{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:JWRLKCN7HJHJ6KVVUN2VUAWUFW","short_pith_number":"pith:JWRLKCN7","canonical_record":{"source":{"id":"1504.01631","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-04-07T15:12:25Z","cross_cats_sorted":[],"title_canon_sha256":"103a43d0e3cce940783013141b816fd8a82613c34ae032604f4755b9539f84cd","abstract_canon_sha256":"13b6f4c2d87c5e1adf358d8116d4b385d3377cd21369ae7df7bd2172e3bcdadf"},"schema_version":"1.0"},"canonical_sha256":"4da2b509bf3a4e9f2ab5a3755a02d42d8b94bd23a9067b5f6c99463db2265f00","source":{"kind":"arxiv","id":"1504.01631","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.01631","created_at":"2026-05-18T02:12:10Z"},{"alias_kind":"arxiv_version","alias_value":"1504.01631v4","created_at":"2026-05-18T02:12:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.01631","created_at":"2026-05-18T02:12:10Z"},{"alias_kind":"pith_short_12","alias_value":"JWRLKCN7HJHJ","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JWRLKCN7HJHJ6KVV","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JWRLKCN7","created_at":"2026-05-18T12:29:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:JWRLKCN7HJHJ6KVVUN2VUAWUFW","target":"record","payload":{"canonical_record":{"source":{"id":"1504.01631","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-04-07T15:12:25Z","cross_cats_sorted":[],"title_canon_sha256":"103a43d0e3cce940783013141b816fd8a82613c34ae032604f4755b9539f84cd","abstract_canon_sha256":"13b6f4c2d87c5e1adf358d8116d4b385d3377cd21369ae7df7bd2172e3bcdadf"},"schema_version":"1.0"},"canonical_sha256":"4da2b509bf3a4e9f2ab5a3755a02d42d8b94bd23a9067b5f6c99463db2265f00","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:12:10.606988Z","signature_b64":"9pA6ZEDNL6tst5zbFEbbIfoaip1GWhdokLVu1pQ2ekVZOyKy+2uST5UtrJwwsbdppGBQxj/eX/aWyjmSvDFxAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4da2b509bf3a4e9f2ab5a3755a02d42d8b94bd23a9067b5f6c99463db2265f00","last_reissued_at":"2026-05-18T02:12:10.606243Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:12:10.606243Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.01631","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:12:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wBXoaRKWrw1Rsr6nE+Nvyxau+MKwv7Ftj9IMvWVwGbiaSMS7UkLYwaTwXKoj2+bAddnY2jaMdTXqFBelcFZ8AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T20:03:56.360367Z"},"content_sha256":"695b535d281b2870cfc3b8b6dfad95e6a961364a0d7414393f2f96067e2dd0f1","schema_version":"1.0","event_id":"sha256:695b535d281b2870cfc3b8b6dfad95e6a961364a0d7414393f2f96067e2dd0f1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:JWRLKCN7HJHJ6KVVUN2VUAWUFW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the non-existence of right almost split maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Jan \\v{S}aroch","submitted_at":"2015-04-07T15:12:25Z","abstract_excerpt":"We show that, over any ring, a module $C$ is a codomain of a right almost split map if and only if $C$ is a finitely presented module with local endomorphism ring; thus we give an answer to a 40 years old question by M. Auslander. Using the tools developed, we also provide a useful sufficient condition for a class of modules to be non-precovering. Finally, we show a non-trivial application in the general context of morphisms determined by object."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01631","kind":"arxiv","version":4},"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":"2026-05-18T02:12:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D+Ma/QuB2diKIkRbNrrOui1D+aIUQMyO0hAHWTYiNfSObQw7YaCfEZf/f9cTsXsTzl/UcdcyRAvhsf446Ey7Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T20:03:56.360718Z"},"content_sha256":"c6b8bf4e1e89ff48847c451a333ac2163ed58ae61e442bbe402db62fdc1ce236","schema_version":"1.0","event_id":"sha256:c6b8bf4e1e89ff48847c451a333ac2163ed58ae61e442bbe402db62fdc1ce236"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JWRLKCN7HJHJ6KVVUN2VUAWUFW/bundle.json","state_url":"https://pith.science