{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:5U7Z5QBEB3VHWYSXOB6X7LRCIA","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":"3165d58aad4872195ec3584cd4e923af2c8ec1ace6268299cf78f31dc5653292","cross_cats_sorted":["cond-mat.stat-mech","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2024-05-14T07:17:42Z","title_canon_sha256":"933b6d14f0c66ebc9723220a7f7f346e9476cd7745c2026f178507210effada0"},"schema_version":"1.0","source":{"id":"2405.08374","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.08374","created_at":"2026-07-05T08:19:45Z"},{"alias_kind":"arxiv_version","alias_value":"2405.08374v1","created_at":"2026-07-05T08:19:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.08374","created_at":"2026-07-05T08:19:45Z"},{"alias_kind":"pith_short_12","alias_value":"5U7Z5QBEB3VH","created_at":"2026-07-05T08:19:45Z"},{"alias_kind":"pith_short_16","alias_value":"5U7Z5QBEB3VHWYSX","created_at":"2026-07-05T08:19:45Z"},{"alias_kind":"pith_short_8","alias_value":"5U7Z5QBE","created_at":"2026-07-05T08:19:45Z"}],"graph_snapshots":[{"event_id":"sha256:5612a4529125d2882c6fc16eea6607a01fef5558cc06a32c6a039026a0e5c38c","target":"graph","created_at":"2026-07-05T08:19:45Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2405.08374/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider polynomial long-range Ising models in one dimension, with ferromagnetic pair interactions decaying with power $2-\\alpha$ (for $0 \\leq \\alpha < 1$), and prepared with randomly chosen boundary conditions. We show that at low temperatures in the thermodynamic limit the finite-volume Gibbs measures do not converge, but have a distributional limit, the so-called metastate. We find that there is a distinction between the values of $\\alpha$ less than or larger than $\\frac{1}{2}$. For moderate, or intermediate, decay $\\alpha < \\frac{1}{2}$, the metastate is very dispersed and supported on ","authors_text":"Aernout C.D. van Enter, Arnaud Le Ny, Eric O. Endo","cross_cats":["cond-mat.stat-mech","math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2024-05-14T07:17:42Z","title":"On Long Range Ising Models with Random Boundary Conditions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.08374","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":"sha256:1e3f4ec495a00a6cd1d56f85b432a8075a27d3ef0820c156139dd586574a0598","target":"record","created_at":"2026-07-05T08:19:45Z","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":"3165d58aad4872195ec3584cd4e923af2c8ec1ace6268299cf78f31dc5653292","cross_cats_sorted":["cond-mat.stat-mech","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2024-05-14T07:17:42Z","title_canon_sha256":"933b6d14f0c66ebc9723220a7f7f346e9476cd7745c2026f178507210effada0"},"schema_version":"1.0","source":{"id":"2405.08374","kind":"arxiv","version":1}},"canonical_sha256":"ed3f9ec0240eea7b6257707d7fae224002405ae05d452902003576940f34384b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ed3f9ec0240eea7b6257707d7fae224002405ae05d452902003576940f34384b","first_computed_at":"2026-07-05T08:19:45.389116Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:19:45.389116Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XokiBQ8YRaXOMIFVeC3c6IgOQkCZVlWgeYCpyqmiMk9Dv7NkvOWOjYtSZGRzJIbWq7iUtkOLxrpqK+1DKnTDDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:19:45.389657Z","signed_message":"canonical_sha256_bytes"},"source_id":"2405.08374","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1e3f4ec495a00a6cd1d56f85b432a8075a27d3ef0820c156139dd586574a0598","sha256:5612a4529125d2882c6fc16eea6607a01fef5558cc06a32c6a039026a0e5c38c"],"state_sha256":"1371c8006c18845f2b9fe0bea6fb1c4367916c7aaf3a69e998b6d10885fbebbe"}