{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:UDHLS4YSVNV7MEKJ6FQIHDCZXK","short_pith_number":"pith:UDHLS4YS","canonical_record":{"source":{"id":"math-ph/0507008","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2005-07-04T06:53:10Z","cross_cats_sorted":["cond-mat.stat-mech","hep-th","math.MP"],"title_canon_sha256":"0450f3fdb7a771120c00d42392b01e9a163d7e484d030f17feb81328bb33a75e","abstract_canon_sha256":"34bf70b1536479ea80ebc6a5ded065e5b13096434a7dba996f243563408da8bf"},"schema_version":"1.0"},"canonical_sha256":"a0ceb97312ab6bf61149f160838c59baa02906122f81221b5609ffa2b945da3f","source":{"kind":"arxiv","id":"math-ph/0507008","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0507008","created_at":"2026-07-04T16:56:35Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0507008v3","created_at":"2026-07-04T16:56:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0507008","created_at":"2026-07-04T16:56:35Z"},{"alias_kind":"pith_short_12","alias_value":"UDHLS4YSVNV7","created_at":"2026-07-04T16:56:35Z"},{"alias_kind":"pith_short_16","alias_value":"UDHLS4YSVNV7MEKJ","created_at":"2026-07-04T16:56:35Z"},{"alias_kind":"pith_short_8","alias_value":"UDHLS4YS","created_at":"2026-07-04T16:56:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:UDHLS4YSVNV7MEKJ6FQIHDCZXK","target":"record","payload":{"canonical_record":{"source":{"id":"math-ph/0507008","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2005-07-04T06:53:10Z","cross_cats_sorted":["cond-mat.stat-mech","hep-th","math.MP"],"title_canon_sha256":"0450f3fdb7a771120c00d42392b01e9a163d7e484d030f17feb81328bb33a75e","abstract_canon_sha256":"34bf70b1536479ea80ebc6a5ded065e5b13096434a7dba996f243563408da8bf"},"schema_version":"1.0"},"canonical_sha256":"a0ceb97312ab6bf61149f160838c59baa02906122f81221b5609ffa2b945da3f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:56:35.956688Z","signature_b64":"OMkEyBYZVlkkWLtM2taZ8VmqWoIKohiYeQLDdasrdEOBJ0d6Ic+Qp9/oJTIARMuPSmU7dv/9vMKvCZ3tW1b4Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a0ceb97312ab6bf61149f160838c59baa02906122f81221b5609ffa2b945da3f","last_reissued_at":"2026-07-04T16:56:35.956271Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:56:35.956271Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math-ph/0507008","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":"2026-07-04T16:56:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WKIzB4uWMV08Sbx3Aw/EeI685oIYpi+6r/VocAGx+t2SrcrpvsvkSDcOLKvzXe1pqATw4QV2Ugz+nfqv8FFTDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T00:56:51.929880Z"},"content_sha256":"e3ba2ff56028137092ba1e0ca1acd6fe0c9ba69ceff03540aa64445fd722bda2","schema_version":"1.0","event_id":"sha256:e3ba2ff56028137092ba1e0ca1acd6fe0c9ba69ceff03540aa64445fd722bda2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:UDHLS4YSVNV7MEKJ6FQIHDCZXK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spectral Gap and Exponential Decay of Correlations","license":"","headline":"","cross_cats":["cond-mat.stat-mech","hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"Matthew B. Hastings, Tohru Koma","submitted_at":"2005-07-04T06:53:10Z","abstract_excerpt":"We study the relation between the spectral gap above the ground state and the decay of the correlations in the ground state in quantum spin and fermion systems with short-range interactions on a wide class of lattices. We prove that, if two observables anticommute with each other at large distance, then the nonvanishing spectral gap implies exponential decay of the corresponding correlation. When two observables commute with each other at large distance, the connected correlation function decays exponentially under the gap assumption. If the observables behave as a vector under the U(1) rotati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0507008","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math-ph/0507008/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T16:56:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i7I/xCPPODTrUefUj1sIuuCgoOqV894rJLCqSYBd4jkjNS366yx/vR18HwT6ZK0d3H0BPxSGAUju28z/Ja9fCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T00:56:51.930384Z"},"content_sha256":"f322dbe7eedb60e014ff883ae3141f116e5816fa18354aa4b7df0af530dd064c","schema_version":"1.0","event_id":"sha256:f322dbe7eedb60e014ff883ae3141f116e5816fa18354aa4b7df0af530dd064c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UDHLS4YSVNV7MEKJ6FQIHDCZXK/bundle.json","state_url":"https://pith.science/pith/UDHLS4YSVNV7MEKJ6FQIHDCZXK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UDHLS4YSVNV7MEKJ6FQIHDCZXK/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":"2026-08-16T00:56:51Z","links":{"resolver":"https://pith.science/pith/UDHLS4YSVNV7MEKJ6FQIHDCZXK","bundle":"https://pith.science/pith/UDHLS4YSVNV7MEKJ6FQIHDCZXK/bundle.json","state":"https://pith.science/pith/UDHLS4YSVNV7MEKJ6FQIHDCZXK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UDHLS4YSVNV7MEKJ6FQIHDCZXK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:UDHLS4YSVNV7MEKJ6FQIHDCZXK","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":"34bf70b1536479ea80ebc6a5ded065e5b13096434a7dba996f243563408da8bf","cross_cats_sorted":["cond-mat.stat-mech","hep-th","math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2005-07-04T06:53:10Z","title_canon_sha256":"0450f3fdb7a771120c00d42392b01e9a163d7e484d030f17feb81328bb33a75e"},"schema_version":"1.0","source":{"id":"math-ph/0507008","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0507008","created_at":"2026-07-04T16:56:35Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0507008v3","created_at":"2026-07-04T16:56:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0507008","created_at":"2026-07-04T16:56:35Z"},{"alias_kind":"pith_short_12","alias_value":"UDHLS4YSVNV7","created_at":"2026-07-04T16:56:35Z"},{"alias_kind":"pith_short_16","alias_value":"UDHLS4YSVNV7MEKJ","created_at":"2026-07-04T16:56:35Z"},{"alias_kind":"pith_short_8","alias_value":"UDHLS4YS","created_at":"2026-07-04T16:56:35Z"}],"graph_snapshots":[{"event_id":"sha256:f322dbe7eedb60e014ff883ae3141f116e5816fa18354aa4b7df0af530dd064c","target":"graph","created_at":"2026-07-04T16:56:35Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math-ph/0507008/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the relation between the spectral gap above the ground state and the decay of the correlations in the ground state in quantum spin and fermion systems with short-range interactions on a wide class of lattices. We prove that, if two observables anticommute with each other at large distance, then the nonvanishing spectral gap implies exponential decay of the corresponding correlation. When two observables commute with each other at large distance, the connected correlation function decays exponentially under the gap assumption. If the observables behave as a vector under the U(1) rotati","authors_text":"Matthew B. Hastings, Tohru Koma","cross_cats":["cond-mat.stat-mech","hep-th","math.MP"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2005-07-04T06:53:10Z","title":"Spectral Gap and Exponential Decay of Correlations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0507008","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:e3ba2ff56028137092ba1e0ca1acd6fe0c9ba69ceff03540aa64445fd722bda2","target":"record","created_at":"2026-07-04T16:56:35Z","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":"34bf70b1536479ea80ebc6a5ded065e5b13096434a7dba996f243563408da8bf","cross_cats_sorted":["cond-mat.stat-mech","hep-th","math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2005-07-04T06:53:10Z","title_canon_sha256":"0450f3fdb7a771120c00d42392b01e9a163d7e484d030f17feb81328bb33a75e"},"schema_version":"1.0","source":{"id":"math-ph/0507008","kind":"arxiv","version":3}},"canonical_sha256":"a0ceb97312ab6bf61149f160838c59baa02906122f81221b5609ffa2b945da3f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a0ceb97312ab6bf61149f160838c59baa02906122f81221b5609ffa2b945da3f","first_computed_at":"2026-07-04T16:56:35.956271Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:56:35.956271Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OMkEyBYZVlkkWLtM2taZ8VmqWoIKohiYeQLDdasrdEOBJ0d6Ic+Qp9/oJTIARMuPSmU7dv/9vMKvCZ3tW1b4Ag==","signature_status":"signed_v1","signed_at":"2026-07-04T16:56:35.956688Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0507008","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e3ba2ff56028137092ba1e0ca1acd6fe0c9ba69ceff03540aa64445fd722bda2","sha256:f322dbe7eedb60e014ff883ae3141f116e5816fa18354aa4b7df0af530dd064c"],"state_sha256":"614606895ee2439b81811e16785c6e02ee1348cbe1e8e1036860014dccdaf8fb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B4tH3zZBMTGx6l/Wpc2aLAfnCt0dVWH00/H2KBXKuilY/9dTw13SjltVO35dm7DUYBkpKYmn0xDjWMzje8sVBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T00:56:51.935030Z","bundle_sha256":"9d3599323efff5ed49f8a12031466164ee823b4bb1741eb63634ec4ecc6e703c"}}