{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:QJ4ULOHFEAKNGISDQX63SV4KSH","short_pith_number":"pith:QJ4ULOHF","schema_version":"1.0","canonical_sha256":"827945b8e52014d3224385fdb9578a91e44ae34c7ff1c8dcc512a995fadcbb5f","source":{"kind":"arxiv","id":"1103.0411","version":3},"attestation_state":"computed","paper":{"title":"Subcritical percolation with a line of defects","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"D. Ioffe, S. Friedli, Y. Velenik","submitted_at":"2011-03-02T12:40:39Z","abstract_excerpt":"We consider the Bernoulli bond percolation process $\\mathbb{P}_{p,p'}$ on the nearest-neighbor edges of $\\mathbb{Z}^d$, which are open independently with probability $p<p_c$, except for those lying on the first coordinate axis, for which this probability is $p'$. Define \\[\\xi_{p,p'}:=-\\lim_{n\\to\\infty}n^{-1}\\log \\mathbb{P}_{p,p'}(0\\leftrightarrow n\\mathbf {e}_1)\\] and $\\xi_p:=\\xi_{p,p}$. We show that there exists $p_c'=p_c'(p,d)$ such that $\\xi_{p,p'}=\\xi_p$ if $p'<p_c'$ and $\\xi_{p,p'}<\\xi_p$ if $p'>p_c'$. Moreover, $p_c'(p,2)=p_c'(p,3)=p$, and $p_c'(p,d)>p$ for $d\\geq 4$. We also analyze the"},"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":"1103.0411","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-03-02T12:40:39Z","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP"],"title_canon_sha256":"1face0272e307e08cf64fe15869433c48089a2ea3e054dc00c1e24fcebce5d5a","abstract_canon_sha256":"ec025ce9a15355e925809e4e05026ddb01e89480479b802b4650dba778994b24"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:44.437253Z","signature_b64":"Sj0ssZcVli8Dp0nb3Z40TonrsydqHx3+c8PPj8AkmuqZTgMLNYKnFaoYNkgq+H3RSEEZEFaHX9QayH0elFDEAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"827945b8e52014d3224385fdb9578a91e44ae34c7ff1c8dcc512a995fadcbb5f","last_reissued_at":"2026-05-18T02:29:44.436761Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:44.436761Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Subcritical percolation with a line of defects","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"D. Ioffe, S. Friedli, Y. Velenik","submitted_at":"2011-03-02T12:40:39Z","abstract_excerpt":"We consider the Bernoulli bond percolation process $\\mathbb{P}_{p,p'}$ on the nearest-neighbor edges of $\\mathbb{Z}^d$, which are open independently with probability $p<p_c$, except for those lying on the first coordinate axis, for which this probability is $p'$. Define \\[\\xi_{p,p'}:=-\\lim_{n\\to\\infty}n^{-1}\\log \\mathbb{P}_{p,p'}(0\\leftrightarrow n\\mathbf {e}_1)\\] and $\\xi_p:=\\xi_{p,p}$. We show that there exists $p_c'=p_c'(p,d)$ such that $\\xi_{p,p'}=\\xi_p$ if $p'<p_c'$ and $\\xi_{p,p'}<\\xi_p$ if $p'>p_c'$. Moreover, $p_c'(p,2)=p_c'(p,3)=p$, and $p_c'(p,d)>p$ for $d\\geq 4$. We also analyze the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.0411","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":"1103.0411","created_at":"2026-05-18T02:29:44.436848+00:00"},{"alias_kind":"arxiv_version","alias_value":"1103.0411v3","created_at":"2026-05-18T02:29:44.436848+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.0411","created_at":"2026-05-18T02:29:44.436848+00:00"},{"alias_kind":"pith_short_12","alias_value":"QJ4ULOHFEAKN","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_16","alias_value":"QJ4ULOHFEAKNGISD","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_8","alias_value":"QJ4ULOHF","created_at":"2026-05-18T12:26:39.201973+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/QJ4ULOHFEAKNGISDQX63SV4KSH","json":"https://pith.science/pith/QJ4ULOHFEAKNGISDQX63SV4KSH.json","graph_json":"https://pith.science/api/pith-number/QJ4ULOHFEAKNGISDQX63SV4KSH/graph.json","events_json":"https://pith.science/api/pith-number/QJ4ULOHFEAKNGISDQX63SV4KSH/events.json","paper":"https://pith.science/paper/QJ4ULOHF"},"agent_actions":{"view_html":"https://pith.science/pith/QJ4ULOHFEAKNGISDQX63SV4KSH","download_json":"https://pith.science/pith/QJ4ULOHFEAKNGISDQX63SV4KSH.json","view_paper":"https://pith.science/paper/QJ4ULOHF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1103.0411&json=true","fetch_graph":"https://pith.science/api/pith-number/QJ4ULOHFEAKNGISDQX63SV4KSH/graph.json","fetch_events":"https://pith.science/api/pith-number/QJ4ULOHFEAKNGISDQX63SV4KSH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QJ4ULOHFEAKNGISDQX63SV4KSH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QJ4ULOHFEAKNGISDQX63SV4KSH/action/storage_attestation","attest_author":"https://pith.science/pith/QJ4ULOHFEAKNGISDQX63SV4KSH/action/author_attestation","sign_citation":"https://pith.science/pith/QJ4ULOHFEAKNGISDQX63SV4KSH/action/citation_signature","submit_replication":"https://pith.science/pith/QJ4ULOHFEAKNGISDQX63SV4KSH/action/replication_record"}},"created_at":"2026-05-18T02:29:44.436848+00:00","updated_at":"2026-05-18T02:29:44.436848+00:00"}