{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:R2RARSVAXQFSPOVN2TN23STXAX","short_pith_number":"pith:R2RARSVA","canonical_record":{"source":{"id":"1704.08669","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.NC","submitted_at":"2017-04-27T17:33:32Z","cross_cats_sorted":["math.PR","physics.comp-ph","physics.data-an"],"title_canon_sha256":"a330a07817c656918c56da0975740c232987cf085f154b94cde90c51b17d39e4","abstract_canon_sha256":"803267bf0b5456a3eb0e61c5e59784b87cfcca51e40aaa1065f343e02e2410b8"},"schema_version":"1.0"},"canonical_sha256":"8ea208caa0bc0b27baadd4dbadca7705fb417228d108371d0dafd5704b897d6f","source":{"kind":"arxiv","id":"1704.08669","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.08669","created_at":"2026-05-18T00:42:57Z"},{"alias_kind":"arxiv_version","alias_value":"1704.08669v1","created_at":"2026-05-18T00:42:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.08669","created_at":"2026-05-18T00:42:57Z"},{"alias_kind":"pith_short_12","alias_value":"R2RARSVAXQFS","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"R2RARSVAXQFSPOVN","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"R2RARSVA","created_at":"2026-05-18T12:31:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:R2RARSVAXQFSPOVN2TN23STXAX","target":"record","payload":{"canonical_record":{"source":{"id":"1704.08669","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.NC","submitted_at":"2017-04-27T17:33:32Z","cross_cats_sorted":["math.PR","physics.comp-ph","physics.data-an"],"title_canon_sha256":"a330a07817c656918c56da0975740c232987cf085f154b94cde90c51b17d39e4","abstract_canon_sha256":"803267bf0b5456a3eb0e61c5e59784b87cfcca51e40aaa1065f343e02e2410b8"},"schema_version":"1.0"},"canonical_sha256":"8ea208caa0bc0b27baadd4dbadca7705fb417228d108371d0dafd5704b897d6f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:57.504816Z","signature_b64":"2DFKXH/Hz6VmYSmHGAXcUo+w4fXUMBpTIuTvbHe29fBeep1ZWBUQnbaW0HKBVOXbYR+vBgk+JU9mFrfM0No+Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8ea208caa0bc0b27baadd4dbadca7705fb417228d108371d0dafd5704b897d6f","last_reissued_at":"2026-05-18T00:42:57.504087Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:57.504087Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.08669","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:42:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VOdZSMEZrQ9bOsZmNoprd//zGscpMisuTOnJhl5faBL7JwNuWADSWEpdgC7DmRhE3Sga1CU4tJkvPn1QJGlHCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T02:55:47.129759Z"},"content_sha256":"d5bb94b08361ade167436138c54454f9232307dcd41fb901b1dac13e8e122291","schema_version":"1.0","event_id":"sha256:d5bb94b08361ade167436138c54454f9232307dcd41fb901b1dac13e8e122291"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:R2RARSVAXQFSPOVN2TN23STXAX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Evolution of moments and correlations in non-renewal escape-time processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","physics.comp-ph","physics.data-an"],"primary_cat":"q-bio.NC","authors_text":"Andr\\'e Longtin, R\\\"udiger Thul, Wilhelm Braun","submitted_at":"2017-04-27T17:33:32Z","abstract_excerpt":"The theoretical description of non-renewal stochastic systems is a challenge. Analytical results are often not available or can only be obtained under strong conditions, limiting their applicability. Also, numerical results have mostly been obtained by ad-hoc Monte--Carlo simulations, which are usually computationally expensive when a high degree of accuracy is needed. To gain quantitative insight into these systems under general conditions, we here introduce a numerical iterated first-passage time approach based on solving the time-dependent Fokker-Planck equation (FPE) to describe the statis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.08669","kind":"arxiv","version":1},"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":"2026-05-18T00:42:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E0fD/rbsxCBB35NmuUaGCMqfXAU5+dPjXpkiMUMOIbILXz3pp7JSBNU8LIbpD4M38JcZJ2DDWHnzdKVU8/a8DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T02:55:47.130104Z"},"content_sha256":"f61ad5838f1b2c79f290536714c2bd27ee5a95e7b80cb51b1e15dcb37b9ee13c","schema_version":"1.0","event_id":"sha256:f61ad5838f1b2c79f290536714c2bd27ee5a95e7b80cb51b1e15dcb37b9ee13c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/R2RARSVAXQFSPOVN2TN23STXAX/bundle.json","state_url":"https://pith.science