/pith/JWRLKCN7HJHJ6KVVUN2VUAWUFW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JWRLKCN7HJHJ6KVVUN2VUAWUFW/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":"2026-06-10T20:03:56Z","links":{"resolver":"https://pith.science/pith/JWRLKCN7HJHJ6KVVUN2VUAWUFW","bundle":"https://pith.science/pith/JWRLKCN7HJHJ6KVVUN2VUAWUFW/bundle.json","state":"https://pith.science/pith/JWRLKCN7HJHJ6KVVUN2VUAWUFW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JWRLKCN7HJHJ6KVVUN2VUAWUFW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:JWRLKCN7HJHJ6KVVUN2VUAWUFW","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":"13b6f4c2d87c5e1adf358d8116d4b385d3377cd21369ae7df7bd2172e3bcdadf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-04-07T15:12:25Z","title_canon_sha256":"103a43d0e3cce940783013141b816fd8a82613c34ae032604f4755b9539f84cd"},"schema_version":"1.0","source":{"id":"1504.01631","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.01631","created_at":"2026-05-18T02:12:10Z"},{"alias_kind":"arxiv_version","alias_value":"1504.01631v4","created_at":"2026-05-18T02:12:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.01631","created_at":"2026-05-18T02:12:10Z"},{"alias_kind":"pith_short_12","alias_value":"JWRLKCN7HJHJ","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JWRLKCN7HJHJ6KVV","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JWRLKCN7","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:c6b8bf4e1e89ff48847c451a333ac2163ed58ae61e442bbe402db62fdc1ce236","target":"graph","created_at":"2026-05-18T02:12:10Z","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":"We show that, over any ring, a module $C$ is a codomain of a right almost split map if and only if $C$ is a finitely presented module with local endomorphism ring; thus we give an answer to a 40 years old question by M. Auslander. Using the tools developed, we also provide a useful sufficient condition for a class of modules to be non-precovering. Finally, we show a non-trivial application in the general context of morphisms determined by object.","authors_text":"Jan \\v{S}aroch","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-04-07T15:12:25Z","title":"On the non-existence of right almost split maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01631","kind":"arxiv","version":4},"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":"sha256:695b535d281b2870cfc3b8b6dfad95e6a961364a0d7414393f2f96067e2dd0f1","target":"record","created_at":"2026-05-18T02:12:10Z","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":"13b6f4c2d87c5e1adf358d8116d4b385d3377cd21369ae7df7bd2172e3bcdadf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-04-07T15:12:25Z","title_canon_sha256":"103a43d0e3cce940783013141b816fd8a82613c34ae032604f4755b9539f84cd"},"schema_version":"1.0","source":{"id":"1504.01631","kind":"arxiv","version":4}},"canonical_sha256":"4da2b509bf3a4e9f2ab5a3755a02d42d8b94bd23a9067b5f6c99463db2265f00","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4da2b509bf3a4e9f2ab5a3755a02d42d8b94bd23a9067b5f6c99463db2265f00","first_computed_at":"2026-05-18T02:12:10.606243Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:12:10.606243Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9pA6ZEDNL6tst5zbFEbbIfoaip1GWhdokLVu1pQ2ekVZOyKy+2uST5UtrJwwsbdppGBQxj/eX/aWyjmSvDFxAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:12:10.606988Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.01631","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:695b535d281b2870cfc3b8b6dfad95e6a961364a0d7414393f2f96067e2dd0f1","sha256:c6b8bf4e1e89ff48847c451a333ac2163ed58ae61e442bbe402db62fdc1ce236"],"state_sha256":"382551a88bdc98245a53e840687fe2d23b241ac0b71711502e4decf73a2910b9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2E29MdZ8kr0WHCnANhEnFSfJFuKSBT+MA53uwhGnhwiUtqw1m0TTAIV+xUbnUurbCAcv36xAwHNWlRRkUC1xDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T20:03:56.362609Z","bundle_sha256":"b6a08912ae77e0f6a085df84a38e49328aa593417314405d752b0a629bcee632"}}