{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:S2DDOR6LTJ7NHFWX4LUOSSX377","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":"c22821ddb24bd3b5ae21c449855610cc40c2646eba20c537a72f376c86469b80","cross_cats_sorted":["cond-mat.dis-nn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-06-17T09:32:24Z","title_canon_sha256":"c69019223e5ba3380bbcb0cafc7ce21775a10b76a539458792c713975927ff68"},"schema_version":"1.0","source":{"id":"1106.3424","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.3424","created_at":"2026-05-18T03:57:40Z"},{"alias_kind":"arxiv_version","alias_value":"1106.3424v2","created_at":"2026-05-18T03:57:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.3424","created_at":"2026-05-18T03:57:40Z"},{"alias_kind":"pith_short_12","alias_value":"S2DDOR6LTJ7N","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"S2DDOR6LTJ7NHFWX","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"S2DDOR6L","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:cd81ac29a73c240f9f87cee177828e4a1d27678f97ec645c0e4d0384cfa1bfa0","target":"graph","created_at":"2026-05-18T03:57:40Z","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":"An exact expression for the spin-spin correlation function is derived for the zero-temperature random-field Ising model defined on a Bethe lattice of arbitrary coordination number. The correlation length describing dynamic spin-spin correlations and separated from the intrinsic topological length scale of the Bethe lattice is shown to diverge as a power law at the critical point. The critical exponents governing the behaviour of the correlation length are consistent with the mean-field values found for a hypercubic lattice with dimension greater than the upper critical dimension.","authors_text":"F.J. Perez-Reche, S.N. Taraskin, T.P. Handford","cross_cats":["cond-mat.dis-nn"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-06-17T09:32:24Z","title":"Exact spin-spin correlation function for the zero-temperature random-field Ising model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.3424","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:bbd0f582e5da364967fd9af3799d4364a66d1cc4eb4c5d0d0ccb197b27c72027","target":"record","created_at":"2026-05-18T03:57:40Z","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":"c22821ddb24bd3b5ae21c449855610cc40c2646eba20c537a72f376c86469b80","cross_cats_sorted":["cond-mat.dis-nn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-06-17T09:32:24Z","title_canon_sha256":"c69019223e5ba3380bbcb0cafc7ce21775a10b76a539458792c713975927ff68"},"schema_version":"1.0","source":{"id":"1106.3424","kind":"arxiv","version":2}},"canonical_sha256":"96863747cb9a7ed396d7e2e8e94afbffe5b2e0db73cfa93ce1f29b76dba28885","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"96863747cb9a7ed396d7e2e8e94afbffe5b2e0db73cfa93ce1f29b76dba28885","first_computed_at":"2026-05-18T03:57:40.608053Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:57:40.608053Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0x+/kqbXVxVjdRvAou6dr9p0C+GQKy0FfDQHB3bTNApCqOsjHX5h+sVjFTMC/8pKHxvhlcbUzIFT5II0RBiqBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:57:40.608834Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.3424","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bbd0f582e5da364967fd9af3799d4364a66d1cc4eb4c5d0d0ccb197b27c72027","sha256:cd81ac29a73c240f9f87cee177828e4a1d27678f97ec645c0e4d0384cfa1bfa0"],"state_sha256":"8745638c422876dd1066d5e2578d1a26f6c27c80170329ee1077bcd84b930dc9"}