{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:FB3ACJV6D3MJUAM5IY75NGI5F3","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":"5aed91231cad9809fb6837d0127c3d7273fd39062c291405385da1ee05c7eda8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-07-11T01:28:26Z","title_canon_sha256":"69fe0665c68b0142363f39fbfbf7e982a95140024222acc81a5b7c86768d5795"},"schema_version":"1.0","source":{"id":"1507.03051","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.03051","created_at":"2026-05-18T01:34:15Z"},{"alias_kind":"arxiv_version","alias_value":"1507.03051v2","created_at":"2026-05-18T01:34:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.03051","created_at":"2026-05-18T01:34:15Z"},{"alias_kind":"pith_short_12","alias_value":"FB3ACJV6D3MJ","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"FB3ACJV6D3MJUAM5","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"FB3ACJV6","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:5a1bead0238bf7db80c74f5fd1d7ec83090951122c0a101ed7350985cb344a82","target":"graph","created_at":"2026-05-18T01:34:15Z","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 the basic properties of determinantal semi-invariants for presentation spaces over any finite dimensional hereditary algebra over any field. These include the virtual generic decomposition theorem, stability theorem and the c-vector theorem which says that the c-vectors of a cluster tilting object are, up to sign, the determinantal weights of the determinantal semi-invariants defined on the cluster tilting objects. Applications of these theorems are given in several concurrently written papers.","authors_text":"Gordana Todorov, Jerzy Weyman, Kent Orr, Kiyoshi Igusa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-07-11T01:28:26Z","title":"Modulated semi-invariants"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.03051","kind":"arxiv","version":2},"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":"sha256:9ed1be7b09ad2c18114215839759254b8e68453f20cdf725c982a166428e2620","target":"record","created_at":"2026-05-18T01:34:15Z","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":"5aed91231cad9809fb6837d0127c3d7273fd39062c291405385da1ee05c7eda8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-07-11T01:28:26Z","title_canon_sha256":"69fe0665c68b0142363f39fbfbf7e982a95140024222acc81a5b7c86768d5795"},"schema_version":"1.0","source":{"id":"1507.03051","kind":"arxiv","version":2}},"canonical_sha256":"28760126be1ed89a019d463fd6991d2eed0339e86026a7307bd8824963b63e5b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"28760126be1ed89a019d463fd6991d2eed0339e86026a7307bd8824963b63e5b","first_computed_at":"2026-05-18T01:34:15.596882Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:15.596882Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VUrutU/KPqmpRXeRUnOkLXDHGdZqpUC0eQHHyU+eeiDVRdUZ+27ORwQreXbeymFjxXMTRmygvGcKk/ERzCQXCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:15.597492Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.03051","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9ed1be7b09ad2c18114215839759254b8e68453f20cdf725c982a166428e2620","sha256:5a1bead0238bf7db80c74f5fd1d7ec83090951122c0a101ed7350985cb344a82"],"state_sha256":"ba1a4737a9cc823748b40791a9b9aa22398096e44014ce0941213e0ff5a5e297"}