{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:GERPXDXGRBZ33INATVUWAHNDNA","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":"60fa84a47ef6c9be32ceda5cdb2475fd293883a476f9122f5ee6bbc6153b5486","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-11-27T14:54:34Z","title_canon_sha256":"ec357f48d55acbcd23657471e1b8d1d718643d5f10ac57e031690840c8d5648c"},"schema_version":"1.0","source":{"id":"1311.6989","kind":"arxiv","version":7}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.6989","created_at":"2026-05-18T00:48:55Z"},{"alias_kind":"arxiv_version","alias_value":"1311.6989v7","created_at":"2026-05-18T00:48:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.6989","created_at":"2026-05-18T00:48:55Z"},{"alias_kind":"pith_short_12","alias_value":"GERPXDXGRBZ3","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"GERPXDXGRBZ33INA","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"GERPXDXG","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:77600f3ce964b9728b1bb0e28d4102014dfb9b009929d2bbc0dc799377ec7da2","target":"graph","created_at":"2026-05-18T00:48:55Z","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 provide a new proof of the Kac positivity conjecture for an arbitrary quiver $Q$. The ingredients are the cohomological integrality theorem in Donaldson-Thomas theory, dimensional reduction, and an easy purity result. These facts imply the purity of the cohomological Donaldson-Thomas invariants for a quiver with potential $(\\tilde{Q},W)$ associated to $Q$, which in turn implies positivity of the Kac polynomials for $Q$.","authors_text":"Ben Davison","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-11-27T14:54:34Z","title":"Purity of critical cohomology and Kac's conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.6989","kind":"arxiv","version":7},"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":"sha256:7c0d47b8fab6f6671fe8f4b2eb6f2c0c128636d9fa7bd8fcd8d4529251f4a063","target":"record","created_at":"2026-05-18T00:48:55Z","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":"60fa84a47ef6c9be32ceda5cdb2475fd293883a476f9122f5ee6bbc6153b5486","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-11-27T14:54:34Z","title_canon_sha256":"ec357f48d55acbcd23657471e1b8d1d718643d5f10ac57e031690840c8d5648c"},"schema_version":"1.0","source":{"id":"1311.6989","kind":"arxiv","version":7}},"canonical_sha256":"3122fb8ee68873bda1a09d69601da36830e167014d2f897d6a90ed07cc4c6673","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3122fb8ee68873bda1a09d69601da36830e167014d2f897d6a90ed07cc4c6673","first_computed_at":"2026-05-18T00:48:55.364607Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:55.364607Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xf37hVG+pMpMHU4KltaDJc2UBLaacP81mlD0Q0TqxYkUktzcFWrVHtMUOxIeN+lXL+N/lRMGTjQajkaKIkgoDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:55.365380Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.6989","source_kind":"arxiv","source_version":7}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7c0d47b8fab6f6671fe8f4b2eb6f2c0c128636d9fa7bd8fcd8d4529251f4a063","sha256:77600f3ce964b9728b1bb0e28d4102014dfb9b009929d2bbc0dc799377ec7da2"],"state_sha256":"1583ead25b61a3fae3e6f50f9fcd249c36e30145c9de2d4991bd4e2bca56cd7e"}