{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:E5OPQVUG6GCX46KGIQJAGSDTT6","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":"176a84d10bd1caa3605dd813e862a8e7f7acc32dd96fec17978239aaf45e5b21","cross_cats_sorted":["math.CT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-10-24T01:27:57Z","title_canon_sha256":"125546f37a1d595bf30ca65e0322045a04fcdf04b16526868d1fa6b5f29b783d"},"schema_version":"1.0","source":{"id":"1510.07098","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.07098","created_at":"2026-05-18T01:29:20Z"},{"alias_kind":"arxiv_version","alias_value":"1510.07098v1","created_at":"2026-05-18T01:29:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.07098","created_at":"2026-05-18T01:29:20Z"},{"alias_kind":"pith_short_12","alias_value":"E5OPQVUG6GCX","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"E5OPQVUG6GCX46KG","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"E5OPQVUG","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:870274b512fc5d7f964145038ee6ae10ac695aff349456b3ab41dda49ccb18b1","target":"graph","created_at":"2026-05-18T01:29:20Z","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":"In an abelian category $\\mathscr{A}$ with small ${\\rm Ext}$ groups, we show that there exists a one-to-one correspondence between any two of the following: balanced pairs, subfunctors $\\mathcal{F}$ of ${\\rm Ext}^{1}_{\\mathscr{A}}(-,-)$ such that $\\mathscr{A}$ has enough $\\mathcal{F}$-projectives and enough $\\mathcal{F}$-injectives and Quillen exact structures $\\mathcal{E}$ with enough $\\mathcal{E}$-projectives and enough $\\mathcal{E}$-injectives. In this case, we get a strengthened version of the translation of the Wakamatsu lemma to the exact context, and also prove that subcategories which a","authors_text":"Junfu Wang, Zhaoyong Huang","cross_cats":["math.CT","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-10-24T01:27:57Z","title":"Applications of Exact Structures in Abelian Categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.07098","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":"sha256:9ed5324f309449a804707db8e87c5cfb16dac9a66fb2f3a19decf4978c0013f5","target":"record","created_at":"2026-05-18T01:29:20Z","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":"176a84d10bd1caa3605dd813e862a8e7f7acc32dd96fec17978239aaf45e5b21","cross_cats_sorted":["math.CT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-10-24T01:27:57Z","title_canon_sha256":"125546f37a1d595bf30ca65e0322045a04fcdf04b16526868d1fa6b5f29b783d"},"schema_version":"1.0","source":{"id":"1510.07098","kind":"arxiv","version":1}},"canonical_sha256":"275cf85686f1857e794644120348739f8403f05d10065675b6125b6d3ffb63c0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"275cf85686f1857e794644120348739f8403f05d10065675b6125b6d3ffb63c0","first_computed_at":"2026-05-18T01:29:20.121073Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:29:20.121073Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kK8suCN22vextSc96ou/J+iMOSAJC5SYGgrjqyOhIzLGpLakKUWWwCI3S+M36XIjfhLOA0uhRLDipVGcsoyPBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:29:20.121830Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.07098","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9ed5324f309449a804707db8e87c5cfb16dac9a66fb2f3a19decf4978c0013f5","sha256:870274b512fc5d7f964145038ee6ae10ac695aff349456b3ab41dda49ccb18b1"],"state_sha256":"d670942a9011ec59567bee2dcba037b9ce000dc121bd586d9d12bb1048d4ee16"}