{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:VKQK4NLPRZCOYXPJ3GAILJBRHQ","short_pith_number":"pith:VKQK4NLP","canonical_record":{"source":{"id":"2409.16951","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2024-09-25T14:05:04Z","cross_cats_sorted":["cond-mat.soft","math-ph","math.MP","math.PR"],"title_canon_sha256":"8eb058e1cd1ac0ca38d527e32a552c6966a76099930ab02f3ad373a68331498e","abstract_canon_sha256":"978a48e08b6302dcff773653551dc2e25da2e6e11a6dee816eba1d2e56992dcc"},"schema_version":"1.0"},"canonical_sha256":"aaa0ae356f8e44ec5de9d98085a4313c26ae5ccde8bf13cbe9bd38762b221f91","source":{"kind":"arxiv","id":"2409.16951","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.16951","created_at":"2026-07-05T10:04:39Z"},{"alias_kind":"arxiv_version","alias_value":"2409.16951v1","created_at":"2026-07-05T10:04:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.16951","created_at":"2026-07-05T10:04:39Z"},{"alias_kind":"pith_short_12","alias_value":"VKQK4NLPRZCO","created_at":"2026-07-05T10:04:39Z"},{"alias_kind":"pith_short_16","alias_value":"VKQK4NLPRZCOYXPJ","created_at":"2026-07-05T10:04:39Z"},{"alias_kind":"pith_short_8","alias_value":"VKQK4NLP","created_at":"2026-07-05T10:04:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:VKQK4NLPRZCOYXPJ3GAILJBRHQ","target":"record","payload":{"canonical_record":{"source":{"id":"2409.16951","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2024-09-25T14:05:04Z","cross_cats_sorted":["cond-mat.soft","math-ph","math.MP","math.PR"],"title_canon_sha256":"8eb058e1cd1ac0ca38d527e32a552c6966a76099930ab02f3ad373a68331498e","abstract_canon_sha256":"978a48e08b6302dcff773653551dc2e25da2e6e11a6dee816eba1d2e56992dcc"},"schema_version":"1.0"},"canonical_sha256":"aaa0ae356f8e44ec5de9d98085a4313c26ae5ccde8bf13cbe9bd38762b221f91","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:04:39.947105Z","signature_b64":"bigjjrdsKMftA0LAdDI3vG4Jcsi3XhwkxcTn4NtkX9SVA0QI1txoK/6e6DsOSG0q3d+gDMtYC5HynZdBqPuCBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aaa0ae356f8e44ec5de9d98085a4313c26ae5ccde8bf13cbe9bd38762b221f91","last_reissued_at":"2026-07-05T10:04:39.946608Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:04:39.946608Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2409.16951","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":"2026-07-05T10:04:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N21BxJlTlyWOJ9cB8MjNGghRopSWVkeUqJNnPhBZ3wDfIP70uCo9nNAIEmVrVbjPTNJzyofJBvM36apwWrxqDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T11:49:05.899963Z"},"content_sha256":"22294326bce66e83c33c9f0616e159bf8dc6ad762709f4b32ba0e3523a365abc","schema_version":"1.0","event_id":"sha256:22294326bce66e83c33c9f0616e159bf8dc6ad762709f4b32ba0e3523a365abc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:VKQK4NLPRZCOYXPJ3GAILJBRHQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Run-and-tumble particle in one-dimensional potentials: mean first-passage time and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.soft","math-ph","math.MP","math.PR"],"primary_cat":"cond-mat.stat-mech","authors_text":"Gregory Schehr, Mathis Gu\\'eneau, Satya N. Majumdar","submitted_at":"2024-09-25T14:05:04Z","abstract_excerpt":"We study a one-dimensional run-and-tumble particle (RTP), which is a prototypical model for active system, moving within an arbitrary external potential. Using backward Fokker-Planck equations, we derive the differential equation satisfied by its mean first-passage time (MFPT) to an absorbing target, which, without any loss of generality, is placed at the origin. Depending on the shape of the potential, we identify four distinct ``phases'', with a corresponding expression for the MFPT in every case, which we derive explicitly. To illustrate these general expressions, we derive explicit formula"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.16951","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/2409.16951/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":"2026-07-05T10:04:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sLf7hnnWso2d3BGFr5W6ESMo8PxIsY/bCj3aMBW3rW5P2yKRYf4nXSPkkFaZQgLA/eZasSZHEz91Dh4P/xvmDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T11:49:05.900290Z"},"content_sha256":"647087d51b6c3a3a7730ed7e821b326d83ad7187755145a1ae22281908d60b36","schema_version":"1.0","event_id":"sha256:647087d51b6c3a3a7730ed7e821b326d83ad7187755145a1ae22281908d60b36"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VKQK4NLPRZCOYXPJ3GAILJBRHQ/bundle.json","state_url":"https