{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:JM3HGAGKU5LBOIAUZJNRH225G5","short_pith_number":"pith:JM3HGAGK","schema_version":"1.0","canonical_sha256":"4b367300caa756172014ca5b13eb5d375f9117ca202b59fa5c492c73446035d9","source":{"kind":"arxiv","id":"1009.3719","version":3},"attestation_state":"computed","paper":{"title":"Percolation in a multiscale Boolean model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jean-Baptiste Gou\\'er\\'e (MAPMO)","submitted_at":"2010-09-20T07:43:30Z","abstract_excerpt":"We consider percolation in a multiscale Boolean model. This model is defined as the union of scaled independent copies of a given Boolean model. The scale factor of the $n^{\\textrm{th}}$ copy is $\\rho^{-n}$. We prove, under optimal integrability assumptions, that no percolation occurs in the multiscale Boolean model for large enough $\\rho$ if the rate of the Boolean model is below some critical value."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1009.3719","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-09-20T07:43:30Z","cross_cats_sorted":[],"title_canon_sha256":"a4d7fbeadf2c4cc0cca11c1857be85a64a8cd68eac385a83621355a4379af396","abstract_canon_sha256":"46ffdd121b4f4f96c0f47026b1bef3770bd7d80d25bf07fca05ba353d793a8c5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:26:56.422248Z","signature_b64":"0hW9i59sz/KLMVbW7S5GjquY3AbzxfYcTdG0Xo7N0fksz+/+XNzMmYpamyjn4k3SkQm8yKleomS6fVmrsY0fBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4b367300caa756172014ca5b13eb5d375f9117ca202b59fa5c492c73446035d9","last_reissued_at":"2026-05-18T04:26:56.421572Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:26:56.421572Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Percolation in a multiscale Boolean model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jean-Baptiste Gou\\'er\\'e (MAPMO)","submitted_at":"2010-09-20T07:43:30Z","abstract_excerpt":"We consider percolation in a multiscale Boolean model. This model is defined as the union of scaled independent copies of a given Boolean model. The scale factor of the $n^{\\textrm{th}}$ copy is $\\rho^{-n}$. We prove, under optimal integrability assumptions, that no percolation occurs in the multiscale Boolean model for large enough $\\rho$ if the rate of the Boolean model is below some critical value."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.3719","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1009.3719","created_at":"2026-05-18T04:26:56.421671+00:00"},{"alias_kind":"arxiv_version","alias_value":"1009.3719v3","created_at":"2026-05-18T04:26:56.421671+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.3719","created_at":"2026-05-18T04:26:56.421671+00:00"},{"alias_kind":"pith_short_12","alias_value":"JM3HGAGKU5LB","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_16","alias_value":"JM3HGAGKU5LBOIAU","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_8","alias_value":"JM3HGAGK","created_at":"2026-05-18T12:26:09.077623+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JM3HGAGKU5LBOIAUZJNRH225G5","json":"https://pith.science/pith/JM3HGAGKU5LBOIAUZJNRH225G5.json","graph_json":"https://pith.science/api/pith-number/JM3HGAGKU5LBOIAUZJNRH225G5/graph.json","events_json":"https://pith.science/api/pith-number/JM3HGAGKU5LBOIAUZJNRH225G5/events.json","paper":"https://pith.science/paper/JM3HGAGK"},"agent_actions":{"view_html":"https://pith.science/pith/JM3HGAGKU5LBOIAUZJNRH225G5","download_json":"https://pith.science/pith/JM3HGAGKU5LBOIAUZJNRH225G5.json","view_paper":"https://pith.science/paper/JM3HGAGK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1009.3719&json=true","fetch_graph":"https://pith.science/api/pith-number/JM3HGAGKU5LBOIAUZJNRH225G5/graph.json","fetch_events":"https://pith.science/api/pith-number/JM3HGAGKU5LBOIAUZJNRH225G5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JM3HGAGKU5LBOIAUZJNRH225G5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JM3HGAGKU5LBOIAUZJNRH225G5/action/storage_attestation","attest_author":"https://pith.science/pith/JM3HGAGKU5LBOIAUZJNRH225G5/action/author_attestation","sign_citation":"https://pith.science/pith/JM3HGAGKU5LBOIAUZJNRH225G5/action/citation_signature","submit_replication":"https://pith.science/pith/JM3HGAGKU5LBOIAUZJNRH225G5/action/replication_record"}},"created_at":"2026-05-18T04:26:56.421671+00:00","updated_at":"2026-05-18T04:26:56.421671+00:00"}