{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:W35W2VSMTOTGBASHF6NP6WR3MX","short_pith_number":"pith:W35W2VSM","schema_version":"1.0","canonical_sha256":"b6fb6d564c9ba66082472f9aff5a3b65ec1f1a649c228eccfb9ed207dac1131e","source":{"kind":"arxiv","id":"1207.3168","version":1},"attestation_state":"computed","paper":{"title":"Oriented percolation in a random environment","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Harry Kesten, Maria Eulalia Vares, Vladas Sidoravicius","submitted_at":"2012-07-13T08:41:51Z","abstract_excerpt":"On the lattice $\\widetilde{\\mathbb Z}^2_+:={(x,y)\\in \\mathbb Z \\times \\mathbb Z_+\\colon x+y \\text{is even}}$ we consider the following oriented (northwest-northeast) site percolation: the lines $H_i:={(x,y)\\in \\widetilde {\\mathbb Z}^2_+ \\colon y=i}$ are first declared to be bad or good with probabilities $\\de$ and $1-\\de$ respectively, independently of each other. Given the configuration of lines, sites on good lines are open with probability $p_{_G}>p_c$, the critical probability for the standard oriented site percolation on $\\mathbb Z_+ \\times \\mathbb Z_+$, and sites on bad lines are open wi"},"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":"1207.3168","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-07-13T08:41:51Z","cross_cats_sorted":[],"title_canon_sha256":"4f7e35e4ee50453e981c4b8ea6f0db06ff1705715164d7d7180cc7b8137a3055","abstract_canon_sha256":"c466fc35f8c67f28bca54e4579cac7b34b46d125c0b13f2f692d064d2cd12067"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:51:12.324489Z","signature_b64":"aXJP30qm5t3oQ8SICQ6tvvq4IwIknZ7xCbNVXwK9x5O5oC/QZrkqjWGyTE/JcYKoeKg84X+RJ2IqxvqeDNtxDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b6fb6d564c9ba66082472f9aff5a3b65ec1f1a649c228eccfb9ed207dac1131e","last_reissued_at":"2026-05-18T03:51:12.323960Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:51:12.323960Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Oriented percolation in a random environment","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Harry Kesten, Maria Eulalia Vares, Vladas Sidoravicius","submitted_at":"2012-07-13T08:41:51Z","abstract_excerpt":"On the lattice $\\widetilde{\\mathbb Z}^2_+:={(x,y)\\in \\mathbb Z \\times \\mathbb Z_+\\colon x+y \\text{is even}}$ we consider the following oriented (northwest-northeast) site percolation: the lines $H_i:={(x,y)\\in \\widetilde {\\mathbb Z}^2_+ \\colon y=i}$ are first declared to be bad or good with probabilities $\\de$ and $1-\\de$ respectively, independently of each other. Given the configuration of lines, sites on good lines are open with probability $p_{_G}>p_c$, the critical probability for the standard oriented site percolation on $\\mathbb Z_+ \\times \\mathbb Z_+$, and sites on bad lines are open wi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.3168","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":"1207.3168","created_at":"2026-05-18T03:51:12.324038+00:00"},{"alias_kind":"arxiv_version","alias_value":"1207.3168v1","created_at":"2026-05-18T03:51:12.324038+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.3168","created_at":"2026-05-18T03:51:12.324038+00:00"},{"alias_kind":"pith_short_12","alias_value":"W35W2VSMTOTG","created_at":"2026-05-18T12:27:25.539911+00:00"},{"alias_kind":"pith_short_16","alias_value":"W35W2VSMTOTGBASH","created_at":"2026-05-18T12:27:25.539911+00:00"},{"alias_kind":"pith_short_8","alias_value":"W35W2VSM","created_at":"2026-05-18T12:27:25.539911+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/W35W2VSMTOTGBASHF6NP6WR3MX","json":"https://pith.science/pith/W35W2VSMTOTGBASHF6NP6WR3MX.json","graph_json":"https://pith.science/api/pith-number/W35W2VSMTOTGBASHF6NP6WR3MX/graph.json","events_json":"https://pith.science/api/pith-number/W35W2VSMTOTGBASHF6NP6WR3MX/events.json","paper":"https://pith.science/paper/W35W2VSM"},"agent_actions":{"view_html":"https://pith.science/pith/W35W2VSMTOTGBASHF6NP6WR3MX","download_json":"https://pith.science/pith/W35W2VSMTOTGBASHF6NP6WR3MX.json","view_paper":"https://pith.science/paper/W35W2VSM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1207.3168&json=true","fetch_graph":"https://pith.science/api/pith-number/W35W2VSMTOTGBASHF6NP6WR3MX/graph.json","fetch_events":"https://pith.science/api/pith-number/W35W2VSMTOTGBASHF6NP6WR3MX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/W35W2VSMTOTGBASHF6NP6WR3MX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/W35W2VSMTOTGBASHF6NP6WR3MX/action/storage_attestation","attest_author":"https://pith.science/pith/W35W2VSMTOTGBASHF6NP6WR3MX/action/author_attestation","sign_citation":"https://pith.science/pith/W35W2VSMTOTGBASHF6NP6WR3MX/action/citation_signature","submit_replication":"https://pith.science/pith/W35W2VSMTOTGBASHF6NP6WR3MX/action/replication_record"}},"created_at":"2026-05-18T03:51:12.324038+00:00","updated_at":"2026-05-18T03:51:12.324038+00:00"}