/pith/R2RARSVAXQFSPOVN2TN23STXAX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/R2RARSVAXQFSPOVN2TN23STXAX/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":"2026-07-05T02:55:47Z","links":{"resolver":"https://pith.science/pith/R2RARSVAXQFSPOVN2TN23STXAX","bundle":"https://pith.science/pith/R2RARSVAXQFSPOVN2TN23STXAX/bundle.json","state":"https://pith.science/pith/R2RARSVAXQFSPOVN2TN23STXAX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/R2RARSVAXQFSPOVN2TN23STXAX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:R2RARSVAXQFSPOVN2TN23STXAX","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":"803267bf0b5456a3eb0e61c5e59784b87cfcca51e40aaa1065f343e02e2410b8","cross_cats_sorted":["math.PR","physics.comp-ph","physics.data-an"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.NC","submitted_at":"2017-04-27T17:33:32Z","title_canon_sha256":"a330a07817c656918c56da0975740c232987cf085f154b94cde90c51b17d39e4"},"schema_version":"1.0","source":{"id":"1704.08669","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.08669","created_at":"2026-05-18T00:42:57Z"},{"alias_kind":"arxiv_version","alias_value":"1704.08669v1","created_at":"2026-05-18T00:42:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.08669","created_at":"2026-05-18T00:42:57Z"},{"alias_kind":"pith_short_12","alias_value":"R2RARSVAXQFS","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"R2RARSVAXQFSPOVN","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"R2RARSVA","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:f61ad5838f1b2c79f290536714c2bd27ee5a95e7b80cb51b1e15dcb37b9ee13c","target":"graph","created_at":"2026-05-18T00:42:57Z","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":"The theoretical description of non-renewal stochastic systems is a challenge. Analytical results are often not available or can only be obtained under strong conditions, limiting their applicability. Also, numerical results have mostly been obtained by ad-hoc Monte--Carlo simulations, which are usually computationally expensive when a high degree of accuracy is needed. To gain quantitative insight into these systems under general conditions, we here introduce a numerical iterated first-passage time approach based on solving the time-dependent Fokker-Planck equation (FPE) to describe the statis","authors_text":"Andr\\'e Longtin, R\\\"udiger Thul, Wilhelm Braun","cross_cats":["math.PR","physics.comp-ph","physics.data-an"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.NC","submitted_at":"2017-04-27T17:33:32Z","title":"Evolution of moments and correlations in non-renewal escape-time processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.08669","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:d5bb94b08361ade167436138c54454f9232307dcd41fb901b1dac13e8e122291","target":"record","created_at":"2026-05-18T00:42:57Z","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":"803267bf0b5456a3eb0e61c5e59784b87cfcca51e40aaa1065f343e02e2410b8","cross_cats_sorted":["math.PR","physics.comp-ph","physics.data-an"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.NC","submitted_at":"2017-04-27T17:33:32Z","title_canon_sha256":"a330a07817c656918c56da0975740c232987cf085f154b94cde90c51b17d39e4"},"schema_version":"1.0","source":{"id":"1704.08669","kind":"arxiv","version":1}},"canonical_sha256":"8ea208caa0bc0b27baadd4dbadca7705fb417228d108371d0dafd5704b897d6f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8ea208caa0bc0b27baadd4dbadca7705fb417228d108371d0dafd5704b897d6f","first_computed_at":"2026-05-18T00:42:57.504087Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:57.504087Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2DFKXH/Hz6VmYSmHGAXcUo+w4fXUMBpTIuTvbHe29fBeep1ZWBUQnbaW0HKBVOXbYR+vBgk+JU9mFrfM0No+Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:57.504816Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.08669","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d5bb94b08361ade167436138c54454f9232307dcd41fb901b1dac13e8e122291","sha256:f61ad5838f1b2c79f290536714c2bd27ee5a95e7b80cb51b1e15dcb37b9ee13c"],"state_sha256":"1e6de59b043b840d66072e8d303c37e245fbc6847c632d83eaccd12f8c3c92f0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7PIlP5jq2eEK74s2CQXuE7rq5jhsYE6A7rcUWDscL6fJlFBHN+Ad3itZkHdUCiMZxTf8VFw7fK0iDU9f+uP4CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T02:55:47.132027Z","bundle_sha256":"ccd9abd885274124a7062623d268e58952e446b22c150be46fc0384cf54b4cda"}}