{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:CYW6IK6C7WB5EDAKCDSHCDLVK3","short_pith_number":"pith:CYW6IK6C","canonical_record":{"source":{"id":"1001.2457","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-01-14T13:31:22Z","cross_cats_sorted":["math.AC","math.AT","math.RA"],"title_canon_sha256":"8fadab8af918d9b9420b0dd91e2059810be188733a60765cab86ca597b3c10b3","abstract_canon_sha256":"e5a544bda363d8008ae169244b9e57bb01a7969ca0fe644dd63075c17d97a058"},"schema_version":"1.0"},"canonical_sha256":"162de42bc2fd83d20c0a10e4710d7556f29988859db343b06d80aa67b17d79f3","source":{"kind":"arxiv","id":"1001.2457","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.2457","created_at":"2026-05-18T04:34:27Z"},{"alias_kind":"arxiv_version","alias_value":"1001.2457v1","created_at":"2026-05-18T04:34:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.2457","created_at":"2026-05-18T04:34:27Z"},{"alias_kind":"pith_short_12","alias_value":"CYW6IK6C7WB5","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"CYW6IK6C7WB5EDAK","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"CYW6IK6C","created_at":"2026-05-18T12:26:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:CYW6IK6C7WB5EDAKCDSHCDLVK3","target":"record","payload":{"canonical_record":{"source":{"id":"1001.2457","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-01-14T13:31:22Z","cross_cats_sorted":["math.AC","math.AT","math.RA"],"title_canon_sha256":"8fadab8af918d9b9420b0dd91e2059810be188733a60765cab86ca597b3c10b3","abstract_canon_sha256":"e5a544bda363d8008ae169244b9e57bb01a7969ca0fe644dd63075c17d97a058"},"schema_version":"1.0"},"canonical_sha256":"162de42bc2fd83d20c0a10e4710d7556f29988859db343b06d80aa67b17d79f3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:34:27.857933Z","signature_b64":"8qtYl0WKW6X/CcB1NidXoEGecH6iM9UjsrjGEJ/QMh+n5m9ZZhpLLtaAviDTi+BmAy3aRXVmQv+yysJdoirNBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"162de42bc2fd83d20c0a10e4710d7556f29988859db343b06d80aa67b17d79f3","last_reissued_at":"2026-05-18T04:34:27.857509Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:34:27.857509Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1001.2457","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:34:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6GI9g6V1N6pmJ7jn0KUq6qSqRSupIlO16YLfSGu7TT0ZYnO0EzdGb4jrwCZY+sKK05oQIvAS9MXRA5tGRBxeDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T15:50:11.566015Z"},"content_sha256":"fd11f5efb26afb6e47d75f7d14ce7381a19635ce5bcb4685fa9d9339b4b32517","schema_version":"1.0","event_id":"sha256:fd11f5efb26afb6e47d75f7d14ce7381a19635ce5bcb4685fa9d9339b4b32517"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:CYW6IK6C7WB5EDAKCDSHCDLVK3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On cellular covers with free kernels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.AT","math.RA"],"primary_cat":"math.GR","authors_text":"Jos\\'e L. Rodr\\'iguez, Lutz Str\\\"ungmann","submitted_at":"2010-01-14T13:31:22Z","abstract_excerpt":"Recall that a homomorphism of $R$-modules $\\pi: G\\to H$ is called a {\\it cellular cover} over $H$ if $\\pi$ induces an isomorphism $\\pi_*: \\Hom_R(G,G)\\cong \\Hom_R(G,H),$ where $\\pi_*(\\varphi)= \\pi \\varphi$ for each $\\varphi \\in \\Hom_R(G,G)$ (where maps are acting on the left). In this paper we show that every cotorsion-free module $K$ of finite rank can be realized as the kernel of a cellular cover of some cotorsion-free module of rank 2. In particular, every free abelian group of any finite rank appears then as the kernel of a cellular cover of a cotorsion-free abelian group of rank 2. This si"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.2457","kind":"arxiv","version":1},"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":"2026-05-18T04:34:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"csZuxo8EE9Zpkaae64GI8vApkRM3V1RAAUryBlZ4DsjyOc68skJkcxFHlr73TQu0OKuTjLVWrbVTXs3L0GyODg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T15:50:11.566388Z"},"content_sha256":"a40fcaad333a7163602d336f88378f256f34683bf870761551b072ccecc3693c","schema_version":"1.0","event_id":"sha256:a40fcaad333a7163602d336f88378f256f34683bf870761551b072ccecc3693c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CYW6IK6C7WB5EDAKCDSHCDLVK3/bundle.json","state_url