{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:CZCOBMI7YJ36WRQ4TT4QKHYJB3","short_pith_number":"pith:CZCOBMI7","canonical_record":{"source":{"id":"0910.3003","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-10-15T21:41:59Z","cross_cats_sorted":["hep-th","quant-ph"],"title_canon_sha256":"e2abdc25fb687e42667462a461a66bc1f05e720ac40bbb80bc21166d5c9121ed","abstract_canon_sha256":"ded9811bef3e381a1aa34b7732a8c952ab79b944d1cf3247e4452adf10227173"},"schema_version":"1.0"},"canonical_sha256":"1644e0b11fc277eb461c9cf9051f090ed15c9e84eae83940c56f419e80bdab4b","source":{"kind":"arxiv","id":"0910.3003","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.3003","created_at":"2026-07-04T17:24:02Z"},{"alias_kind":"arxiv_version","alias_value":"0910.3003v2","created_at":"2026-07-04T17:24:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.3003","created_at":"2026-07-04T17:24:02Z"},{"alias_kind":"pith_short_12","alias_value":"CZCOBMI7YJ36","created_at":"2026-07-04T17:24:02Z"},{"alias_kind":"pith_short_16","alias_value":"CZCOBMI7YJ36WRQ4","created_at":"2026-07-04T17:24:02Z"},{"alias_kind":"pith_short_8","alias_value":"CZCOBMI7","created_at":"2026-07-04T17:24:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:CZCOBMI7YJ36WRQ4TT4QKHYJB3","target":"record","payload":{"canonical_record":{"source":{"id":"0910.3003","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-10-15T21:41:59Z","cross_cats_sorted":["hep-th","quant-ph"],"title_canon_sha256":"e2abdc25fb687e42667462a461a66bc1f05e720ac40bbb80bc21166d5c9121ed","abstract_canon_sha256":"ded9811bef3e381a1aa34b7732a8c952ab79b944d1cf3247e4452adf10227173"},"schema_version":"1.0"},"canonical_sha256":"1644e0b11fc277eb461c9cf9051f090ed15c9e84eae83940c56f419e80bdab4b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T17:24:02.580774Z","signature_b64":"FLgmBonM+6iAjCN2am/3iYcX/rmA3XVJlOgPG40pjFkBjgd/HXx3qoynY3fi2fThDiuBvk7Xk1Yl/uLC6ml9DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1644e0b11fc277eb461c9cf9051f090ed15c9e84eae83940c56f419e80bdab4b","last_reissued_at":"2026-07-04T17:24:02.580409Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T17:24:02.580409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0910.3003","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T17:24:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7weXviYzxa0j/G3yMny7i4ngFHzAa0I53RpDoxcSGRY51uWjAZc4uMqnpVV1b6rPTnQvO75ycZE3jfZzjfI4Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T16:27:02.815082Z"},"content_sha256":"563d0e21b11c6dcc54a6478b812c11915a2efab2b0e5c3e84fa1f9992ab4b58b","schema_version":"1.0","event_id":"sha256:563d0e21b11c6dcc54a6478b812c11915a2efab2b0e5c3e84fa1f9992ab4b58b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:CZCOBMI7YJ36WRQ4TT4QKHYJB3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Entanglement entropy and the complex plane of replicas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","quant-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"F. Gliozzi, L. Tagliacozzo","submitted_at":"2009-10-15T21:41:59Z","abstract_excerpt":"The entanglement entropy of a subsystem $A$ of a quantum system is expressed, in the replica method, through analytic continuation with respect to n of the trace of the n-th power of the reduced density matrix $\\tr\\rho_A^n$. We study the analytic properties of this quantity as a function of n in some quantum critical Ising-like models in 1+1 and 2+1 dimensions. Although we find no true singularities for n>0, there is a threshold value of n close to 2 which separates two very different `phases'. The region with larger n is characterized by rapidly convergent Taylor expansions and is very smooth"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.3003","kind":"arxiv","version":2},"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/0910.3003/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":"2026-07-04T17:24:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o9JwpgKYyz+V9z8GoBYfX08TPx/WQ7eF5+9iw5g83oCC0k3OCJ8WpzNB/rb2nQG+RBUmJWojKBg1I7+3KwuOAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T16:27:02.815674Z"},"content_sha256":"3ef7240848e557480338f588474ebab0bb18648d25edeffe42d88a71a56231b3","schema_version":"1.0","event_id":"sha256:3ef7240848e557480338f588474ebab0bb18648d25edeffe42d88a71a56231b3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CZCOBMI7YJ36WRQ4TT4QKHYJB3/bundle.json","state_url":"https://pith.science/pith/CZCOBMI7YJ36WRQ4TT4QKHYJB3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CZCOBMI7YJ36WRQ4TT4QKHYJB3/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":"2026-08-18T16:27:02Z","links":{"resolver":"https://pith.science/pith/CZCOBMI7YJ36WRQ4TT4QKHYJB3","bundle":"https://pith.science/pith/CZCOBMI7YJ36WRQ4TT4QKHYJB3/bundle.json","state":"https://pith.science/pith/CZCOBMI7YJ36WRQ4TT4QKHYJB3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CZCOBMI7YJ36WRQ4TT4QKHYJB3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:CZCOBMI7YJ36WRQ4TT4QKHYJB3","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":"ded9811bef3e381a1aa34b7732a8c952ab79b944d1cf3247e4452adf10227173","cross_cats_sorted":["hep-th","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-10-15T21:41:59Z","title_canon_sha256":"e2abdc25fb687e42667462a461a66bc1f05e720ac40bbb80bc21166d5c9121ed"},"schema_version":"1.0","source":{"id":"0910.3003","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.3003","created_at":"2026-07-04T17:24:02Z"},{"alias_kind":"arxiv_version","alias_value":"0910.3003v2","created_at":"2026-07-04T17:24:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.3003","created_at":"2026-07-04T17:24:02Z"},{"alias_kind":"pith_short_12","alias_value":"CZCOBMI7YJ36","created_at":"2026-07-04T17:24:02Z"},{"alias_kind":"pith_short_16","alias_value":"CZCOBMI7YJ36WRQ4","created_at":"2026-07-04T17:24:02Z"},{"alias_kind":"pith_short_8","alias_value":"CZCOBMI7","created_at":"2026-07-04T17:24:02Z"}],"graph_snapshots":[{"event_id":"sha256:3ef7240848e557480338f588474ebab0bb18648d25edeffe42d88a71a56231b3","target":"graph","created_at":"2026-07-04T17:24:02Z","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/0910.3003/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The entanglement entropy of a subsystem $A$ of a quantum system is expressed, in the replica method, through analytic continuation with respect to n of the trace of the n-th power of the reduced density matrix $\\tr\\rho_A^n$. We study the analytic properties of this quantity as a function of n in some quantum critical Ising-like models in 1+1 and 2+1 dimensions. Although we find no true singularities for n>0, there is a threshold value of n close to 2 which separates two very different `phases'. The region with larger n is characterized by rapidly convergent Taylor expansions and is very smooth","authors_text":"F. Gliozzi, L. Tagliacozzo","cross_cats":["hep-th","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-10-15T21:41:59Z","title":"Entanglement entropy and the complex plane of replicas"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.3003","kind":"arxiv","version":2},"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":"sha256:563d0e21b11c6dcc54a6478b812c11915a2efab2b0e5c3e84fa1f9992ab4b58b","target":"record","created_at":"2026-07-04T17:24:02Z","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":"ded9811bef3e381a1aa34b7732a8c952ab79b944d1cf3247e4452adf10227173","cross_cats_sorted":["hep-th","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-10-15T21:41:59Z","title_canon_sha256":"e2abdc25fb687e42667462a461a66bc1f05e720ac40bbb80bc21166d5c9121ed"},"schema_version":"1.0","source":{"id":"0910.3003","kind":"arxiv","version":2}},"canonical_sha256":"1644e0b11fc277eb461c9cf9051f090ed15c9e84eae83940c56f419e80bdab4b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1644e0b11fc277eb461c9cf9051f090ed15c9e84eae83940c56f419e80bdab4b","first_computed_at":"2026-07-04T17:24:02.580409Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T17:24:02.580409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FLgmBonM+6iAjCN2am/3iYcX/rmA3XVJlOgPG40pjFkBjgd/HXx3qoynY3fi2fThDiuBvk7Xk1Yl/uLC6ml9DQ==","signature_status":"signed_v1","signed_at":"2026-07-04T17:24:02.580774Z","signed_message":"canonical_sha256_bytes"},"source_id":"0910.3003","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:563d0e21b11c6dcc54a6478b812c11915a2efab2b0e5c3e84fa1f9992ab4b58b","sha256:3ef7240848e557480338f588474ebab0bb18648d25edeffe42d88a71a56231b3"],"state_sha256":"90e73092fdff94d42619dba4b41a3ace2aad022fae4cb85081ada832fbb480dd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XLYG5sSntCitctqqWv/f3ugZOe/I4o/xErVCAMfCsGEn0V1UsN7kbpSA5wRGKEZ2z8hJqhVSpD80F+VOPuL/AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T16:27:02.821315Z","bundle_sha256":"76e0cbc5dcc43573bfbd309b34c905465af4dd5e8821281f9ae0631ff253e0dd"}}