{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:MOVROLGVFCC2JFO33Z36L5I56U","short_pith_number":"pith:MOVROLGV","schema_version":"1.0","canonical_sha256":"63ab172cd52885a495dbde77e5f51df51fa14b910f0fe3b8271e4893d2da8830","source":{"kind":"arxiv","id":"1812.02469","version":2},"attestation_state":"computed","paper":{"title":"Uniqueness and Non-Uniqueness for Spin-Glass Ground States on Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Johannes B\\\"aumler","submitted_at":"2018-12-06T11:30:38Z","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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1812.02469","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-12-06T11:30:38Z","cross_cats_sorted":[],"title_canon_sha256":"1a46c205893b059174fc87ed39c506565e955d8ca2c8918813f4052e9783ba70","abstract_canon_sha256":"8607549903212ed0ad6fc5ae0d55887b08c82a7cdf3ed6c9b7586c2e2187d173"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:33.985418Z","signature_b64":"QOBNnVMcv0IEV7k553ZMWbH0GNS2coz6xkVF02XiQKll/U7na+9VkRxK53hKh0JUMfjIWEJqOV3NNAf/vu7dCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"63ab172cd52885a495dbde77e5f51df51fa14b910f0fe3b8271e4893d2da8830","last_reissued_at":"2026-05-17T23:40:33.984741Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:33.984741Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Uniqueness and Non-Uniqueness for Spin-Glass Ground States on Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Johannes B\\\"aumler","submitted_at":"2018-12-06T11:30:38Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.02469","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1812.02469","created_at":"2026-05-17T23:40:33.984855+00:00"},{"alias_kind":"arxiv_version","alias_value":"1812.02469v2","created_at":"2026-05-17T23:40:33.984855+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.02469","created_at":"2026-05-17T23:40:33.984855+00:00"},{"alias_kind":"pith_short_12","alias_value":"MOVROLGVFCC2","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_16","alias_value":"MOVROLGVFCC2JFO3","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_8","alias_value":"MOVROLGV","created_at":"2026-05-18T12:32:37.024351+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MOVROLGVFCC2JFO33Z36L5I56U","json":"https://pith.science/pith/MOVROLGVFCC2JFO33Z36L5I56U.json","graph_json":"https://pith.science/api/pith-number/MOVROLGVFCC2JFO33Z36L5I56U/graph.json","events_json":"https://pith.science/api/pith-number/MOVROLGVFCC2JFO33Z36L5I56U/events.json","paper":"https://pith.science/paper/MOVROLGV"},"agent_actions":{"view_html":"https://pith.science/pith/MOVROLGVFCC2JFO33Z36L5I56U","download_json":"https://pith.science/pith/MOVROLGVFCC2JFO33Z36L5I56U.json","view_paper":"https://pith.science/paper/MOVROLGV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1812.02469&json=true","fetch_graph":"https://pith.science/api/pith-number/MOVROLGVFCC2JFO33Z36L5I56U/graph.json","fetch_events":"https://pith.science/api/pith-number/MOVROLGVFCC2JFO33Z36L5I56U/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MOVROLGVFCC2JFO33Z36L5I56U/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MOVROLGVFCC2JFO33Z36L5I56U/action/storage_attestation","attest_author":"https://pith.science/pith/MOVROLGVFCC2JFO33Z36L5I56U/action/author_attestation","sign_citation":"https://pith.science/pith/MOVROLGVFCC2JFO33Z36L5I56U/action/citation_signature","submit_replication":"https://pith.science/pith/MOVROLGVFCC2JFO33Z36L5I56U/action/replication_record"}},"created_at":"2026-05-17T23:40:33.984855+00:00","updated_at":"2026-05-17T23:40:33.984855+00:00"}