{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:PB23IKYP7DHH7LR6WY6FRB2IBX","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":"7fe43efeb637c5b1ab98c8c3dc6341eeb55e1d4cb1e321bde8388e7dd3c79fc0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-03-27T02:21:33Z","title_canon_sha256":"af525a1f38c03a06d8fd3b6d6a83a252606f86c391d002e31c6fa2b1757e224d"},"schema_version":"1.0","source":{"id":"1503.07945","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.07945","created_at":"2026-05-18T01:30:42Z"},{"alias_kind":"arxiv_version","alias_value":"1503.07945v2","created_at":"2026-05-18T01:30:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.07945","created_at":"2026-05-18T01:30:42Z"},{"alias_kind":"pith_short_12","alias_value":"PB23IKYP7DHH","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"PB23IKYP7DHH7LR6","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"PB23IKYP","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:eb9721bd9e32f334ffa3f919a269312dfcc1712b44d4ebd5509afae8d0d806c9","target":"graph","created_at":"2026-05-18T01:30:42Z","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 use semi-invariant pictures to prove two conjectures about maximal green sequences. First: if $Q$ is any acyclic valued quiver with an arrow $j\\to i$ of infinite type then any maximal green sequence for $Q$ must mutate at $i$ before mutating at $j$. Second: for any quiver $Q'$ obtained by mutating an acyclic valued quiver $Q$ of tame type, there are only finitely many maximal green sequences for $Q'$. Both statements follow from the Rotation Lemma for reddening sequences and this in turn follows from the Mutation Formula for the semi-invariant picture for $Q$.","authors_text":"Gordana Todorov, Kiyoshi Igusa, Stephen Hermes, Thomas Br\\\"ustle","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-03-27T02:21:33Z","title":"Semi-invariant pictures and two conjectures on maximal green sequences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.07945","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":"sha256:48cb7f91e885ed4e70efd2403bdbe733ce2f6da649188d2b7be1482538e33e66","target":"record","created_at":"2026-05-18T01:30:42Z","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":"7fe43efeb637c5b1ab98c8c3dc6341eeb55e1d4cb1e321bde8388e7dd3c79fc0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-03-27T02:21:33Z","title_canon_sha256":"af525a1f38c03a06d8fd3b6d6a83a252606f86c391d002e31c6fa2b1757e224d"},"schema_version":"1.0","source":{"id":"1503.07945","kind":"arxiv","version":2}},"canonical_sha256":"7875b42b0ff8ce7fae3eb63c5887480df0c2436377ebe48665dc3fd65cd7d709","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7875b42b0ff8ce7fae3eb63c5887480df0c2436377ebe48665dc3fd65cd7d709","first_computed_at":"2026-05-18T01:30:42.996850Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:42.996850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GMPgyDyVhwlRDoz8No42wytnU3eF+OEu5Xcuz/nXW5Qf4HIt+9a0Pm7J7XCZ7K/cfnotRDxZx59HbBeBPw3TAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:42.997636Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.07945","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:48cb7f91e885ed4e70efd2403bdbe733ce2f6da649188d2b7be1482538e33e66","sha256:eb9721bd9e32f334ffa3f919a269312dfcc1712b44d4ebd5509afae8d0d806c9"],"state_sha256":"c4b997ff26d207d7affa7ac0a83f12f0eb12dda9dadbab59b7258fe1a5eff8b7"}