{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:5RZSJKGZZUZB22LOCVMGBZVHD4","short_pith_number":"pith:5RZSJKGZ","canonical_record":{"source":{"id":"1307.5890","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-07-22T21:14:18Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"5d6343a7095fd7a78f6f328688ce0cbfa3584ac6fa292669ca82e75231f9b5a1","abstract_canon_sha256":"50f6f2c13057f954c9e2e575589563c264cd820a9a21bba01dd73e4853af7c0d"},"schema_version":"1.0"},"canonical_sha256":"ec7324a8d9cd321d696e155860e6a71f0e044d6763e59c14e4e874461f45e7e7","source":{"kind":"arxiv","id":"1307.5890","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.5890","created_at":"2026-05-18T03:17:45Z"},{"alias_kind":"arxiv_version","alias_value":"1307.5890v1","created_at":"2026-05-18T03:17:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.5890","created_at":"2026-05-18T03:17:45Z"},{"alias_kind":"pith_short_12","alias_value":"5RZSJKGZZUZB","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"5RZSJKGZZUZB22LO","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"5RZSJKGZ","created_at":"2026-05-18T12:27:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:5RZSJKGZZUZB22LOCVMGBZVHD4","target":"record","payload":{"canonical_record":{"source":{"id":"1307.5890","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-07-22T21:14:18Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"5d6343a7095fd7a78f6f328688ce0cbfa3584ac6fa292669ca82e75231f9b5a1","abstract_canon_sha256":"50f6f2c13057f954c9e2e575589563c264cd820a9a21bba01dd73e4853af7c0d"},"schema_version":"1.0"},"canonical_sha256":"ec7324a8d9cd321d696e155860e6a71f0e044d6763e59c14e4e874461f45e7e7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:17:45.867466Z","signature_b64":"ZQSMtGuJrZv5OhF7GAKTgkNAa0cIxWFLu6tTU6NzXMScLsOEW++mh4TWCvc5SZaKSHUykXLl0bdhO502vOefDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ec7324a8d9cd321d696e155860e6a71f0e044d6763e59c14e4e874461f45e7e7","last_reissued_at":"2026-05-18T03:17:45.866940Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:17:45.866940Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.5890","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":"2026-05-18T03:17:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"09QNBYZAPt2HuRCLYqzxSp9zcL6whO09GzxC+AW6DA3uAyCJREv6oBNpemvfoqGFHint9z08nK5DVDyVdAN+AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T02:55:54.578907Z"},"content_sha256":"e7577abe0ca41566173b34bd427e5c815d01d9eb3ac45372b9eb20c8ad4d2346","schema_version":"1.0","event_id":"sha256:e7577abe0ca41566173b34bd427e5c815d01d9eb3ac45372b9eb20c8ad4d2346"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:5RZSJKGZZUZB22LOCVMGBZVHD4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Chirality and principal graph obstructions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.OA","authors_text":"David Penneys","submitted_at":"2013-07-22T21:14:18Z","abstract_excerpt":"Determining which bipartite graphs can be principal graphs of subfactors is an important and difficult question in subfactor theory. Using only planar algebra techniques, we prove a triple point obstruction which generalizes all known initial triple point obstructions to possible principal graphs. We also prove a similar quadruple point obstruction with the same technique. Using our obstructions, we eliminate some infinite families of possible principal graphs with initial triple and quadruple points which were a major hurdle in extending subfactor classification results above index 5."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.5890","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":"2026-05-18T03:17:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eRs3L6+B4uBNlmNsamsyeyBwBFXUDm8nFVl09Ao4yNSwbhFP/kbk99pDNhuTk02UVO0Hbu/32O9v608F4Wk9BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T02:55:54.579246Z"},"content_sha256":"82954d67d833c81255434612e3b71baa0cd9ce7d4aebaf8fbf693cca32492095","schema_version":"1.0","event_id":"sha256:82954d67d833c81255434612e3b71baa0cd9ce7d4aebaf8fbf693cca32492095"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5RZSJKGZZUZB22LOCVMGBZVHD4/bundle.json","