{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1998:PRQ4O5LJYBT5UM43WUWJA4RNZK","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"102c7c8e7f7f26f04155578f8ffd6f7b6293dfaf183e44af03700953cea54bfd","cross_cats_sorted":[],"license":"","primary_cat":"math.PR","submitted_at":"1998-10-15T09:49:46Z","title_canon_sha256":"4170c3e6211b71d719f7c0588cf4ce4b83e5564d12330176fe7dc5c7e5daad51"},"schema_version":"1.0","source":{"id":"math/9810094","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9810094","created_at":"2026-05-18T01:38:22Z"},{"alias_kind":"arxiv_version","alias_value":"math/9810094v1","created_at":"2026-05-18T01:38:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9810094","created_at":"2026-05-18T01:38:22Z"},{"alias_kind":"pith_short_12","alias_value":"PRQ4O5LJYBT5","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"PRQ4O5LJYBT5UM43","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"PRQ4O5LJ","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:8fcea03f1cb5fefa8d992c539557a5e39ce28995565872cb6462021c9579a66b","target":"graph","created_at":"2026-05-18T01:38:22Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We discuss the status of recent Gibbsian descriptions of the restriction (projection) of the Ising phases to a layer. We concentrate on the projection of the two-dimensional low temperature Ising phases for which we prove a variational principle.","authors_text":"A. Van Moffaert, C. Maes, F. Redig","cross_cats":[],"headline":"","license":"","primary_cat":"math.PR","submitted_at":"1998-10-15T09:49:46Z","title":"The restriction of the Ising model to a layer"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9810094","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:db3257ce6ba8db4b550c9e257e8061157dc15a0b06e0cbdfcfa2b1b23160bfc9","target":"record","created_at":"2026-05-18T01:38:22Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"102c7c8e7f7f26f04155578f8ffd6f7b6293dfaf183e44af03700953cea54bfd","cross_cats_sorted":[],"license":"","primary_cat":"math.PR","submitted_at":"1998-10-15T09:49:46Z","title_canon_sha256":"4170c3e6211b71d719f7c0588cf4ce4b83e5564d12330176fe7dc5c7e5daad51"},"schema_version":"1.0","source":{"id":"math/9810094","kind":"arxiv","version":1}},"canonical_sha256":"7c61c77569c067da339bb52c90722dca88ecfa5d30f7416493f31e90d88220b2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7c61c77569c067da339bb52c90722dca88ecfa5d30f7416493f31e90d88220b2","first_computed_at":"2026-05-18T01:38:22.750968Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:22.750968Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QDkiQbDOpgkcBJyVj20QlSdS8cFQrN/XT9oyxtuATw9yPJvprnCCCeR+GrG/G8kjpLU7sRLG9wRgXa+20BDlDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:22.751673Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9810094","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:db3257ce6ba8db4b550c9e257e8061157dc15a0b06e0cbdfcfa2b1b23160bfc9","sha256:8fcea03f1cb5fefa8d992c539557a5e39ce28995565872cb6462021c9579a66b"],"state_sha256":"bf711a0745f2e3ca4e3e004f3abc125e704d10816c2dbb0a029fd03ee893f0b4"}