{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:ITXI4H6ER3Q7VKSFR6RNWMHLAN","short_pith_number":"pith:ITXI4H6E","canonical_record":{"source":{"id":"1710.00097","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-09-29T21:25:34Z","cross_cats_sorted":[],"title_canon_sha256":"8f27a0c091e2d4955f3731454457582d23db0c8bb616b396b08c595dfb5ba619","abstract_canon_sha256":"7c8c6295bf3dd8b6bd7873513a35b54a131353d472d75c866f44879a6142660e"},"schema_version":"1.0"},"canonical_sha256":"44ee8e1fc48ee1faaa458fa2db30eb03763b54178aaa74241abe8fe2712d4193","source":{"kind":"arxiv","id":"1710.00097","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.00097","created_at":"2026-05-18T00:33:57Z"},{"alias_kind":"arxiv_version","alias_value":"1710.00097v1","created_at":"2026-05-18T00:33:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.00097","created_at":"2026-05-18T00:33:57Z"},{"alias_kind":"pith_short_12","alias_value":"ITXI4H6ER3Q7","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"ITXI4H6ER3Q7VKSF","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"ITXI4H6E","created_at":"2026-05-18T12:31:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:ITXI4H6ER3Q7VKSFR6RNWMHLAN","target":"record","payload":{"canonical_record":{"source":{"id":"1710.00097","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-09-29T21:25:34Z","cross_cats_sorted":[],"title_canon_sha256":"8f27a0c091e2d4955f3731454457582d23db0c8bb616b396b08c595dfb5ba619","abstract_canon_sha256":"7c8c6295bf3dd8b6bd7873513a35b54a131353d472d75c866f44879a6142660e"},"schema_version":"1.0"},"canonical_sha256":"44ee8e1fc48ee1faaa458fa2db30eb03763b54178aaa74241abe8fe2712d4193","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:57.918604Z","signature_b64":"Yeft5n3pcYSG7sQ4lVe7tj7+tQpn0t0UU+Y8kXaZ0m/NQ1jiyuUORC9UrNQzeLNIZNucQRGPTnNS3n91QJTODA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"44ee8e1fc48ee1faaa458fa2db30eb03763b54178aaa74241abe8fe2712d4193","last_reissued_at":"2026-05-18T00:33:57.918027Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:57.918027Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.00097","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":"2026-05-18T00:33:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7MCVfQz8Ng9vN7kXevwI2kGb8K+pfHB22c9g+vckk/HDSwOEwwnQwNRI/tcC2aLuaenI7LCXK0q4pNS00GDKDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T00:41:40.366551Z"},"content_sha256":"5d590b990fb2b3b4a3b00fa99618410b967cf5f44a36b8ab9001d54d64f19d91","schema_version":"1.0","event_id":"sha256:5d590b990fb2b3b4a3b00fa99618410b967cf5f44a36b8ab9001d54d64f19d91"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:ITXI4H6ER3Q7VKSFR6RNWMHLAN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Equivalence of Some Homological Conditions for Ring Epimorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Alberto Facchini, Zahra Nazemian","submitted_at":"2017-09-29T21:25:34Z","abstract_excerpt":"Let $R$ be a right and left Ore ring, $S$ its set of regular elements and $Q = R[S^{-1}] = [S^{-1}] R$ the classical ring of quotients of $R$. We prove that if F.dim$(Q_Q) = 0$, then the following conditions are equivalent: $(i)$ Flat right $R$-modules are strongly flat. $ (ii)$ Matlis-cotorsion right $R$-modules are Enochs-cotorsion. $(iii) $ $h$-divisible right $R$-modules are weak-injective. $(iv)$ Homomorphic images of weak-injective right $R$-modules are weak-injective. $(v)$ Homomorphic images of injective right $R$-modules are weak-injective. $(vi)$ Right $R$-modules of weak dimension $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.00097","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":"2026-05-18T00:33:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+mhNx+bNA57SdeLgTt0ydbz+2MSEFqUKS3aIPffJfgVq90jC2C+ZwbUp0pEQVUfVNeZzdrBVuReYZcz+8VOUBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T00:41:40.367083Z"},"content_sha256":"702094f49e27b67e844898c24375b7405921460b3e2d7f1c20783fb088707a36","schema_version":"1.0","event_id":"sha256:702094f49e27b67e844898c24375b7405921460b3e2d7f1c20783fb088707a36"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ITXI4H6ER3Q7VKSFR6RNWMHLAN/bundle.json","state_url":"https