{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:AYZ5U4CIG5KVW5LLYJKIX5KRTU","short_pith_number":"pith:AYZ5U4CI","canonical_record":{"source":{"id":"1405.2302","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-05-09T18:22:57Z","cross_cats_sorted":["math.AP","math.MP"],"title_canon_sha256":"4440d14c66559d8262d7c9985dda0abbcf95505e5eb5054ac807a0b65bf21a80","abstract_canon_sha256":"97dd25286109772463354cfa26e951740559dedf1a1cae5d7423b1a95a1ecaf4"},"schema_version":"1.0"},"canonical_sha256":"0633da704837555b756bc2548bf5519d350ff027475c5e544df732716c4c5935","source":{"kind":"arxiv","id":"1405.2302","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.2302","created_at":"2026-05-18T02:35:47Z"},{"alias_kind":"arxiv_version","alias_value":"1405.2302v2","created_at":"2026-05-18T02:35:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.2302","created_at":"2026-05-18T02:35:47Z"},{"alias_kind":"pith_short_12","alias_value":"AYZ5U4CIG5KV","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"AYZ5U4CIG5KVW5LL","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"AYZ5U4CI","created_at":"2026-05-18T12:28:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:AYZ5U4CIG5KVW5LLYJKIX5KRTU","target":"record","payload":{"canonical_record":{"source":{"id":"1405.2302","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-05-09T18:22:57Z","cross_cats_sorted":["math.AP","math.MP"],"title_canon_sha256":"4440d14c66559d8262d7c9985dda0abbcf95505e5eb5054ac807a0b65bf21a80","abstract_canon_sha256":"97dd25286109772463354cfa26e951740559dedf1a1cae5d7423b1a95a1ecaf4"},"schema_version":"1.0"},"canonical_sha256":"0633da704837555b756bc2548bf5519d350ff027475c5e544df732716c4c5935","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:35:47.351799Z","signature_b64":"mqVtGr/d9xaWcNoQpz29/bY7lRxtWM096Hhbetr90Fp9jqx4s37rrGrIrpuCmJEVW1faE/g0tXs7TwTAhR/lDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0633da704837555b756bc2548bf5519d350ff027475c5e544df732716c4c5935","last_reissued_at":"2026-05-18T02:35:47.351392Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:35:47.351392Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.2302","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:35:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UrVZTQeFLxuUBp6lJlZWFnV+iAkWacjTQ3vebZ6Ge5Adqy+787q2r4ru4DA7x1XcF8nPqEvlR6bNYPaGMISBCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T04:11:27.281209Z"},"content_sha256":"e1dcb9c9acb36ea10ece1303a151452a43ce324db787284ab8f49192334f8747","schema_version":"1.0","event_id":"sha256:e1dcb9c9acb36ea10ece1303a151452a43ce324db787284ab8f49192334f8747"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:AYZ5U4CIG5KVW5LLYJKIX5KRTU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mean first passage time for a small rotating trap inside a reflective disk","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Justin C. Tzou, Theodore Kolokolnikov","submitted_at":"2014-05-09T18:22:57Z","abstract_excerpt":"We compute the mean first passage time (MFPT) for a Brownian particle inside a two-dimensional disk with reflective boundaries and a small interior trap that is rotating at a constant angular velocity. The inherent symmetry of the problem allows for a detailed analytic study of the situation. For a given angular velocity, we determine the optimal radius of rotation that minimizes the average MFPT over the disk. Several distinct regimes are observed, depending on the ratio between the angular velocity $\\omega$ and the trap size $\\varepsilon$, and several intricate transitions are analyzed using"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.2302","kind":"arxiv","version":2},"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":"2026-05-18T02:35:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jMYMEcNHzxj/OmeUPPYqH5MlB4KvTnOw7HgnfMkX+j+WCEYY/6HjKs8PvS0Z/hpg/hjOwftBqg64gTW29Y7iAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T04:11:27.281983Z"},"content_sha256":"1baa3158129c1ad47f4a883aa7d08557e180f6242e0821e651b182d6326e2dea","schema_version":"1.0","event_id":"sha256:1baa3158129c1ad47f4a883aa7d08557e180f6242e0821e651b182d6326e2dea"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AYZ5U4CIG5KVW5LLYJKIX5KRTU/bundle.json","state_url":"https://pith.science/pith/AYZ5U4CIG5KVW5LLYJKIX5KRTU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AYZ5U4CIG5KVW5LLYJKIX5KRTU/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":"2026-05-30T04:11:27Z","links":{"resolver":"https://pith.science/pith/AYZ5U4CIG5KVW5LLYJKIX5KRTU","bundle":"https://pith.science/pith/AYZ5U4CIG5KVW5LLYJKIX5KRTU/bundle.json","state":"https://pith.science/pith/AYZ5U4CIG5KVW5LLYJKIX5KRTU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AYZ5U4CIG5KVW5LLYJKIX5KRTU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:AYZ5U4CIG5KVW5LLYJKIX5KRTU","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":"97dd25286109772463354cfa26e951740559dedf1a1cae5d7423b1a95a1ecaf4","cross_cats_sorted":["math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-05-09T18:22:57Z","title_canon_sha256":"4440d14c66559d8262d7c9985dda0abbcf95505e5eb5054ac807a0b65bf21a80"},"schema_version":"1.0","source":{"id":"1405.2302","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.2302","created_at":"2026-05-18T02:35:47Z"},{"alias_kind":"arxiv_version","alias_value":"1405.2302v2","created_at":"2026-05-18T02:35:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.2302","created_at":"2026-05-18T02:35:47Z"},{"alias_kind":"pith_short_12","alias_value":"AYZ5U4CIG5KV","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"AYZ5U4CIG5KVW5LL","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"AYZ5U4CI","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:1baa3158129c1ad47f4a883aa7d08557e180f6242e0821e651b182d6326e2dea","target":"graph","created_at":"2026-05-18T02:35:47Z","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":"We compute the mean first passage time (MFPT) for a Brownian particle inside a two-dimensional disk with reflective boundaries and a small interior trap that is rotating at a constant angular velocity. The inherent symmetry of the problem allows for a detailed analytic study of the situation. For a given angular velocity, we determine the optimal radius of rotation that minimizes the average MFPT over the disk. Several distinct regimes are observed, depending on the ratio between the angular velocity $\\omega$ and the trap size $\\varepsilon$, and several intricate transitions are analyzed using","authors_text":"Justin C. Tzou, Theodore Kolokolnikov","cross_cats":["math.AP","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-05-09T18:22:57Z","title":"Mean first passage time for a small rotating trap inside a reflective disk"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.2302","kind":"arxiv","version":2},"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:e1dcb9c9acb36ea10ece1303a151452a43ce324db787284ab8f49192334f8747","target":"record","created_at":"2026-05-18T02:35:47Z","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":"97dd25286109772463354cfa26e951740559dedf1a1cae5d7423b1a95a1ecaf4","cross_cats_sorted":["math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-05-09T18:22:57Z","title_canon_sha256":"4440d14c66559d8262d7c9985dda0abbcf95505e5eb5054ac807a0b65bf21a80"},"schema_version":"1.0","source":{"id":"1405.2302","kind":"arxiv","version":2}},"canonical_sha256":"0633da704837555b756bc2548bf5519d350ff027475c5e544df732716c4c5935","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0633da704837555b756bc2548bf5519d350ff027475c5e544df732716c4c5935","first_computed_at":"2026-05-18T02:35:47.351392Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:35:47.351392Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mqVtGr/d9xaWcNoQpz29/bY7lRxtWM096Hhbetr90Fp9jqx4s37rrGrIrpuCmJEVW1faE/g0tXs7TwTAhR/lDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:35:47.351799Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.2302","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e1dcb9c9acb36ea10ece1303a151452a43ce324db787284ab8f49192334f8747","sha256:1baa3158129c1ad47f4a883aa7d08557e180f6242e0821e651b182d6326e2dea"],"state_sha256":"8f8374ebb1bdab130ad17e16e4359ba880bf8b71d7a9928e037e06b6052d6ad1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hb0iDCBhuAG7EJb5LnOkMIKuzR+Z3o8UosSA7Kwnb4xgkzhMH5Kg/OpMHFiT2fCvxUkqXbOliKsQ89BjFQEeDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T04:11:27.285658Z","bundle_sha256":"115db8c1690357eb84f123cee89d0b7dd6a0733ea9c4a08a1ce32342c44081a5"}}