{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:SMTWC3ABNJ7FVIPH6CNF223WL4","short_pith_number":"pith:SMTWC3AB","canonical_record":{"source":{"id":"2606.08387","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2026-06-07T00:50:53Z","cross_cats_sorted":[],"title_canon_sha256":"0c7d6982eb58e0431afd547c71cc31104404de71e33e44a29fd97534dc06d152","abstract_canon_sha256":"5aeeb018f99d79c7f321c2102898238403897fdb9fa8bc9a42561cb4e54e92f1"},"schema_version":"1.0"},"canonical_sha256":"9327616c016a7e5aa1e7f09a5d6b765f25dcc74b266d079890e0f88fa00af803","source":{"kind":"arxiv","id":"2606.08387","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.08387","created_at":"2026-06-09T01:05:35Z"},{"alias_kind":"arxiv_version","alias_value":"2606.08387v1","created_at":"2026-06-09T01:05:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.08387","created_at":"2026-06-09T01:05:35Z"},{"alias_kind":"pith_short_12","alias_value":"SMTWC3ABNJ7F","created_at":"2026-06-09T01:05:35Z"},{"alias_kind":"pith_short_16","alias_value":"SMTWC3ABNJ7FVIPH","created_at":"2026-06-09T01:05:35Z"},{"alias_kind":"pith_short_8","alias_value":"SMTWC3AB","created_at":"2026-06-09T01:05:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:SMTWC3ABNJ7FVIPH6CNF223WL4","target":"record","payload":{"canonical_record":{"source":{"id":"2606.08387","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2026-06-07T00:50:53Z","cross_cats_sorted":[],"title_canon_sha256":"0c7d6982eb58e0431afd547c71cc31104404de71e33e44a29fd97534dc06d152","abstract_canon_sha256":"5aeeb018f99d79c7f321c2102898238403897fdb9fa8bc9a42561cb4e54e92f1"},"schema_version":"1.0"},"canonical_sha256":"9327616c016a7e5aa1e7f09a5d6b765f25dcc74b266d079890e0f88fa00af803","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T01:05:35.357218Z","signature_b64":"WvHcUpYwqeFz1e4P8FFjlZkOpvdTbrbM6IznQjd0sdxwRv1oe5S195gV5txHYfY9MThEJNb5yek9w81R9Z6vBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9327616c016a7e5aa1e7f09a5d6b765f25dcc74b266d079890e0f88fa00af803","last_reissued_at":"2026-06-09T01:05:35.356808Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T01:05:35.356808Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.08387","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":"2026-06-09T01:05:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oY4PdJeSGY2xCqWhBUz2JuutavrgK1GBVixt/1LR+itz51DGYY0Vv9yfKsW+/BUTuBz0c3k/C5VHLEmxUROuDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T18:14:58.927387Z"},"content_sha256":"f74368a6ed219a8ad91c9eccae1bf25c9f63ae00c7052a0d4cf149b9136761ce","schema_version":"1.0","event_id":"sha256:f74368a6ed219a8ad91c9eccae1bf25c9f63ae00c7052a0d4cf149b9136761ce"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:SMTWC3ABNJ7FVIPH6CNF223WL4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Notes on noninvertible quantum symmetries in two dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"E. Sharpe, P. Banerjee","submitted_at":"2026-06-07T00:50:53Z","abstract_excerpt":"In this note we describe a systematic procedure for computing partition functions of noninvertible Rep ($G$) quantum symmetry actions on two-dimensional nonabelian $G$ orbifolds. We apply this procedure to multiplicity-free examples for several nonabelian groups, and check explicitly in those examples that the partition function of a two-dimensional Rep ($G$)-gauged $G$ orbifold, for nonabelian $G$, matches that of the original theory, as expected on general principles. This fills a minor gap in the literature, making quantum symmetries in two-dimensional nonabelian orbifolds more concrete."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.08387","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.08387/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":"2026-06-09T01:05:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pBALCOUvFDB6QMgI+RlCmUYcCSkUWvQq4KGqIZJRR6VWcJHAaZDXVx31ocu0bMdvP11V5GkjHVYIPyxfC2whBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T18:14:58.927766Z"},"content_sha256":"ab55cd07ffcd6352a3bc7c2e835a058b305d840532de57407f18b3f3a8de2613","schema_version":"1.0","event_id":"sha256:ab55cd07ffcd6352a3bc7c2e835a058b305d840532de57407f18b3f3a8de2613"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SMTWC3ABNJ7FVIPH6CNF223WL4/bundle.json","state_url":"https://pith.science