://pith.science/pith/VKQK4NLPRZCOYXPJ3GAILJBRHQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VKQK4NLPRZCOYXPJ3GAILJBRHQ/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":"2026-08-05T11:49:05Z","links":{"resolver":"https://pith.science/pith/VKQK4NLPRZCOYXPJ3GAILJBRHQ","bundle":"https://pith.science/pith/VKQK4NLPRZCOYXPJ3GAILJBRHQ/bundle.json","state":"https://pith.science/pith/VKQK4NLPRZCOYXPJ3GAILJBRHQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VKQK4NLPRZCOYXPJ3GAILJBRHQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:VKQK4NLPRZCOYXPJ3GAILJBRHQ","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":"978a48e08b6302dcff773653551dc2e25da2e6e11a6dee816eba1d2e56992dcc","cross_cats_sorted":["cond-mat.soft","math-ph","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2024-09-25T14:05:04Z","title_canon_sha256":"8eb058e1cd1ac0ca38d527e32a552c6966a76099930ab02f3ad373a68331498e"},"schema_version":"1.0","source":{"id":"2409.16951","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.16951","created_at":"2026-07-05T10:04:39Z"},{"alias_kind":"arxiv_version","alias_value":"2409.16951v1","created_at":"2026-07-05T10:04:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.16951","created_at":"2026-07-05T10:04:39Z"},{"alias_kind":"pith_short_12","alias_value":"VKQK4NLPRZCO","created_at":"2026-07-05T10:04:39Z"},{"alias_kind":"pith_short_16","alias_value":"VKQK4NLPRZCOYXPJ","created_at":"2026-07-05T10:04:39Z"},{"alias_kind":"pith_short_8","alias_value":"VKQK4NLP","created_at":"2026-07-05T10:04:39Z"}],"graph_snapshots":[{"event_id":"sha256:647087d51b6c3a3a7730ed7e821b326d83ad7187755145a1ae22281908d60b36","target":"graph","created_at":"2026-07-05T10:04:39Z","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/2409.16951/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study a one-dimensional run-and-tumble particle (RTP), which is a prototypical model for active system, moving within an arbitrary external potential. Using backward Fokker-Planck equations, we derive the differential equation satisfied by its mean first-passage time (MFPT) to an absorbing target, which, without any loss of generality, is placed at the origin. Depending on the shape of the potential, we identify four distinct ``phases'', with a corresponding expression for the MFPT in every case, which we derive explicitly. To illustrate these general expressions, we derive explicit formula","authors_text":"Gregory Schehr, Mathis Gu\\'eneau, Satya N. Majumdar","cross_cats":["cond-mat.soft","math-ph","math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2024-09-25T14:05:04Z","title":"Run-and-tumble particle in one-dimensional potentials: mean first-passage time and applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.16951","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":"sha256:22294326bce66e83c33c9f0616e159bf8dc6ad762709f4b32ba0e3523a365abc","target":"record","created_at":"2026-07-05T10:04:39Z","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":"978a48e08b6302dcff773653551dc2e25da2e6e11a6dee816eba1d2e56992dcc","cross_cats_sorted":["cond-mat.soft","math-ph","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2024-09-25T14:05:04Z","title_canon_sha256":"8eb058e1cd1ac0ca38d527e32a552c6966a76099930ab02f3ad373a68331498e"},"schema_version":"1.0","source":{"id":"2409.16951","kind":"arxiv","version":1}},"canonical_sha256":"aaa0ae356f8e44ec5de9d98085a4313c26ae5ccde8bf13cbe9bd38762b221f91","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aaa0ae356f8e44ec5de9d98085a4313c26ae5ccde8bf13cbe9bd38762b221f91","first_computed_at":"2026-07-05T10:04:39.946608Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:04:39.946608Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bigjjrdsKMftA0LAdDI3vG4Jcsi3XhwkxcTn4NtkX9SVA0QI1txoK/6e6DsOSG0q3d+gDMtYC5HynZdBqPuCBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:04:39.947105Z","signed_message":"canonical_sha256_bytes"},"source_id":"2409.16951","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:22294326bce66e83c33c9f0616e159bf8dc6ad762709f4b32ba0e3523a365abc","sha256:647087d51b6c3a3a7730ed7e821b326d83ad7187755145a1ae22281908d60b36"],"state_sha256":"ae02f786449c0e83c886df26f1ad162c69423284620850d31cfd2bbc6470d445"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2Mko57HzeB5TkmODrlIRqkAd9N6oSzYfxWFaknaqciGJCil/yFXCg4TYFdrKv1Xen0NXPhXEw+8Pbl41xHZ7AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T11:49:05.903181Z","bundle_sha256":"0a87baaf920fde59aa41452a4a149da5a7336eb0513eeea1ee3248e710c5cc0a"}}