{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:DWO4W7TXESV6YAP3VOF2G5SBR4","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":"3ebbda717e67d05f034007ab24fb476ac26b5f99509465109a6fd4a2a5f81de8","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2025-03-05T18:56:07Z","title_canon_sha256":"49a5818b8c90cea7ffc4ab1896e3b72f8c2175603599084bbd00b6489a336d31"},"schema_version":"1.0","source":{"id":"2503.03741","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.03741","created_at":"2026-07-05T11:42:26Z"},{"alias_kind":"arxiv_version","alias_value":"2503.03741v3","created_at":"2026-07-05T11:42:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.03741","created_at":"2026-07-05T11:42:26Z"},{"alias_kind":"pith_short_12","alias_value":"DWO4W7TXESV6","created_at":"2026-07-05T11:42:26Z"},{"alias_kind":"pith_short_16","alias_value":"DWO4W7TXESV6YAP3","created_at":"2026-07-05T11:42:26Z"},{"alias_kind":"pith_short_8","alias_value":"DWO4W7TX","created_at":"2026-07-05T11:42:26Z"}],"graph_snapshots":[{"event_id":"sha256:f256ca50dc6efe1fa094f5a5485549e504ac184945132f9f519bb0f56549dab1","target":"graph","created_at":"2026-07-05T11:42:26Z","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/2503.03741/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $G$ be a finite abelian group written multiplicatively, with $\\hat{G} = G\\sqcup \\{0\\}$ the pointed abelian group formed by adjoining an absorbing element $0$. There is an associated finitary, proto-abelian category $\\operatorname{Vect}_{\\hat{G}}$, whose objects can be thought of as finite-dimensional vector spaces over $\\hat{G}$. The class of $\\hat{G}$-linear monoids are then defined in terms of this category. In this paper, we study the finitary, proto-abelian category $\\operatorname{Rep}(M,\\hat{G})$ of finite-dimensional $\\hat{G}$-linear representations of a $\\hat{G}$-linear monoid $M$. ","authors_text":"Alexander Sistko","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2025-03-05T18:56:07Z","title":"On Semisimple Proto-Abelian Categories Associated to Inverse Monoids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.03741","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":"sha256:605a0d44ccb139ffb53d79d725a839a9f4e16132b81a7b34ebc8c1e990c590f0","target":"record","created_at":"2026-07-05T11:42:26Z","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":"3ebbda717e67d05f034007ab24fb476ac26b5f99509465109a6fd4a2a5f81de8","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2025-03-05T18:56:07Z","title_canon_sha256":"49a5818b8c90cea7ffc4ab1896e3b72f8c2175603599084bbd00b6489a336d31"},"schema_version":"1.0","source":{"id":"2503.03741","kind":"arxiv","version":3}},"canonical_sha256":"1d9dcb7e7724abec01fbab8ba376418f17c30adada92f06c64167b57dfe46d9d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1d9dcb7e7724abec01fbab8ba376418f17c30adada92f06c64167b57dfe46d9d","first_computed_at":"2026-07-05T11:42:26.787867Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:42:26.787867Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XbKPUz4UPNqugTbitYCg91+W5fM7gOeeB6lrevLcApxJE6d4wHvOr9Go+hxeblkGyBoDr6z/165xBlMHCUmsDw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:42:26.788346Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.03741","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:605a0d44ccb139ffb53d79d725a839a9f4e16132b81a7b34ebc8c1e990c590f0","sha256:f256ca50dc6efe1fa094f5a5485549e504ac184945132f9f519bb0f56549dab1"],"state_sha256":"74307478936e22acb645d4502d853b7a10caa80f9a396eb35f3ec3dad570264a"}