{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:BG24OTEVDLHYBFGKHFSER5XJRW","short_pith_number":"pith:BG24OTEV","canonical_record":{"source":{"id":"1111.1362","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-11-06T01:04:47Z","cross_cats_sorted":[],"title_canon_sha256":"a2556a350c143cbb1fc8fa3ed94419d0be0a0e2af6de3520d8b690c6a5866009","abstract_canon_sha256":"3b4a8d433b3baab4ce538519c3b57fb3996e960fc4039a1663f1194508d76ddf"},"schema_version":"1.0"},"canonical_sha256":"09b5c74c951acf8094ca396448f6e98da5604d61a72f41b725b3f355f818d3fc","source":{"kind":"arxiv","id":"1111.1362","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.1362","created_at":"2026-05-18T04:09:26Z"},{"alias_kind":"arxiv_version","alias_value":"1111.1362v1","created_at":"2026-05-18T04:09:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.1362","created_at":"2026-05-18T04:09:26Z"},{"alias_kind":"pith_short_12","alias_value":"BG24OTEVDLHY","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"BG24OTEVDLHYBFGK","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"BG24OTEV","created_at":"2026-05-18T12:26:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:BG24OTEVDLHYBFGKHFSER5XJRW","target":"record","payload":{"canonical_record":{"source":{"id":"1111.1362","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-11-06T01:04:47Z","cross_cats_sorted":[],"title_canon_sha256":"a2556a350c143cbb1fc8fa3ed94419d0be0a0e2af6de3520d8b690c6a5866009","abstract_canon_sha256":"3b4a8d433b3baab4ce538519c3b57fb3996e960fc4039a1663f1194508d76ddf"},"schema_version":"1.0"},"canonical_sha256":"09b5c74c951acf8094ca396448f6e98da5604d61a72f41b725b3f355f818d3fc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:09:26.377152Z","signature_b64":"/Oa2vXAqiWYn2RG3/z9jzJZwI/nYXGgrcemtqNnk1Dcp76NxvGeLv9BZ7VPIpkV/AG+XTO5ZVLiaX6LG+1ssBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"09b5c74c951acf8094ca396448f6e98da5604d61a72f41b725b3f355f818d3fc","last_reissued_at":"2026-05-18T04:09:26.376459Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:09:26.376459Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.1362","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":"2026-05-18T04:09:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tDrIhEhf06dp681Go8t9p1TbpOkr0apTrtqRYDuEJmb5GzOLoHxkd1vU8RS72XL4UX+IxmcHB1HVYvnBScgyAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T17:27:46.910367Z"},"content_sha256":"5660874a3227afb67c52c457b2e04e1674a289527ee32f9a76dfaec8aa065579","schema_version":"1.0","event_id":"sha256:5660874a3227afb67c52c457b2e04e1674a289527ee32f9a76dfaec8aa065579"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:BG24OTEVDLHYBFGKHFSER5XJRW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Subfactors, Planar Algebras and Rotations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Michael Burns","submitted_at":"2011-11-06T01:04:47Z","abstract_excerpt":"Growing out of the initial connections between subfactors and knot theory that gave rise to the Jones polynomial, Jones' axiomatization of the standard invariant of an extremal finite index $II_1$ subfactor as a spherical $C^*$-planar algebra, presented in arXiv:math.QA/9909027, is the most elegant and powerful description available. We make the natural extension of this axiomatization to the case of finite index subfactors of arbitrary type. We also provide the first steps toward a limited planar structure in the infinite index case. The central role of rotations, which provide the main non-t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.1362","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":"2026-05-18T04:09:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qXrW5dO5c1iYqwaGVAAV8ZGC2A5/xm8QjTFjYB9vIy+CLPYYjIR/VDvHPuEtd0P21W9V2FGwGaX54O3D3cD6Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T17:27:46.910841Z"},"content_sha256":"f710bf199a98f0ae1f7a20f1667a3cac700b084f5cd66f35d1e36005a0189b20","schema_version":"1.0","event_id":"sha256:f710bf199a98f0ae1f7a20f1667a3cac700b084f5cd66f35d1e36005a0189b20"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BG24OTEVDLHYBFGKHFSER5XJRW/bundle.json","state_url":"https