{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:IAPJUA5IB5B5X3RQOB5LCYDAJA","short_pith_number":"pith:IAPJUA5I","canonical_record":{"source":{"id":"1704.02041","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-04-06T23:00:56Z","cross_cats_sorted":[],"title_canon_sha256":"999680c53be60772eef546502475afa71539a108c239a0045a484196d7c70875","abstract_canon_sha256":"f60eb17425e58459e9ddae6987cd059aeb6386ed442c31425b5ff989646378bb"},"schema_version":"1.0"},"canonical_sha256":"401e9a03a80f43dbee30707ab16060481d1bae624feeefde5df368601e060953","source":{"kind":"arxiv","id":"1704.02041","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.02041","created_at":"2026-05-18T00:09:56Z"},{"alias_kind":"arxiv_version","alias_value":"1704.02041v2","created_at":"2026-05-18T00:09:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.02041","created_at":"2026-05-18T00:09:56Z"},{"alias_kind":"pith_short_12","alias_value":"IAPJUA5IB5B5","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"IAPJUA5IB5B5X3RQ","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"IAPJUA5I","created_at":"2026-05-18T12:31:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:IAPJUA5IB5B5X3RQOB5LCYDAJA","target":"record","payload":{"canonical_record":{"source":{"id":"1704.02041","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-04-06T23:00:56Z","cross_cats_sorted":[],"title_canon_sha256":"999680c53be60772eef546502475afa71539a108c239a0045a484196d7c70875","abstract_canon_sha256":"f60eb17425e58459e9ddae6987cd059aeb6386ed442c31425b5ff989646378bb"},"schema_version":"1.0"},"canonical_sha256":"401e9a03a80f43dbee30707ab16060481d1bae624feeefde5df368601e060953","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:56.083720Z","signature_b64":"uRI9DAPwQbies9iRdhiX53vKxQElafv0gA07OsqUGjXquXpBu3oAUXk4e2ep12765+eThG81xSTpzDLwnT8kCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"401e9a03a80f43dbee30707ab16060481d1bae624feeefde5df368601e060953","last_reissued_at":"2026-05-18T00:09:56.083074Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:56.083074Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.02041","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":"2026-05-18T00:09:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"531DHxnb2K8nUK+MS4j1d2LFZiV//2lqa+LBxRNtUCqqadldaxO7IXfQUWY1OkwauBi5FW72m2UtyH1zNEV6Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T17:04:24.027602Z"},"content_sha256":"79ed2edfdc30645704fc9b6b36c59ad8e4417d5f57718ccb95979eca6007b433","schema_version":"1.0","event_id":"sha256:79ed2edfdc30645704fc9b6b36c59ad8e4417d5f57718ccb95979eca6007b433"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:IAPJUA5IB5B5X3RQOB5LCYDAJA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Congruence Subgroups and Super-Modular Categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Eric C. Rowell, Parsa Bonderson, Qing Zhang, Zhenghan Wang","submitted_at":"2017-04-06T23:00:56Z","abstract_excerpt":"A super-modular category is a unitary pre-modular category with M\\\"uger center equivalent to the symmetric unitary category of super-vector spaces. Super-modular categories are important alternatives to modular categories as any unitary pre-modular category is the equivariantization of a either a modular or super-modular category. Physically, super-modular categories describe universal properties of quasiparticles in fermionic topological phases of matter. In general one does not have a representation of the modular group $\\mathrm{SL}(2,\\mathbb{Z})$ associated to a super-modular category, but "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.02041","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":"2026-05-18T00:09:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XU4rh2jrkRn1l206KNSgVbsyYmSaGi8UdXoIm9TtaIVG7cI2KjiKzykbHtq9TDSYCx4PZ6gIog37VakVsGm1Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T17:04:24.027968Z"},"content_sha256":"7da4741a8a0cd7919fc31f7c83d4930394b8c9deb00ee3deaf37d44f9e91b7cf","schema_version":"1.0","event_id":"sha256:7da4741a8a0cd7919fc31f7c83d4930394b8c9deb00ee3deaf37d44f9e91b7cf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IAPJUA5IB5B5X3RQOB5LCYDAJA/bundle.json","state_url":"https