{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:FRQDSWR2Z3YJFKMDIRRMH6E5V2","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":"bdd58b7b17711f3f8341be3a00e4ab2968dce2117c177cb7d893004142139417","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.RT","submitted_at":"2025-01-27T07:04:43Z","title_canon_sha256":"a41585ab3c2f7fb1fe217ac737bdb3bdd3bddf36f2a0be4ddadca1ff9a95b730"},"schema_version":"1.0","source":{"id":"2501.15822","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.15822","created_at":"2026-06-23T01:12:44Z"},{"alias_kind":"arxiv_version","alias_value":"2501.15822v3","created_at":"2026-06-23T01:12:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.15822","created_at":"2026-06-23T01:12:44Z"},{"alias_kind":"pith_short_12","alias_value":"FRQDSWR2Z3YJ","created_at":"2026-06-23T01:12:44Z"},{"alias_kind":"pith_short_16","alias_value":"FRQDSWR2Z3YJFKMD","created_at":"2026-06-23T01:12:44Z"},{"alias_kind":"pith_short_8","alias_value":"FRQDSWR2","created_at":"2026-06-23T01:12:44Z"}],"graph_snapshots":[{"event_id":"sha256:4f8110222489a893247e10a987e6c7bfa206323b9dd89cf94b159981eb42ffa5","target":"graph","created_at":"2026-06-23T01:12:44Z","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/2501.15822/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper studies the wall-chamber structures of finite-dimensional ($\\tau$-tilting infinite) algebras via generic decompositions of g-vectors. In particular, we examine regions outside the chambers. We show that the cones of g-vectors are rational and simplicial. Moreover, we prove that the open cone of a given g-vector coincides with the interior of its $\\TF$-equivalence class if and only if the two have the same dimension. Furthermore, we establish that g-vectors satisfy the ray condition when they are sufficiently far from the origin. As an application, we generalize several results of As","authors_text":"Mohamad Haerizadeh, Siamak Yassemi","cross_cats":[],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.RT","submitted_at":"2025-01-27T07:04:43Z","title":"The cones of g-vectors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.15822","kind":"arxiv","version":3},"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":"sha256:723721cb9bebaeccb1766a509e47cf8226815c37e6a93c4f5f4b48154b149a9f","target":"record","created_at":"2026-06-23T01:12:44Z","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":"bdd58b7b17711f3f8341be3a00e4ab2968dce2117c177cb7d893004142139417","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.RT","submitted_at":"2025-01-27T07:04:43Z","title_canon_sha256":"a41585ab3c2f7fb1fe217ac737bdb3bdd3bddf36f2a0be4ddadca1ff9a95b730"},"schema_version":"1.0","source":{"id":"2501.15822","kind":"arxiv","version":3}},"canonical_sha256":"2c60395a3acef092a9834462c3f89daea9bd37a35b2b3a1f2baaf89f77c7185c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2c60395a3acef092a9834462c3f89daea9bd37a35b2b3a1f2baaf89f77c7185c","first_computed_at":"2026-06-23T01:12:44.915083Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-23T01:12:44.915083Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o3BGZbIDn12/XsEwnSW00ouK1hOMz9NNIua3PKFdqY4crWwoX7cCwpBQQLVyb7JfSZ5EXrofbO0mccbmgu5uDw==","signature_status":"signed_v1","signed_at":"2026-06-23T01:12:44.915682Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.15822","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:723721cb9bebaeccb1766a509e47cf8226815c37e6a93c4f5f4b48154b149a9f","sha256:4f8110222489a893247e10a987e6c7bfa206323b9dd89cf94b159981eb42ffa5"],"state_sha256":"9418edacff188cfe0e28f768d37d2bde604c3ff41fbdbeba95f081bf888c5d24"}