{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:MOVROLGVFCC2JFO33Z36L5I56U","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":"8607549903212ed0ad6fc5ae0d55887b08c82a7cdf3ed6c9b7586c2e2187d173","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-12-06T11:30:38Z","title_canon_sha256":"1a46c205893b059174fc87ed39c506565e955d8ca2c8918813f4052e9783ba70"},"schema_version":"1.0","source":{"id":"1812.02469","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.02469","created_at":"2026-05-17T23:40:33Z"},{"alias_kind":"arxiv_version","alias_value":"1812.02469v2","created_at":"2026-05-17T23:40:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.02469","created_at":"2026-05-17T23:40:33Z"},{"alias_kind":"pith_short_12","alias_value":"MOVROLGVFCC2","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"MOVROLGVFCC2JFO3","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"MOVROLGV","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:99dc01f196963559a0b1977a0422e9c8172be61bad61fca55ddb4cc852e9525b","target":"graph","created_at":"2026-05-17T23:40:33Z","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 a Spin Glass at temperature $T = 0$ where the underlying graph is a locally finite tree. We prove for a wide range of coupling distributions that uniqueness of ground states is equivalent to the maximal flow from any vertex to $\\infty$ (where each edge $e$ has capacity $|J_{e}|$) being equal to zero which is equivalent to recurrence of the simple random walk on the tree.","authors_text":"Johannes B\\\"aumler","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-12-06T11:30:38Z","title":"Uniqueness and Non-Uniqueness for Spin-Glass Ground States on Trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.02469","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:cadd84c60165d6f17dd2108127cf4696525c4977fca789df29734681238f6486","target":"record","created_at":"2026-05-17T23:40:33Z","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":"8607549903212ed0ad6fc5ae0d55887b08c82a7cdf3ed6c9b7586c2e2187d173","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-12-06T11:30:38Z","title_canon_sha256":"1a46c205893b059174fc87ed39c506565e955d8ca2c8918813f4052e9783ba70"},"schema_version":"1.0","source":{"id":"1812.02469","kind":"arxiv","version":2}},"canonical_sha256":"63ab172cd52885a495dbde77e5f51df51fa14b910f0fe3b8271e4893d2da8830","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"63ab172cd52885a495dbde77e5f51df51fa14b910f0fe3b8271e4893d2da8830","first_computed_at":"2026-05-17T23:40:33.984741Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:33.984741Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QOBNnVMcv0IEV7k553ZMWbH0GNS2coz6xkVF02XiQKll/U7na+9VkRxK53hKh0JUMfjIWEJqOV3NNAf/vu7dCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:33.985418Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.02469","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cadd84c60165d6f17dd2108127cf4696525c4977fca789df29734681238f6486","sha256:99dc01f196963559a0b1977a0422e9c8172be61bad61fca55ddb4cc852e9525b"],"state_sha256":"8ca76196f828fd53de74123064dc5655d738abab91ad3a637e9e69a6bbf678f5"}