{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:56Z4XHU7IWOMP4ZXJPLSODF3IK","short_pith_number":"pith:56Z4XHU7","canonical_record":{"source":{"id":"0809.0262","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2008-09-01T15:06:04Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"a7631e19ab217ccb7ac0f1f523a1be540e24cad1526a840c28cc7c751aa01fca","abstract_canon_sha256":"c24fdd35e634e6701aacc97d9339b36e40ecc1a03ce134eba060264b97526991"},"schema_version":"1.0"},"canonical_sha256":"efb3cb9e9f459cc7f3374bd7270cbb42bce1da8ab614d6efd48f58edfa6e7ebf","source":{"kind":"arxiv","id":"0809.0262","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0809.0262","created_at":"2026-05-17T23:41:31Z"},{"alias_kind":"arxiv_version","alias_value":"0809.0262v1","created_at":"2026-05-17T23:41:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0809.0262","created_at":"2026-05-17T23:41:31Z"},{"alias_kind":"pith_short_12","alias_value":"56Z4XHU7IWOM","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"56Z4XHU7IWOMP4ZX","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"56Z4XHU7","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:56Z4XHU7IWOMP4ZXJPLSODF3IK","target":"record","payload":{"canonical_record":{"source":{"id":"0809.0262","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2008-09-01T15:06:04Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"a7631e19ab217ccb7ac0f1f523a1be540e24cad1526a840c28cc7c751aa01fca","abstract_canon_sha256":"c24fdd35e634e6701aacc97d9339b36e40ecc1a03ce134eba060264b97526991"},"schema_version":"1.0"},"canonical_sha256":"efb3cb9e9f459cc7f3374bd7270cbb42bce1da8ab614d6efd48f58edfa6e7ebf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:31.685230Z","signature_b64":"CDmLcQDKzLyvSd9zYm0QkJIHSD5tVNcmV5thTGhBtybXnjEUXSSMXisxekAWe2xegPt9Z6yavv5nDYBBgarwDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"efb3cb9e9f459cc7f3374bd7270cbb42bce1da8ab614d6efd48f58edfa6e7ebf","last_reissued_at":"2026-05-17T23:41:31.684547Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:31.684547Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0809.0262","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":"2026-05-17T23:41:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dkSlKULJSIyjUPXx+3l1HYrseH2S8qSYzct9B+mzfrWqb/LRfcuTx+Vt/xkW4BZSCTxuLKLpLTvf3zlP2BUHCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T12:05:42.963755Z"},"content_sha256":"e4adcedad95ec706b7f3dfe33edcda6a749523159650dd88a88b75aadb099b78","schema_version":"1.0","event_id":"sha256:e4adcedad95ec706b7f3dfe33edcda6a749523159650dd88a88b75aadb099b78"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:56Z4XHU7IWOMP4ZXJPLSODF3IK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Replica overlap and covering time for the Wiener sausages among Poissonian obstacles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Ryoki Fukushima","submitted_at":"2008-09-01T15:06:04Z","abstract_excerpt":"We study two objects concerning the Wiener sausage among Poissonian obstacles. The first is the asymptotics for the \\textit{replica overlap}, which is the intersection of two independent Wiener sausages. We show that it is asymptotically equal to their union. This result confirms that the localizing effect of the media is so strong as to completely determine the motional range of particles. The second is an estimate on the \\textit{covering time}. It is known that the Wiener sausage avoiding Poissonian obstacles up to time $t$ is confined in some `clearing' ball near the origin and almost fills"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.0262","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":"2026-05-17T23:41:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GTff6FfbpC9Udz4mxVzeGdUiA8wtPrFYp83XyqT/NPw7QoP1Rc6Ft0WAUutGf1KP3xu0cDIbner+pMy8sBfwAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T12:05:42.964479Z"},"content_sha256":"9bc073dde98451d9651da7e915e048908df1399c1812ff1c0ad32913eaca12ca","schema_version":"1.0","event_id":"sha256:9bc073dde98451d9651da7e915e048908df1399c1812ff1c0ad32913eaca12ca"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/56Z4XHU7IWOMP4ZXJPLSODF3IK/bundle.json","state_url":"https://pith.science