{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:IDCJSS5QIBNOBH4YQZMZF7DWCQ","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":"a49b628a9eac68ecfd44cab5a16de7acb64651d085b89428ada8d5aed8c444cd","cross_cats_sorted":["cond-mat.soft","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2017-09-02T08:07:48Z","title_canon_sha256":"f69d5bef2a159c1f3e13a0c28bf075bab98063d538a38640fa4581b1088fe56e"},"schema_version":"1.0","source":{"id":"1709.00543","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.00543","created_at":"2026-05-17T23:46:55Z"},{"alias_kind":"arxiv_version","alias_value":"1709.00543v3","created_at":"2026-05-17T23:46:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.00543","created_at":"2026-05-17T23:46:55Z"},{"alias_kind":"pith_short_12","alias_value":"IDCJSS5QIBNO","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"IDCJSS5QIBNOBH4Y","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"IDCJSS5Q","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:d8c73ac0c110b7ba14469737f373958dc32ca6283974d241ef31b2e4a735f377","target":"graph","created_at":"2026-05-17T23:46:55Z","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 consider the ferromagnetic Ising model on the Cayley tree and we investigate the decomposition of the free state into extremal states below the spin glass temperature. We show that this decomposition has uncountably many components. The tail observable showing that the free state is not extremal is related to the Edwards-Anderson parameter, measuring the variance of the (random) magnetization obtained from drawing boundary conditions from the free state.","authors_text":"Christian Maes, Daniel Gandolfo, Jean Ruiz, Senya Shlosman","cross_cats":["cond-mat.soft","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2017-09-02T08:07:48Z","title":"Glassy states: the free Ising model on a tree"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.00543","kind":"arxiv","version":3},"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":"sha256:5298a804d735bd23d9d168b1bc295ff4bb3c383c4ddea4cd6d57ccee9fe4918b","target":"record","created_at":"2026-05-17T23:46:55Z","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":"a49b628a9eac68ecfd44cab5a16de7acb64651d085b89428ada8d5aed8c444cd","cross_cats_sorted":["cond-mat.soft","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2017-09-02T08:07:48Z","title_canon_sha256":"f69d5bef2a159c1f3e13a0c28bf075bab98063d538a38640fa4581b1088fe56e"},"schema_version":"1.0","source":{"id":"1709.00543","kind":"arxiv","version":3}},"canonical_sha256":"40c4994bb0405ae09f98865992fc76140558880f775b9f6603c78e3f27291c68","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"40c4994bb0405ae09f98865992fc76140558880f775b9f6603c78e3f27291c68","first_computed_at":"2026-05-17T23:46:55.673368Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:55.673368Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Q81Ell5MeP9knABhvWC9emfPXnz48DQnaaWlJjb/5VvJIxl9/lnik+XMQZyNcvnmMdsUSk1hCn8RbOhmUTGuCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:55.673856Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.00543","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5298a804d735bd23d9d168b1bc295ff4bb3c383c4ddea4cd6d57ccee9fe4918b","sha256:d8c73ac0c110b7ba14469737f373958dc32ca6283974d241ef31b2e4a735f377"],"state_sha256":"6c2422a8940541c2723e0ed669307da6c261270c93babfe73fc997ab75c34d1c"}