{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:UKVVHWPXVUJDECYUPWX2KLUJON","short_pith_number":"pith:UKVVHWPX","schema_version":"1.0","canonical_sha256":"a2ab53d9f7ad12320b147dafa52e89735e5a52f947fe8c3a1088df370ac296cc","source":{"kind":"arxiv","id":"1505.06069","version":1},"attestation_state":"computed","paper":{"title":"Homogenization via sprinkling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Itai Benjamini, Vincent Tassion","submitted_at":"2015-05-22T13:33:42Z","abstract_excerpt":"We show that a superposition of an $\\varepsilon$-Bernoulli bond percolation and any everywhere percolating subgraph of $\\mathbb Z^d$, $d\\ge 2$, results in a connected subgraph, which after a renormalization dominates supercritical Bernoulli percolation. This result, which confirms a conjecture of the first author together with H\\\"aggstr\\\"om and Schramm (2000), is mainly motivated by obtaining finite volume characterizations of uniqueness for general percolation processes."},"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":"1505.06069","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-05-22T13:33:42Z","cross_cats_sorted":[],"title_canon_sha256":"2f290fb71206123e0e77184ade0817d95cdd1024a6a84ccd2fae36168ed3d9b3","abstract_canon_sha256":"0b40867223721994a7463538e08cf27a3560cb70462fe1933c018db97d86330e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:03:49.224040Z","signature_b64":"XIVZ6o5dGuTARvcil8iAXKAlsEVzI7Ppx1laMt7WqqOwGP7XBBuDrdnLq4F51k9Gj6nioqp1IOWQ9TQ8WDleDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a2ab53d9f7ad12320b147dafa52e89735e5a52f947fe8c3a1088df370ac296cc","last_reissued_at":"2026-05-18T02:03:49.223396Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:03:49.223396Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Homogenization via sprinkling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Itai Benjamini, Vincent Tassion","submitted_at":"2015-05-22T13:33:42Z","abstract_excerpt":"We show that a superposition of an $\\varepsilon$-Bernoulli bond percolation and any everywhere percolating subgraph of $\\mathbb Z^d$, $d\\ge 2$, results in a connected subgraph, which after a renormalization dominates supercritical Bernoulli percolation. This result, which confirms a conjecture of the first author together with H\\\"aggstr\\\"om and Schramm (2000), is mainly motivated by obtaining finite volume characterizations of uniqueness for general percolation processes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06069","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1505.06069","created_at":"2026-05-18T02:03:49.223511+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.06069v1","created_at":"2026-05-18T02:03:49.223511+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.06069","created_at":"2026-05-18T02:03:49.223511+00:00"},{"alias_kind":"pith_short_12","alias_value":"UKVVHWPXVUJD","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_16","alias_value":"UKVVHWPXVUJDECYU","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_8","alias_value":"UKVVHWPX","created_at":"2026-05-18T12:29:44.643036+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/UKVVHWPXVUJDECYUPWX2KLUJON","json":"https://pith.science/pith/UKVVHWPXVUJDECYUPWX2KLUJON.json","graph_json":"https://pith.science/api/pith-number/UKVVHWPXVUJDECYUPWX2KLUJON/graph.json","events_json":"https://pith.science/api/pith-number/UKVVHWPXVUJDECYUPWX2KLUJON/events.json","paper":"https://pith.science/paper/UKVVHWPX"},"agent_actions":{"view_html":"https://pith.science/pith/UKVVHWPXVUJDECYUPWX2KLUJON","download_json":"https://pith.science/pith/UKVVHWPXVUJDECYUPWX2KLUJON.json","view_paper":"https://pith.science/paper/UKVVHWPX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.06069&json=true","fetch_graph":"https://pith.science/api/pith-number/UKVVHWPXVUJDECYUPWX2KLUJON/graph.json","fetch_events":"https://pith.science/api/pith-number/UKVVHWPXVUJDECYUPWX2KLUJON/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UKVVHWPXVUJDECYUPWX2KLUJON/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UKVVHWPXVUJDECYUPWX2KLUJON/action/storage_attestation","attest_author":"https://pith.science/pith/UKVVHWPXVUJDECYUPWX2KLUJON/action/author_attestation","sign_citation":"https://pith.science/pith/UKVVHWPXVUJDECYUPWX2KLUJON/action/citation_signature","submit_replication":"https://pith.science/pith/UKVVHWPXVUJDECYUPWX2KLUJON/action/replication_record"}},"created_at":"2026-05-18T02:03:49.223511+00:00","updated_at":"2026-05-18T02:03:49.223511+00:00"}