{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:QAHYLAJJKSDDLOZG4VUQGZSYWX","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":"410db4b6ebacb28fad69f5e217edd8aa613f2968d382ca36501f0a7094ff3bd1","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-07-06T13:06:27Z","title_canon_sha256":"7dab2ec8cb3492ae66bcd7bd223201f85043312882349dad561c56e4f5b87388"},"schema_version":"1.0","source":{"id":"1007.0882","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.0882","created_at":"2026-05-18T00:59:42Z"},{"alias_kind":"arxiv_version","alias_value":"1007.0882v1","created_at":"2026-05-18T00:59:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.0882","created_at":"2026-05-18T00:59:42Z"},{"alias_kind":"pith_short_12","alias_value":"QAHYLAJJKSDD","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"QAHYLAJJKSDDLOZG","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"QAHYLAJJ","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:a9738df834d60a7b6dbf17c458f6a52ba19245e746e3955cb2c459fe7da85527","target":"graph","created_at":"2026-05-18T00:59:42Z","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 symmetric quiver $(Q,\\sigma)$ is a finite quiver without oriented cycles $Q=(Q_0,Q_1)$ equipped with a contravariant involution $\\sigma$ on $Q_0\\sqcup Q_1$. The involution allows us to define a nondegenerate bilinear form $<,>$ on a representation $V$ of $Q$. We shall say that $V$ is orthogonal if $<,>$ is symmetric and symplectic if $<,>$ is skew-symmetric. Moreover, we define an action of products of classical groups on the space of orthogonal representations and on the space of symplectic representations. So we prove that if $(Q,\\sigma)$ is a symmetric quiver of tame type then the rings o","authors_text":"Riccardo Aragona","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-07-06T13:06:27Z","title":"Semi-invariants of symmetric quivers of tame type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.0882","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":"sha256:7206d77711988b937c7865425b7a3bf318f17bcc8f16ef435a4e9a03d65f7824","target":"record","created_at":"2026-05-18T00:59:42Z","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":"410db4b6ebacb28fad69f5e217edd8aa613f2968d382ca36501f0a7094ff3bd1","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-07-06T13:06:27Z","title_canon_sha256":"7dab2ec8cb3492ae66bcd7bd223201f85043312882349dad561c56e4f5b87388"},"schema_version":"1.0","source":{"id":"1007.0882","kind":"arxiv","version":1}},"canonical_sha256":"800f858129548635bb26e569036658b5e24517674f019a3014c27266563e18b7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"800f858129548635bb26e569036658b5e24517674f019a3014c27266563e18b7","first_computed_at":"2026-05-18T00:59:42.606750Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:42.606750Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cs70W6AbQIeg1KsRjpZ47pDBFXBxyVi026PrUPTRolp+4WR4bONmwa4l71IJRhRBN0BcJB0M021cqdxL79iMBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:42.607385Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.0882","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7206d77711988b937c7865425b7a3bf318f17bcc8f16ef435a4e9a03d65f7824","sha256:a9738df834d60a7b6dbf17c458f6a52ba19245e746e3955cb2c459fe7da85527"],"state_sha256":"f20b80331d2a490f338f4399aa81127e666c65ca2542f78f9b56e686d19ada92"}