://pith.science/pith/ITXI4H6ER3Q7VKSFR6RNWMHLAN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ITXI4H6ER3Q7VKSFR6RNWMHLAN/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":"2026-06-09T00:41:40Z","links":{"resolver":"https://pith.science/pith/ITXI4H6ER3Q7VKSFR6RNWMHLAN","bundle":"https://pith.science/pith/ITXI4H6ER3Q7VKSFR6RNWMHLAN/bundle.json","state":"https://pith.science/pith/ITXI4H6ER3Q7VKSFR6RNWMHLAN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ITXI4H6ER3Q7VKSFR6RNWMHLAN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ITXI4H6ER3Q7VKSFR6RNWMHLAN","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":"7c8c6295bf3dd8b6bd7873513a35b54a131353d472d75c866f44879a6142660e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-09-29T21:25:34Z","title_canon_sha256":"8f27a0c091e2d4955f3731454457582d23db0c8bb616b396b08c595dfb5ba619"},"schema_version":"1.0","source":{"id":"1710.00097","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.00097","created_at":"2026-05-18T00:33:57Z"},{"alias_kind":"arxiv_version","alias_value":"1710.00097v1","created_at":"2026-05-18T00:33:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.00097","created_at":"2026-05-18T00:33:57Z"},{"alias_kind":"pith_short_12","alias_value":"ITXI4H6ER3Q7","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"ITXI4H6ER3Q7VKSF","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"ITXI4H6E","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:702094f49e27b67e844898c24375b7405921460b3e2d7f1c20783fb088707a36","target":"graph","created_at":"2026-05-18T00:33:57Z","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":"Let $R$ be a right and left Ore ring, $S$ its set of regular elements and $Q = R[S^{-1}] = [S^{-1}] R$ the classical ring of quotients of $R$. We prove that if F.dim$(Q_Q) = 0$, then the following conditions are equivalent: $(i)$ Flat right $R$-modules are strongly flat. $ (ii)$ Matlis-cotorsion right $R$-modules are Enochs-cotorsion. $(iii) $ $h$-divisible right $R$-modules are weak-injective. $(iv)$ Homomorphic images of weak-injective right $R$-modules are weak-injective. $(v)$ Homomorphic images of injective right $R$-modules are weak-injective. $(vi)$ Right $R$-modules of weak dimension $","authors_text":"Alberto Facchini, Zahra Nazemian","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-09-29T21:25:34Z","title":"Equivalence of Some Homological Conditions for Ring Epimorphisms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.00097","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":"sha256:5d590b990fb2b3b4a3b00fa99618410b967cf5f44a36b8ab9001d54d64f19d91","target":"record","created_at":"2026-05-18T00:33:57Z","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":"7c8c6295bf3dd8b6bd7873513a35b54a131353d472d75c866f44879a6142660e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-09-29T21:25:34Z","title_canon_sha256":"8f27a0c091e2d4955f3731454457582d23db0c8bb616b396b08c595dfb5ba619"},"schema_version":"1.0","source":{"id":"1710.00097","kind":"arxiv","version":1}},"canonical_sha256":"44ee8e1fc48ee1faaa458fa2db30eb03763b54178aaa74241abe8fe2712d4193","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"44ee8e1fc48ee1faaa458fa2db30eb03763b54178aaa74241abe8fe2712d4193","first_computed_at":"2026-05-18T00:33:57.918027Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:57.918027Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Yeft5n3pcYSG7sQ4lVe7tj7+tQpn0t0UU+Y8kXaZ0m/NQ1jiyuUORC9UrNQzeLNIZNucQRGPTnNS3n91QJTODA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:57.918604Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.00097","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d590b990fb2b3b4a3b00fa99618410b967cf5f44a36b8ab9001d54d64f19d91","sha256:702094f49e27b67e844898c24375b7405921460b3e2d7f1c20783fb088707a36"],"state_sha256":"7d0a096d614da1031301e5fcf4b367cfb88f508ef34a88f6bed4bdb7bf5e961f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D5aRdId+y54FabOyisXWLrV3fHwW+yWJU8/kUuD7rmlcDarWgIBahbhw/GaRGhG34/cNvIxb+aV5ebiQVGppDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T00:41:40.369638Z","bundle_sha256":"222a15ac58c8be42343e3a3a18206c9da0567394b766979f0e5a35551ed36adf"}}