{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NGIR4GDIKWBJV5E3UVM5UNQKL7","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":"d0fd61dfa837b9473b338155709796b344af16d0cf835d98ed0773e9969b5087","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-07-23T19:52:49Z","title_canon_sha256":"ca1402bf569991dd96a44b05fb86b9c42799145ec96cdb9cd2fc52055465c01e"},"schema_version":"1.0","source":{"id":"1607.06968","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.06968","created_at":"2026-05-18T00:53:59Z"},{"alias_kind":"arxiv_version","alias_value":"1607.06968v1","created_at":"2026-05-18T00:53:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.06968","created_at":"2026-05-18T00:53:59Z"},{"alias_kind":"pith_short_12","alias_value":"NGIR4GDIKWBJ","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"NGIR4GDIKWBJV5E3","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"NGIR4GDI","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:00490b9cc4e863c5b9f7808c71db3f28330e62e732c77919a92bf0eb70563745","target":"graph","created_at":"2026-05-18T00:53:59Z","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 study phase-transitions of the ferromagnetic $q$-state Potts chain with random nearest-neighbour couplings having a variance $\\Delta^2$ and with homogeneous long-range interactions, which decay with the distance as a power $r^{-(1+\\sigma)}$, $\\sigma>0$. In the large-$q$ limit the free-energy of random samples of length $L \\le 2048$ is calculated exactly by a combinatorial optimization algorithm. The phase-transition stays first-order for $\\sigma < \\sigma_c(\\Delta) \\le 0.5$, while the correlation length becomes divergent at the transition point for $\\sigma_c(\\Delta) < \\sigma < 1$. In the lat","authors_text":"Ferenc Igl\\'oi, Jean-Christian Angl\\`es d'Auriac","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-07-23T19:52:49Z","title":"Phase-transitions of the random bond Potts chain with long-range interactions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.06968","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":"sha256:4d949b1ba95548bb9c1b37bc03c0e4025404ebc3cfdf9220df7fde2f20eaaf2f","target":"record","created_at":"2026-05-18T00:53:59Z","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":"d0fd61dfa837b9473b338155709796b344af16d0cf835d98ed0773e9969b5087","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-07-23T19:52:49Z","title_canon_sha256":"ca1402bf569991dd96a44b05fb86b9c42799145ec96cdb9cd2fc52055465c01e"},"schema_version":"1.0","source":{"id":"1607.06968","kind":"arxiv","version":1}},"canonical_sha256":"69911e186855829af49ba559da360a5ff4e40138df17fb5f3c38b47f0a0b5f8f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"69911e186855829af49ba559da360a5ff4e40138df17fb5f3c38b47f0a0b5f8f","first_computed_at":"2026-05-18T00:53:59.638975Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:59.638975Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Z97Qw+tr7R7ogeC1Ebnr7bW9XqtLS4dHcB2+gJuJZUZ8b7FUgbxqHqsfag3lWJNu+XpYMvkLQ8qVV5WbFS5JAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:59.639570Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.06968","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4d949b1ba95548bb9c1b37bc03c0e4025404ebc3cfdf9220df7fde2f20eaaf2f","sha256:00490b9cc4e863c5b9f7808c71db3f28330e62e732c77919a92bf0eb70563745"],"state_sha256":"7493af83a19aa57307693e6ffa4358ad8ad17ab0e0bf36554672688047205e8d"}