{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:GHA3GOUOBX2WDBS36YP6GOLX56","short_pith_number":"pith:GHA3GOUO","canonical_record":{"source":{"id":"2508.14202","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-08-19T18:50:05Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"3fc78045ae579d735c5386c05dfc857a9f2b22e356700e9ece627b688f148d2f","abstract_canon_sha256":"0a765c211240f8118b2fc68f401f64cbd813d06e62362ea80109ce288e8a17c6"},"schema_version":"1.0"},"canonical_sha256":"31c1b33a8e0df561865bf61fe33977efaac95cf26fb21c2f8b01bd5bf8cd6cba","source":{"kind":"arxiv","id":"2508.14202","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.14202","created_at":"2026-07-05T11:56:27Z"},{"alias_kind":"arxiv_version","alias_value":"2508.14202v1","created_at":"2026-07-05T11:56:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.14202","created_at":"2026-07-05T11:56:27Z"},{"alias_kind":"pith_short_12","alias_value":"GHA3GOUOBX2W","created_at":"2026-07-05T11:56:27Z"},{"alias_kind":"pith_short_16","alias_value":"GHA3GOUOBX2WDBS3","created_at":"2026-07-05T11:56:27Z"},{"alias_kind":"pith_short_8","alias_value":"GHA3GOUO","created_at":"2026-07-05T11:56:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:GHA3GOUOBX2WDBS36YP6GOLX56","target":"record","payload":{"canonical_record":{"source":{"id":"2508.14202","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-08-19T18:50:05Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"3fc78045ae579d735c5386c05dfc857a9f2b22e356700e9ece627b688f148d2f","abstract_canon_sha256":"0a765c211240f8118b2fc68f401f64cbd813d06e62362ea80109ce288e8a17c6"},"schema_version":"1.0"},"canonical_sha256":"31c1b33a8e0df561865bf61fe33977efaac95cf26fb21c2f8b01bd5bf8cd6cba","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:56:27.979197Z","signature_b64":"1T4PTCIcn0hNAp/nnPpJf5pdgGYQa0DpbIBmPjHatsEQczJrmlxQQeJ0P8m/ZPz5vMbIxUZ2t6pCIAEpoMmUAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"31c1b33a8e0df561865bf61fe33977efaac95cf26fb21c2f8b01bd5bf8cd6cba","last_reissued_at":"2026-07-05T11:56:27.978821Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:56:27.978821Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2508.14202","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":"2026-07-05T11:56:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5VESu+tviCQET3LDu/LVWC4j2UjO1KqoDfhqMwktjvwSlgPWI22ov8ah/5ZsbEr2JmDT+t8gE7luAEE7g6IKAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T16:28:16.093308Z"},"content_sha256":"41804fb15cf63bc0fea4d715bab8feba91ffac60aa7e8e5f3cf813a69ea1ffbc","schema_version":"1.0","event_id":"sha256:41804fb15cf63bc0fea4d715bab8feba91ffac60aa7e8e5f3cf813a69ea1ffbc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:GHA3GOUOBX2WDBS36YP6GOLX56","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Passage times of fast inhomogeneous immigration processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"math.PR","authors_text":"Hwai-Ray Tung, Sean D Lawley","submitted_at":"2025-08-19T18:50:05Z","abstract_excerpt":"In many biophysical systems, key events are triggered when the fastest of many random searchers find a target. Most mathematical models of such systems assume that all searchers are initially present in the search domain, which permits the use of classical extreme value theory. In this paper, we explore $k$th passage times of inhomogeneous immigration processes where searchers are added to the domain over time either through time inhomogeneous rates or a Yule (pure birth) process. We rigorously prove convergence in distribution and convergence of moments of the $k$th passage times for both pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.14202","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2508.14202/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T11:56:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JVHibGi0Jphf2VmuEPBi3YcEQv4pqS46YlStZuNfZjxjMUP2UNaZDr/IhEN2or8p0PWVm7MLMWBSNM4D+GjSDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T16:28:16.094533Z"},"content_sha256":"51c650a4975648676f37b6164c2f49ff012ba42e99cfabd3826584cf41f1382f","schema_version":"1.0","event_id":"sha256:51c650a4975648676f37b6164c2f49ff012ba42e99cfabd3826584cf41f1382f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GHA3GOUOBX2WDBS36YP6GOLX56/bundle.json","state_url":"https://