{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:GAM2DLXUBVELYB6MA2N7WW2GIX","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":"12eb39c813b53847dbbba7350b357cfa435e5d9929b0a577a2fccabab4c988ee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-12-18T16:46:07Z","title_canon_sha256":"813d444bf10cd69e04ff665aea9162c5c436a7c2d8280431e228d03cf07fe66e"},"schema_version":"1.0","source":{"id":"1212.4421","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.4421","created_at":"2026-05-18T01:52:30Z"},{"alias_kind":"arxiv_version","alias_value":"1212.4421v3","created_at":"2026-05-18T01:52:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.4421","created_at":"2026-05-18T01:52:30Z"},{"alias_kind":"pith_short_12","alias_value":"GAM2DLXUBVEL","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"GAM2DLXUBVELYB6M","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"GAM2DLXU","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:c151d07c42850d18cc3e83d70e25e440addc0400f3de62338407c87a78b584a7","target":"graph","created_at":"2026-05-18T01:52:30Z","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 singleton deformation of the AdS4 higher-spin theory dual to the three-dimensional O(N) vector model. The singleton couples to the higher-spin multiplet only through a marginal boundary interaction. We argue that the effect of such a deformation is to shift N to N+1 in both sides of the holographic correspondance and we show how the gap equations of the three-dimensional O(N) vector model arise from the higher-spin theory. The singleton deformation breaks higher-spin symmetry and gives rise to the well-known 1/N anomalous dimensions of the boundary theory.","authors_text":"Anastasios C. Petkou, Robert G. Leigh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-12-18T16:46:07Z","title":"Singleton deformation of higher-spin theory and the phase structure of the three-dimensional O(N) vector model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.4421","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":"sha256:46fa49cf4db37cd6c2b2d8033e3f9302c44a72cbea0c47adb23809e894166ac5","target":"record","created_at":"2026-05-18T01:52:30Z","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":"12eb39c813b53847dbbba7350b357cfa435e5d9929b0a577a2fccabab4c988ee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-12-18T16:46:07Z","title_canon_sha256":"813d444bf10cd69e04ff665aea9162c5c436a7c2d8280431e228d03cf07fe66e"},"schema_version":"1.0","source":{"id":"1212.4421","kind":"arxiv","version":3}},"canonical_sha256":"3019a1aef40d48bc07cc069bfb5b4645ce448f7d0b33ec370d83cf8e389b7746","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3019a1aef40d48bc07cc069bfb5b4645ce448f7d0b33ec370d83cf8e389b7746","first_computed_at":"2026-05-18T01:52:30.907934Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:52:30.907934Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"39S5zr7Xngbg8ZJyHWho1pg80NBeJqJ1qoSMpBhDx9v6nZnGNdetQesbWISO4+lp2BGQq/xDYkqgbIbreEHwBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:52:30.908552Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.4421","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:46fa49cf4db37cd6c2b2d8033e3f9302c44a72cbea0c47adb23809e894166ac5","sha256:c151d07c42850d18cc3e83d70e25e440addc0400f3de62338407c87a78b584a7"],"state_sha256":"a4dc64e8639c7b95e24fe16dd1350c18a764b186658108c2971312c5be798cde"}