{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:M4YDMJZMACSH3R6JTNPYWY3OZP","short_pith_number":"pith:M4YDMJZM","schema_version":"1.0","canonical_sha256":"673036272c00a47dc7c99b5f8b636ecbe4bb5d379beff48740ad6f1e86731957","source":{"kind":"arxiv","id":"0905.3040","version":2},"attestation_state":"computed","paper":{"title":"On the mixing time of the 2D stochastic Ising model with \"plus\" boundary conditions at low temperature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"ENS Lyon), F. Martinelli (Matematica, F. Toninelli (CNRS, Roma 3)","submitted_at":"2009-05-19T08:08:50Z","abstract_excerpt":"We consider the Glauber dynamics for the 2D Ising model in a box of side L, at inverse temperature $\\beta$ and random boundary conditions $\\tau$ whose distribution P either stochastically dominates the extremal plus phase (hence the quotation marks in the title) or is stochastically dominated by the extremal minus phase. A particular case is when P is concentrated on the homogeneous configuration identically equal to + (equal to -). For $\\beta$ large enough we show that for any $\\epsilon$ there exists $c=c(\\beta,\\epsilon)$ such that the corresponding mixing time $T_{mix}$ satisfies $\\lim_{L\\to"},"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":"0905.3040","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-05-19T08:08:50Z","cross_cats_sorted":[],"title_canon_sha256":"b1116e6367a2cd58155505eb62287890a788008b28305e281dfd98b50a58df88","abstract_canon_sha256":"ca87c612a0b5a8fa52a976d49232709067082000b0ab26afff93d5b6d3bed59d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:06:21.252439Z","signature_b64":"E6lcDZNArlUwPEXkYPeppZlUkE9TEm0Ag7GdqA6HoaafuZX1ivmfSDkJiXUjff+Os+Zo5fu6A3tKy6Crouk6CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"673036272c00a47dc7c99b5f8b636ecbe4bb5d379beff48740ad6f1e86731957","last_reissued_at":"2026-05-18T04:06:21.251762Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:06:21.251762Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the mixing time of the 2D stochastic Ising model with \"plus\" boundary conditions at low temperature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"ENS Lyon), F. Martinelli (Matematica, F. Toninelli (CNRS, Roma 3)","submitted_at":"2009-05-19T08:08:50Z","abstract_excerpt":"We consider the Glauber dynamics for the 2D Ising model in a box of side L, at inverse temperature $\\beta$ and random boundary conditions $\\tau$ whose distribution P either stochastically dominates the extremal plus phase (hence the quotation marks in the title) or is stochastically dominated by the extremal minus phase. A particular case is when P is concentrated on the homogeneous configuration identically equal to + (equal to -). For $\\beta$ large enough we show that for any $\\epsilon$ there exists $c=c(\\beta,\\epsilon)$ such that the corresponding mixing time $T_{mix}$ satisfies $\\lim_{L\\to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.3040","kind":"arxiv","version":2},"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":"0905.3040","created_at":"2026-05-18T04:06:21.251869+00:00"},{"alias_kind":"arxiv_version","alias_value":"0905.3040v2","created_at":"2026-05-18T04:06:21.251869+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.3040","created_at":"2026-05-18T04:06:21.251869+00:00"},{"alias_kind":"pith_short_12","alias_value":"M4YDMJZMACSH","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_16","alias_value":"M4YDMJZMACSH3R6J","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_8","alias_value":"M4YDMJZM","created_at":"2026-05-18T12:26:00.592388+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/M4YDMJZMACSH3R6JTNPYWY3OZP","json":"https://pith.science/pith/M4YDMJZMACSH3R6JTNPYWY3OZP.json","graph_json":"https://pith.science/api/pith-number/M4YDMJZMACSH3R6JTNPYWY3OZP/graph.json","events_json":"https://pith.science/api/pith-number/M4YDMJZMACSH3R6JTNPYWY3OZP/events.json","paper":"https://pith.science/paper/M4YDMJZM"},"agent_actions":{"view_html":"https://pith.science/pith/M4YDMJZMACSH3R6JTNPYWY3OZP","download_json":"https://pith.science/pith/M4YDMJZMACSH3R6JTNPYWY3OZP.json","view_paper":"https://pith.science/paper/M4YDMJZM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0905.3040&json=true","fetch_graph":"https://pith.science/api/pith-number/M4YDMJZMACSH3R6JTNPYWY3OZP/graph.json","fetch_events":"https://pith.science/api/pith-number/M4YDMJZMACSH3R6JTNPYWY3OZP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/M4YDMJZMACSH3R6JTNPYWY3OZP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/M4YDMJZMACSH3R6JTNPYWY3OZP/action/storage_attestation","attest_author":"https://pith.science/pith/M4YDMJZMACSH3R6JTNPYWY3OZP/action/author_attestation","sign_citation":"https://pith.science/pith/M4YDMJZMACSH3R6JTNPYWY3OZP/action/citation_signature","submit_replication":"https://pith.science/pith/M4YDMJZMACSH3R6JTNPYWY3OZP/action/replication_record"}},"created_at":"2026-05-18T04:06:21.251869+00:00","updated_at":"2026-05-18T04:06:21.251869+00:00"}