{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1998:3C2AQC42W5I5XMBUAMG2MRWFMK","short_pith_number":"pith:3C2AQC42","canonical_record":{"source":{"id":"hep-th/9812110","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1998-12-14T14:26:12Z","cross_cats_sorted":[],"title_canon_sha256":"07dd09296532685d269ea438966659def12513f49767ee863481749a5bcfe99c","abstract_canon_sha256":"78b0e79695c50a8e5dded2d5fd89f5f1714fce7c9f11bc67a5d1d0c2f6c8a2d3"},"schema_version":"1.0"},"canonical_sha256":"d8b4080b9ab751dbb034030da646c5628c4d872a2d32cb04549a1bd63897f775","source":{"kind":"arxiv","id":"hep-th/9812110","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9812110","created_at":"2026-07-04T16:10:06Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9812110v2","created_at":"2026-07-04T16:10:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9812110","created_at":"2026-07-04T16:10:06Z"},{"alias_kind":"pith_short_12","alias_value":"3C2AQC42W5I5","created_at":"2026-07-04T16:10:06Z"},{"alias_kind":"pith_short_16","alias_value":"3C2AQC42W5I5XMBU","created_at":"2026-07-04T16:10:06Z"},{"alias_kind":"pith_short_8","alias_value":"3C2AQC42","created_at":"2026-07-04T16:10:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1998:3C2AQC42W5I5XMBUAMG2MRWFMK","target":"record","payload":{"canonical_record":{"source":{"id":"hep-th/9812110","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1998-12-14T14:26:12Z","cross_cats_sorted":[],"title_canon_sha256":"07dd09296532685d269ea438966659def12513f49767ee863481749a5bcfe99c","abstract_canon_sha256":"78b0e79695c50a8e5dded2d5fd89f5f1714fce7c9f11bc67a5d1d0c2f6c8a2d3"},"schema_version":"1.0"},"canonical_sha256":"d8b4080b9ab751dbb034030da646c5628c4d872a2d32cb04549a1bd63897f775","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:10:06.310177Z","signature_b64":"urbQsET9p8fcAu4MTu8nvhxyWBuKDb7fl1+S75y5N/GK1XtHjAKPyxZmzcI9pthLaqkt3Z4fKrqV/kmso5REBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d8b4080b9ab751dbb034030da646c5628c4d872a2d32cb04549a1bd63897f775","last_reissued_at":"2026-07-04T16:10:06.309756Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:10:06.309756Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"hep-th/9812110","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":"2026-07-04T16:10:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TF5htKbEjTakwBVI0ZEemwQ2dtyA2yHG3r/slcn7q3FK2uQ+T7ebaxh/XbXjIX/hzlCtDr7aa9ImpIU26fQBDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T05:33:54.142687Z"},"content_sha256":"f0ab6f039c0ed1b3cd7056084b5b2e2302b1e53b15ca704daf1a7eec54c84e54","schema_version":"1.0","event_id":"sha256:f0ab6f039c0ed1b3cd7056084b5b2e2302b1e53b15ca704daf1a7eec54c84e54"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1998:3C2AQC42W5I5XMBUAMG2MRWFMK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Modular Invariants, Graphs and $\\alpha$-Induction for Nets of Subfactors. III","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"D.E. Evans, J. B\\\"ockenhauer","submitted_at":"1998-12-14T14:26:12Z","abstract_excerpt":"In this paper we further develop the theory of $\\alpha$-induction for nets of subfactors, in particular in view of the system of sectors obtained by mixing the two kinds of induction arising from the two choices of braiding. We construct a relative braiding between the irreducible subsectors of the two ``chiral'' induced systems, providing a proper braiding on their intersection. We also express the principal and dual principal graphs of the local subfactors in terms of the induced sector systems. This extended theory is again applied to conformal or orbifold embeddings of SU(n) WZW models. A "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9812110","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/hep-th/9812110/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T16:10:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Nr1iTisTbWOqlNfrV7KKOhQLq9vzVcyWhBsOffl+f3TxcnMPuEfaXpzeYm7/faG68+6MZKfb5wUhi839SzA4AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T05:33:54.143216Z"},"content_sha256":"c88bef87c4445ec10685a18580fd333dca7c0c766d9ac1ba1b5fafb4e2cccf1f","schema_version":"1.0","event_id":"sha256:c88bef87c4445ec10685a18580fd333dca7c0c766d9ac1ba1b5fafb4e2cccf1f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3C2AQC42W5I5XMBUAMG2MRWFMK/bundle.json","state_url":"https://pith.science