{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:FWMIITOJOQRE5NEYUPR2FVO6RL","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":"8e5e06c545d52290ac06a4f1cfdb432a677aef2f359e14919da986b0e2e2b167","cross_cats_sorted":["math-ph","math.MP","math.QA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2025-06-02T10:35:19Z","title_canon_sha256":"d053b172ce9bd08dc2583ddb043606ac28970dc8b0ec2e6c11a775299e462011"},"schema_version":"1.0","source":{"id":"2506.01521","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.01521","created_at":"2026-06-08T01:05:01Z"},{"alias_kind":"arxiv_version","alias_value":"2506.01521v2","created_at":"2026-06-08T01:05:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.01521","created_at":"2026-06-08T01:05:01Z"},{"alias_kind":"pith_short_12","alias_value":"FWMIITOJOQRE","created_at":"2026-06-08T01:05:01Z"},{"alias_kind":"pith_short_16","alias_value":"FWMIITOJOQRE5NEY","created_at":"2026-06-08T01:05:01Z"},{"alias_kind":"pith_short_8","alias_value":"FWMIITOJ","created_at":"2026-06-08T01:05:01Z"}],"graph_snapshots":[{"event_id":"sha256:542387616eaa6b913d3a26928b9aabce5c29f560308f0a31636708d607f80236","target":"graph","created_at":"2026-06-08T01:05:01Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2506.01521/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We invesigate the relation between projective and anomalous representations of categories, and show how to any anomaly $J\\colon \\mathcal{C}\\to 2\\mathrm{Vect}$ one can associate an extension $\\mathcal{C}^J$ of $\\mathcal{C}$ and a subcategory $\\mathcal{C}^J_{\\mathrm{ST}}$ of $\\mathcal{C}^J$ with the property that: (i) anomalous representations of $\\mathcal{C}$ with anomaly $J$ are equivalent to $\\mathrm{Vect}$-linear functors $E\\colon \\mathcal{C}^J\\to \\mathrm{Vect}$, and (ii) these are in turn equivalent to linear representations of $\\mathcal{C}^J_{\\mathrm{ST}}$ where \"$J$ acts as scalars\". This","authors_text":"Chetan Vuppulury, Domenico Fiorenza","cross_cats":["math-ph","math.MP","math.QA","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2025-06-02T10:35:19Z","title":"Projective and anomalous representations of categories and their linearizations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.01521","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":"sha256:84939a0184e803df87a547d5e62eaf20e0473ddae49562ab02826011f8964170","target":"record","created_at":"2026-06-08T01:05:01Z","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":"8e5e06c545d52290ac06a4f1cfdb432a677aef2f359e14919da986b0e2e2b167","cross_cats_sorted":["math-ph","math.MP","math.QA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2025-06-02T10:35:19Z","title_canon_sha256":"d053b172ce9bd08dc2583ddb043606ac28970dc8b0ec2e6c11a775299e462011"},"schema_version":"1.0","source":{"id":"2506.01521","kind":"arxiv","version":2}},"canonical_sha256":"2d98844dc974224eb498a3e3a2d5de8ad284d8fa59a1e77c02cb90ea23014fef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2d98844dc974224eb498a3e3a2d5de8ad284d8fa59a1e77c02cb90ea23014fef","first_computed_at":"2026-06-08T01:05:01.153613Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-08T01:05:01.153613Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oOliUEZocBHsysk/sFK4rOY/Fewn6Uq5dsav0/LDvDno6Y/3JSp+cumF/CmLcWZ0I59ZR+lM5bd9rF08/cw4Cg==","signature_status":"signed_v1","signed_at":"2026-06-08T01:05:01.154184Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.01521","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:84939a0184e803df87a547d5e62eaf20e0473ddae49562ab02826011f8964170","sha256:542387616eaa6b913d3a26928b9aabce5c29f560308f0a31636708d607f80236"],"state_sha256":"b63b55370b2a249f57d9bede6060f272f434e04cca677ae4318518916c89529a"}