{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:IOSJANGXEZIW4OFMCHRI4L6XTH","short_pith_number":"pith:IOSJANGX","canonical_record":{"source":{"id":"math-ph/0606046","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2006-06-19T21:00:45Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"1518160220bef4994a716966b537e5b500c630d40a3f881b25279ea49cd95cad","abstract_canon_sha256":"e7dba8d7fc94994788184361a3d637a121a95dade9e6327fc19bcd2d41ec69fe"},"schema_version":"1.0"},"canonical_sha256":"43a49034d726516e38ac11e28e2fd799f35cffe7bb07b5f344a0dabad66aeb63","source":{"kind":"arxiv","id":"math-ph/0606046","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0606046","created_at":"2026-05-18T04:13:07Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0606046v1","created_at":"2026-05-18T04:13:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0606046","created_at":"2026-05-18T04:13:07Z"},{"alias_kind":"pith_short_12","alias_value":"IOSJANGXEZIW","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"IOSJANGXEZIW4OFM","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"IOSJANGX","created_at":"2026-05-18T12:25:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:IOSJANGXEZIW4OFMCHRI4L6XTH","target":"record","payload":{"canonical_record":{"source":{"id":"math-ph/0606046","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2006-06-19T21:00:45Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"1518160220bef4994a716966b537e5b500c630d40a3f881b25279ea49cd95cad","abstract_canon_sha256":"e7dba8d7fc94994788184361a3d637a121a95dade9e6327fc19bcd2d41ec69fe"},"schema_version":"1.0"},"canonical_sha256":"43a49034d726516e38ac11e28e2fd799f35cffe7bb07b5f344a0dabad66aeb63","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:13:07.379833Z","signature_b64":"epARVwHrUrRDPXjqRVmp6uWR8YkDE70Y7iUURFu9p0iLfJRBKb9dF1kjnIhApzwjU/xPNjFU31p99VEFTWUeAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"43a49034d726516e38ac11e28e2fd799f35cffe7bb07b5f344a0dabad66aeb63","last_reissued_at":"2026-05-18T04:13:07.379250Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:13:07.379250Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math-ph/0606046","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":"2026-05-18T04:13:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r5fwDV85GR67kG1eRfDu950zgcWpXE4A5+Mu3as6Q5/75KNVz7RPEAcwuTwS+oSD/Z8zeq4bQjMgTnyJ/mU5BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T13:41:44.221202Z"},"content_sha256":"a054c70a5b4fd7fc2be58e5492c7966fd9bf8072988875a6412ffc1c9f4b3737","schema_version":"1.0","event_id":"sha256:a054c70a5b4fd7fc2be58e5492c7966fd9bf8072988875a6412ffc1c9f4b3737"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:IOSJANGXEZIW4OFMCHRI4L6XTH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some Recent Results on Pair Correlation Functions and Susceptibilities in Exactly Solvable Models","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Helen Au-Yang, Jacques H.H. Perk","submitted_at":"2006-06-19T21:00:45Z","abstract_excerpt":"Using detailed exact results on pair-correlation functions of Z-invariant Ising models, we can write and run algorithms of polynomial complexity to obtain wavevector-dependent susceptibilities for a variety of Ising systems. Reviewing recent work we compare various periodic and quasiperiodic models, where the couplings and/or the lattice may be aperiodic, and where the Ising couplings may be either ferromagnetic, or antiferromagnetic, or of mixed sign. We present some of our results on the square-lattice fully-frustrated Ising model. Finally, we make a few remarks on our recent works on the pe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0606046","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":"2026-05-18T04:13:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n6jMvgu7qA/ZWvs/pVUC+LjRFmscDr+MST9JsqeTp8cf4eC0hTbOMJF5MuDsT6vHcBM3OAU8dTM27ZPn9PR6Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T13:41:44.221566Z"},"content_sha256":"1f9f14ee8cdfbba372740901d686db0bafb5447c8ca9fd78a67a3f1aa7c5771e","schema_version":"1.0","event_id":"sha256:1f9f14ee8cdfbba372740901d686db0bafb5447c8ca9fd78a67a3f1aa7c5771e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IOSJANGXEZIW4OFMCHRI4L6XTH/bundle.json","state_url":"https://pith.science/pith