{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:FZQ7EFR7FCCATRGA3FZHQTFPNK","short_pith_number":"pith:FZQ7EFR7","canonical_record":{"source":{"id":"1110.6385","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-lat","submitted_at":"2011-10-28T16:15:02Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"a3b8ca01a8b01f8b157e490ec9caa11dfe6c5cc44da479b71269aaed97dde2c5","abstract_canon_sha256":"8d5e56d3be4720fab33d0c74f55361e2b850ead1afe3948f0d0c2bdea15e5fcb"},"schema_version":"1.0"},"canonical_sha256":"2e61f2163f288409c4c0d972784caf6aaf85ca4a473001f36053338ac3f33bba","source":{"kind":"arxiv","id":"1110.6385","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.6385","created_at":"2026-05-18T04:09:56Z"},{"alias_kind":"arxiv_version","alias_value":"1110.6385v1","created_at":"2026-05-18T04:09:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.6385","created_at":"2026-05-18T04:09:56Z"},{"alias_kind":"pith_short_12","alias_value":"FZQ7EFR7FCCA","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"FZQ7EFR7FCCATRGA","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"FZQ7EFR7","created_at":"2026-05-18T12:26:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:FZQ7EFR7FCCATRGA3FZHQTFPNK","target":"record","payload":{"canonical_record":{"source":{"id":"1110.6385","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-lat","submitted_at":"2011-10-28T16:15:02Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"a3b8ca01a8b01f8b157e490ec9caa11dfe6c5cc44da479b71269aaed97dde2c5","abstract_canon_sha256":"8d5e56d3be4720fab33d0c74f55361e2b850ead1afe3948f0d0c2bdea15e5fcb"},"schema_version":"1.0"},"canonical_sha256":"2e61f2163f288409c4c0d972784caf6aaf85ca4a473001f36053338ac3f33bba","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:09:56.863221Z","signature_b64":"/0vvIWMY6waG43rXFTryePbC8M5DnsvM1c9wWEefd7JAscHUXhAvsPyrE5wR3pQxmo4Dq04nq8DOOJ5TPTNLCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e61f2163f288409c4c0d972784caf6aaf85ca4a473001f36053338ac3f33bba","last_reissued_at":"2026-05-18T04:09:56.862395Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:09:56.862395Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.6385","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:09:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DVjjMW9OfCX+7GGc2i9J6e4CvYBcryKB/aHWGMakI8yhuU3dBXTVEDRSf+mlTBhvHC80OD07GXK+wMlSkhPQAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T12:54:16.164416Z"},"content_sha256":"eebec6c01735e857ea50017ab291bf6b4d44d2a479a23a89224fd0f8920c56bf","schema_version":"1.0","event_id":"sha256:eebec6c01735e857ea50017ab291bf6b4d44d2a479a23a89224fd0f8920c56bf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:FZQ7EFR7FCCATRGA3FZHQTFPNK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Critical properties of 2D Z(N) vector models for N>4","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"hep-lat","authors_text":"Alessandro Papa, Gennaro Cortese, Mario Gravina, Oleg Borisenko, Roberto Fiore","submitted_at":"2011-10-28T16:15:02Z","abstract_excerpt":"We investigate the critical properties of two-dimensional Z(N) vector models for N larger than 4. In particular, critical points of the two phase transitions are located and some critical indices are determined. We study also the behavior of the helicity modulus and the dependence of the critical points on N."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6385","kind":"arxiv","version":1},"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":"2026-05-18T04:09:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s4/QxhfPQNB4fsMwW5xJIoeg0BX/jZCsENoxSvVAspJn2tffYc4NRa2uTiAgxrivGzktr6MAT0zYKttPiRIVBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T12:54:16.165036Z"},"content_sha256":"9dd0eac09ac2702395af635b7a10a6311322d4fecad97f9d2ef5459926e8235a","schema_version":"1.0","event_id":"sha256:9dd0eac09ac2702395af635b7a10a6311322d4fecad97f9d2ef5459926e8235a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FZQ7EFR7FCCATRGA3FZHQTFPNK/bundle.json","state_url":"https