/pith/SMTWC3ABNJ7FVIPH6CNF223WL4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SMTWC3ABNJ7FVIPH6CNF223WL4/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":"2026-06-30T18:14:58Z","links":{"resolver":"https://pith.science/pith/SMTWC3ABNJ7FVIPH6CNF223WL4","bundle":"https://pith.science/pith/SMTWC3ABNJ7FVIPH6CNF223WL4/bundle.json","state":"https://pith.science/pith/SMTWC3ABNJ7FVIPH6CNF223WL4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SMTWC3ABNJ7FVIPH6CNF223WL4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:SMTWC3ABNJ7FVIPH6CNF223WL4","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":"5aeeb018f99d79c7f321c2102898238403897fdb9fa8bc9a42561cb4e54e92f1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2026-06-07T00:50:53Z","title_canon_sha256":"0c7d6982eb58e0431afd547c71cc31104404de71e33e44a29fd97534dc06d152"},"schema_version":"1.0","source":{"id":"2606.08387","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.08387","created_at":"2026-06-09T01:05:35Z"},{"alias_kind":"arxiv_version","alias_value":"2606.08387v1","created_at":"2026-06-09T01:05:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.08387","created_at":"2026-06-09T01:05:35Z"},{"alias_kind":"pith_short_12","alias_value":"SMTWC3ABNJ7F","created_at":"2026-06-09T01:05:35Z"},{"alias_kind":"pith_short_16","alias_value":"SMTWC3ABNJ7FVIPH","created_at":"2026-06-09T01:05:35Z"},{"alias_kind":"pith_short_8","alias_value":"SMTWC3AB","created_at":"2026-06-09T01:05:35Z"}],"graph_snapshots":[{"event_id":"sha256:ab55cd07ffcd6352a3bc7c2e835a058b305d840532de57407f18b3f3a8de2613","target":"graph","created_at":"2026-06-09T01:05:35Z","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/2606.08387/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this note we describe a systematic procedure for computing partition functions of noninvertible Rep ($G$) quantum symmetry actions on two-dimensional nonabelian $G$ orbifolds. We apply this procedure to multiplicity-free examples for several nonabelian groups, and check explicitly in those examples that the partition function of a two-dimensional Rep ($G$)-gauged $G$ orbifold, for nonabelian $G$, matches that of the original theory, as expected on general principles. This fills a minor gap in the literature, making quantum symmetries in two-dimensional nonabelian orbifolds more concrete.","authors_text":"E. Sharpe, P. Banerjee","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2026-06-07T00:50:53Z","title":"Notes on noninvertible quantum symmetries in two dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.08387","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:f74368a6ed219a8ad91c9eccae1bf25c9f63ae00c7052a0d4cf149b9136761ce","target":"record","created_at":"2026-06-09T01:05:35Z","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":"5aeeb018f99d79c7f321c2102898238403897fdb9fa8bc9a42561cb4e54e92f1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2026-06-07T00:50:53Z","title_canon_sha256":"0c7d6982eb58e0431afd547c71cc31104404de71e33e44a29fd97534dc06d152"},"schema_version":"1.0","source":{"id":"2606.08387","kind":"arxiv","version":1}},"canonical_sha256":"9327616c016a7e5aa1e7f09a5d6b765f25dcc74b266d079890e0f88fa00af803","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9327616c016a7e5aa1e7f09a5d6b765f25dcc74b266d079890e0f88fa00af803","first_computed_at":"2026-06-09T01:05:35.356808Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-09T01:05:35.356808Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WvHcUpYwqeFz1e4P8FFjlZkOpvdTbrbM6IznQjd0sdxwRv1oe5S195gV5txHYfY9MThEJNb5yek9w81R9Z6vBQ==","signature_status":"signed_v1","signed_at":"2026-06-09T01:05:35.357218Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.08387","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f74368a6ed219a8ad91c9eccae1bf25c9f63ae00c7052a0d4cf149b9136761ce","sha256:ab55cd07ffcd6352a3bc7c2e835a058b305d840532de57407f18b3f3a8de2613"],"state_sha256":"e6107a868ce03b23a1fe35ef1e8f53eeb993b20aad714b5f6414d3af4127b62c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qB9TlHj6hYCmWUWIiS3NhWxfclEAfZPuQKAr/P9iN7E5l2s0nh6u3Tj2JyyYWSduSgYkEjV+rBxbY5W6kXOOCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T18:14:58.930003Z","bundle_sha256":"9c28142aa61444e49783e9a9996edd63dcb3dcbf2aa9827c2e26393c7dd41c8d"}}