{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:AGXG6XG44GK6PWSZNJ65XWIEUG","short_pith_number":"pith:AGXG6XG4","canonical_record":{"source":{"id":"1603.09294","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-03-30T17:58:15Z","cross_cats_sorted":[],"title_canon_sha256":"f3591e5b4461b540c7b6526eb2f037b85cdd6aa2c2312193b523a92dc8ba6488","abstract_canon_sha256":"c1cfaf07730638058a90fde0e530dda86846ee1481f36c40614e7c09a07d4b39"},"schema_version":"1.0"},"canonical_sha256":"01ae6f5cdce195e7da596a7ddbd904a19ad5d2daffdcd7f6fef90b2f73cfa813","source":{"kind":"arxiv","id":"1603.09294","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.09294","created_at":"2026-05-18T00:44:01Z"},{"alias_kind":"arxiv_version","alias_value":"1603.09294v3","created_at":"2026-05-18T00:44:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.09294","created_at":"2026-05-18T00:44:01Z"},{"alias_kind":"pith_short_12","alias_value":"AGXG6XG44GK6","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"AGXG6XG44GK6PWSZ","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"AGXG6XG4","created_at":"2026-05-18T12:30:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:AGXG6XG44GK6PWSZNJ65XWIEUG","target":"record","payload":{"canonical_record":{"source":{"id":"1603.09294","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-03-30T17:58:15Z","cross_cats_sorted":[],"title_canon_sha256":"f3591e5b4461b540c7b6526eb2f037b85cdd6aa2c2312193b523a92dc8ba6488","abstract_canon_sha256":"c1cfaf07730638058a90fde0e530dda86846ee1481f36c40614e7c09a07d4b39"},"schema_version":"1.0"},"canonical_sha256":"01ae6f5cdce195e7da596a7ddbd904a19ad5d2daffdcd7f6fef90b2f73cfa813","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:01.295120Z","signature_b64":"SAwlXh0XRfPDqP7j11a/Qc1H82k7V3F3uNavxCD0wOAVoMvMBN0B6IfhD/35sfZLnaY1W6i8lHQHynjQfvcIDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"01ae6f5cdce195e7da596a7ddbd904a19ad5d2daffdcd7f6fef90b2f73cfa813","last_reissued_at":"2026-05-18T00:44:01.294652Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:01.294652Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.09294","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:44:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FT5CExcLXLyVids6zvLXoTVjaYrBFVQ0lxFJtz6BS/gQnIrMDwuoDVwhMX3KzZK5ReOyccdz3vYqdtlpI7sRDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T10:03:28.701136Z"},"content_sha256":"57ac494eb119ea4c20a00910f132f1e15cd432d9d9e26ef45d9d6afcc0813931","schema_version":"1.0","event_id":"sha256:57ac494eb119ea4c20a00910f132f1e15cd432d9d9e26ef45d9d6afcc0813931"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:AGXG6XG44GK6PWSZNJ65XWIEUG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fermionic Modular Categories and the 16-fold Way","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Cesar Galindo, Eric C. Rowell, Julia Yael Plavnik, Paul Bruillard, Siu-Hung Ng, Tobias Hagge, Zhenghan Wang","submitted_at":"2016-03-30T17:58:15Z","abstract_excerpt":"We study spin and super-modular categories systematically as inspired by fermionic topological phases of matter, which are always fermion parity enriched and modelled by spin TQFTs at low energy. We formulate a $16$-fold way conjecture for the minimal modular extensions of super-modular categories to spin modular categories, which is a categorical formulation of gauging the fermion parity. We investigate general properties of super-modular categories such as fermions in twisted Drinfeld doubles, Verlinde formulas for naive quotients, and explicit extensions of $PSU(2)_{4m+2}$ with an eye towar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.09294","kind":"arxiv","version":3},"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":"2026-05-18T00:44:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tiM9OAnwBVR/qJkW5b2TSSojx6LXRGC3w+DtgU+jUPt9HXupmg1zyqXtZFbydOAqko49IL/sUTtDtbhURttbBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T10:03:28.701483Z"},"content_sha256":"62dfa1ff49c1fa966998ac0dfc8f0c2323bc916906d060fbfb9b2fe511519da7","schema_version":"1.0","event_id":"sha256:62dfa1ff49c1fa966998ac0dfc8f0c2323bc916906d060fbfb9b2fe511519da7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AGXG6XG44GK6PWSZNJ65XWIEUG/bundle.json","state_url":"https://pith.science/pith/AGXG6XG44GK6PWSZNJ65XWIEUG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AGXG6XG44GK6PWSZNJ65XWIEUG/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":"2026-06-02T10:03:28Z","links":{"resolver":"https://pith.science/pith/AGXG6XG44GK6PWSZNJ65XWIEUG","bundle":"https://pith.science/pith/AGXG6XG44GK6PWSZNJ65XWIEUG/bundle.json","state":"https://pith.science/pith/AGXG6XG44GK6PWSZNJ65XWIEUG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AGXG6XG44GK6PWSZNJ65XWIEUG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:AGXG6XG44GK6PWSZNJ65XWIEUG","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":"c1cfaf07730638058a90fde0e530dda86846ee1481f36c40614e7c09a07d4b39","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-03-30T17:58:15Z","title_canon_sha256":"f3591e5b4461b540c7b6526eb2f037b85cdd6aa2c2312193b523a92dc8ba6488"},"schema_version":"1.0","source":{"id":"1603.09294","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.09294","created_at":"2026-05-18T00:44:01Z"},{"alias_kind":"arxiv_version","alias_value":"1603.09294v3","created_at":"2026-05-18T00:44:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.09294","created_at":"2026-05-18T00:44:01Z"},{"alias_kind":"pith_short_12","alias_value":"AGXG6XG44GK6","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"AGXG6XG44GK6PWSZ","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"AGXG6XG4","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:62dfa1ff49c1fa966998ac0dfc8f0c2323bc916906d060fbfb9b2fe511519da7","target":"graph","created_at":"2026-05-18T00:44:01Z","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 study spin and super-modular categories systematically as inspired by fermionic topological phases of matter, which are always fermion parity enriched and modelled by spin TQFTs at low energy. We formulate a $16$-fold way conjecture for the minimal modular extensions of super-modular categories to spin modular categories, which is a categorical formulation of gauging the fermion parity. We investigate general properties of super-modular categories such as fermions in twisted Drinfeld doubles, Verlinde formulas for naive quotients, and explicit extensions of $PSU(2)_{4m+2}$ with an eye towar","authors_text":"Cesar Galindo, Eric C. Rowell, Julia Yael Plavnik, Paul Bruillard, Siu-Hung Ng, Tobias Hagge, Zhenghan Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-03-30T17:58:15Z","title":"Fermionic Modular Categories and the 16-fold Way"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.09294","kind":"arxiv","version":3},"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":"sha256:57ac494eb119ea4c20a00910f132f1e15cd432d9d9e26ef45d9d6afcc0813931","target":"record","created_at":"2026-05-18T00:44:01Z","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":"c1cfaf07730638058a90fde0e530dda86846ee1481f36c40614e7c09a07d4b39","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-03-30T17:58:15Z","title_canon_sha256":"f3591e5b4461b540c7b6526eb2f037b85cdd6aa2c2312193b523a92dc8ba6488"},"schema_version":"1.0","source":{"id":"1603.09294","kind":"arxiv","version":3}},"canonical_sha256":"01ae6f5cdce195e7da596a7ddbd904a19ad5d2daffdcd7f6fef90b2f73cfa813","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"01ae6f5cdce195e7da596a7ddbd904a19ad5d2daffdcd7f6fef90b2f73cfa813","first_computed_at":"2026-05-18T00:44:01.294652Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:01.294652Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SAwlXh0XRfPDqP7j11a/Qc1H82k7V3F3uNavxCD0wOAVoMvMBN0B6IfhD/35sfZLnaY1W6i8lHQHynjQfvcIDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:01.295120Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.09294","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:57ac494eb119ea4c20a00910f132f1e15cd432d9d9e26ef45d9d6afcc0813931","sha256:62dfa1ff49c1fa966998ac0dfc8f0c2323bc916906d060fbfb9b2fe511519da7"],"state_sha256":"d81e4134e959c99a175ed240b994ae42e5a01093cfad7cb6e9c7c283ee80c580"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kH/dO8IetD8bAFBlzQX/4g3rK4BBS4/kGPkm0BdU8jRx7G5niz4dig43xzgSqK5fTpuN8ImPWophXW0Jyi9YDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T10:03:28.703313Z","bundle_sha256":"269e018a740b0f584a56b2a6a5e5b854b8f85ceec0ab84e71c3956bceb31ad1e"}}