://pith.science/pith/FZQ7EFR7FCCATRGA3FZHQTFPNK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FZQ7EFR7FCCATRGA3FZHQTFPNK/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":"2026-05-31T12:54:16Z","links":{"resolver":"https://pith.science/pith/FZQ7EFR7FCCATRGA3FZHQTFPNK","bundle":"https://pith.science/pith/FZQ7EFR7FCCATRGA3FZHQTFPNK/bundle.json","state":"https://pith.science/pith/FZQ7EFR7FCCATRGA3FZHQTFPNK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FZQ7EFR7FCCATRGA3FZHQTFPNK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:FZQ7EFR7FCCATRGA3FZHQTFPNK","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":"8d5e56d3be4720fab33d0c74f55361e2b850ead1afe3948f0d0c2bdea15e5fcb","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-lat","submitted_at":"2011-10-28T16:15:02Z","title_canon_sha256":"a3b8ca01a8b01f8b157e490ec9caa11dfe6c5cc44da479b71269aaed97dde2c5"},"schema_version":"1.0","source":{"id":"1110.6385","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.6385","created_at":"2026-05-18T04:09:56Z"},{"alias_kind":"arxiv_version","alias_value":"1110.6385v1","created_at":"2026-05-18T04:09:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.6385","created_at":"2026-05-18T04:09:56Z"},{"alias_kind":"pith_short_12","alias_value":"FZQ7EFR7FCCA","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"FZQ7EFR7FCCATRGA","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"FZQ7EFR7","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:9dd0eac09ac2702395af635b7a10a6311322d4fecad97f9d2ef5459926e8235a","target":"graph","created_at":"2026-05-18T04:09:56Z","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 investigate the critical properties of two-dimensional Z(N) vector models for N larger than 4. In particular, critical points of the two phase transitions are located and some critical indices are determined. We study also the behavior of the helicity modulus and the dependence of the critical points on N.","authors_text":"Alessandro Papa, Gennaro Cortese, Mario Gravina, Oleg Borisenko, Roberto Fiore","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-lat","submitted_at":"2011-10-28T16:15:02Z","title":"Critical properties of 2D Z(N) vector models for N>4"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6385","kind":"arxiv","version":1},"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:eebec6c01735e857ea50017ab291bf6b4d44d2a479a23a89224fd0f8920c56bf","target":"record","created_at":"2026-05-18T04:09:56Z","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":"8d5e56d3be4720fab33d0c74f55361e2b850ead1afe3948f0d0c2bdea15e5fcb","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-lat","submitted_at":"2011-10-28T16:15:02Z","title_canon_sha256":"a3b8ca01a8b01f8b157e490ec9caa11dfe6c5cc44da479b71269aaed97dde2c5"},"schema_version":"1.0","source":{"id":"1110.6385","kind":"arxiv","version":1}},"canonical_sha256":"2e61f2163f288409c4c0d972784caf6aaf85ca4a473001f36053338ac3f33bba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2e61f2163f288409c4c0d972784caf6aaf85ca4a473001f36053338ac3f33bba","first_computed_at":"2026-05-18T04:09:56.862395Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:09:56.862395Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/0vvIWMY6waG43rXFTryePbC8M5DnsvM1c9wWEefd7JAscHUXhAvsPyrE5wR3pQxmo4Dq04nq8DOOJ5TPTNLCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:09:56.863221Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.6385","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eebec6c01735e857ea50017ab291bf6b4d44d2a479a23a89224fd0f8920c56bf","sha256:9dd0eac09ac2702395af635b7a10a6311322d4fecad97f9d2ef5459926e8235a"],"state_sha256":"29fd608212f9e3d2a859b033058f6afbe32f0ae581e911c35468c1fac6dd8bce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gQ42IOQJ+aujVgADr9xNhsF4nsjGAPmB5jyWME6MCT9gMs++Ppq9QZ9/G/r1hNWVEF4iNkNpiNuPV8fJuc9jDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T12:54:16.168095Z","bundle_sha256":"c25d0db88cd45ccb09ca3f976c80451629c9f1b4e3a1971517cf79d8f8aec4ae"}}