{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:CJRECBZGWCAOJD325GSU7V5FAM","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":"5a2aaac02e0a919d3b34b7924a2ad7b630a64cd9286d21a3dba98fe3a5abed90","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-02-12T06:15:58Z","title_canon_sha256":"e0b15d3eaa226180bfe7c87594b153f5d62af6ee055cb1d7c0e812114ee76b61"},"schema_version":"1.0","source":{"id":"1302.2709","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.2709","created_at":"2026-05-18T00:42:24Z"},{"alias_kind":"arxiv_version","alias_value":"1302.2709v4","created_at":"2026-05-18T00:42:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.2709","created_at":"2026-05-18T00:42:24Z"},{"alias_kind":"pith_short_12","alias_value":"CJRECBZGWCAO","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"CJRECBZGWCAOJD32","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"CJRECBZG","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:4d2f450024ff12baf15e613997a6a2ed37fa363d5a70d61646bcd2e10848cd9a","target":"graph","created_at":"2026-05-18T00:42:24Z","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":"The class of support $\\tau$-tilting modules was introduced recently by Adachi, Iyama and Reiten. These modules complete the class of tilting modules from the point of view of mutations. Given a finite dimensional algebra $A$, we study all basic support $\\tau$-tilting $A$-modules which have given basic $\\tau$-rigid $A$-module as a direct summand. We show that there exist an algebra $C$ such that there exists an order-preserving bijection between these modules and all basic support $\\tau$-tilting $C$-modules; we call this process $\\tau$-tilting reduction. An important step in this process is the","authors_text":"Gustavo Jasso","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-02-12T06:15:58Z","title":"Reduction of $\\tau$-tilting modules and torsion pairs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.2709","kind":"arxiv","version":4},"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:cd2d805175ac82f91f4b0c488d4f80f7580d3c87ee0098f76f2ebd245d32db1f","target":"record","created_at":"2026-05-18T00:42:24Z","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":"5a2aaac02e0a919d3b34b7924a2ad7b630a64cd9286d21a3dba98fe3a5abed90","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-02-12T06:15:58Z","title_canon_sha256":"e0b15d3eaa226180bfe7c87594b153f5d62af6ee055cb1d7c0e812114ee76b61"},"schema_version":"1.0","source":{"id":"1302.2709","kind":"arxiv","version":4}},"canonical_sha256":"1262410726b080e48f7ae9a54fd7a503213c29c81ce6b672837f83e2346731d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1262410726b080e48f7ae9a54fd7a503213c29c81ce6b672837f83e2346731d8","first_computed_at":"2026-05-18T00:42:24.274031Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:24.274031Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qX6S2Ry/krDT32UI+lDYA3fbWPXPOok1bsLuSOBZkiDC4/k6V3diV7BS2c2/VxIqmp4mA/ES4wXKAUoC1eA4CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:24.274623Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.2709","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd2d805175ac82f91f4b0c488d4f80f7580d3c87ee0098f76f2ebd245d32db1f","sha256:4d2f450024ff12baf15e613997a6a2ed37fa363d5a70d61646bcd2e10848cd9a"],"state_sha256":"4b76b9bb3f452efdd3a0695839e386f73f10f1807a7b3b666dd8cae38de4f268"}