{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:5MQ2ARBNLGN52NWFVVAYS42JVE","short_pith_number":"pith:5MQ2ARBN","canonical_record":{"source":{"id":"0911.2096","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-11-11T10:06:34Z","cross_cats_sorted":["cond-mat.stat-mech","hep-lat"],"title_canon_sha256":"c480d524a7e97bb35613ef2235d65f03e2be96f26681b037b6ecdb317d4e11cf","abstract_canon_sha256":"6135b215733e38d06327b0942d4d5ca1fb0e8a045dbb296dbc19912fada30e4e"},"schema_version":"1.0"},"canonical_sha256":"eb21a0442d599bdd36c5ad41897349a910740be6e95726e18025a32ee5b40fcc","source":{"kind":"arxiv","id":"0911.2096","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.2096","created_at":"2026-05-18T02:34:11Z"},{"alias_kind":"arxiv_version","alias_value":"0911.2096v3","created_at":"2026-05-18T02:34:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.2096","created_at":"2026-05-18T02:34:11Z"},{"alias_kind":"pith_short_12","alias_value":"5MQ2ARBNLGN5","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"5MQ2ARBNLGN52NWF","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"5MQ2ARBN","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:5MQ2ARBNLGN52NWFVVAYS42JVE","target":"record","payload":{"canonical_record":{"source":{"id":"0911.2096","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-11-11T10:06:34Z","cross_cats_sorted":["cond-mat.stat-mech","hep-lat"],"title_canon_sha256":"c480d524a7e97bb35613ef2235d65f03e2be96f26681b037b6ecdb317d4e11cf","abstract_canon_sha256":"6135b215733e38d06327b0942d4d5ca1fb0e8a045dbb296dbc19912fada30e4e"},"schema_version":"1.0"},"canonical_sha256":"eb21a0442d599bdd36c5ad41897349a910740be6e95726e18025a32ee5b40fcc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:34:11.271374Z","signature_b64":"wpw6uknLJhjrRhgCuYYttMWnqZY61LSmqYrPc93pHL4WEgqIR1w5Rewi8DswF4gvPqktevsimhoDUU2hDD0PDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eb21a0442d599bdd36c5ad41897349a910740be6e95726e18025a32ee5b40fcc","last_reissued_at":"2026-05-18T02:34:11.270966Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:34:11.270966Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0911.2096","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:34:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g+rvlGUNAGHEPIJWzYGQPGPX6AZn3JOECk8/XAf+8jGB1g/m1KkAvtlhTwwijt7Icqtf5RFEsfG7zzR9DWzNDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T20:16:35.903180Z"},"content_sha256":"b5900d992d85b95ced2dd07efd3eef8d57d165f4549212282cfd81c840f02390","schema_version":"1.0","event_id":"sha256:b5900d992d85b95ced2dd07efd3eef8d57d165f4549212282cfd81c840f02390"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:5MQ2ARBNLGN52NWFVVAYS42JVE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mapping all classical spin models to a lattice gauge theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","hep-lat"],"primary_cat":"quant-ph","authors_text":"G. De las Cuevas, H. J. Briegel, M. A. Martin-Delgado, W. D\\\"ur","submitted_at":"2009-11-11T10:06:34Z","abstract_excerpt":"In our recent work [Phys. Rev. Lett. 102, 230502 (2009)] we showed that the partition function of all classical spin models, including all discrete standard statistical models and all Abelian discrete lattice gauge theories (LGTs), can be expressed as a special instance of the partition function of a 4-dimensional pure LGT with gauge group Z_2 (4D Z_2 LGT). This provides a unification of models with apparently very different features into a single complete model. The result uses an equality between the Hamilton function of any classical spin model and the Hamilton function of a model with all "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.2096","kind":"arxiv","version":3},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:34:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LJH9jHrm68vj2Q/+qXjeBNIuLS68VvWXf+BaBIWVlLpLzQ+VkOMHS+LghPRnFz7W1scq56/6XmD8mVuEcAnGDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T20:16:35.903533Z"},"content_sha256":"295ce06723bec2fec5f9a7514aee8d57a4058baff03839e61fdc34bece87bfe4","schema_version":"1.0","event_id":"sha256:295ce06723bec2fec5f9a7514aee8d57a4058baff03839e61fdc34bece87bfe4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5MQ2ARBNLGN52NWFVVAYS42JVE/bundle.json","state_url":"https://pith.science/pith/5MQ2ARBNLGN52NWFVVAYS42JVE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5MQ2ARBNLGN52NWFVVAYS42JVE/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-27T20:16:35Z","links":{"resolver":"https://pith.science/pith/5MQ2ARBNLGN52NWFVVAYS42JVE","bundle":"https://pith.science/pith/5MQ2ARBNLGN52NWFVVAYS42JVE/bundle.json","state":"https://pith.science/pith/5MQ2ARBNLGN52NWFVVAYS42JVE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5MQ2ARBNLGN52NWFVVAYS42JVE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:5MQ2ARBNLGN52NWFVVAYS42JVE","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":"6135b215733e38d06327b0942d4d5ca1fb0e8a045dbb296dbc19912fada30e4e","cross_cats_sorted":["cond-mat.stat-mech","hep-lat"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-11-11T10:06:34Z","title_canon_sha256":"c480d524a7e97bb35613ef2235d65f03e2be96f26681b037b6ecdb317d4e11cf"},"schema_version":"1.0","source":{"id":"0911.2096","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.2096","created_at":"2026-05-18T02:34:11Z"},{"alias_kind":"arxiv_version","alias_value":"0911.2096v3","created_at":"2026-05-18T02:34:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.2096","created_at":"2026-05-18T02:34:11Z"},{"alias_kind":"pith_short_12","alias_value":"5MQ2ARBNLGN5","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"5MQ2ARBNLGN52NWF","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"5MQ2ARBN","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:295ce06723bec2fec5f9a7514aee8d57a4058baff03839e61fdc34bece87bfe4","target":"graph","created_at":"2026-05-18T02:34:11Z","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":"In our recent work [Phys. Rev. Lett. 102, 230502 (2009)] we showed that the partition function of all classical spin models, including all discrete standard statistical models and all Abelian discrete lattice gauge theories (LGTs), can be expressed as a special instance of the partition function of a 4-dimensional pure LGT with gauge group Z_2 (4D Z_2 LGT). This provides a unification of models with apparently very different features into a single complete model. The result uses an equality between the Hamilton function of any classical spin model and the Hamilton function of a model with all ","authors_text":"G. De las Cuevas, H. J. Briegel, M. A. Martin-Delgado, W. D\\\"ur","cross_cats":["cond-mat.stat-mech","hep-lat"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-11-11T10:06:34Z","title":"Mapping all classical spin models to a lattice gauge theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.2096","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:b5900d992d85b95ced2dd07efd3eef8d57d165f4549212282cfd81c840f02390","target":"record","created_at":"2026-05-18T02:34:11Z","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":"6135b215733e38d06327b0942d4d5ca1fb0e8a045dbb296dbc19912fada30e4e","cross_cats_sorted":["cond-mat.stat-mech","hep-lat"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-11-11T10:06:34Z","title_canon_sha256":"c480d524a7e97bb35613ef2235d65f03e2be96f26681b037b6ecdb317d4e11cf"},"schema_version":"1.0","source":{"id":"0911.2096","kind":"arxiv","version":3}},"canonical_sha256":"eb21a0442d599bdd36c5ad41897349a910740be6e95726e18025a32ee5b40fcc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb21a0442d599bdd36c5ad41897349a910740be6e95726e18025a32ee5b40fcc","first_computed_at":"2026-05-18T02:34:11.270966Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:34:11.270966Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wpw6uknLJhjrRhgCuYYttMWnqZY61LSmqYrPc93pHL4WEgqIR1w5Rewi8DswF4gvPqktevsimhoDUU2hDD0PDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:34:11.271374Z","signed_message":"canonical_sha256_bytes"},"source_id":"0911.2096","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b5900d992d85b95ced2dd07efd3eef8d57d165f4549212282cfd81c840f02390","sha256:295ce06723bec2fec5f9a7514aee8d57a4058baff03839e61fdc34bece87bfe4"],"state_sha256":"d4b8b979f2a6a808f9c17ba5200f3108ba6c2ab2b3720aeb5e0d1fe604765f46"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Npm2TtGpDo4fcDKzEuOxCa5nBZPbWtpwV2e4Ne7qp2FtJvaIUwLG7FBhttotjBvIgTJxfrjnbw+x86fauryLDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T20:16:35.905369Z","bundle_sha256":"dcc838bc70fdcbf4c56349b5bb1624de864c6ba5e690231cd59e9ecd186d2e26"}}