pith.science/pith/GHA3GOUOBX2WDBS36YP6GOLX56/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GHA3GOUOBX2WDBS36YP6GOLX56/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":"2026-08-12T16:28:16Z","links":{"resolver":"https://pith.science/pith/GHA3GOUOBX2WDBS36YP6GOLX56","bundle":"https://pith.science/pith/GHA3GOUOBX2WDBS36YP6GOLX56/bundle.json","state":"https://pith.science/pith/GHA3GOUOBX2WDBS36YP6GOLX56/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GHA3GOUOBX2WDBS36YP6GOLX56/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:GHA3GOUOBX2WDBS36YP6GOLX56","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":"0a765c211240f8118b2fc68f401f64cbd813d06e62362ea80109ce288e8a17c6","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-08-19T18:50:05Z","title_canon_sha256":"3fc78045ae579d735c5386c05dfc857a9f2b22e356700e9ece627b688f148d2f"},"schema_version":"1.0","source":{"id":"2508.14202","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.14202","created_at":"2026-07-05T11:56:27Z"},{"alias_kind":"arxiv_version","alias_value":"2508.14202v1","created_at":"2026-07-05T11:56:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.14202","created_at":"2026-07-05T11:56:27Z"},{"alias_kind":"pith_short_12","alias_value":"GHA3GOUOBX2W","created_at":"2026-07-05T11:56:27Z"},{"alias_kind":"pith_short_16","alias_value":"GHA3GOUOBX2WDBS3","created_at":"2026-07-05T11:56:27Z"},{"alias_kind":"pith_short_8","alias_value":"GHA3GOUO","created_at":"2026-07-05T11:56:27Z"}],"graph_snapshots":[{"event_id":"sha256:51c650a4975648676f37b6164c2f49ff012ba42e99cfabd3826584cf41f1382f","target":"graph","created_at":"2026-07-05T11:56:27Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2508.14202/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In many biophysical systems, key events are triggered when the fastest of many random searchers find a target. Most mathematical models of such systems assume that all searchers are initially present in the search domain, which permits the use of classical extreme value theory. In this paper, we explore $k$th passage times of inhomogeneous immigration processes where searchers are added to the domain over time either through time inhomogeneous rates or a Yule (pure birth) process. We rigorously prove convergence in distribution and convergence of moments of the $k$th passage times for both pro","authors_text":"Hwai-Ray Tung, Sean D Lawley","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-08-19T18:50:05Z","title":"Passage times of fast inhomogeneous immigration processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.14202","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":"sha256:41804fb15cf63bc0fea4d715bab8feba91ffac60aa7e8e5f3cf813a69ea1ffbc","target":"record","created_at":"2026-07-05T11:56:27Z","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":"0a765c211240f8118b2fc68f401f64cbd813d06e62362ea80109ce288e8a17c6","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-08-19T18:50:05Z","title_canon_sha256":"3fc78045ae579d735c5386c05dfc857a9f2b22e356700e9ece627b688f148d2f"},"schema_version":"1.0","source":{"id":"2508.14202","kind":"arxiv","version":1}},"canonical_sha256":"31c1b33a8e0df561865bf61fe33977efaac95cf26fb21c2f8b01bd5bf8cd6cba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"31c1b33a8e0df561865bf61fe33977efaac95cf26fb21c2f8b01bd5bf8cd6cba","first_computed_at":"2026-07-05T11:56:27.978821Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:56:27.978821Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1T4PTCIcn0hNAp/nnPpJf5pdgGYQa0DpbIBmPjHatsEQczJrmlxQQeJ0P8m/ZPz5vMbIxUZ2t6pCIAEpoMmUAw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:56:27.979197Z","signed_message":"canonical_sha256_bytes"},"source_id":"2508.14202","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:41804fb15cf63bc0fea4d715bab8feba91ffac60aa7e8e5f3cf813a69ea1ffbc","sha256:51c650a4975648676f37b6164c2f49ff012ba42e99cfabd3826584cf41f1382f"],"state_sha256":"43ef7b87a57263cbbd131f09f1a0968c7b5b5ab413c1bdc382c7628580812bff"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1qbs+pa/gUkuIC3MC7f9B2VAU9hvRFeadwMbJ+qVb4dKlaYlS/5xJ6hcTUA1VGfPSHQ2Zb0wYSZeQ6xXifiPCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T16:28:16.101890Z","bundle_sha256":"24195817d5616112d27a7c6c3d1b5af58e2a3d22b04409b8b98b384dcd5daa16"}}