{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:X66HS5AICVRK3T3YOI6YEZ4PBP","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":"e7a7d0bee0b72a20349b0a6b8824ea34d67fe199e722443bea8c989b54188537","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-02-03T06:54:46Z","title_canon_sha256":"1caa2600c82493f576e8c0f399ac3aac49a3fe9f69bd0e4ebf5db47af028eb6f"},"schema_version":"1.0","source":{"id":"1602.01207","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.01207","created_at":"2026-05-18T01:21:20Z"},{"alias_kind":"arxiv_version","alias_value":"1602.01207v1","created_at":"2026-05-18T01:21:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.01207","created_at":"2026-05-18T01:21:20Z"},{"alias_kind":"pith_short_12","alias_value":"X66HS5AICVRK","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"X66HS5AICVRK3T3Y","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"X66HS5AI","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:36196cfaecc9090362868995b76a204b5cacd448e44167aa0395b42f5eca5f73","target":"graph","created_at":"2026-05-18T01:21:20Z","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":"We prove that the number of geometrically indecomposable representations of fixed dimension vector d of a canonical algebra C defined over a finite field Fq is given by a polynomial in q (depending on C and d). We prove a similar result for squid algebras (and for any almost concealed canonical algebra). Finally we express the volume of the moduli stacks of representations of these algebras of a fixed dimension vector in terms of the corresponding Kac polynomials.","authors_text":"O. Schiffmann, P.-G. Plamondon","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-02-03T06:54:46Z","title":"Kac polynomials for canonical algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.01207","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:caadc3ac58daa9478315d1d8231d8ccf99356de08df31991364a4a5071202b55","target":"record","created_at":"2026-05-18T01:21:20Z","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":"e7a7d0bee0b72a20349b0a6b8824ea34d67fe199e722443bea8c989b54188537","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-02-03T06:54:46Z","title_canon_sha256":"1caa2600c82493f576e8c0f399ac3aac49a3fe9f69bd0e4ebf5db47af028eb6f"},"schema_version":"1.0","source":{"id":"1602.01207","kind":"arxiv","version":1}},"canonical_sha256":"bfbc7974081562adcf78723d82678f0bd6c0767837be0368dc1cd7e5a3d4ee5e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bfbc7974081562adcf78723d82678f0bd6c0767837be0368dc1cd7e5a3d4ee5e","first_computed_at":"2026-05-18T01:21:20.807704Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:20.807704Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NuPcbMO0ng30RSpD+chS9rE1d3ip3sJoYA3RjpEUhPUysN3EbCXvlFn9hQFJgKfCGrNVlzBcgT8XwF7Vg6EdDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:20.808244Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.01207","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:caadc3ac58daa9478315d1d8231d8ccf99356de08df31991364a4a5071202b55","sha256:36196cfaecc9090362868995b76a204b5cacd448e44167aa0395b42f5eca5f73"],"state_sha256":"7688e4e618480597a4612f74dfeb6a8a4eb2f43e0085a13a1995d34558c7f229"}