{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:OTHGU2PQWDD6YG2JQIKJICMR7Y","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":"30fe8a9a78f60b18fc6c50df8a11dfa7211a9c55f1364aab47fc9962fc33df60","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-06-16T12:43:59Z","title_canon_sha256":"4f2fd01314de649a817b7551ba5d5385e73227d251351c3de2f02eb870fae77a"},"schema_version":"1.0","source":{"id":"1606.05161","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.05161","created_at":"2026-05-18T01:12:21Z"},{"alias_kind":"arxiv_version","alias_value":"1606.05161v1","created_at":"2026-05-18T01:12:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.05161","created_at":"2026-05-18T01:12:21Z"},{"alias_kind":"pith_short_12","alias_value":"OTHGU2PQWDD6","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"OTHGU2PQWDD6YG2J","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"OTHGU2PQ","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:8bebf17a188379cabf7c62b1f3fb2a25b00f049c21993ccb2669870582a2d656","target":"graph","created_at":"2026-05-18T01:12:21Z","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 characterize the indecomposable transjective modules over an arbitrary cluster-tilted algebra that do not lie on a local slice, and we provide a sharp upper bound for the number of (isoclasses of) these modules.","authors_text":"Ibrahim Assem, Khrystyna Serhiyenko, Ralf Schiffler","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-06-16T12:43:59Z","title":"Modules over cluster-tilted algebras that do not lie on local slices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.05161","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:b9314f2e05fb739dd4257e2795551a265f46867b36051ddcfcb775a888d074e1","target":"record","created_at":"2026-05-18T01:12:21Z","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":"30fe8a9a78f60b18fc6c50df8a11dfa7211a9c55f1364aab47fc9962fc33df60","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-06-16T12:43:59Z","title_canon_sha256":"4f2fd01314de649a817b7551ba5d5385e73227d251351c3de2f02eb870fae77a"},"schema_version":"1.0","source":{"id":"1606.05161","kind":"arxiv","version":1}},"canonical_sha256":"74ce6a69f0b0c7ec1b498214940991fe1cc642a0e7e2b2da5a606c00863d1fcd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"74ce6a69f0b0c7ec1b498214940991fe1cc642a0e7e2b2da5a606c00863d1fcd","first_computed_at":"2026-05-18T01:12:21.912290Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:21.912290Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2OMch1y7agUOAajW194F1i6sjPgyYzROqeZaTXXHLFc4AXGXptO1W0KI+DwIvERd18BygYwOuNMkI/ohi2oDCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:21.912661Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.05161","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b9314f2e05fb739dd4257e2795551a265f46867b36051ddcfcb775a888d074e1","sha256:8bebf17a188379cabf7c62b1f3fb2a25b00f049c21993ccb2669870582a2d656"],"state_sha256":"7f842776377cb9845a49410e7b6fbc1a007c3186f980af7a6f5089adf8e47a00"}