{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:6J7AXA3MDLZX67QE3G5WCI5R7J","short_pith_number":"pith:6J7AXA3M","canonical_record":{"source":{"id":"math-ph/0505035","kind":"arxiv","version":6},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2005-05-11T09:56:10Z","cross_cats_sorted":["math.FA","math.MP"],"title_canon_sha256":"32b386f982e950f50d7784de6f2075c11d83d343322dac53f49dbc1244d5be0d","abstract_canon_sha256":"51209fc142ddfb37f21371973cd8eed2d0bfcf7b2c68a8c0625d2fda7cf1fdb5"},"schema_version":"1.0"},"canonical_sha256":"f27e0b836c1af37f7e04d9bb6123b1fa72a39a9927ae688d00c09490f1d9348c","source":{"kind":"arxiv","id":"math-ph/0505035","version":6},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0505035","created_at":"2026-05-18T03:09:20Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0505035v6","created_at":"2026-05-18T03:09:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0505035","created_at":"2026-05-18T03:09:20Z"},{"alias_kind":"pith_short_12","alias_value":"6J7AXA3MDLZX","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"6J7AXA3MDLZX67QE","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"6J7AXA3M","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:6J7AXA3MDLZX67QE3G5WCI5R7J","target":"record","payload":{"canonical_record":{"source":{"id":"math-ph/0505035","kind":"arxiv","version":6},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2005-05-11T09:56:10Z","cross_cats_sorted":["math.FA","math.MP"],"title_canon_sha256":"32b386f982e950f50d7784de6f2075c11d83d343322dac53f49dbc1244d5be0d","abstract_canon_sha256":"51209fc142ddfb37f21371973cd8eed2d0bfcf7b2c68a8c0625d2fda7cf1fdb5"},"schema_version":"1.0"},"canonical_sha256":"f27e0b836c1af37f7e04d9bb6123b1fa72a39a9927ae688d00c09490f1d9348c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:09:20.594165Z","signature_b64":"YaelcihDu4qE4bbBOpsOGkdAMhSMWoSQUNuXJa8SV2gJO0Hn63ZuKrGob1ShqejS6l2hgqRyuXjD4N3491YBCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f27e0b836c1af37f7e04d9bb6123b1fa72a39a9927ae688d00c09490f1d9348c","last_reissued_at":"2026-05-18T03:09:20.593446Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:09:20.593446Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math-ph/0505035","source_version":6,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:09:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9pC+OhWAmeMOlA6/9LlMgda3yBe/Xl5Sx4fPGjxMMwFS/aEt9shDeuhdBoMkSHufp8mcdN+ic/8bVMQabnzXCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:54:01.279933Z"},"content_sha256":"42a8245acc53155e0bbfe3f8d9dcd458f751104dd9e7a6b5c0b2669033a25fe2","schema_version":"1.0","event_id":"sha256:42a8245acc53155e0bbfe3f8d9dcd458f751104dd9e7a6b5c0b2669033a25fe2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:6J7AXA3MDLZX67QE3G5WCI5R7J","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Phase transition and split property in quantum spin chain","license":"","headline":"","cross_cats":["math.FA","math.MP"],"primary_cat":"math-ph","authors_text":"Anilesh Mohari","submitted_at":"2005-05-11T09:56:10Z","abstract_excerpt":"In this exposition we investigate further the general methodology proposed in [Mo2] to study properties of the ground states of a translation invariant Hamiltonian for one lattice dimensional quantum spin chain $\\cla=\\otimes_{\\IZ}M_d$, where $M_d$ is the matrix of $d \\times d$ complex matrices. We introduce a notion of quantum detailed balance [Mo1] for a translation invariant state on $\\cla$ and prove that such a pure state is uniformly mixing [BR,Ma2] if and only if the lattice space correlation functions decay exponentially. Furthermore we also prove that a pure lattice symmetric, translati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0505035","kind":"arxiv","version":6},"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":"2026-05-18T03:09:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q1oTM57vyGEQJ78CKh8xauT/Td64rnBeA7qjoXEq1BpFPO9Zp4jV6ibg0IOVAKzMZ60GixP/7pog2rUfDbsjDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:54:01.280593Z"},"content_sha256":"1d861eca3bc89bc3711c1bf715d42d7491735a164fd73436db21a90f793458fc","schema_version":"1.0","event_id":"sha256:1d861eca3bc89bc3711c1bf715d42d7491735a164fd73436db21a90f793458fc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6J7AXA3MDLZX67QE3G5WCI5R7J/bundle.json","state