{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:JVNGSCRR5VIGTC6VCTHUXCEXOE","short_pith_number":"pith:JVNGSCRR","canonical_record":{"source":{"id":"1306.2628","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-06-11T19:57:50Z","cross_cats_sorted":[],"title_canon_sha256":"9bef2034294642c22de4b31463dcf465a0f01719774107c73536c79a6e9f3350","abstract_canon_sha256":"facf4cf71add9d6ae8bda088ea06af4e0fdc719be6ce001a8d54ffb5e44ff414"},"schema_version":"1.0"},"canonical_sha256":"4d5a690a31ed50698bd514cf4b88977126f93b720fd220f2a6d7eff44d85ff1a","source":{"kind":"arxiv","id":"1306.2628","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.2628","created_at":"2026-05-18T00:13:38Z"},{"alias_kind":"arxiv_version","alias_value":"1306.2628v3","created_at":"2026-05-18T00:13:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.2628","created_at":"2026-05-18T00:13:38Z"},{"alias_kind":"pith_short_12","alias_value":"JVNGSCRR5VIG","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JVNGSCRR5VIGTC6V","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JVNGSCRR","created_at":"2026-05-18T12:27:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:JVNGSCRR5VIGTC6VCTHUXCEXOE","target":"record","payload":{"canonical_record":{"source":{"id":"1306.2628","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-06-11T19:57:50Z","cross_cats_sorted":[],"title_canon_sha256":"9bef2034294642c22de4b31463dcf465a0f01719774107c73536c79a6e9f3350","abstract_canon_sha256":"facf4cf71add9d6ae8bda088ea06af4e0fdc719be6ce001a8d54ffb5e44ff414"},"schema_version":"1.0"},"canonical_sha256":"4d5a690a31ed50698bd514cf4b88977126f93b720fd220f2a6d7eff44d85ff1a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:38.404219Z","signature_b64":"+26beUR/KPI2RQC1/IwhKO9saimbzxhghkoe/9gOQgBEU74tXiX/EcDZMgKivXNNKg6v3dQkg9VWkGhq9VReDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4d5a690a31ed50698bd514cf4b88977126f93b720fd220f2a6d7eff44d85ff1a","last_reissued_at":"2026-05-18T00:13:38.403617Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:38.403617Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.2628","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:13:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5kOVOiJPXiKIJAv5LBp0Rpqb1XLmyf4YK27Bm7YqjpgBhjSROFvsxnjm0bykIdCe7ma4ci8xLhDm7taYRzwGBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T21:57:09.716922Z"},"content_sha256":"3c94162c29d613613e7a5b36e474d6368e9c982d315158bde04d38fa5848caec","schema_version":"1.0","event_id":"sha256:3c94162c29d613613e7a5b36e474d6368e9c982d315158bde04d38fa5848caec"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:JVNGSCRR5VIGTC6VCTHUXCEXOE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Greedy Clearing of Persistent Poissonian Dust","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Laurent Tournier, Leonardo T. Rolla, Vladas Sidoravicius","submitted_at":"2013-06-11T19:57:50Z","abstract_excerpt":"Given a Poisson point process on R, assign either one or two marks to each point of this process, independently of the others. We study the motion of a particle that jumps deterministically from its current location to the nearest point of the Poisson point process which still contains at least one mark, and removes one mark per each visit. A point of the Poisson point process which is left with no marks is removed from the system. We prove that the presence of any positive density of double marks leads to the eventual removal of every Poissonian point."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.2628","kind":"arxiv","version":3},"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":"2026-05-18T00:13:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IGFODY16WvJCdKXbPXkCk8J4sZSYolH0upyQWJilp3b+tG2bvgs3pmGDFlQ23yvOIatHubP/MOdXylsbouFWAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T21:57:09.717623Z"},"content_sha256":"87edb6cda0039453785330a869fcabdefb5e8ffaeadb74d7d10d6ff5378d0a68","schema_version":"1.0","event_id":"sha256:87edb6cda0039453785330a869fcabdefb5e8ffaeadb74d7d10d6ff5378d0a68"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JVNGSCRR5VIGTC6VCTHUXCEXOE/bundle.json","state_url":"https://pith.science