{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:FNUKOUQIFCZ2ZIUZ5TTQPOVMFN","short_pith_number":"pith:FNUKOUQI","schema_version":"1.0","canonical_sha256":"2b68a7520828b3aca299ece707baac2b59c1a0fddbe4e9bb3e2e6331274e285b","source":{"kind":"arxiv","id":"1802.02059","version":2},"attestation_state":"computed","paper":{"title":"One-sided continuity properties for the Schonmann projection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Diana Conache, Stein Andreas Bethuelsen","submitted_at":"2018-02-06T16:41:59Z","abstract_excerpt":"We consider the plus-phase of the two-dimensional Ising model below the critical temperature. In $1989$ Schonmann proved that the projection of this measure onto a one-dimensional line is not a Gibbs measure. After many years of continued research which have revealed further properties of this measure, the question whether or not it is a Gibbs measure in an almost sure sense remains open.\n  In this paper we study the same measure by interpreting it as a temporal process. One of our main results is that the Schonmann projection is almost surely a regular $g$-measure. That is, it does possess th"},"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":"1802.02059","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-02-06T16:41:59Z","cross_cats_sorted":[],"title_canon_sha256":"16f7599757f5af062e1362e9e86da1864ddd0e33c095ed0723063431fde7474a","abstract_canon_sha256":"a5b069ac2cb25a384225619b6513b770c8f8f52d4c2d1664cc2d4faf151fd9d4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:16.336984Z","signature_b64":"6DdczjupDlwlpsTmM3+6+MvS/WmDNgXWNCwnx94LzmTnq1r4IH5IgcIDZ2lNNc4mkpOI8L/zM8rLSgMYAEqwCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b68a7520828b3aca299ece707baac2b59c1a0fddbe4e9bb3e2e6331274e285b","last_reissued_at":"2026-05-18T00:09:16.336260Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:16.336260Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"One-sided continuity properties for the Schonmann projection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Diana Conache, Stein Andreas Bethuelsen","submitted_at":"2018-02-06T16:41:59Z","abstract_excerpt":"We consider the plus-phase of the two-dimensional Ising model below the critical temperature. In $1989$ Schonmann proved that the projection of this measure onto a one-dimensional line is not a Gibbs measure. After many years of continued research which have revealed further properties of this measure, the question whether or not it is a Gibbs measure in an almost sure sense remains open.\n  In this paper we study the same measure by interpreting it as a temporal process. One of our main results is that the Schonmann projection is almost surely a regular $g$-measure. That is, it does possess th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.02059","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":"1802.02059","created_at":"2026-05-18T00:09:16.336400+00:00"},{"alias_kind":"arxiv_version","alias_value":"1802.02059v2","created_at":"2026-05-18T00:09:16.336400+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.02059","created_at":"2026-05-18T00:09:16.336400+00:00"},{"alias_kind":"pith_short_12","alias_value":"FNUKOUQIFCZ2","created_at":"2026-05-18T12:32:25.280505+00:00"},{"alias_kind":"pith_short_16","alias_value":"FNUKOUQIFCZ2ZIUZ","created_at":"2026-05-18T12:32:25.280505+00:00"},{"alias_kind":"pith_short_8","alias_value":"FNUKOUQI","created_at":"2026-05-18T12:32:25.280505+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/FNUKOUQIFCZ2ZIUZ5TTQPOVMFN","json":"https://pith.science/pith/FNUKOUQIFCZ2ZIUZ5TTQPOVMFN.json","graph_json":"https://pith.science/api/pith-number/FNUKOUQIFCZ2ZIUZ5TTQPOVMFN/graph.json","events_json":"https://pith.science/api/pith-number/FNUKOUQIFCZ2ZIUZ5TTQPOVMFN/events.json","paper":"https://pith.science/paper/FNUKOUQI"},"agent_actions":{"view_html":"https://pith.science/pith/FNUKOUQIFCZ2ZIUZ5TTQPOVMFN","download_json":"https://pith.science/pith/FNUKOUQIFCZ2ZIUZ5TTQPOVMFN.json","view_paper":"https://pith.science/paper/FNUKOUQI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1802.02059&json=true","fetch_graph":"https://pith.science/api/pith-number/FNUKOUQIFCZ2ZIUZ5TTQPOVMFN/graph.json","fetch_events":"https://pith.science/api/pith-number/FNUKOUQIFCZ2ZIUZ5TTQPOVMFN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FNUKOUQIFCZ2ZIUZ5TTQPOVMFN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FNUKOUQIFCZ2ZIUZ5TTQPOVMFN/action/storage_attestation","attest_author":"https://pith.science/pith/FNUKOUQIFCZ2ZIUZ5TTQPOVMFN/action/author_attestation","sign_citation":"https://pith.science/pith/FNUKOUQIFCZ2ZIUZ5TTQPOVMFN/action/citation_signature","submit_replication":"https://pith.science/pith/FNUKOUQIFCZ2ZIUZ5TTQPOVMFN/action/replication_record"}},"created_at":"2026-05-18T00:09:16.336400+00:00","updated_at":"2026-05-18T00:09:16.336400+00:00"}