{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:D2YYVNYVLAENWJVV4KE72OLC63","short_pith_number":"pith:D2YYVNYV","canonical_record":{"source":{"id":"1304.0056","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-03-30T00:59:22Z","cross_cats_sorted":[],"title_canon_sha256":"64d9f2845d8cd2f16df5ea747eb22b3db2c550754f0a9a8208a6e8fa8b36e010","abstract_canon_sha256":"762cc5313655e990cd6723f5215695963250ad8dd5ce3b3cac4f7e8b649a5e46"},"schema_version":"1.0"},"canonical_sha256":"1eb18ab7155808db26b5e289fd3962f6e9755f46105a6dce1648d8e7f81c3a72","source":{"kind":"arxiv","id":"1304.0056","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:D2YYVNYVLAENWJVV4KE72OLC63","target":"record","payload":{"canonical_record":{"source":{"id":"1304.0056","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-03-30T00:59:22Z","cross_cats_sorted":[],"title_canon_sha256":"64d9f2845d8cd2f16df5ea747eb22b3db2c550754f0a9a8208a6e8fa8b36e010","abstract_canon_sha256":"762cc5313655e990cd6723f5215695963250ad8dd5ce3b3cac4f7e8b649a5e46"},"schema_version":"1.0"},"canonical_sha256":"1eb18ab7155808db26b5e289fd3962f6e9755f46105a6dce1648d8e7f81c3a72","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:25:45.659897Z","signature_b64":"6KKA6s5TyIMeFmhZb+iFZRUT53pqzLwFXPLcrXJo8StHSij7LI71MUjTQhY/xkhXmvJ91TEPBy3JkvzZLDUCCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1eb18ab7155808db26b5e289fd3962f6e9755f46105a6dce1648d8e7f81c3a72","last_reissued_at":"2026-05-18T03:25:45.659070Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:25:45.659070Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.0056","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:25:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RdShcdekCAre+o4JA3Mrqicw7MvyPJJKldMKTlyjFki5nEiG8tMY3AmKfLd51OPh44kPHyrnL1OnAp3nZTqgAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T05:17:51.411385Z"},"content_sha256":"9cd7e21a08273fc2ef0166a1d07f6d3da2d57ecea6a93ee8f269f72cd626cc34","schema_version":"1.0","event_id":"sha256:9cd7e21a08273fc2ef0166a1d07f6d3da2d57ecea6a93ee8f269f72cd626cc34"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:D2YYVNYVLAENWJVV4KE72OLC63","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Automorphism-invariant modules satisfy the exchange property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Ashish K. Srivastava, Pedro A Guil Asensio","submitted_at":"2013-03-30T00:59:22Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0056","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:25:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gFs+EaKUj67M/4jQclmOw7Haq3i57QHa3DwGqhrabtKnlYNYwm+lVvzqrUbDHnhwDaIkAxOHoYWlrsta83jLAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T05:17:51.411728Z"},"content_sha256":"4549b171d87b39a91d468241c78ae4d5e5f2e1abfbac8981bfef7e663d8895bd","schema_version":"1.0","event_id":"sha256:4549b171d87b39a91d468241c78ae4d5e5f2e1abfbac8981bfef7e663d8895bd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D2YYVNYVLAENWJVV4KE72OLC63/bundle.json","state_url":"https://pith.science/pith/D2YYVNYVLAENWJVV4KE72OLC63/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D2YYVNYVLAENWJVV4KE72OLC63/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-20T05:17:51Z","links":{"resolver":"https://pith.science/pith/D2YYVNYVLAENWJVV4KE72OLC63","bundle":"https://pith.science/pith/D2YYVNYVLAENWJVV4KE72OLC63/bundle.json","state":"https://pith.science/pith/D2YYVNYVLAENWJVV4KE72OLC63/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D2YYVNYVLAENWJVV4KE72OLC63/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZZcdu02/+rUgWCvUwrxyVf6Rqgg6nnoDS0yad3ZL/sxPHoSle/B9MymXCuB95z9wxmt0KXAWLGpeZ5ZcYwXtDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T05:17:51.413586Z","bundle_sha256":"8cdfbfc24f49445c332a15a9d327c5605aaa6d5ca0c2299dbc534df6706c2e25"}}