://pith.science/pith/BG24OTEVDLHYBFGKHFSER5XJRW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BG24OTEVDLHYBFGKHFSER5XJRW/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":"2026-08-16T17:27:46Z","links":{"resolver":"https://pith.science/pith/BG24OTEVDLHYBFGKHFSER5XJRW","bundle":"https://pith.science/pith/BG24OTEVDLHYBFGKHFSER5XJRW/bundle.json","state":"https://pith.science/pith/BG24OTEVDLHYBFGKHFSER5XJRW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BG24OTEVDLHYBFGKHFSER5XJRW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:BG24OTEVDLHYBFGKHFSER5XJRW","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":"3b4a8d433b3baab4ce538519c3b57fb3996e960fc4039a1663f1194508d76ddf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-11-06T01:04:47Z","title_canon_sha256":"a2556a350c143cbb1fc8fa3ed94419d0be0a0e2af6de3520d8b690c6a5866009"},"schema_version":"1.0","source":{"id":"1111.1362","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.1362","created_at":"2026-05-18T04:09:26Z"},{"alias_kind":"arxiv_version","alias_value":"1111.1362v1","created_at":"2026-05-18T04:09:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.1362","created_at":"2026-05-18T04:09:26Z"},{"alias_kind":"pith_short_12","alias_value":"BG24OTEVDLHY","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"BG24OTEVDLHYBFGK","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"BG24OTEV","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:f710bf199a98f0ae1f7a20f1667a3cac700b084f5cd66f35d1e36005a0189b20","target":"graph","created_at":"2026-05-18T04:09:26Z","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":"Growing out of the initial connections between subfactors and knot theory that gave rise to the Jones polynomial, Jones' axiomatization of the standard invariant of an extremal finite index $II_1$ subfactor as a spherical $C^*$-planar algebra, presented in arXiv:math.QA/9909027, is the most elegant and powerful description available. We make the natural extension of this axiomatization to the case of finite index subfactors of arbitrary type. We also provide the first steps toward a limited planar structure in the infinite index case. The central role of rotations, which provide the main non-t","authors_text":"Michael Burns","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-11-06T01:04:47Z","title":"Subfactors, Planar Algebras and Rotations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.1362","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":"sha256:5660874a3227afb67c52c457b2e04e1674a289527ee32f9a76dfaec8aa065579","target":"record","created_at":"2026-05-18T04:09:26Z","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":"3b4a8d433b3baab4ce538519c3b57fb3996e960fc4039a1663f1194508d76ddf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-11-06T01:04:47Z","title_canon_sha256":"a2556a350c143cbb1fc8fa3ed94419d0be0a0e2af6de3520d8b690c6a5866009"},"schema_version":"1.0","source":{"id":"1111.1362","kind":"arxiv","version":1}},"canonical_sha256":"09b5c74c951acf8094ca396448f6e98da5604d61a72f41b725b3f355f818d3fc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"09b5c74c951acf8094ca396448f6e98da5604d61a72f41b725b3f355f818d3fc","first_computed_at":"2026-05-18T04:09:26.376459Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:09:26.376459Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/Oa2vXAqiWYn2RG3/z9jzJZwI/nYXGgrcemtqNnk1Dcp76NxvGeLv9BZ7VPIpkV/AG+XTO5ZVLiaX6LG+1ssBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:09:26.377152Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.1362","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5660874a3227afb67c52c457b2e04e1674a289527ee32f9a76dfaec8aa065579","sha256:f710bf199a98f0ae1f7a20f1667a3cac700b084f5cd66f35d1e36005a0189b20"],"state_sha256":"bda758259c8c7f1fb7a37e759000e0f78082aebfe6fce856e827d5ba92d88f69"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mhsFtd/SnZTQVP+NwAyNMVZwfMLjWn0i0R6SxVV7l3JTmcD7tKyF/su9WugUjs/LidyQnlmI2ZlatYZg59DgAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T17:27:46.917167Z","bundle_sha256":"7ca18712d9380a01d565d53b0f18a2da274cb6bc299bd5f8f0e500cdddcaffcd"}}