/pith/56Z4XHU7IWOMP4ZXJPLSODF3IK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/56Z4XHU7IWOMP4ZXJPLSODF3IK/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":"2026-06-07T12:05:42Z","links":{"resolver":"https://pith.science/pith/56Z4XHU7IWOMP4ZXJPLSODF3IK","bundle":"https://pith.science/pith/56Z4XHU7IWOMP4ZXJPLSODF3IK/bundle.json","state":"https://pith.science/pith/56Z4XHU7IWOMP4ZXJPLSODF3IK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/56Z4XHU7IWOMP4ZXJPLSODF3IK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:56Z4XHU7IWOMP4ZXJPLSODF3IK","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":"c24fdd35e634e6701aacc97d9339b36e40ecc1a03ce134eba060264b97526991","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2008-09-01T15:06:04Z","title_canon_sha256":"a7631e19ab217ccb7ac0f1f523a1be540e24cad1526a840c28cc7c751aa01fca"},"schema_version":"1.0","source":{"id":"0809.0262","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0809.0262","created_at":"2026-05-17T23:41:31Z"},{"alias_kind":"arxiv_version","alias_value":"0809.0262v1","created_at":"2026-05-17T23:41:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0809.0262","created_at":"2026-05-17T23:41:31Z"},{"alias_kind":"pith_short_12","alias_value":"56Z4XHU7IWOM","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"56Z4XHU7IWOMP4ZX","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"56Z4XHU7","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:9bc073dde98451d9651da7e915e048908df1399c1812ff1c0ad32913eaca12ca","target":"graph","created_at":"2026-05-17T23:41:31Z","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 study two objects concerning the Wiener sausage among Poissonian obstacles. The first is the asymptotics for the \\textit{replica overlap}, which is the intersection of two independent Wiener sausages. We show that it is asymptotically equal to their union. This result confirms that the localizing effect of the media is so strong as to completely determine the motional range of particles. The second is an estimate on the \\textit{covering time}. It is known that the Wiener sausage avoiding Poissonian obstacles up to time $t$ is confined in some `clearing' ball near the origin and almost fills","authors_text":"Ryoki Fukushima","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2008-09-01T15:06:04Z","title":"Replica overlap and covering time for the Wiener sausages among Poissonian obstacles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.0262","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:e4adcedad95ec706b7f3dfe33edcda6a749523159650dd88a88b75aadb099b78","target":"record","created_at":"2026-05-17T23:41:31Z","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":"c24fdd35e634e6701aacc97d9339b36e40ecc1a03ce134eba060264b97526991","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2008-09-01T15:06:04Z","title_canon_sha256":"a7631e19ab217ccb7ac0f1f523a1be540e24cad1526a840c28cc7c751aa01fca"},"schema_version":"1.0","source":{"id":"0809.0262","kind":"arxiv","version":1}},"canonical_sha256":"efb3cb9e9f459cc7f3374bd7270cbb42bce1da8ab614d6efd48f58edfa6e7ebf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"efb3cb9e9f459cc7f3374bd7270cbb42bce1da8ab614d6efd48f58edfa6e7ebf","first_computed_at":"2026-05-17T23:41:31.684547Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:31.684547Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CDmLcQDKzLyvSd9zYm0QkJIHSD5tVNcmV5thTGhBtybXnjEUXSSMXisxekAWe2xegPt9Z6yavv5nDYBBgarwDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:31.685230Z","signed_message":"canonical_sha256_bytes"},"source_id":"0809.0262","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e4adcedad95ec706b7f3dfe33edcda6a749523159650dd88a88b75aadb099b78","sha256:9bc073dde98451d9651da7e915e048908df1399c1812ff1c0ad32913eaca12ca"],"state_sha256":"0dcc358925fdbeb7f2b25ed725f2edc3c47e06eca00353c8118fdd755fbbae5e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tYDqYkScjkH6YWqCuOtbfmSxD3ihUtAmexwRH13nePkgy5Xwm52e0dzrwtsLeUZQokbGcAFSlG2r1URZhDMWAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T12:05:42.968132Z","bundle_sha256":"f8f3441e873993e4136277c6d4c0acea736b987602981aa0cae30ed41fc21540"}}