{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:I6DYZFTFNQA6G4I5MRT5Y5Q7PP","short_pith_number":"pith:I6DYZFTF","schema_version":"1.0","canonical_sha256":"47878c96656c01e3711d6467dc761f7bc0d0294a794eb7e3c6e2f7a5758bacb7","source":{"kind":"arxiv","id":"1611.02310","version":1},"attestation_state":"computed","paper":{"title":"Phase separation for the long range one--dimensional ising model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Immacolata Merola, Marzio Cassandro, Pierre Picco","submitted_at":"2016-11-07T21:32:13Z","abstract_excerpt":"We consider the phase separation problem for the one--dimensional ferromagnetic Ising model with long--range two--body interaction, $J(n)=n^{-2+\\a}$ where $n\\in \\N$ denotes the distance of the two spins and $ \\alpha \\in ]0,\\a_+[$ with $\\a_+=(\\log 3)/(\\log 2) -1$. We prove that given $m\\in ]-1,+1[$, if the temperature is small enough, then typical configuration for the $\\mu^{+}$ Gibbs measure conditionally to have a empirical magnetization of the order $m$ are made of a single interval that occupy almost a proportion $\\frac{1}{2}(1-\\frac{m}{m_\\b})$ of the volume with the minus phase inside and "},"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":"1611.02310","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-11-07T21:32:13Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"b324bab24f1e595fb88ca7af67293543900a18b78dad78f7652422db4404926d","abstract_canon_sha256":"363dd0824d70acd43d5afa4375ee8f3330b379109b4dddd5726720b7f313bf09"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:47.554961Z","signature_b64":"h1Rr2H5n0VvFiVyFHYpgdJaPBtd5RMNIXx/qJUkIsEz+rfpSbU+9E/QDpl/ZEAab6Y5jJCv2Dr7USVANQ5J2CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"47878c96656c01e3711d6467dc761f7bc0d0294a794eb7e3c6e2f7a5758bacb7","last_reissued_at":"2026-05-18T00:45:47.554454Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:47.554454Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Phase separation for the long range one--dimensional ising model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Immacolata Merola, Marzio Cassandro, Pierre Picco","submitted_at":"2016-11-07T21:32:13Z","abstract_excerpt":"We consider the phase separation problem for the one--dimensional ferromagnetic Ising model with long--range two--body interaction, $J(n)=n^{-2+\\a}$ where $n\\in \\N$ denotes the distance of the two spins and $ \\alpha \\in ]0,\\a_+[$ with $\\a_+=(\\log 3)/(\\log 2) -1$. We prove that given $m\\in ]-1,+1[$, if the temperature is small enough, then typical configuration for the $\\mu^{+}$ Gibbs measure conditionally to have a empirical magnetization of the order $m$ are made of a single interval that occupy almost a proportion $\\frac{1}{2}(1-\\frac{m}{m_\\b})$ of the volume with the minus phase inside and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.02310","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":"1611.02310","created_at":"2026-05-18T00:45:47.554542+00:00"},{"alias_kind":"arxiv_version","alias_value":"1611.02310v1","created_at":"2026-05-18T00:45:47.554542+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.02310","created_at":"2026-05-18T00:45:47.554542+00:00"},{"alias_kind":"pith_short_12","alias_value":"I6DYZFTFNQA6","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_16","alias_value":"I6DYZFTFNQA6G4I5","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_8","alias_value":"I6DYZFTF","created_at":"2026-05-18T12:30:22.444734+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/I6DYZFTFNQA6G4I5MRT5Y5Q7PP","json":"https://pith.science/pith/I6DYZFTFNQA6G4I5MRT5Y5Q7PP.json","graph_json":"https://pith.science/api/pith-number/I6DYZFTFNQA6G4I5MRT5Y5Q7PP/graph.json","events_json":"https://pith.science/api/pith-number/I6DYZFTFNQA6G4I5MRT5Y5Q7PP/events.json","paper":"https://pith.science/paper/I6DYZFTF"},"agent_actions":{"view_html":"https://pith.science/pith/I6DYZFTFNQA6G4I5MRT5Y5Q7PP","download_json":"https://pith.science/pith/I6DYZFTFNQA6G4I5MRT5Y5Q7PP.json","view_paper":"https://pith.science/paper/I6DYZFTF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1611.02310&json=true","fetch_graph":"https://pith.science/api/pith-number/I6DYZFTFNQA6G4I5MRT5Y5Q7PP/graph.json","fetch_events":"https://pith.science/api/pith-number/I6DYZFTFNQA6G4I5MRT5Y5Q7PP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I6DYZFTFNQA6G4I5MRT5Y5Q7PP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I6DYZFTFNQA6G4I5MRT5Y5Q7PP/action/storage_attestation","attest_author":"https://pith.science/pith/I6DYZFTFNQA6G4I5MRT5Y5Q7PP/action/author_attestation","sign_citation":"https://pith.science/pith/I6DYZFTFNQA6G4I5MRT5Y5Q7PP/action/citation_signature","submit_replication":"https://pith.science/pith/I6DYZFTFNQA6G4I5MRT5Y5Q7PP/action/replication_record"}},"created_at":"2026-05-18T00:45:47.554542+00:00","updated_at":"2026-05-18T00:45:47.554542+00:00"}