{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:4WRV2NI34CV3QDYIGINXQVLYQX","short_pith_number":"pith:4WRV2NI3","canonical_record":{"source":{"id":"1106.0913","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-06-05T16:47:04Z","cross_cats_sorted":[],"title_canon_sha256":"6060f6f5cf71088e3908537587af7ddaaaf8d7e921b3a320d6fd58e7832f9221","abstract_canon_sha256":"ee41ded333c50df4fcbb5469d62737a058bba87e06d2289d6d2484e66e26b427"},"schema_version":"1.0"},"canonical_sha256":"e5a35d351be0abb80f08321b78557885d404a827b2440bbdc93739a906edbb6a","source":{"kind":"arxiv","id":"1106.0913","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.0913","created_at":"2026-05-18T04:20:37Z"},{"alias_kind":"arxiv_version","alias_value":"1106.0913v1","created_at":"2026-05-18T04:20:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.0913","created_at":"2026-05-18T04:20:37Z"},{"alias_kind":"pith_short_12","alias_value":"4WRV2NI34CV3","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"4WRV2NI34CV3QDYI","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"4WRV2NI3","created_at":"2026-05-18T12:26:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:4WRV2NI34CV3QDYIGINXQVLYQX","target":"record","payload":{"canonical_record":{"source":{"id":"1106.0913","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-06-05T16:47:04Z","cross_cats_sorted":[],"title_canon_sha256":"6060f6f5cf71088e3908537587af7ddaaaf8d7e921b3a320d6fd58e7832f9221","abstract_canon_sha256":"ee41ded333c50df4fcbb5469d62737a058bba87e06d2289d6d2484e66e26b427"},"schema_version":"1.0"},"canonical_sha256":"e5a35d351be0abb80f08321b78557885d404a827b2440bbdc93739a906edbb6a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:20:37.035807Z","signature_b64":"z5+u8tDxQ8Ej5ly7eBqRPmz7Ez0BNGtniBp7Ad71UyX4+PVbozCrDVm4Lkb9zukLs8b+oyPYkQgB9o+fXDxdDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e5a35d351be0abb80f08321b78557885d404a827b2440bbdc93739a906edbb6a","last_reissued_at":"2026-05-18T04:20:37.035049Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:20:37.035049Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1106.0913","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":"2026-05-18T04:20:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ONlQ4ObahLIM7UU4C4LfwDItrfKfsVFPiubbkQySr3Qnn1+2G86umw7ZE68hHepBhAhUwDG5gBRY2J4qFSuGCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T05:17:36.981620Z"},"content_sha256":"cff929270393aee555c1f1620da30e1bc12ed1c4839bcce734bb8a1fd3d2844f","schema_version":"1.0","event_id":"sha256:cff929270393aee555c1f1620da30e1bc12ed1c4839bcce734bb8a1fd3d2844f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:4WRV2NI34CV3QDYIGINXQVLYQX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Square-Free Rings With Local Units","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Martin Montgomery","submitted_at":"2011-06-05T16:47:04Z","abstract_excerpt":"Recently, the author characterized all artinian square-free rings with identity. Here, those results are extended to the setting of rings with local units. We use this characterization of square-free rings to derive many results similar to the artinian case and to determine, in cohomological terms, exactly when a square-free ring has an associated square-free algebra structure."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.0913","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":"2026-05-18T04:20:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5D9c6zt65pU+27U0fa0c1+ExagDBHB8W3QDrC8GAhJsQjUdm5W6eHOVrCNA3UtVxU/ENxLSZl3a4X33T+vmZAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T05:17:36.982000Z"},"content_sha256":"57fcfa07d3542e92a3800703f62695247fd9531028238ad5de07d261482ffb48","schema_version":"1.0","event_id":"sha256:57fcfa07d3542e92a3800703f62695247fd9531028238ad5de07d261482ffb48"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4WRV2NI34CV3QDYIGINXQVLYQX/bundle.json","state_url":"