{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:AQSLY5LR25MNP2XW3HHFSS4U6E","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":"453203b9f32b24ee8be7a0f810e6a3ad9a35a78f5e37e33c0b067935188303f8","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2025-01-23T14:19:30Z","title_canon_sha256":"4e583b81d732274e20f51448a431b566095bdd7f3c4bb2a4471cbb2ac4416c55"},"schema_version":"1.0","source":{"id":"2501.13694","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.13694","created_at":"2026-07-05T10:04:32Z"},{"alias_kind":"arxiv_version","alias_value":"2501.13694v1","created_at":"2026-07-05T10:04:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.13694","created_at":"2026-07-05T10:04:32Z"},{"alias_kind":"pith_short_12","alias_value":"AQSLY5LR25MN","created_at":"2026-07-05T10:04:32Z"},{"alias_kind":"pith_short_16","alias_value":"AQSLY5LR25MNP2XW","created_at":"2026-07-05T10:04:32Z"},{"alias_kind":"pith_short_8","alias_value":"AQSLY5LR","created_at":"2026-07-05T10:04:32Z"}],"graph_snapshots":[{"event_id":"sha256:ce4817066a798a2940c88b08b983f2f544e8aff29e90a7ac36fccfab7390bdef","target":"graph","created_at":"2026-07-05T10:04:32Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2501.13694/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A mutation operation for $\\tau$-exceptional sequences of modules over any finite-dimensional algebra was recently introduced, generalising the mutation for exceptional sequences of modules over hereditary algebras. We interpret this mutation in terms of TF-ordered $\\tau$-rigid modules, which are in bijection with $\\tau$-exceptional sequences. As an application we show that the mutation is transitive for Nakayama algebras, by providing an explicit combinatorial description of mutation over this class of algebras.","authors_text":"Aslak B. Buan, H{\\aa}vard U. Terland, Maximilian Kaipel","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2025-01-23T14:19:30Z","title":"Mutating ordered $\\tau$-rigid modules with applications to Nakayama algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.13694","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":"sha256:5f367ad5f556daf06bb4ab53d15a9fd70ac4a9f8e0567b2447b8cdebb7001c2c","target":"record","created_at":"2026-07-05T10:04:32Z","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":"453203b9f32b24ee8be7a0f810e6a3ad9a35a78f5e37e33c0b067935188303f8","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2025-01-23T14:19:30Z","title_canon_sha256":"4e583b81d732274e20f51448a431b566095bdd7f3c4bb2a4471cbb2ac4416c55"},"schema_version":"1.0","source":{"id":"2501.13694","kind":"arxiv","version":1}},"canonical_sha256":"0424bc7571d758d7eaf6d9ce594b94f11e90c4e6809a76e65b09626f27f118ce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0424bc7571d758d7eaf6d9ce594b94f11e90c4e6809a76e65b09626f27f118ce","first_computed_at":"2026-07-05T10:04:32.707657Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:04:32.707657Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oHIMoPqdyp92ikxHO4OfEkP10mUmVev4t/Njq20d+GbGWQ4XmfBhU/w9BLnJdkm0HIdlVhqLlbBxPXCsoX+hDA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:04:32.708254Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.13694","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5f367ad5f556daf06bb4ab53d15a9fd70ac4a9f8e0567b2447b8cdebb7001c2c","sha256:ce4817066a798a2940c88b08b983f2f544e8aff29e90a7ac36fccfab7390bdef"],"state_sha256":"b16eb5da66a29fcedeae36008589fd560a5014448e403f9f20ae956971d93fae"}