{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:44XMTYUC4MEJGLD7IT4VSH4GWP","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":"6ab38645b09398a3f675c10ffbbea495ab56cfa3151e44b8d49c52583077d939","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.RT","submitted_at":"2025-01-23T11:36:36Z","title_canon_sha256":"e9f85da0168686994f460a3ec765d5b0c53c3ce5033d4373aa457c1b21c6cd14"},"schema_version":"1.0","source":{"id":"2501.13578","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.13578","created_at":"2026-07-05T10:04:31Z"},{"alias_kind":"arxiv_version","alias_value":"2501.13578v1","created_at":"2026-07-05T10:04:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.13578","created_at":"2026-07-05T10:04:31Z"},{"alias_kind":"pith_short_12","alias_value":"44XMTYUC4MEJ","created_at":"2026-07-05T10:04:31Z"},{"alias_kind":"pith_short_16","alias_value":"44XMTYUC4MEJGLD7","created_at":"2026-07-05T10:04:31Z"},{"alias_kind":"pith_short_8","alias_value":"44XMTYUC","created_at":"2026-07-05T10:04:31Z"}],"graph_snapshots":[{"event_id":"sha256:2a2d89bd9a085476e270fc50bb2b7c2918b14c63103c164773e0cacdd4eb35e9","target":"graph","created_at":"2026-07-05T10:04:31Z","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/2501.13578/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We extend the notion of stability in the non-abelian category of poset representations (introduced by Futorny and Iusenko) to the category of socle-projective representations of a given $r$-peak poset $\\P$. When $\\P$ is a poset of type $\\mathbb{A}$, we demonstrate in two distinct ways that every indecomposable peak $\\P$-space is stable. First, this is shown using a bilinear form associated with the poset. Second, we prove it by observing that a stability function derived from a geometric model ensures that all indecomposable objects are stable. Along the way, we provide a new geometric realiza","authors_text":"Gabriel Bravo Rios, Kostiantyn Iusenko, Robinson-Julian Serna","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.RT","submitted_at":"2025-01-23T11:36:36Z","title":"Stability for socle-projective categories of type $\\mathbb{A}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.13578","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":"sha256:96e9ef5e8e9960d368e6662d711d3f5200494e9c489b41c17a88a94516a0c862","target":"record","created_at":"2026-07-05T10:04:31Z","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":"6ab38645b09398a3f675c10ffbbea495ab56cfa3151e44b8d49c52583077d939","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.RT","submitted_at":"2025-01-23T11:36:36Z","title_canon_sha256":"e9f85da0168686994f460a3ec765d5b0c53c3ce5033d4373aa457c1b21c6cd14"},"schema_version":"1.0","source":{"id":"2501.13578","kind":"arxiv","version":1}},"canonical_sha256":"e72ec9e282e308932c7f44f9591f86b3fbf8b763544365393998a6085c2df07c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e72ec9e282e308932c7f44f9591f86b3fbf8b763544365393998a6085c2df07c","first_computed_at":"2026-07-05T10:04:31.075730Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:04:31.075730Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"H6XBhcm2c5ujAwQtKTfIggsRO6l2d07xYQ3iRTrZL2KiRvcgUK1lYRYkYzrHB/cXVo+29EDoPW74Iz1PJAMyCg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:04:31.076200Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.13578","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:96e9ef5e8e9960d368e6662d711d3f5200494e9c489b41c17a88a94516a0c862","sha256:2a2d89bd9a085476e270fc50bb2b7c2918b14c63103c164773e0cacdd4eb35e9"],"state_sha256":"39e8ef5615d7e20fdfff7929ebec267246f054d2969f004f7bda712700ea9fb6"}