{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:DZP55S2MVPJMSKQHAF72K3B565","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":"10745d975dbc5bc971335d741dc28e519bd4df95103933babf5a640fbd693416","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-01-13T18:42:54Z","title_canon_sha256":"4e5ebb50fa7ca74c890b406ce87c46969d4628cde9bc4bdaf37bd3c96c9d949b"},"schema_version":"1.0","source":{"id":"1501.03103","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.03103","created_at":"2026-05-18T02:29:30Z"},{"alias_kind":"arxiv_version","alias_value":"1501.03103v1","created_at":"2026-05-18T02:29:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.03103","created_at":"2026-05-18T02:29:30Z"},{"alias_kind":"pith_short_12","alias_value":"DZP55S2MVPJM","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DZP55S2MVPJMSKQH","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DZP55S2M","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:c5f51326b3de294d916302c4d19ad2e8782b8b06cf718e6245fc452d9172f877","target":"graph","created_at":"2026-05-18T02:29:30Z","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":"Let $\\Gamma$ be a non-commutative free group on finitely many generators. In a previous work two of the authors have constructed the class of multiplicative representations of $\\Gamma$ and proved them irreducible as representation of $\\Gamma\\ltimes_\\lambda C(\\Omega)$. In this paper we analyze multiplicative representations as representations of $\\Gamma$ and we prove a criterium for irreducibility based on the growth of their matrix coefficients.","authors_text":"M. Gabriella Kuhn, Sandra Saliani, Tim Steger","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-01-13T18:42:54Z","title":"Free Group Representations from Vector-Valued Multiplicative Functions, II"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.03103","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":"sha256:9218ceb3830f0aa27ec614ea23a1131b7a6a8877f45edad59814331f61e853f4","target":"record","created_at":"2026-05-18T02:29:30Z","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":"10745d975dbc5bc971335d741dc28e519bd4df95103933babf5a640fbd693416","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-01-13T18:42:54Z","title_canon_sha256":"4e5ebb50fa7ca74c890b406ce87c46969d4628cde9bc4bdaf37bd3c96c9d949b"},"schema_version":"1.0","source":{"id":"1501.03103","kind":"arxiv","version":1}},"canonical_sha256":"1e5fdecb4cabd2c92a07017fa56c3df740f60ffab86cda0fe1de68d426687c15","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1e5fdecb4cabd2c92a07017fa56c3df740f60ffab86cda0fe1de68d426687c15","first_computed_at":"2026-05-18T02:29:30.506977Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:30.506977Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pZ3aN1TFANH9+VnT/93AqacncdL48op5eljSvXXa6L8rrC543VVYaBi/zIY1WAlAxuoyNYROoU03ZYlKwmdMBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:30.507390Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.03103","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9218ceb3830f0aa27ec614ea23a1131b7a6a8877f45edad59814331f61e853f4","sha256:c5f51326b3de294d916302c4d19ad2e8782b8b06cf718e6245fc452d9172f877"],"state_sha256":"4ef17a75a55f38e108df4a4d1abfbb0c0b2d47c1b3427d43944abab4f8b79784"}