{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:ZPW4TUH2W643WIFJTDRKOO3EIG","short_pith_number":"pith:ZPW4TUH2","canonical_record":{"source":{"id":"1705.05293","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-05-15T15:28:06Z","cross_cats_sorted":[],"title_canon_sha256":"28ddc42c6299672e6b0b2ae4e1f7f89cd44c53322c7a13551475bebc218c541a","abstract_canon_sha256":"0dfb8edc044b50d6eb9590388033570bc6d7413d64d761062a6889a101e21be2"},"schema_version":"1.0"},"canonical_sha256":"cbedc9d0fab7b9bb20a998e2a73b6441bac13f16b61075713c172b11e271abfa","source":{"kind":"arxiv","id":"1705.05293","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.05293","created_at":"2026-05-18T00:01:53Z"},{"alias_kind":"arxiv_version","alias_value":"1705.05293v2","created_at":"2026-05-18T00:01:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.05293","created_at":"2026-05-18T00:01:53Z"},{"alias_kind":"pith_short_12","alias_value":"ZPW4TUH2W643","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZPW4TUH2W643WIFJ","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZPW4TUH2","created_at":"2026-05-18T12:31:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:ZPW4TUH2W643WIFJTDRKOO3EIG","target":"record","payload":{"canonical_record":{"source":{"id":"1705.05293","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-05-15T15:28:06Z","cross_cats_sorted":[],"title_canon_sha256":"28ddc42c6299672e6b0b2ae4e1f7f89cd44c53322c7a13551475bebc218c541a","abstract_canon_sha256":"0dfb8edc044b50d6eb9590388033570bc6d7413d64d761062a6889a101e21be2"},"schema_version":"1.0"},"canonical_sha256":"cbedc9d0fab7b9bb20a998e2a73b6441bac13f16b61075713c172b11e271abfa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:53.660822Z","signature_b64":"dj67nogjmY38hxP51EQf5UCO9PfItd3dRsieo6UkBZAQKhjzS5M/Ndnc2Q73Av+oSNOR8OOdcWejlaVXTZPkCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cbedc9d0fab7b9bb20a998e2a73b6441bac13f16b61075713c172b11e271abfa","last_reissued_at":"2026-05-18T00:01:53.660376Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:53.660376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.05293","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":"2026-05-18T00:01:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2eUFbcAjntCAqceOB94SZAlzspMhZ7r17ej1i6wV0GF/0TO22xJUeVPHTxA4Hd5LFkakmxPDUi7t0/GY9X/EAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T06:48:16.846627Z"},"content_sha256":"1f5cd0f2b8066997ffdc581b03e56fb41870cb36ceb39f8fa2f4a168b5e1a63e","schema_version":"1.0","event_id":"sha256:1f5cd0f2b8066997ffdc581b03e56fb41870cb36ceb39f8fa2f4a168b5e1a63e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:ZPW4TUH2W643WIFJTDRKOO3EIG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Classification of super-modular categories by rank","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"C\\'esar Galindo, Eric C. Rowell, Julia Yael Plavnik, Paul Bruillard, Siu-Hung Ng, Zhenghan Wang","submitted_at":"2017-05-15T15:28:06Z","abstract_excerpt":"We pursue a classification of low-rank super-modular categories parallel to that of modular categories. We classify all super-modular categories up to rank=$6$, and spin modular categories up to rank=$11$. In particular, we show that, up to fusion rules, there is exactly one non-split super-modular category of rank $2,4$ and $6$, namely $PSU(2)_{4k+2}$ for $k=0,1$ and $2$. This classification is facilitated by adapting and extending well-known constraints from modular categories to super-modular categories, such as Verlinde and Frobenius-Schur indicator formulae."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.05293","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":"2026-05-18T00:01:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"//XJS8U3hx4jGZQWTkv1xS2qnpn4+PcFUxxyPHiMQQy3W8SFCdFX8/BhPhPs0Z20sgycoq4blHU1s9UOOuH4AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T06:48:16.846973Z"},"content_sha256":"78f1025162928420ff66d46ca364cc74741df27d9d76d20f9ec01cb193f59019","schema_version":"1.0","event_id":"sha256:78f1025162928420ff66d46ca364cc74741df27d9d76d20f9ec01cb193f59019"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZPW4TUH2W643WIFJTDRKOO3EIG/bundle.json","state_url