https://pith.science/pith/4WRV2NI34CV3QDYIGINXQVLYQX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4WRV2NI34CV3QDYIGINXQVLYQX/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":"2026-05-31T05:17:36Z","links":{"resolver":"https://pith.science/pith/4WRV2NI34CV3QDYIGINXQVLYQX","bundle":"https://pith.science/pith/4WRV2NI34CV3QDYIGINXQVLYQX/bundle.json","state":"https://pith.science/pith/4WRV2NI34CV3QDYIGINXQVLYQX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4WRV2NI34CV3QDYIGINXQVLYQX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:4WRV2NI34CV3QDYIGINXQVLYQX","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":"ee41ded333c50df4fcbb5469d62737a058bba87e06d2289d6d2484e66e26b427","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-06-05T16:47:04Z","title_canon_sha256":"6060f6f5cf71088e3908537587af7ddaaaf8d7e921b3a320d6fd58e7832f9221"},"schema_version":"1.0","source":{"id":"1106.0913","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.0913","created_at":"2026-05-18T04:20:37Z"},{"alias_kind":"arxiv_version","alias_value":"1106.0913v1","created_at":"2026-05-18T04:20:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.0913","created_at":"2026-05-18T04:20:37Z"},{"alias_kind":"pith_short_12","alias_value":"4WRV2NI34CV3","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"4WRV2NI34CV3QDYI","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"4WRV2NI3","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:57fcfa07d3542e92a3800703f62695247fd9531028238ad5de07d261482ffb48","target":"graph","created_at":"2026-05-18T04:20:37Z","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":"Recently, the author characterized all artinian square-free rings with identity. Here, those results are extended to the setting of rings with local units. We use this characterization of square-free rings to derive many results similar to the artinian case and to determine, in cohomological terms, exactly when a square-free ring has an associated square-free algebra structure.","authors_text":"Martin Montgomery","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-06-05T16:47:04Z","title":"Square-Free Rings With Local Units"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.0913","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:cff929270393aee555c1f1620da30e1bc12ed1c4839bcce734bb8a1fd3d2844f","target":"record","created_at":"2026-05-18T04:20:37Z","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":"ee41ded333c50df4fcbb5469d62737a058bba87e06d2289d6d2484e66e26b427","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-06-05T16:47:04Z","title_canon_sha256":"6060f6f5cf71088e3908537587af7ddaaaf8d7e921b3a320d6fd58e7832f9221"},"schema_version":"1.0","source":{"id":"1106.0913","kind":"arxiv","version":1}},"canonical_sha256":"e5a35d351be0abb80f08321b78557885d404a827b2440bbdc93739a906edbb6a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e5a35d351be0abb80f08321b78557885d404a827b2440bbdc93739a906edbb6a","first_computed_at":"2026-05-18T04:20:37.035049Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:20:37.035049Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z5+u8tDxQ8Ej5ly7eBqRPmz7Ez0BNGtniBp7Ad71UyX4+PVbozCrDVm4Lkb9zukLs8b+oyPYkQgB9o+fXDxdDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:20:37.035807Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.0913","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cff929270393aee555c1f1620da30e1bc12ed1c4839bcce734bb8a1fd3d2844f","sha256:57fcfa07d3542e92a3800703f62695247fd9531028238ad5de07d261482ffb48"],"state_sha256":"0674c487fe5a155e827269e368e7f4e4f23db1cc90d18dcdcbca0df874b5a3a9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VHBeMYxlqS0g1hPXTfEyI7DIONX2k1PLIdHxa6nx1dt/jBglWyqqtFGhEotlybf9/9VzaPDvhAnuqn3muTTaDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T05:17:36.984065Z","bundle_sha256":"a6ffc0d9484a37ae0c2e2171826b0c6151999ec7ea04ea5a56c9269ed1741a15"}}