{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:ZWX4SE4KVO3GZKZC2YFXAWY5P5","short_pith_number":"pith:ZWX4SE4K","canonical_record":{"source":{"id":"1408.2904","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-08-13T03:03:43Z","cross_cats_sorted":["math.CT","math.RT"],"title_canon_sha256":"4dde265fb29f41e7f9b4bfb5b20abe0844d806c24030b9b934e78cfa84ff5e17","abstract_canon_sha256":"e146db15d4b413515605490108e9438e49a71e93d62433a0d3e96471d749db6a"},"schema_version":"1.0"},"canonical_sha256":"cdafc9138aabb66cab22d60b705b1d7f631898f5d03e34a4f59bbb5cf3e298a7","source":{"kind":"arxiv","id":"1408.2904","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.2904","created_at":"2026-05-18T02:30:08Z"},{"alias_kind":"arxiv_version","alias_value":"1408.2904v2","created_at":"2026-05-18T02:30:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.2904","created_at":"2026-05-18T02:30:08Z"},{"alias_kind":"pith_short_12","alias_value":"ZWX4SE4KVO3G","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZWX4SE4KVO3GZKZC","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZWX4SE4K","created_at":"2026-05-18T12:28:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:ZWX4SE4KVO3GZKZC2YFXAWY5P5","target":"record","payload":{"canonical_record":{"source":{"id":"1408.2904","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-08-13T03:03:43Z","cross_cats_sorted":["math.CT","math.RT"],"title_canon_sha256":"4dde265fb29f41e7f9b4bfb5b20abe0844d806c24030b9b934e78cfa84ff5e17","abstract_canon_sha256":"e146db15d4b413515605490108e9438e49a71e93d62433a0d3e96471d749db6a"},"schema_version":"1.0"},"canonical_sha256":"cdafc9138aabb66cab22d60b705b1d7f631898f5d03e34a4f59bbb5cf3e298a7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:08.001068Z","signature_b64":"B68THSHkR/jkstC3cxJ6MUChr1Jz7OTRRZg/0xXt91HDBQP5IQtjELk5WshzY17q4kWQcBH8chdwdz6pazhuCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cdafc9138aabb66cab22d60b705b1d7f631898f5d03e34a4f59bbb5cf3e298a7","last_reissued_at":"2026-05-18T02:30:08.000605Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:08.000605Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1408.2904","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:30:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2OTvvxCTn2wmx890oDtqt8NuvPESwXQfgIK/5iWPwP2VB4vD9eBmjwns/fPxuABxprR2YCkEXjd8fBHP+Ib5CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T03:52:48.707291Z"},"content_sha256":"47a9f057da9632ee5619281817ee8b52b1fdd40b06487672d5da82d461eb0a8e","schema_version":"1.0","event_id":"sha256:47a9f057da9632ee5619281817ee8b52b1fdd40b06487672d5da82d461eb0a8e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:ZWX4SE4KVO3GZKZC2YFXAWY5P5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The stable category of a left hereditary ring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.RT"],"primary_cat":"math.RA","authors_text":"Alex Martsinkovsky, Dali Zangurashvili","submitted_at":"2014-08-13T03:03:43Z","abstract_excerpt":"The (co)completeness problem for the (projectively) stable module category of an associative ring is studied. (Normal) monomorphisms and (normal) epimorphisms in such a category are characterized. As an application, we give a criterion for the stable category of a left hereditary ring to be abelian. By a structure theorem of Colby-Rutter, this leads to an explicit description of all such rings."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.2904","kind":"arxiv","version":2},"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":"2026-05-18T02:30:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pIbYW9ALQX2tx2ILpg6PqSOaIJbW7sLen1CKJJkQJpux3XCKKqjLlAlgKP9w+jkmX35XkNLIv1/n7/zD/8f1Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T03:52:48.707996Z"},"content_sha256":"e2e55083f70f24bca69614fc97e0b54d2f05f3ef34b1bf90a51550b12bfc33f0","schema_version":"1.0","event_id":"sha256:e2e55083f70f24bca69614fc97e0b54d2f05f3ef34b1bf90a51550b12bfc33f0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZWX4SE4KVO3GZKZC2YFXAWY5P5/bundle.json","state_url":"https://pith.science