/pith/3C2AQC42W5I5XMBUAMG2MRWFMK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3C2AQC42W5I5XMBUAMG2MRWFMK/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":"2026-08-12T05:33:54Z","links":{"resolver":"https://pith.science/pith/3C2AQC42W5I5XMBUAMG2MRWFMK","bundle":"https://pith.science/pith/3C2AQC42W5I5XMBUAMG2MRWFMK/bundle.json","state":"https://pith.science/pith/3C2AQC42W5I5XMBUAMG2MRWFMK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3C2AQC42W5I5XMBUAMG2MRWFMK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1998:3C2AQC42W5I5XMBUAMG2MRWFMK","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":"78b0e79695c50a8e5dded2d5fd89f5f1714fce7c9f11bc67a5d1d0c2f6c8a2d3","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"1998-12-14T14:26:12Z","title_canon_sha256":"07dd09296532685d269ea438966659def12513f49767ee863481749a5bcfe99c"},"schema_version":"1.0","source":{"id":"hep-th/9812110","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9812110","created_at":"2026-07-04T16:10:06Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9812110v2","created_at":"2026-07-04T16:10:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9812110","created_at":"2026-07-04T16:10:06Z"},{"alias_kind":"pith_short_12","alias_value":"3C2AQC42W5I5","created_at":"2026-07-04T16:10:06Z"},{"alias_kind":"pith_short_16","alias_value":"3C2AQC42W5I5XMBU","created_at":"2026-07-04T16:10:06Z"},{"alias_kind":"pith_short_8","alias_value":"3C2AQC42","created_at":"2026-07-04T16:10:06Z"}],"graph_snapshots":[{"event_id":"sha256:c88bef87c4445ec10685a18580fd333dca7c0c766d9ac1ba1b5fafb4e2cccf1f","target":"graph","created_at":"2026-07-04T16:10:06Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/hep-th/9812110/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we further develop the theory of $\\alpha$-induction for nets of subfactors, in particular in view of the system of sectors obtained by mixing the two kinds of induction arising from the two choices of braiding. We construct a relative braiding between the irreducible subsectors of the two ``chiral'' induced systems, providing a proper braiding on their intersection. We also express the principal and dual principal graphs of the local subfactors in terms of the induced sector systems. This extended theory is again applied to conformal or orbifold embeddings of SU(n) WZW models. A ","authors_text":"D.E. Evans, J. B\\\"ockenhauer","cross_cats":[],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"1998-12-14T14:26:12Z","title":"Modular Invariants, Graphs and $\\alpha$-Induction for Nets of Subfactors. III"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9812110","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:f0ab6f039c0ed1b3cd7056084b5b2e2302b1e53b15ca704daf1a7eec54c84e54","target":"record","created_at":"2026-07-04T16:10:06Z","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":"78b0e79695c50a8e5dded2d5fd89f5f1714fce7c9f11bc67a5d1d0c2f6c8a2d3","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"1998-12-14T14:26:12Z","title_canon_sha256":"07dd09296532685d269ea438966659def12513f49767ee863481749a5bcfe99c"},"schema_version":"1.0","source":{"id":"hep-th/9812110","kind":"arxiv","version":2}},"canonical_sha256":"d8b4080b9ab751dbb034030da646c5628c4d872a2d32cb04549a1bd63897f775","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d8b4080b9ab751dbb034030da646c5628c4d872a2d32cb04549a1bd63897f775","first_computed_at":"2026-07-04T16:10:06.309756Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:10:06.309756Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"urbQsET9p8fcAu4MTu8nvhxyWBuKDb7fl1+S75y5N/GK1XtHjAKPyxZmzcI9pthLaqkt3Z4fKrqV/kmso5REBQ==","signature_status":"signed_v1","signed_at":"2026-07-04T16:10:06.310177Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/9812110","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f0ab6f039c0ed1b3cd7056084b5b2e2302b1e53b15ca704daf1a7eec54c84e54","sha256:c88bef87c4445ec10685a18580fd333dca7c0c766d9ac1ba1b5fafb4e2cccf1f"],"state_sha256":"7a3fd38efe76508cde80e488a5d39e0ffb735ae9d5459511980b404bc1638253"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/15fWFd9HllT8Nz0SIEqcxQgfo6BCDNZrmEPOfzPbOiHyvf+hZ0WlksbRvbpgaA8mwVZBdDJyhbLq+Dd+d3/Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T05:33:54.147152Z","bundle_sha256":"fb32f16cfb2bce34f2f733584d1b906e563b848528dd5073b7e78ebbfc855023"}}