{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:PB25FLW7V4ESJP7QTGKKNCAHPU","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":"466964ccf17092e76f7d1bac2a221cdf19e5e7fb60a03de10aa238cd877aeef2","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-10-30T12:27:26Z","title_canon_sha256":"0c1ee6277fe4ca5947beef5727bcf471526fcf7d6f7562859ba5ed18b4bbb3b1"},"schema_version":"1.0","source":{"id":"1210.7981","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.7981","created_at":"2026-05-18T01:53:35Z"},{"alias_kind":"arxiv_version","alias_value":"1210.7981v1","created_at":"2026-05-18T01:53:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.7981","created_at":"2026-05-18T01:53:35Z"},{"alias_kind":"pith_short_12","alias_value":"PB25FLW7V4ES","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PB25FLW7V4ESJP7Q","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PB25FLW7","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:2024118dc323bac29eaa90155eb5274a28b3cae361fb7aa80eb94f492f443883","target":"graph","created_at":"2026-05-18T01:53:35Z","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 establish a Mermin--Wagner type theorem for Gibbs states on infinite random Lorentzian triangulations (LT) arising in models of quantum gravity. Such a triangulation is naturally related to the distribution $\\sf P$ of a critical Galton--Watson tree, conditional upon non-extinction. At the vertices of the triangles we place classical spins taking values in a torus $M$ of dimension $d$, with a given group action of a torus ${\\tt G}$ of dimension $d'\\leq d$. In the main body of the paper we assume that the spins interact via a two-body nearest-neighbor potential $U(x,y)$ invariant under the ac","authors_text":"A. Yambartsev, M. Kelbert, Yu. Suhov","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-10-30T12:27:26Z","title":"A Mermin--Wagner theorem for Gibbs states on Lorentzian triangulations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.7981","kind":"arxiv","version":1},"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":"sha256:2f9d082e7986350830cb320f6278aeafc3591117f53705ad1eb8be95f69cd64f","target":"record","created_at":"2026-05-18T01:53:35Z","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":"466964ccf17092e76f7d1bac2a221cdf19e5e7fb60a03de10aa238cd877aeef2","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-10-30T12:27:26Z","title_canon_sha256":"0c1ee6277fe4ca5947beef5727bcf471526fcf7d6f7562859ba5ed18b4bbb3b1"},"schema_version":"1.0","source":{"id":"1210.7981","kind":"arxiv","version":1}},"canonical_sha256":"7875d2aedfaf0924bff09994a688077d3c855eb957c3d4f20de5c15eaba2ce38","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7875d2aedfaf0924bff09994a688077d3c855eb957c3d4f20de5c15eaba2ce38","first_computed_at":"2026-05-18T01:53:35.691002Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:53:35.691002Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j4YwI1kKdbRAcSK4qGaVuUELSXjS72usjq0uMiqOJ21firkDShyRMGAS3hDqwhyK2HzTYKxcYR17NoYYWRVKCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:53:35.691686Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.7981","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2f9d082e7986350830cb320f6278aeafc3591117f53705ad1eb8be95f69cd64f","sha256:2024118dc323bac29eaa90155eb5274a28b3cae361fb7aa80eb94f492f443883"],"state_sha256":"4bd2df38ea049fa64b8dabd6b370332dce182c0320b939c4cf4067a69ba1a2b7"}