{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:3Q7M2HHLARPBL3EFNPZQTXMLJM","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":"f68ec85520b0b669bec149dc3263bdbe44462c7caf4e9cb8afef2a0c924fe1d9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2022-03-23T02:16:16Z","title_canon_sha256":"ae3087a89f80aeb661891a6d036d9133a14074c4be374b41d05d106084bc8bae"},"schema_version":"1.0","source":{"id":"2203.12140","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2203.12140","created_at":"2026-07-05T07:37:36Z"},{"alias_kind":"arxiv_version","alias_value":"2203.12140v3","created_at":"2026-07-05T07:37:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.12140","created_at":"2026-07-05T07:37:36Z"},{"alias_kind":"pith_short_12","alias_value":"3Q7M2HHLARPB","created_at":"2026-07-05T07:37:36Z"},{"alias_kind":"pith_short_16","alias_value":"3Q7M2HHLARPBL3EF","created_at":"2026-07-05T07:37:36Z"},{"alias_kind":"pith_short_8","alias_value":"3Q7M2HHL","created_at":"2026-07-05T07:37:36Z"}],"graph_snapshots":[{"event_id":"sha256:f3c81cc50cabeebdea9b25a7a9c78f8888086f89c05260801bcd20f245554cc0","target":"graph","created_at":"2026-07-05T07:37:36Z","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/2203.12140/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"From the notion of (co)generator in relative homological algebra, we present the concept of finite balanced system $[(\\mathcal{X} , \\omega ); (\\nu, \\mathcal{Y})]$ as a tool to induce balanced pairs $(\\mathcal{X} , \\mathcal{Y} )$ for the $\\mathrm{Hom}$ functor with domain determined by the finiteness of homological dimensions relative to $\\mathcal{X}$ and $\\mathcal{Y}$.\n  This approach to balance will cover several well known ambients where right derived functors of $\\mathrm{Hom}$ are obtained relative to certain classes of objects in an abelian category, such as Gorenstein projective and injec","authors_text":"Marco A. P\\'erez, Octavio Mendoza, V\\'ictor Becerril","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2022-03-23T02:16:16Z","title":"Balanced systems for $\\mathrm{Hom}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.12140","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":"sha256:2b7ee651b2369a70665a61479b59ba2cdd25fe40ca529855773587e58bd5d09d","target":"record","created_at":"2026-07-05T07:37:36Z","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":"f68ec85520b0b669bec149dc3263bdbe44462c7caf4e9cb8afef2a0c924fe1d9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2022-03-23T02:16:16Z","title_canon_sha256":"ae3087a89f80aeb661891a6d036d9133a14074c4be374b41d05d106084bc8bae"},"schema_version":"1.0","source":{"id":"2203.12140","kind":"arxiv","version":3}},"canonical_sha256":"dc3ecd1ceb045e15ec856bf309dd8b4b3e7dc420356d8982fe934ff6b138c153","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dc3ecd1ceb045e15ec856bf309dd8b4b3e7dc420356d8982fe934ff6b138c153","first_computed_at":"2026-07-05T07:37:36.517916Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:37:36.517916Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZqaCrlI0hoWeGvR2Tbe4fdreUaabOTYkooF9OSFuAL37/05HkEsPTP4NmtQLsPCdg36kwt2JkwiX1F0zw0bLCg==","signature_status":"signed_v1","signed_at":"2026-07-05T07:37:36.518479Z","signed_message":"canonical_sha256_bytes"},"source_id":"2203.12140","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2b7ee651b2369a70665a61479b59ba2cdd25fe40ca529855773587e58bd5d09d","sha256:f3c81cc50cabeebdea9b25a7a9c78f8888086f89c05260801bcd20f245554cc0"],"state_sha256":"6c5f825345f8254fcecd2437883bf4bb7ecabf73aa38eeb9cfc3351bd26a60a4"}