{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:CDLCUZGC7FH6ZGLRONHAWHZQ72","short_pith_number":"pith:CDLCUZGC","schema_version":"1.0","canonical_sha256":"10d62a64c2f94fec9971734e0b1f30fe88d83bf69a4bd60b14e8b2cba322b1cb","source":{"kind":"arxiv","id":"1205.1361","version":1},"attestation_state":"computed","paper":{"title":"Symmetries of a mean-field spin model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"cond-mat.stat-mech","authors_text":"Rytis Pa\\v{s}kauskas","submitted_at":"2012-05-07T12:39:07Z","abstract_excerpt":"Thermodynamic limit evolution of a closed quantum Heisenberg-type spin model with mean-field interactions is characterized by classifying all the symmetries of the equations of motion. It is shown that parameters of the model induce a structure in the Hilbert space by partitioning it into invariant subspaces, decoupled by the underlying Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy. All possible partitions are classified in terms of a $3\\times3$ matrix of effective, thermodynamic limit coupling constants. It is found that there are either 1, 2, 4, or O(N) invariant subspaces. The BBGKY"},"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":"1205.1361","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-05-07T12:39:07Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"61027b7880d21c1e5fa5300aa4a0ed6e3eb05de47e133959f7b6e88d1d3ba216","abstract_canon_sha256":"53bdb134d6c57ab37d4b2a7330513d95dadaf9a82c8eb6d3905d5d677dd10535"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:57:37.366168Z","signature_b64":"Cast5Q9qHbgu/4OuZO1bD5dQNsTvA271u/6e/6h/S0qBMLQcnOsushz2X2OLZhJzYq38tPn2aWxk0odr4ZzyDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"10d62a64c2f94fec9971734e0b1f30fe88d83bf69a4bd60b14e8b2cba322b1cb","last_reissued_at":"2026-05-18T01:57:37.365143Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:57:37.365143Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Symmetries of a mean-field spin model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"cond-mat.stat-mech","authors_text":"Rytis Pa\\v{s}kauskas","submitted_at":"2012-05-07T12:39:07Z","abstract_excerpt":"Thermodynamic limit evolution of a closed quantum Heisenberg-type spin model with mean-field interactions is characterized by classifying all the symmetries of the equations of motion. It is shown that parameters of the model induce a structure in the Hilbert space by partitioning it into invariant subspaces, decoupled by the underlying Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy. All possible partitions are classified in terms of a $3\\times3$ matrix of effective, thermodynamic limit coupling constants. It is found that there are either 1, 2, 4, or O(N) invariant subspaces. The BBGKY"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1361","kind":"arxiv","version":1},"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":"1205.1361","created_at":"2026-05-18T01:57:37.365248+00:00"},{"alias_kind":"arxiv_version","alias_value":"1205.1361v1","created_at":"2026-05-18T01:57:37.365248+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.1361","created_at":"2026-05-18T01:57:37.365248+00:00"},{"alias_kind":"pith_short_12","alias_value":"CDLCUZGC7FH6","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_16","alias_value":"CDLCUZGC7FH6ZGLR","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_8","alias_value":"CDLCUZGC","created_at":"2026-05-18T12:27:01.376967+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/CDLCUZGC7FH6ZGLRONHAWHZQ72","json":"https://pith.science/pith/CDLCUZGC7FH6ZGLRONHAWHZQ72.json","graph_json":"https://pith.science/api/pith-number/CDLCUZGC7FH6ZGLRONHAWHZQ72/graph.json","events_json":"https://pith.science/api/pith-number/CDLCUZGC7FH6ZGLRONHAWHZQ72/events.json","paper":"https://pith.science/paper/CDLCUZGC"},"agent_actions":{"view_html":"https://pith.science/pith/CDLCUZGC7FH6ZGLRONHAWHZQ72","download_json":"https://pith.science/pith/CDLCUZGC7FH6ZGLRONHAWHZQ72.json","view_paper":"https://pith.science/paper/CDLCUZGC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1205.1361&json=true","fetch_graph":"https://pith.science/api/pith-number/CDLCUZGC7FH6ZGLRONHAWHZQ72/graph.json","fetch_events":"https://pith.science/api/pith-number/CDLCUZGC7FH6ZGLRONHAWHZQ72/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CDLCUZGC7FH6ZGLRONHAWHZQ72/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CDLCUZGC7FH6ZGLRONHAWHZQ72/action/storage_attestation","attest_author":"https://pith.science/pith/CDLCUZGC7FH6ZGLRONHAWHZQ72/action/author_attestation","sign_citation":"https://pith.science/pith/CDLCUZGC7FH6ZGLRONHAWHZQ72/action/citation_signature","submit_replication":"https://pith.science/pith/CDLCUZGC7FH6ZGLRONHAWHZQ72/action/replication_record"}},"created_at":"2026-05-18T01:57:37.365248+00:00","updated_at":"2026-05-18T01:57:37.365248+00:00"}