/pith/ZWX4SE4KVO3GZKZC2YFXAWY5P5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZWX4SE4KVO3GZKZC2YFXAWY5P5/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":"2026-06-09T03:52:48Z","links":{"resolver":"https://pith.science/pith/ZWX4SE4KVO3GZKZC2YFXAWY5P5","bundle":"https://pith.science/pith/ZWX4SE4KVO3GZKZC2YFXAWY5P5/bundle.json","state":"https://pith.science/pith/ZWX4SE4KVO3GZKZC2YFXAWY5P5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZWX4SE4KVO3GZKZC2YFXAWY5P5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ZWX4SE4KVO3GZKZC2YFXAWY5P5","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":"e146db15d4b413515605490108e9438e49a71e93d62433a0d3e96471d749db6a","cross_cats_sorted":["math.CT","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-08-13T03:03:43Z","title_canon_sha256":"4dde265fb29f41e7f9b4bfb5b20abe0844d806c24030b9b934e78cfa84ff5e17"},"schema_version":"1.0","source":{"id":"1408.2904","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.2904","created_at":"2026-05-18T02:30:08Z"},{"alias_kind":"arxiv_version","alias_value":"1408.2904v2","created_at":"2026-05-18T02:30:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.2904","created_at":"2026-05-18T02:30:08Z"},{"alias_kind":"pith_short_12","alias_value":"ZWX4SE4KVO3G","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZWX4SE4KVO3GZKZC","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZWX4SE4K","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:e2e55083f70f24bca69614fc97e0b54d2f05f3ef34b1bf90a51550b12bfc33f0","target":"graph","created_at":"2026-05-18T02:30:08Z","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":"The (co)completeness problem for the (projectively) stable module category of an associative ring is studied. (Normal) monomorphisms and (normal) epimorphisms in such a category are characterized. As an application, we give a criterion for the stable category of a left hereditary ring to be abelian. By a structure theorem of Colby-Rutter, this leads to an explicit description of all such rings.","authors_text":"Alex Martsinkovsky, Dali Zangurashvili","cross_cats":["math.CT","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-08-13T03:03:43Z","title":"The stable category of a left hereditary ring"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.2904","kind":"arxiv","version":2},"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":"sha256:47a9f057da9632ee5619281817ee8b52b1fdd40b06487672d5da82d461eb0a8e","target":"record","created_at":"2026-05-18T02:30:08Z","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":"e146db15d4b413515605490108e9438e49a71e93d62433a0d3e96471d749db6a","cross_cats_sorted":["math.CT","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-08-13T03:03:43Z","title_canon_sha256":"4dde265fb29f41e7f9b4bfb5b20abe0844d806c24030b9b934e78cfa84ff5e17"},"schema_version":"1.0","source":{"id":"1408.2904","kind":"arxiv","version":2}},"canonical_sha256":"cdafc9138aabb66cab22d60b705b1d7f631898f5d03e34a4f59bbb5cf3e298a7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cdafc9138aabb66cab22d60b705b1d7f631898f5d03e34a4f59bbb5cf3e298a7","first_computed_at":"2026-05-18T02:30:08.000605Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:30:08.000605Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B68THSHkR/jkstC3cxJ6MUChr1Jz7OTRRZg/0xXt91HDBQP5IQtjELk5WshzY17q4kWQcBH8chdwdz6pazhuCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:30:08.001068Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.2904","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47a9f057da9632ee5619281817ee8b52b1fdd40b06487672d5da82d461eb0a8e","sha256:e2e55083f70f24bca69614fc97e0b54d2f05f3ef34b1bf90a51550b12bfc33f0"],"state_sha256":"96f96ab6578d4b9a936ae8810a43e25b53bc52e9587bb130ccf9a5d495b0cab1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tnxs6BPDcayMmlglvach//W3pmkNU6Ujjt+BQj079u7u8QpQ+ksuLwLZH+IbLpTsWm9q1DmhPOFXrgUpqWfZCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T03:52:48.712267Z","bundle_sha256":"4fa77846242ebea1e72c08847f0144a5f6b08a78f63799ab4ba9abdafb996118"}}