_url":"https://pith.science/pith/6J7AXA3MDLZX67QE3G5WCI5R7J/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6J7AXA3MDLZX67QE3G5WCI5R7J/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":"2026-05-27T11:54:01Z","links":{"resolver":"https://pith.science/pith/6J7AXA3MDLZX67QE3G5WCI5R7J","bundle":"https://pith.science/pith/6J7AXA3MDLZX67QE3G5WCI5R7J/bundle.json","state":"https://pith.science/pith/6J7AXA3MDLZX67QE3G5WCI5R7J/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6J7AXA3MDLZX67QE3G5WCI5R7J/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:6J7AXA3MDLZX67QE3G5WCI5R7J","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":"51209fc142ddfb37f21371973cd8eed2d0bfcf7b2c68a8c0625d2fda7cf1fdb5","cross_cats_sorted":["math.FA","math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2005-05-11T09:56:10Z","title_canon_sha256":"32b386f982e950f50d7784de6f2075c11d83d343322dac53f49dbc1244d5be0d"},"schema_version":"1.0","source":{"id":"math-ph/0505035","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0505035","created_at":"2026-05-18T03:09:20Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0505035v6","created_at":"2026-05-18T03:09:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0505035","created_at":"2026-05-18T03:09:20Z"},{"alias_kind":"pith_short_12","alias_value":"6J7AXA3MDLZX","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"6J7AXA3MDLZX67QE","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"6J7AXA3M","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:1d861eca3bc89bc3711c1bf715d42d7491735a164fd73436db21a90f793458fc","target":"graph","created_at":"2026-05-18T03:09:20Z","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 this exposition we investigate further the general methodology proposed in [Mo2] to study properties of the ground states of a translation invariant Hamiltonian for one lattice dimensional quantum spin chain $\\cla=\\otimes_{\\IZ}M_d$, where $M_d$ is the matrix of $d \\times d$ complex matrices. We introduce a notion of quantum detailed balance [Mo1] for a translation invariant state on $\\cla$ and prove that such a pure state is uniformly mixing [BR,Ma2] if and only if the lattice space correlation functions decay exponentially. Furthermore we also prove that a pure lattice symmetric, translati","authors_text":"Anilesh Mohari","cross_cats":["math.FA","math.MP"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2005-05-11T09:56:10Z","title":"Phase transition and split property in quantum spin chain"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0505035","kind":"arxiv","version":6},"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":"sha256:42a8245acc53155e0bbfe3f8d9dcd458f751104dd9e7a6b5c0b2669033a25fe2","target":"record","created_at":"2026-05-18T03:09:20Z","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":"51209fc142ddfb37f21371973cd8eed2d0bfcf7b2c68a8c0625d2fda7cf1fdb5","cross_cats_sorted":["math.FA","math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2005-05-11T09:56:10Z","title_canon_sha256":"32b386f982e950f50d7784de6f2075c11d83d343322dac53f49dbc1244d5be0d"},"schema_version":"1.0","source":{"id":"math-ph/0505035","kind":"arxiv","version":6}},"canonical_sha256":"f27e0b836c1af37f7e04d9bb6123b1fa72a39a9927ae688d00c09490f1d9348c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f27e0b836c1af37f7e04d9bb6123b1fa72a39a9927ae688d00c09490f1d9348c","first_computed_at":"2026-05-18T03:09:20.593446Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:09:20.593446Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YaelcihDu4qE4bbBOpsOGkdAMhSMWoSQUNuXJa8SV2gJO0Hn63ZuKrGob1ShqejS6l2hgqRyuXjD4N3491YBCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:09:20.594165Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0505035","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:42a8245acc53155e0bbfe3f8d9dcd458f751104dd9e7a6b5c0b2669033a25fe2","sha256:1d861eca3bc89bc3711c1bf715d42d7491735a164fd73436db21a90f793458fc"],"state_sha256":"f2605c3ece476c4b643534f18b78b3e6d8a21c1a3afcf8a89e79fcfbf0a2be5a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"chNnO5dnNXNHwNF6wj6P4ELue9j6uKYmHRXyqueYC27a0UJbjZvxM6vf+QxZC4LBsPbggIr794jPrqE8CvhwCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T11:54:01.283975Z","bundle_sha256":"bbf2cbccf1d3c75484c52ba11ece504526dfd58e50583ed049ba892c5e9b64f6"}}