state_url":"https://pith.science/pith/5RZSJKGZZUZB22LOCVMGBZVHD4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5RZSJKGZZUZB22LOCVMGBZVHD4/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":"2026-06-03T02:55:54Z","links":{"resolver":"https://pith.science/pith/5RZSJKGZZUZB22LOCVMGBZVHD4","bundle":"https://pith.science/pith/5RZSJKGZZUZB22LOCVMGBZVHD4/bundle.json","state":"https://pith.science/pith/5RZSJKGZZUZB22LOCVMGBZVHD4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5RZSJKGZZUZB22LOCVMGBZVHD4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:5RZSJKGZZUZB22LOCVMGBZVHD4","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":"50f6f2c13057f954c9e2e575589563c264cd820a9a21bba01dd73e4853af7c0d","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-07-22T21:14:18Z","title_canon_sha256":"5d6343a7095fd7a78f6f328688ce0cbfa3584ac6fa292669ca82e75231f9b5a1"},"schema_version":"1.0","source":{"id":"1307.5890","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.5890","created_at":"2026-05-18T03:17:45Z"},{"alias_kind":"arxiv_version","alias_value":"1307.5890v1","created_at":"2026-05-18T03:17:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.5890","created_at":"2026-05-18T03:17:45Z"},{"alias_kind":"pith_short_12","alias_value":"5RZSJKGZZUZB","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"5RZSJKGZZUZB22LO","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"5RZSJKGZ","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:82954d67d833c81255434612e3b71baa0cd9ce7d4aebaf8fbf693cca32492095","target":"graph","created_at":"2026-05-18T03:17:45Z","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":"Determining which bipartite graphs can be principal graphs of subfactors is an important and difficult question in subfactor theory. Using only planar algebra techniques, we prove a triple point obstruction which generalizes all known initial triple point obstructions to possible principal graphs. We also prove a similar quadruple point obstruction with the same technique. Using our obstructions, we eliminate some infinite families of possible principal graphs with initial triple and quadruple points which were a major hurdle in extending subfactor classification results above index 5.","authors_text":"David Penneys","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-07-22T21:14:18Z","title":"Chirality and principal graph obstructions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.5890","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:e7577abe0ca41566173b34bd427e5c815d01d9eb3ac45372b9eb20c8ad4d2346","target":"record","created_at":"2026-05-18T03:17:45Z","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":"50f6f2c13057f954c9e2e575589563c264cd820a9a21bba01dd73e4853af7c0d","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-07-22T21:14:18Z","title_canon_sha256":"5d6343a7095fd7a78f6f328688ce0cbfa3584ac6fa292669ca82e75231f9b5a1"},"schema_version":"1.0","source":{"id":"1307.5890","kind":"arxiv","version":1}},"canonical_sha256":"ec7324a8d9cd321d696e155860e6a71f0e044d6763e59c14e4e874461f45e7e7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ec7324a8d9cd321d696e155860e6a71f0e044d6763e59c14e4e874461f45e7e7","first_computed_at":"2026-05-18T03:17:45.866940Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:17:45.866940Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZQSMtGuJrZv5OhF7GAKTgkNAa0cIxWFLu6tTU6NzXMScLsOEW++mh4TWCvc5SZaKSHUykXLl0bdhO502vOefDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:17:45.867466Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.5890","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e7577abe0ca41566173b34bd427e5c815d01d9eb3ac45372b9eb20c8ad4d2346","sha256:82954d67d833c81255434612e3b71baa0cd9ce7d4aebaf8fbf693cca32492095"],"state_sha256":"706759e290e4db5e84e25c6f44607ee02bf70a45f2f77eb71b7506cb924dac81"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X9CnAdo4yp8gbbCgfz3pdMjhh0XaJ8mUvq0W/GaUwE2AMaYZjev1gvy4hhjDn2gHKO6Zcs/ovFEfjztJd6OnAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T02:55:54.581150Z","bundle_sha256":"ca042349b5ce5fbcfd64caa84b9e03042b7b96ada98c3eb4ed12217b90ee35f9"}}