/IOSJANGXEZIW4OFMCHRI4L6XTH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IOSJANGXEZIW4OFMCHRI4L6XTH/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":"2026-06-01T13:41:44Z","links":{"resolver":"https://pith.science/pith/IOSJANGXEZIW4OFMCHRI4L6XTH","bundle":"https://pith.science/pith/IOSJANGXEZIW4OFMCHRI4L6XTH/bundle.json","state":"https://pith.science/pith/IOSJANGXEZIW4OFMCHRI4L6XTH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IOSJANGXEZIW4OFMCHRI4L6XTH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:IOSJANGXEZIW4OFMCHRI4L6XTH","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":"e7dba8d7fc94994788184361a3d637a121a95dade9e6327fc19bcd2d41ec69fe","cross_cats_sorted":["math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2006-06-19T21:00:45Z","title_canon_sha256":"1518160220bef4994a716966b537e5b500c630d40a3f881b25279ea49cd95cad"},"schema_version":"1.0","source":{"id":"math-ph/0606046","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0606046","created_at":"2026-05-18T04:13:07Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0606046v1","created_at":"2026-05-18T04:13:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0606046","created_at":"2026-05-18T04:13:07Z"},{"alias_kind":"pith_short_12","alias_value":"IOSJANGXEZIW","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"IOSJANGXEZIW4OFM","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"IOSJANGX","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:1f9f14ee8cdfbba372740901d686db0bafb5447c8ca9fd78a67a3f1aa7c5771e","target":"graph","created_at":"2026-05-18T04:13:07Z","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":"Using detailed exact results on pair-correlation functions of Z-invariant Ising models, we can write and run algorithms of polynomial complexity to obtain wavevector-dependent susceptibilities for a variety of Ising systems. Reviewing recent work we compare various periodic and quasiperiodic models, where the couplings and/or the lattice may be aperiodic, and where the Ising couplings may be either ferromagnetic, or antiferromagnetic, or of mixed sign. We present some of our results on the square-lattice fully-frustrated Ising model. Finally, we make a few remarks on our recent works on the pe","authors_text":"Helen Au-Yang, Jacques H.H. Perk","cross_cats":["math.MP"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2006-06-19T21:00:45Z","title":"Some Recent Results on Pair Correlation Functions and Susceptibilities in Exactly Solvable Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0606046","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:a054c70a5b4fd7fc2be58e5492c7966fd9bf8072988875a6412ffc1c9f4b3737","target":"record","created_at":"2026-05-18T04:13:07Z","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":"e7dba8d7fc94994788184361a3d637a121a95dade9e6327fc19bcd2d41ec69fe","cross_cats_sorted":["math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2006-06-19T21:00:45Z","title_canon_sha256":"1518160220bef4994a716966b537e5b500c630d40a3f881b25279ea49cd95cad"},"schema_version":"1.0","source":{"id":"math-ph/0606046","kind":"arxiv","version":1}},"canonical_sha256":"43a49034d726516e38ac11e28e2fd799f35cffe7bb07b5f344a0dabad66aeb63","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"43a49034d726516e38ac11e28e2fd799f35cffe7bb07b5f344a0dabad66aeb63","first_computed_at":"2026-05-18T04:13:07.379250Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:13:07.379250Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"epARVwHrUrRDPXjqRVmp6uWR8YkDE70Y7iUURFu9p0iLfJRBKb9dF1kjnIhApzwjU/xPNjFU31p99VEFTWUeAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:13:07.379833Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0606046","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a054c70a5b4fd7fc2be58e5492c7966fd9bf8072988875a6412ffc1c9f4b3737","sha256:1f9f14ee8cdfbba372740901d686db0bafb5447c8ca9fd78a67a3f1aa7c5771e"],"state_sha256":"50a42adca995f53d0889318dd5b50b27bd0e974a392aba2b7149234a8ea04bfa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CPWbtp7IuivXPF8jWW7Rl8whb45PRAsmWLAJWilEFHE5myMsC61lv1VQjeOLIzklTWPpeSHLhrKmvJghKVp+Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T13:41:44.223560Z","bundle_sha256":"b724059f22c2e8e3570fa1f4015e45a663ca33cc67bafd50a65625428bbb8cee"}}