":"https://pith.science/pith/ZPW4TUH2W643WIFJTDRKOO3EIG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZPW4TUH2W643WIFJTDRKOO3EIG/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":"2026-06-02T06:48:16Z","links":{"resolver":"https://pith.science/pith/ZPW4TUH2W643WIFJTDRKOO3EIG","bundle":"https://pith.science/pith/ZPW4TUH2W643WIFJTDRKOO3EIG/bundle.json","state":"https://pith.science/pith/ZPW4TUH2W643WIFJTDRKOO3EIG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZPW4TUH2W643WIFJTDRKOO3EIG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ZPW4TUH2W643WIFJTDRKOO3EIG","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":"0dfb8edc044b50d6eb9590388033570bc6d7413d64d761062a6889a101e21be2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-05-15T15:28:06Z","title_canon_sha256":"28ddc42c6299672e6b0b2ae4e1f7f89cd44c53322c7a13551475bebc218c541a"},"schema_version":"1.0","source":{"id":"1705.05293","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.05293","created_at":"2026-05-18T00:01:53Z"},{"alias_kind":"arxiv_version","alias_value":"1705.05293v2","created_at":"2026-05-18T00:01:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.05293","created_at":"2026-05-18T00:01:53Z"},{"alias_kind":"pith_short_12","alias_value":"ZPW4TUH2W643","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZPW4TUH2W643WIFJ","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZPW4TUH2","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:78f1025162928420ff66d46ca364cc74741df27d9d76d20f9ec01cb193f59019","target":"graph","created_at":"2026-05-18T00:01:53Z","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":"We pursue a classification of low-rank super-modular categories parallel to that of modular categories. We classify all super-modular categories up to rank=$6$, and spin modular categories up to rank=$11$. In particular, we show that, up to fusion rules, there is exactly one non-split super-modular category of rank $2,4$ and $6$, namely $PSU(2)_{4k+2}$ for $k=0,1$ and $2$. This classification is facilitated by adapting and extending well-known constraints from modular categories to super-modular categories, such as Verlinde and Frobenius-Schur indicator formulae.","authors_text":"C\\'esar Galindo, Eric C. Rowell, Julia Yael Plavnik, Paul Bruillard, Siu-Hung Ng, Zhenghan Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-05-15T15:28:06Z","title":"Classification of super-modular categories by rank"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.05293","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":"sha256:1f5cd0f2b8066997ffdc581b03e56fb41870cb36ceb39f8fa2f4a168b5e1a63e","target":"record","created_at":"2026-05-18T00:01:53Z","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":"0dfb8edc044b50d6eb9590388033570bc6d7413d64d761062a6889a101e21be2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-05-15T15:28:06Z","title_canon_sha256":"28ddc42c6299672e6b0b2ae4e1f7f89cd44c53322c7a13551475bebc218c541a"},"schema_version":"1.0","source":{"id":"1705.05293","kind":"arxiv","version":2}},"canonical_sha256":"cbedc9d0fab7b9bb20a998e2a73b6441bac13f16b61075713c172b11e271abfa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cbedc9d0fab7b9bb20a998e2a73b6441bac13f16b61075713c172b11e271abfa","first_computed_at":"2026-05-18T00:01:53.660376Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:53.660376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dj67nogjmY38hxP51EQf5UCO9PfItd3dRsieo6UkBZAQKhjzS5M/Ndnc2Q73Av+oSNOR8OOdcWejlaVXTZPkCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:53.660822Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.05293","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f5cd0f2b8066997ffdc581b03e56fb41870cb36ceb39f8fa2f4a168b5e1a63e","sha256:78f1025162928420ff66d46ca364cc74741df27d9d76d20f9ec01cb193f59019"],"state_sha256":"49ed34d2948b4967e2744b901475b2f0892fdfefaa3a24e94d6fc4454624efc8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3PYmZAXXOI3nYr2Htnhe+cH6wMaCPBwjfU6svV+5BYV0ZhfRzVCIQarcDUBf1HebZKK0/uuSL+6dUHD6EbJiCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T06:48:16.849209Z","bundle_sha256":"c588170f40a8cb7fa15fc58b6e6948d2c5835c2f01b327a498de7d0e70772cfc"}}