{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:NWHCEM57BHHHZ4VGELQD2AF5HI","short_pith_number":"pith:NWHCEM57","schema_version":"1.0","canonical_sha256":"6d8e2233bf09ce7cf2a622e03d00bd3a1b3a90083d3403382e3666043ecd2233","source":{"kind":"arxiv","id":"1504.06767","version":1},"attestation_state":"computed","paper":{"title":"Layered systems at the mean field critical temperature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Domingos H. U. Marchetti, Errico Presutti, Immacolata Merola, Luiz Renato Fontes, Maria Eulalia Vares","submitted_at":"2015-04-25T22:36:54Z","abstract_excerpt":"We consider the Ising model on $\\mathbb Z\\times \\mathbb Z$ where on each horizontal line $\\{(x,i), x\\in \\mathbb Z\\}$, the interaction is given by a ferromagnetic Kac potential with coupling strength $J_\\gamma(x,y)\\sim \\gamma J(\\gamma (x-y))$ at the mean field critical temperature. We then add a nearest neighbor ferromagnetic vertical interaction of strength $\\epsilon$ and prove that for every $\\epsilon >0$ the systems exhibits phase transition provided $\\gamma>0$ is small enough."},"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":"1504.06767","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-04-25T22:36:54Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"4fbdd027455075b8697f4e5c40e975357ec027e2a7a01232acbbe25f95a32c6c","abstract_canon_sha256":"4bef0b2b7953bdbfc5d0bb1a069190b409d13aa8dde7a320f26ffe674ac1506c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:31:39.454209Z","signature_b64":"e1i1XTuXZiD8RhPHYNIAKd91loMGTSHUgWhurqFd7hhwXPqC4sKAET2dAANdw716o6Kks9emcKI3tFZ4aLZCAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6d8e2233bf09ce7cf2a622e03d00bd3a1b3a90083d3403382e3666043ecd2233","last_reissued_at":"2026-05-18T01:31:39.453718Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:31:39.453718Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Layered systems at the mean field critical temperature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Domingos H. U. Marchetti, Errico Presutti, Immacolata Merola, Luiz Renato Fontes, Maria Eulalia Vares","submitted_at":"2015-04-25T22:36:54Z","abstract_excerpt":"We consider the Ising model on $\\mathbb Z\\times \\mathbb Z$ where on each horizontal line $\\{(x,i), x\\in \\mathbb Z\\}$, the interaction is given by a ferromagnetic Kac potential with coupling strength $J_\\gamma(x,y)\\sim \\gamma J(\\gamma (x-y))$ at the mean field critical temperature. We then add a nearest neighbor ferromagnetic vertical interaction of strength $\\epsilon$ and prove that for every $\\epsilon >0$ the systems exhibits phase transition provided $\\gamma>0$ is small enough."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.06767","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":"1504.06767","created_at":"2026-05-18T01:31:39.453802+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.06767v1","created_at":"2026-05-18T01:31:39.453802+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.06767","created_at":"2026-05-18T01:31:39.453802+00:00"},{"alias_kind":"pith_short_12","alias_value":"NWHCEM57BHHH","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_16","alias_value":"NWHCEM57BHHHZ4VG","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_8","alias_value":"NWHCEM57","created_at":"2026-05-18T12:29:34.919912+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/NWHCEM57BHHHZ4VGELQD2AF5HI","json":"https://pith.science/pith/NWHCEM57BHHHZ4VGELQD2AF5HI.json","graph_json":"https://pith.science/api/pith-number/NWHCEM57BHHHZ4VGELQD2AF5HI/graph.json","events_json":"https://pith.science/api/pith-number/NWHCEM57BHHHZ4VGELQD2AF5HI/events.json","paper":"https://pith.science/paper/NWHCEM57"},"agent_actions":{"view_html":"https://pith.science/pith/NWHCEM57BHHHZ4VGELQD2AF5HI","download_json":"https://pith.science/pith/NWHCEM57BHHHZ4VGELQD2AF5HI.json","view_paper":"https://pith.science/paper/NWHCEM57","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.06767&json=true","fetch_graph":"https://pith.science/api/pith-number/NWHCEM57BHHHZ4VGELQD2AF5HI/graph.json","fetch_events":"https://pith.science/api/pith-number/NWHCEM57BHHHZ4VGELQD2AF5HI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NWHCEM57BHHHZ4VGELQD2AF5HI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NWHCEM57BHHHZ4VGELQD2AF5HI/action/storage_attestation","attest_author":"https://pith.science/pith/NWHCEM57BHHHZ4VGELQD2AF5HI/action/author_attestation","sign_citation":"https://pith.science/pith/NWHCEM57BHHHZ4VGELQD2AF5HI/action/citation_signature","submit_replication":"https://pith.science/pith/NWHCEM57BHHHZ4VGELQD2AF5HI/action/replication_record"}},"created_at":"2026-05-18T01:31:39.453802+00:00","updated_at":"2026-05-18T01:31:39.453802+00:00"}