{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:HUJVAHF3JDBKGQEARGY5BUKTIO","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":"796ba74f972202d5fab4333d493fe99b043fa8d5a27c2d68a6700d909eeee103","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2017-03-07T15:23:56Z","title_canon_sha256":"7ad2212e491b83af7f9c664bced12d71b06a00187e7494cf8a46f941cc221aaa"},"schema_version":"1.0","source":{"id":"1703.02431","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.02431","created_at":"2026-05-18T00:26:00Z"},{"alias_kind":"arxiv_version","alias_value":"1703.02431v2","created_at":"2026-05-18T00:26:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.02431","created_at":"2026-05-18T00:26:00Z"},{"alias_kind":"pith_short_12","alias_value":"HUJVAHF3JDBK","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"HUJVAHF3JDBKGQEA","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"HUJVAHF3","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:97c3f694e2294379541dc600dfb1da61103c5dd117a18d40430ba109fdbeffaa","target":"graph","created_at":"2026-05-18T00:26:00Z","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":"Multiplex networks consist of a fixed set of nodes connected by several sets of edges which are generated separately and correspond to different networks (\"layers\"). Here, a simple variant of the Ising model on multiplex networks with two layers is considered, with spins located in the nodes and edges corresponding to ferromagnetic interactions between them. Critical temperatures for the ferromagnetic transition are evaluated for the layers in the form of random Erd\\\"os-R\\'enyi graphs or heterogeneous scale-free networks using the mean-field approximation and the replica method, from the repli","authors_text":"Andrzej Krawiecki","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2017-03-07T15:23:56Z","title":"Ferromagnetic transition in a simple variant of the Ising model on multiplex networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.02431","kind":"arxiv","version":2},"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":"sha256:64ddd5cf4d430eb1e1f2b1597a90e042df5a2ea8e22bec5032b6de4bb919174e","target":"record","created_at":"2026-05-18T00:26:00Z","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":"796ba74f972202d5fab4333d493fe99b043fa8d5a27c2d68a6700d909eeee103","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2017-03-07T15:23:56Z","title_canon_sha256":"7ad2212e491b83af7f9c664bced12d71b06a00187e7494cf8a46f941cc221aaa"},"schema_version":"1.0","source":{"id":"1703.02431","kind":"arxiv","version":2}},"canonical_sha256":"3d13501cbb48c2a3408089b1d0d15343ab52ca7ab1715f9af525dbbf544c2f73","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3d13501cbb48c2a3408089b1d0d15343ab52ca7ab1715f9af525dbbf544c2f73","first_computed_at":"2026-05-18T00:26:00.904550Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:00.904550Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"d0ERHtDJ2WCVj26+MbTQ7egjscLdpfRQvCuKq2YKRFgNM6iubs1oBHUjB5AIX1DWT9GQK7VRdjG20hz29LcVDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:00.905304Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.02431","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:64ddd5cf4d430eb1e1f2b1597a90e042df5a2ea8e22bec5032b6de4bb919174e","sha256:97c3f694e2294379541dc600dfb1da61103c5dd117a18d40430ba109fdbeffaa"],"state_sha256":"188d630796b5ccc8a22f9284ce10df277b301bf3213f15498b2dd3805f02a877"}