://pith.science/pith/IAPJUA5IB5B5X3RQOB5LCYDAJA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IAPJUA5IB5B5X3RQOB5LCYDAJA/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":"2026-05-30T17:04:24Z","links":{"resolver":"https://pith.science/pith/IAPJUA5IB5B5X3RQOB5LCYDAJA","bundle":"https://pith.science/pith/IAPJUA5IB5B5X3RQOB5LCYDAJA/bundle.json","state":"https://pith.science/pith/IAPJUA5IB5B5X3RQOB5LCYDAJA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IAPJUA5IB5B5X3RQOB5LCYDAJA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:IAPJUA5IB5B5X3RQOB5LCYDAJA","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":"f60eb17425e58459e9ddae6987cd059aeb6386ed442c31425b5ff989646378bb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-04-06T23:00:56Z","title_canon_sha256":"999680c53be60772eef546502475afa71539a108c239a0045a484196d7c70875"},"schema_version":"1.0","source":{"id":"1704.02041","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.02041","created_at":"2026-05-18T00:09:56Z"},{"alias_kind":"arxiv_version","alias_value":"1704.02041v2","created_at":"2026-05-18T00:09:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.02041","created_at":"2026-05-18T00:09:56Z"},{"alias_kind":"pith_short_12","alias_value":"IAPJUA5IB5B5","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"IAPJUA5IB5B5X3RQ","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"IAPJUA5I","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:7da4741a8a0cd7919fc31f7c83d4930394b8c9deb00ee3deaf37d44f9e91b7cf","target":"graph","created_at":"2026-05-18T00:09:56Z","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":"A super-modular category is a unitary pre-modular category with M\\\"uger center equivalent to the symmetric unitary category of super-vector spaces. Super-modular categories are important alternatives to modular categories as any unitary pre-modular category is the equivariantization of a either a modular or super-modular category. Physically, super-modular categories describe universal properties of quasiparticles in fermionic topological phases of matter. In general one does not have a representation of the modular group $\\mathrm{SL}(2,\\mathbb{Z})$ associated to a super-modular category, but ","authors_text":"Eric C. Rowell, Parsa Bonderson, Qing Zhang, Zhenghan Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-04-06T23:00:56Z","title":"Congruence Subgroups and Super-Modular Categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.02041","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":"sha256:79ed2edfdc30645704fc9b6b36c59ad8e4417d5f57718ccb95979eca6007b433","target":"record","created_at":"2026-05-18T00:09:56Z","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":"f60eb17425e58459e9ddae6987cd059aeb6386ed442c31425b5ff989646378bb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-04-06T23:00:56Z","title_canon_sha256":"999680c53be60772eef546502475afa71539a108c239a0045a484196d7c70875"},"schema_version":"1.0","source":{"id":"1704.02041","kind":"arxiv","version":2}},"canonical_sha256":"401e9a03a80f43dbee30707ab16060481d1bae624feeefde5df368601e060953","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"401e9a03a80f43dbee30707ab16060481d1bae624feeefde5df368601e060953","first_computed_at":"2026-05-18T00:09:56.083074Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:09:56.083074Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uRI9DAPwQbies9iRdhiX53vKxQElafv0gA07OsqUGjXquXpBu3oAUXk4e2ep12765+eThG81xSTpzDLwnT8kCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:09:56.083720Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.02041","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:79ed2edfdc30645704fc9b6b36c59ad8e4417d5f57718ccb95979eca6007b433","sha256:7da4741a8a0cd7919fc31f7c83d4930394b8c9deb00ee3deaf37d44f9e91b7cf"],"state_sha256":"bc4889e7c1201d170d27e2c0f28241a82445942e25e6b33a715eb49fa357b1bf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k23wNWUzHmaREHY8wRAtMe0gDnwFEm/gkVvo3HIjMx4Dm2asX2KjY3w9G1tZPSxrgC8HyCtT1YWc+8vV4ZCkBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T17:04:24.031531Z","bundle_sha256":"8789284dcd3176c23851aae8fa4cd53986bc34b5f336f9e9cc2053cb415e3a11"}}