{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:D2YYVNYVLAENWJVV4KE72OLC63","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":"762cc5313655e990cd6723f5215695963250ad8dd5ce3b3cac4f7e8b649a5e46","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-03-30T00:59:22Z","title_canon_sha256":"64d9f2845d8cd2f16df5ea747eb22b3db2c550754f0a9a8208a6e8fa8b36e010"},"schema_version":"1.0","source":{"id":"1304.0056","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.0056","created_at":"2026-05-18T03:25:45Z"},{"alias_kind":"arxiv_version","alias_value":"1304.0056v3","created_at":"2026-05-18T03:25:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.0056","created_at":"2026-05-18T03:25:45Z"},{"alias_kind":"pith_short_12","alias_value":"D2YYVNYVLAEN","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"D2YYVNYVLAENWJVV","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"D2YYVNYV","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:4549b171d87b39a91d468241c78ae4d5e5f2e1abfbac8981bfef7e663d8895bd","target":"graph","created_at":"2026-05-18T03:25:45Z","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":"Warfield proved that every injective module has the exchange property. This was generalized by Fuchs who showed that quasi-injective modules satisfy the exchange property. We extend this further and prove that a module invariant under automorphisms of its injective hull satisfies the exchange property. We also show that automorphism-invariant modules are clean and that directly-finite automorphism-invariant modules satisfy the internal cancellation and hence the cancellation property.","authors_text":"Ashish K. Srivastava, Pedro A Guil Asensio","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-03-30T00:59:22Z","title":"Automorphism-invariant modules satisfy the exchange property"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0056","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":"sha256:9cd7e21a08273fc2ef0166a1d07f6d3da2d57ecea6a93ee8f269f72cd626cc34","target":"record","created_at":"2026-05-18T03:25:45Z","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":"762cc5313655e990cd6723f5215695963250ad8dd5ce3b3cac4f7e8b649a5e46","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-03-30T00:59:22Z","title_canon_sha256":"64d9f2845d8cd2f16df5ea747eb22b3db2c550754f0a9a8208a6e8fa8b36e010"},"schema_version":"1.0","source":{"id":"1304.0056","kind":"arxiv","version":3}},"canonical_sha256":"1eb18ab7155808db26b5e289fd3962f6e9755f46105a6dce1648d8e7f81c3a72","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1eb18ab7155808db26b5e289fd3962f6e9755f46105a6dce1648d8e7f81c3a72","first_computed_at":"2026-05-18T03:25:45.659070Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:25:45.659070Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6KKA6s5TyIMeFmhZb+iFZRUT53pqzLwFXPLcrXJo8StHSij7LI71MUjTQhY/xkhXmvJ91TEPBy3JkvzZLDUCCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:25:45.659897Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.0056","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9cd7e21a08273fc2ef0166a1d07f6d3da2d57ecea6a93ee8f269f72cd626cc34","sha256:4549b171d87b39a91d468241c78ae4d5e5f2e1abfbac8981bfef7e663d8895bd"],"state_sha256":"a89730fe59ba29f03d837e041aa65e32093a74f4e7b740e3ee98c6121387bf7d"}