{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:4TOEZFRPOONVTXG4U7SP26SS2N","short_pith_number":"pith:4TOEZFRP","canonical_record":{"source":{"id":"1110.5527","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-10-23T01:10:39Z","cross_cats_sorted":[],"title_canon_sha256":"0e826b6ee29bfbb586bc7d0222d3cf624be911067e6bb933408a257ca96ae519","abstract_canon_sha256":"3d362cc0d994b86eb991ac54d6a419d5a38472e6287f6c76803da39c9f59a5bc"},"schema_version":"1.0"},"canonical_sha256":"e4dc4c962f739b59dcdca7e4fd7a52d370f3f71fab8f0dc743da21102e8a2f39","source":{"kind":"arxiv","id":"1110.5527","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.5527","created_at":"2026-05-18T03:39:14Z"},{"alias_kind":"arxiv_version","alias_value":"1110.5527v2","created_at":"2026-05-18T03:39:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.5527","created_at":"2026-05-18T03:39:14Z"},{"alias_kind":"pith_short_12","alias_value":"4TOEZFRPOONV","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"4TOEZFRPOONVTXG4","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"4TOEZFRP","created_at":"2026-05-18T12:26:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:4TOEZFRPOONVTXG4U7SP26SS2N","target":"record","payload":{"canonical_record":{"source":{"id":"1110.5527","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-10-23T01:10:39Z","cross_cats_sorted":[],"title_canon_sha256":"0e826b6ee29bfbb586bc7d0222d3cf624be911067e6bb933408a257ca96ae519","abstract_canon_sha256":"3d362cc0d994b86eb991ac54d6a419d5a38472e6287f6c76803da39c9f59a5bc"},"schema_version":"1.0"},"canonical_sha256":"e4dc4c962f739b59dcdca7e4fd7a52d370f3f71fab8f0dc743da21102e8a2f39","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:39:14.689792Z","signature_b64":"Uvi/n53L4/64R9AQuj0Nr7ujacgg/D5EcGDxNkCdWIHb8akaUtbzpb8muI5BBWlwTY8BO4/WjD01NojfcwwDCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e4dc4c962f739b59dcdca7e4fd7a52d370f3f71fab8f0dc743da21102e8a2f39","last_reissued_at":"2026-05-18T03:39:14.689126Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:39:14.689126Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.5527","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":"2026-05-18T03:39:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EjO/VJjeA++nObz/weEJ/UP1GBYZZGOmti4IY5ZdnEjRRcmQIbfMjBUU9yHFdyLBNaeLhEOZVsIRCU9oL8mQDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T08:29:21.610498Z"},"content_sha256":"586dbd80822b7d807ff9319548904c7a62b847a70e07a2e7d59861ac503da747","schema_version":"1.0","event_id":"sha256:586dbd80822b7d807ff9319548904c7a62b847a70e07a2e7d59861ac503da747"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:4TOEZFRPOONVTXG4U7SP26SS2N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Conformal invariance in the three dimensional (3D) Ising model and quaternionic geometric phase in quaternionic Hilbert space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Norman H. March, Zhidong Zhang","submitted_at":"2011-10-23T01:10:39Z","abstract_excerpt":"Based on the quaternionic approach developed by one of us [Z.D. Zhang, Phil. Mag. 87 (2007) 5309.] for the three-dimensional (3D) Ising model, we study in this work conformal invariance in three dimensions. We develop a procedure for treating the 3D conformal field theory. The 2D conformal field theory is generalized to be appropriate for three dimensions, within the framework of quaternionic coordinates with complex weights. The Virasoro algebra still works, but for each complex plane of quaternionic coordinates. The quaternionic geometric phases appear in quaternionic Hilbert space as a resu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.5527","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":""},"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":"2026-05-18T03:39:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"99VY2dUIBpXNkcRP/6Y0Ng/F3wWThtOQLQSPkCdq9VNJWHPvdzJ9GQl9K/nYkrrZEYPRj1vK7u7iEsZn5LaLDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T08:29:21.610833Z"},"content_sha256":"22954ca5d7eac9824bd2007db5a9e55d0ae0f5dc593ca9a025b87871b709ca59","schema_version":"1.0","event_id":"sha256:22954ca5d7eac9824bd2007db5a9e55d0ae0f5dc593ca9a025b87871b709ca59"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4TOEZFRPOONVTXG4U7SP26