":"https://pith.science/pith/CYW6IK6C7WB5EDAKCDSHCDLVK3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CYW6IK6C7WB5EDAKCDSHCDLVK3/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":"2026-06-05T15:50:11Z","links":{"resolver":"https://pith.science/pith/CYW6IK6C7WB5EDAKCDSHCDLVK3","bundle":"https://pith.science/pith/CYW6IK6C7WB5EDAKCDSHCDLVK3/bundle.json","state":"https://pith.science/pith/CYW6IK6C7WB5EDAKCDSHCDLVK3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CYW6IK6C7WB5EDAKCDSHCDLVK3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:CYW6IK6C7WB5EDAKCDSHCDLVK3","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":"e5a544bda363d8008ae169244b9e57bb01a7969ca0fe644dd63075c17d97a058","cross_cats_sorted":["math.AC","math.AT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-01-14T13:31:22Z","title_canon_sha256":"8fadab8af918d9b9420b0dd91e2059810be188733a60765cab86ca597b3c10b3"},"schema_version":"1.0","source":{"id":"1001.2457","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.2457","created_at":"2026-05-18T04:34:27Z"},{"alias_kind":"arxiv_version","alias_value":"1001.2457v1","created_at":"2026-05-18T04:34:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.2457","created_at":"2026-05-18T04:34:27Z"},{"alias_kind":"pith_short_12","alias_value":"CYW6IK6C7WB5","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"CYW6IK6C7WB5EDAK","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"CYW6IK6C","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:a40fcaad333a7163602d336f88378f256f34683bf870761551b072ccecc3693c","target":"graph","created_at":"2026-05-18T04:34:27Z","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":"Recall that a homomorphism of $R$-modules $\\pi: G\\to H$ is called a {\\it cellular cover} over $H$ if $\\pi$ induces an isomorphism $\\pi_*: \\Hom_R(G,G)\\cong \\Hom_R(G,H),$ where $\\pi_*(\\varphi)= \\pi \\varphi$ for each $\\varphi \\in \\Hom_R(G,G)$ (where maps are acting on the left). In this paper we show that every cotorsion-free module $K$ of finite rank can be realized as the kernel of a cellular cover of some cotorsion-free module of rank 2. In particular, every free abelian group of any finite rank appears then as the kernel of a cellular cover of a cotorsion-free abelian group of rank 2. This si","authors_text":"Jos\\'e L. Rodr\\'iguez, Lutz Str\\\"ungmann","cross_cats":["math.AC","math.AT","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-01-14T13:31:22Z","title":"On cellular covers with free kernels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.2457","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:fd11f5efb26afb6e47d75f7d14ce7381a19635ce5bcb4685fa9d9339b4b32517","target":"record","created_at":"2026-05-18T04:34:27Z","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":"e5a544bda363d8008ae169244b9e57bb01a7969ca0fe644dd63075c17d97a058","cross_cats_sorted":["math.AC","math.AT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-01-14T13:31:22Z","title_canon_sha256":"8fadab8af918d9b9420b0dd91e2059810be188733a60765cab86ca597b3c10b3"},"schema_version":"1.0","source":{"id":"1001.2457","kind":"arxiv","version":1}},"canonical_sha256":"162de42bc2fd83d20c0a10e4710d7556f29988859db343b06d80aa67b17d79f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"162de42bc2fd83d20c0a10e4710d7556f29988859db343b06d80aa67b17d79f3","first_computed_at":"2026-05-18T04:34:27.857509Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:34:27.857509Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8qtYl0WKW6X/CcB1NidXoEGecH6iM9UjsrjGEJ/QMh+n5m9ZZhpLLtaAviDTi+BmAy3aRXVmQv+yysJdoirNBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:34:27.857933Z","signed_message":"canonical_sha256_bytes"},"source_id":"1001.2457","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd11f5efb26afb6e47d75f7d14ce7381a19635ce5bcb4685fa9d9339b4b32517","sha256:a40fcaad333a7163602d336f88378f256f34683bf870761551b072ccecc3693c"],"state_sha256":"bc06cb8b941acf06be1905af105d7ca0f51361a27d15fb1b8e5e7097293ffc6c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7TMHmVBhYfGdhwo2JeuFBi7pO81uCy1EitvQXMt1GV1EKJV5z+lvj7tEsVycXt5w3Ym1aDMSax6lllU7zV1RCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T15:50:11.569098Z","bundle_sha256":"e7fe04e971661e2ade436d5210c8e94afd86ecd08fd8725d64de888a4b352b19"}}