{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:VGAZP7HZTOHLIH3PGQF5TQ67HD","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":"31602c74e1dbc5f92568c0ad6fb5ebc51652cc69a11804cc5906a105ec488529","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2020-04-20T07:56:32Z","title_canon_sha256":"c6e7a650565e3e8ccaa265ee2d94fcd53bf3238d7bcb47a052ca1f8dd7aaaa34"},"schema_version":"1.0","source":{"id":"2004.09111","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2004.09111","created_at":"2026-07-05T03:27:54Z"},{"alias_kind":"arxiv_version","alias_value":"2004.09111v3","created_at":"2026-07-05T03:27:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2004.09111","created_at":"2026-07-05T03:27:54Z"},{"alias_kind":"pith_short_12","alias_value":"VGAZP7HZTOHL","created_at":"2026-07-05T03:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"VGAZP7HZTOHLIH3P","created_at":"2026-07-05T03:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"VGAZP7HZ","created_at":"2026-07-05T03:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:6c147539d1411d1c8ba8357c3c658875cf4c93057f1661ec929911d6697f312d","target":"graph","created_at":"2026-07-05T03:27:54Z","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/2004.09111/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Frobenius-Perron theory of an endofunctor of a category was introduced in recent years [12, 13]. We apply this theory to monoidal (or tensor) triangulated structures of quiver representations.","authors_text":"J.-H. Zhou, J. J. Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2020-04-20T07:56:32Z","title":"Frobenius-Perron Theory of Representations of Quivers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2004.09111","kind":"arxiv","version":3},"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":"sha256:814c87dd8b844097e6fcbfc26a2a7361ee694710366eff53f1702c12eafea94e","target":"record","created_at":"2026-07-05T03:27:54Z","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":"31602c74e1dbc5f92568c0ad6fb5ebc51652cc69a11804cc5906a105ec488529","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2020-04-20T07:56:32Z","title_canon_sha256":"c6e7a650565e3e8ccaa265ee2d94fcd53bf3238d7bcb47a052ca1f8dd7aaaa34"},"schema_version":"1.0","source":{"id":"2004.09111","kind":"arxiv","version":3}},"canonical_sha256":"a98197fcf99b8eb41f6f340bd9c3df38d325a7b15e2cdb3608e818db84773841","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a98197fcf99b8eb41f6f340bd9c3df38d325a7b15e2cdb3608e818db84773841","first_computed_at":"2026-07-05T03:27:54.622718Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:27:54.622718Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"l/rR6KmScK0a8w4ByBxc1Ph+t7jiRXqsK0cebOKUJ4rOtT2mukMKWn/qIYNNM2Gleth6Cbb2nEdVEekz2j71CA==","signature_status":"signed_v1","signed_at":"2026-07-05T03:27:54.623134Z","signed_message":"canonical_sha256_bytes"},"source_id":"2004.09111","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:814c87dd8b844097e6fcbfc26a2a7361ee694710366eff53f1702c12eafea94e","sha256:6c147539d1411d1c8ba8357c3c658875cf4c93057f1661ec929911d6697f312d"],"state_sha256":"d733bcc07a306eade8f31674946ff86b18a521b7d5c22f52c42d0e727fe82c0d"}