{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:4RD4M32QUNMX4LCWSS7MSIZALZ","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":"ec2b1481a582dfbd8def52df518736f710a3322faa7ec4e2e3ea321198a9c3ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-03-13T16:52:47Z","title_canon_sha256":"cb8c393dd0d8c3911c6b03725d6013522fe8ecbb334832483017bd579d67cc97"},"schema_version":"1.0","source":{"id":"1203.2859","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.2859","created_at":"2026-05-18T03:53:44Z"},{"alias_kind":"arxiv_version","alias_value":"1203.2859v2","created_at":"2026-05-18T03:53:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.2859","created_at":"2026-05-18T03:53:44Z"},{"alias_kind":"pith_short_12","alias_value":"4RD4M32QUNMX","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"4RD4M32QUNMX4LCW","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"4RD4M32Q","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:ac3241f4d27d60cf4515cf7afe1b954c0857b46fb52626674b25b5bf30fc5b0b","target":"graph","created_at":"2026-05-18T03:53:44Z","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 analytically, in one dimension, the survival probability $P_{s}(t)$ up to time $t$ of an immobile target surrounded by mutually noninteracting traps each performing a continuous-time random walk (CTRW) in continuous space. We consider a general CTRW with symmetric and continuous (but otherwise arbitrary) jump length distribution $f(\\eta)$ and arbitrary waiting time distribution $\\psi(\\tau)$. The traps are initially distributed uniformly in space with density $\\rho$. We prove an exact relation, valid for all time $t$, between $P_s(t)$ and the expected maximum $E[M(t)]$ of the trap proc","authors_text":"Jasper Franke, Satya N. Majumdar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-03-13T16:52:47Z","title":"Survival probability of an immobile target surrounded by mobile traps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.2859","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":"sha256:8b70d16214f03a25f509761c5704a5ac7024fecf3112472cc05016502c88858d","target":"record","created_at":"2026-05-18T03:53:44Z","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":"ec2b1481a582dfbd8def52df518736f710a3322faa7ec4e2e3ea321198a9c3ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-03-13T16:52:47Z","title_canon_sha256":"cb8c393dd0d8c3911c6b03725d6013522fe8ecbb334832483017bd579d67cc97"},"schema_version":"1.0","source":{"id":"1203.2859","kind":"arxiv","version":2}},"canonical_sha256":"e447c66f50a3597e2c5694bec923205e615c34a27c56a920775da65c03dd929c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e447c66f50a3597e2c5694bec923205e615c34a27c56a920775da65c03dd929c","first_computed_at":"2026-05-18T03:53:44.807599Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:53:44.807599Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QPBJgUfSBA16yrxWRyWo4Xs7hUPHeRxdVjfpeADAScAVlFTwl97tL1heZ/HJWYO4ADDjFbtr1NNVTNT/ya+KCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:53:44.808101Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.2859","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8b70d16214f03a25f509761c5704a5ac7024fecf3112472cc05016502c88858d","sha256:ac3241f4d27d60cf4515cf7afe1b954c0857b46fb52626674b25b5bf30fc5b0b"],"state_sha256":"1f261849fe230180ce20ae214bdd78174007dc9c3e875f4b7e189564db05c78c"}