/pith/JVNGSCRR5VIGTC6VCTHUXCEXOE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JVNGSCRR5VIGTC6VCTHUXCEXOE/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":"2026-05-28T21:57:09Z","links":{"resolver":"https://pith.science/pith/JVNGSCRR5VIGTC6VCTHUXCEXOE","bundle":"https://pith.science/pith/JVNGSCRR5VIGTC6VCTHUXCEXOE/bundle.json","state":"https://pith.science/pith/JVNGSCRR5VIGTC6VCTHUXCEXOE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JVNGSCRR5VIGTC6VCTHUXCEXOE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:JVNGSCRR5VIGTC6VCTHUXCEXOE","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":"facf4cf71add9d6ae8bda088ea06af4e0fdc719be6ce001a8d54ffb5e44ff414","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-06-11T19:57:50Z","title_canon_sha256":"9bef2034294642c22de4b31463dcf465a0f01719774107c73536c79a6e9f3350"},"schema_version":"1.0","source":{"id":"1306.2628","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.2628","created_at":"2026-05-18T00:13:38Z"},{"alias_kind":"arxiv_version","alias_value":"1306.2628v3","created_at":"2026-05-18T00:13:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.2628","created_at":"2026-05-18T00:13:38Z"},{"alias_kind":"pith_short_12","alias_value":"JVNGSCRR5VIG","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JVNGSCRR5VIGTC6V","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JVNGSCRR","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:87edb6cda0039453785330a869fcabdefb5e8ffaeadb74d7d10d6ff5378d0a68","target":"graph","created_at":"2026-05-18T00:13:38Z","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":"Given a Poisson point process on R, assign either one or two marks to each point of this process, independently of the others. We study the motion of a particle that jumps deterministically from its current location to the nearest point of the Poisson point process which still contains at least one mark, and removes one mark per each visit. A point of the Poisson point process which is left with no marks is removed from the system. We prove that the presence of any positive density of double marks leads to the eventual removal of every Poissonian point.","authors_text":"Laurent Tournier, Leonardo T. Rolla, Vladas Sidoravicius","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-06-11T19:57:50Z","title":"Greedy Clearing of Persistent Poissonian Dust"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.2628","kind":"arxiv","version":3},"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":"sha256:3c94162c29d613613e7a5b36e474d6368e9c982d315158bde04d38fa5848caec","target":"record","created_at":"2026-05-18T00:13:38Z","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":"facf4cf71add9d6ae8bda088ea06af4e0fdc719be6ce001a8d54ffb5e44ff414","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-06-11T19:57:50Z","title_canon_sha256":"9bef2034294642c22de4b31463dcf465a0f01719774107c73536c79a6e9f3350"},"schema_version":"1.0","source":{"id":"1306.2628","kind":"arxiv","version":3}},"canonical_sha256":"4d5a690a31ed50698bd514cf4b88977126f93b720fd220f2a6d7eff44d85ff1a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4d5a690a31ed50698bd514cf4b88977126f93b720fd220f2a6d7eff44d85ff1a","first_computed_at":"2026-05-18T00:13:38.403617Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:38.403617Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+26beUR/KPI2RQC1/IwhKO9saimbzxhghkoe/9gOQgBEU74tXiX/EcDZMgKivXNNKg6v3dQkg9VWkGhq9VReDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:38.404219Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.2628","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3c94162c29d613613e7a5b36e474d6368e9c982d315158bde04d38fa5848caec","sha256:87edb6cda0039453785330a869fcabdefb5e8ffaeadb74d7d10d6ff5378d0a68"],"state_sha256":"baf16cb8e082296c0336d4d44319a01f399468f7612ad551f0e407d87bb54e1f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SaMwRO3fBZOFXofxWbkc5VnYDfSpJYnKLagbpXyWyflt+7KTMMTJ0SPhTMxVObCDTmagTJLFzlqlV7jOm+rcDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T21:57:09.722116Z","bundle_sha256":"c23414398eef910c9b769b8da26f9ad0ef135ba5b9bb6de099ca1e5d392ffab5"}}