SS2N/bundle.json","state_url":"https://pith.science/pith/4TOEZFRPOONVTXG4U7SP26SS2N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4TOEZFRPOONVTXG4U7SP26SS2N/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":"2026-06-25T08:29:21Z","links":{"resolver":"https://pith.science/pith/4TOEZFRPOONVTXG4U7SP26SS2N","bundle":"https://pith.science/pith/4TOEZFRPOONVTXG4U7SP26SS2N/bundle.json","state":"https://pith.science/pith/4TOEZFRPOONVTXG4U7SP26SS2N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4TOEZFRPOONVTXG4U7SP26SS2N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:4TOEZFRPOONVTXG4U7SP26SS2N","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":"3d362cc0d994b86eb991ac54d6a419d5a38472e6287f6c76803da39c9f59a5bc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-10-23T01:10:39Z","title_canon_sha256":"0e826b6ee29bfbb586bc7d0222d3cf624be911067e6bb933408a257ca96ae519"},"schema_version":"1.0","source":{"id":"1110.5527","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.5527","created_at":"2026-05-18T03:39:14Z"},{"alias_kind":"arxiv_version","alias_value":"1110.5527v2","created_at":"2026-05-18T03:39:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.5527","created_at":"2026-05-18T03:39:14Z"},{"alias_kind":"pith_short_12","alias_value":"4TOEZFRPOONV","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"4TOEZFRPOONVTXG4","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"4TOEZFRP","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:22954ca5d7eac9824bd2007db5a9e55d0ae0f5dc593ca9a025b87871b709ca59","target":"graph","created_at":"2026-05-18T03:39:14Z","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":"Based on the quaternionic approach developed by one of us [Z.D. Zhang, Phil. Mag. 87 (2007) 5309.] for the three-dimensional (3D) Ising model, we study in this work conformal invariance in three dimensions. We develop a procedure for treating the 3D conformal field theory. The 2D conformal field theory is generalized to be appropriate for three dimensions, within the framework of quaternionic coordinates with complex weights. The Virasoro algebra still works, but for each complex plane of quaternionic coordinates. The quaternionic geometric phases appear in quaternionic Hilbert space as a resu","authors_text":"Norman H. March, Zhidong Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-10-23T01:10:39Z","title":"Conformal invariance in the three dimensional (3D) Ising model and quaternionic geometric phase in quaternionic Hilbert space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.5527","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":"sha256:586dbd80822b7d807ff9319548904c7a62b847a70e07a2e7d59861ac503da747","target":"record","created_at":"2026-05-18T03:39:14Z","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":"3d362cc0d994b86eb991ac54d6a419d5a38472e6287f6c76803da39c9f59a5bc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-10-23T01:10:39Z","title_canon_sha256":"0e826b6ee29bfbb586bc7d0222d3cf624be911067e6bb933408a257ca96ae519"},"schema_version":"1.0","source":{"id":"1110.5527","kind":"arxiv","version":2}},"canonical_sha256":"e4dc4c962f739b59dcdca7e4fd7a52d370f3f71fab8f0dc743da21102e8a2f39","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e4dc4c962f739b59dcdca7e4fd7a52d370f3f71fab8f0dc743da21102e8a2f39","first_computed_at":"2026-05-18T03:39:14.689126Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:39:14.689126Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Uvi/n53L4/64R9AQuj0Nr7ujacgg/D5EcGDxNkCdWIHb8akaUtbzpb8muI5BBWlwTY8BO4/WjD01NojfcwwDCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:39:14.689792Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.5527","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:586dbd80822b7d807ff9319548904c7a62b847a70e07a2e7d59861ac503da747","sha256:22954ca5d7eac9824bd2007db5a9e55d0ae0f5dc593ca9a025b87871b709ca59"],"state_sha256":"c54e63a87963be09ccdb182bf563a7f8ddd28dad6a73fc7219d38b79a17c63e1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RbL9a4yxQCAUk9wL/nQNwANgZ/C1BBUVgLsHeAO5q6dHZ4+AnOWPfU8Y9KEPPq2cLnZXkxy+0p5OgOlgK1u0Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T08:29:21.612750Z","bundle_sha256":"da18a8d339050286cb9278003684725a084eb7e47648631915d60d9d455ea7ea"}}