{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:2C7NCS7BB4D247PLGL3CV32HYM","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":"37c034eb1dd79083472eae9a5b5a39b93491705efb4d006daf1c1df1368f313a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2026-05-26T16:57:55Z","title_canon_sha256":"a08c6a8a62fc55b421415bdd4572775eaad9cd46559a764e5547cb046cc6fffc"},"schema_version":"1.0","source":{"id":"2605.27280","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.27280","created_at":"2026-05-27T02:06:15Z"},{"alias_kind":"arxiv_version","alias_value":"2605.27280v1","created_at":"2026-05-27T02:06:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.27280","created_at":"2026-05-27T02:06:15Z"},{"alias_kind":"pith_short_12","alias_value":"2C7NCS7BB4D2","created_at":"2026-05-27T02:06:15Z"},{"alias_kind":"pith_short_16","alias_value":"2C7NCS7BB4D247PL","created_at":"2026-05-27T02:06:15Z"},{"alias_kind":"pith_short_8","alias_value":"2C7NCS7B","created_at":"2026-05-27T02:06:15Z"}],"graph_snapshots":[{"event_id":"sha256:822cf15fa244feff9182bf56d9c5c1f30953db91d9769a882ecb28f55d055635","target":"graph","created_at":"2026-05-27T02:06:15Z","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/2605.27280/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The first part of this article is devoted to characterizing the cocycles $\\alpha$ of a finite group $G$ that give rise to faithful projective representations of $G$. We prove that a $p$-group $G$ admits a faithful irreducible projective representation if and only if the cohomology class $[\\alpha]$ does not lie in the image of the inflation map $\\operatorname{inf}: \\mathrm{H}^2\\!\\left(G / N, \\mathbb{C}^{\\times}\\right) \\longrightarrow \\mathrm{H}^2\\!\\left(G, \\mathbb{C}^{\\times}\\right)$ for any non-trivial central subgroup $N$ of $G$. In the case where $[\\alpha] \\in \\operatorname{Im}(\\operatorname","authors_text":"Poonam Nayak, Sumana Hatui","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2026-05-26T16:57:55Z","title":"On the Faithful Projective Representations of Finite Groups and their Minimal Dimension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.27280","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":"sha256:46dd610c29cf6e268851e28f5176a5c5b618a209ab26310dd475ba3996a00b1f","target":"record","created_at":"2026-05-27T02:06:15Z","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":"37c034eb1dd79083472eae9a5b5a39b93491705efb4d006daf1c1df1368f313a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2026-05-26T16:57:55Z","title_canon_sha256":"a08c6a8a62fc55b421415bdd4572775eaad9cd46559a764e5547cb046cc6fffc"},"schema_version":"1.0","source":{"id":"2605.27280","kind":"arxiv","version":1}},"canonical_sha256":"d0bed14be10f07ae7deb32f62aef47c3233feaca7f2892410e37e32a96b64396","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d0bed14be10f07ae7deb32f62aef47c3233feaca7f2892410e37e32a96b64396","first_computed_at":"2026-05-27T02:06:15.130350Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-27T02:06:15.130350Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hY45qtMFOXLLYvn/hCPRzSsbAc3QjnjqhofyFj08pCw6f3758lUa1wP0ygQuddl+m77+pKMEkO3DorVffh+8BQ==","signature_status":"signed_v1","signed_at":"2026-05-27T02:06:15.131157Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.27280","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:46dd610c29cf6e268851e28f5176a5c5b618a209ab26310dd475ba3996a00b1f","sha256:822cf15fa244feff9182bf56d9c5c1f30953db91d9769a882ecb28f55d055635"],"state_sha256":"3e96ce58b22e902f49fd1953b8372d24e473ca8038c6ac8bf11eafd4cab39c12"}