical version counting the number of observed crossings. But is there a better way? In this paper, for a wide class of piecewise smooth processes, we propose estimators of the average number of continuous crossings of an hypersurface based on Kac-Rice formulae. We revisit these formulae in the un","authors_text":"Alexandre Genadot, Romain Aza\\\"is","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2017-03-29T18:34:48Z","title":"Estimation of the average number of continuous crossings for non-stationary non-diffusion processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.10192","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":"sha256:17eec27f174b54d97d900608c9041d774969a4530dfff703f21622f1cff45572","target":"record","created_at":"2026-05-18T00:18:37Z","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":"d4ef74ad6d4333f03f47f27fc653baa48e7000221a8447dd493542815319cd1f","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2017-03-29T18:34:48Z","title_canon_sha256":"dbe7025b557c09324ae8ce616493fc1cc4704432eea626ddf26d104e6dc562b4"},"schema_version":"1.0","source":{"id":"1703.10192","kind":"arxiv","version":3}},"canonical_sha256":"860b75182735e14e766553437a9b1ba70d8f5f56b89f0a0e05d1ca0f2ce2f7f1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"860b75182735e14e766553437a9b1ba70d8f5f56b89f0a0e05d1ca0f2ce2f7f1","first_computed_at":"2026-05-18T00:18:37.118658Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:37.118658Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lVXsfbkfZAkkOxiUPlWsWjYz5cxpOvCpqg/zHMvOVrwv5GNpqWLx7of5wnF5svmkaNFmxLfoLoOBIGyMt76gBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:37.119279Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.10192","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:17eec27f174b54d97d900608c9041d774969a4530dfff703f21622f1cff45572","sha256:4ab4451a688a29d4a7bc3df32f999dbe8607ffc482aed5df1e40ced0bcf945fa"],"state_sha256":"d3092d316bd7b108a63315f7eaa931a0be562ab27e57904122431fa4d3e2331a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M1c8eHWQdYVYfSAB3u0iPqH/ekfvcMDLqKB4OwBfWjuxXlXTMof+nGZW9TlYxtZkCp2+Nvb7rd6qi5qL9oziBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T13:31:16.283349Z","bundle_sha256":"7f2f3651139b1e1334a9a6c8c67a807a4c445bf8c0b73a2ba8a0f665407116b4"}}