{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:QAHYLAJJKSDDLOZG4VUQGZSYWX","short_pith_number":"pith:QAHYLAJJ","schema_version":"1.0","canonical_sha256":"800f858129548635bb26e569036658b5e24517674f019a3014c27266563e18b7","source":{"kind":"arxiv","id":"1007.0882","version":1},"attestation_state":"computed","paper":{"title":"Semi-invariants of symmetric quivers of tame type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Riccardo Aragona","submitted_at":"2010-07-06T13:06:27Z","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1007.0882","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-07-06T13:06:27Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"7dab2ec8cb3492ae66bcd7bd223201f85043312882349dad561c56e4f5b87388","abstract_canon_sha256":"410db4b6ebacb28fad69f5e217edd8aa613f2968d382ca36501f0a7094ff3bd1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:59:42.607385Z","signature_b64":"cs70W6AbQIeg1KsRjpZ47pDBFXBxyVi026PrUPTRolp+4WR4bONmwa4l71IJRhRBN0BcJB0M021cqdxL79iMBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"800f858129548635bb26e569036658b5e24517674f019a3014c27266563e18b7","last_reissued_at":"2026-05-18T00:59:42.606750Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:59:42.606750Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Semi-invariants of symmetric quivers of tame type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Riccardo Aragona","submitted_at":"2010-07-06T13:06:27Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.0882","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1007.0882","created_at":"2026-05-18T00:59:42.606839+00:00"},{"alias_kind":"arxiv_version","alias_value":"1007.0882v1","created_at":"2026-05-18T00:59:42.606839+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.0882","created_at":"2026-05-18T00:59:42.606839+00:00"},{"alias_kind":"pith_short_12","alias_value":"QAHYLAJJKSDD","created_at":"2026-05-18T12:26:12.377268+00:00"},{"alias_kind":"pith_short_16","alias_value":"QAHYLAJJKSDDLOZG","created_at":"2026-05-18T12:26:12.377268+00:00"},{"alias_kind":"pith_short_8","alias_value":"QAHYLAJJ","created_at":"2026-05-18T12:26:12.377268+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QAHYLAJJKSDDLOZG4VUQGZSYWX","json":"https://pith.science/pith/QAHYLAJJKSDDLOZG4VUQGZSYWX.json","graph_json":"https://pith.science/api/pith-number/QAHYLAJJKSDDLOZG4VUQGZSYWX/graph.json","events_json":"https://pith.science/api/pith-number/QAHYLAJJKSDDLOZG4VUQGZSYWX/events.json","paper":"https://pith.science/paper/QAHYLAJJ"},"agent_actions":{"view_html":"https://pith.science/pith/QAHYLAJJKSDDLOZG4VUQGZSYWX","download_json":"https://pith.science/pith/QAHYLAJJKSDDLOZG4VUQGZSYWX.json","view_paper":"https://pith.science/paper/QAHYLAJJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1007.0882&json=true","fetch_graph":"https://pith.science/api/pith-number/QAHYLAJJKSDDLOZG4VUQGZSYWX/graph.json","fetch_events":"https://pith.science/api/pith-number/QAHYLAJJKSDDLOZG4VUQGZSYWX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QAHYLAJJKSDDLOZG4VUQGZSYWX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QAHYLAJJKSDDLOZG4VUQGZSYWX/action/storage_attestation","attest_author":"https://pith.science/pith/QAHYLAJJKSDDLOZG4VUQGZSYWX/action/author_attestation","sign_citation":"https://pith.science/pith/QAHYLAJJKSDDLOZG4VUQGZSYWX/action/citation_signature","submit_replication":"https://pith.science/pith/QAHYLAJJKSDDLOZG4VUQGZSYWX/action/replication_record"}},"created_at":"2026-05-18T00:59:42.606839+00:00","updated_at":"2026-05-18T00:59:42.606839+00:00"}