{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:YB2NFHBD2TIUCY6ALOZ7VTRD46","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":"4530395cf77956c567eb73a8cb6e82cb222f1d6922e6acde11ae93145bdd1da6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-03-19T08:56:49Z","title_canon_sha256":"13c43d152482b2a20755a270d93e6543b5ef300fb166092da93f1645f877970a"},"schema_version":"1.0","source":{"id":"1703.06404","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.06404","created_at":"2026-05-18T00:48:23Z"},{"alias_kind":"arxiv_version","alias_value":"1703.06404v1","created_at":"2026-05-18T00:48:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.06404","created_at":"2026-05-18T00:48:23Z"},{"alias_kind":"pith_short_12","alias_value":"YB2NFHBD2TIU","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"YB2NFHBD2TIUCY6A","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"YB2NFHBD","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:ed1b769cba29fbf277bf8feb8f01711a532c0df250c8441f65e419d2032fa53b","target":"graph","created_at":"2026-05-18T00:48:23Z","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":"Let $\\Lambda$ be a finite dimensional string algebra over a field with the quiver $Q$ such that the underlying graph of $Q$ is a tree, and let $|\\Det(\\Lambda)|$ be the number of the minimal right determiners of all irreducible morphisms between indecomposable left $\\Lambda$-modules. Then we have $$|\\Det(\\Lambda)|=2n-p-q-1,$$ where $n$ is the number of vertices in $Q$, $p=|\\{i\\mid i$ is a source in $Q$ with two neighbours$\\}|$ and $q$ is the number of non-zero vertex ideals of $\\Lambda$.","authors_text":"Xiaoxing Wu, Zhaoyong Huang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-03-19T08:56:49Z","title":"Minimal right determiners of irreducible morphisms in string algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.06404","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:ecd2e437e5b68e11e2981dca341620a242f945bd2153be4f13be1b6842b7892e","target":"record","created_at":"2026-05-18T00:48:23Z","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":"4530395cf77956c567eb73a8cb6e82cb222f1d6922e6acde11ae93145bdd1da6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-03-19T08:56:49Z","title_canon_sha256":"13c43d152482b2a20755a270d93e6543b5ef300fb166092da93f1645f877970a"},"schema_version":"1.0","source":{"id":"1703.06404","kind":"arxiv","version":1}},"canonical_sha256":"c074d29c23d4d14163c05bb3face23e7ad58a55cc388dab20b2f0cf1f80caedd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c074d29c23d4d14163c05bb3face23e7ad58a55cc388dab20b2f0cf1f80caedd","first_computed_at":"2026-05-18T00:48:23.002677Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:23.002677Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xUFSnJt8XiLqHRz5YkcGUTca6B4fuexn365ixsRCITDgsJYGh1W5zPkuOZdMJbzuokF3eVYZbDxlG4tCkho7CA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:23.003288Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.06404","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ecd2e437e5b68e11e2981dca341620a242f945bd2153be4f13be1b6842b7892e","sha256:ed1b769cba29fbf277bf8feb8f01711a532c0df250c8441f65e419d2032fa53b"],"state_sha256":"72337ded5d5fc46cce2ef482a1fec633e2b78b6f6a8384662c8875d78d46ba8a"}