{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:IF4J3QLXDQQ7O6SHNQKHE3YXL2","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":"8dda73ce481824278c9292fcff2ed530a6649e82c7d03ac2414a10f07bdefcae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-01-11T20:20:57Z","title_canon_sha256":"08c6e8d135645a777cd55312cc38db3a0e8f02a8d85d8741651d3857c52947a0"},"schema_version":"1.0","source":{"id":"1501.02491","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.02491","created_at":"2026-05-18T00:35:36Z"},{"alias_kind":"arxiv_version","alias_value":"1501.02491v2","created_at":"2026-05-18T00:35:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.02491","created_at":"2026-05-18T00:35:36Z"},{"alias_kind":"pith_short_12","alias_value":"IF4J3QLXDQQ7","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"IF4J3QLXDQQ7O6SH","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"IF4J3QLX","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:b9bc62f305bb920db46880f9bb0864198b1108b246e643635e5415bb754f9ec4","target":"graph","created_at":"2026-05-18T00:35:36Z","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":"Jir\\'asko introduced the concepts of L-injective module as a generalization of injective module. The aim of this paper is to study L-injective modules and some related concepts.","authors_text":"Akeel Ramadan Mehdi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-01-11T20:20:57Z","title":"On L-Injective Modules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.02491","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:af42301f530514695206d85020ae88d28bc8dd1d10cd6873c9f0ef52222b7d2c","target":"record","created_at":"2026-05-18T00:35:36Z","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":"8dda73ce481824278c9292fcff2ed530a6649e82c7d03ac2414a10f07bdefcae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-01-11T20:20:57Z","title_canon_sha256":"08c6e8d135645a777cd55312cc38db3a0e8f02a8d85d8741651d3857c52947a0"},"schema_version":"1.0","source":{"id":"1501.02491","kind":"arxiv","version":2}},"canonical_sha256":"41789dc1771c21f77a476c14726f175e9b8c5b80b717d28a72a0bd6790fb87f4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"41789dc1771c21f77a476c14726f175e9b8c5b80b717d28a72a0bd6790fb87f4","first_computed_at":"2026-05-18T00:35:36.056535Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:36.056535Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+f2vACS9aTYaeTVSi2Mpv6NAgcbQVYNWK5KPwQ8dSHugbu+zDVXEOCqsaP62Kl8B+aZs58VwAOUkGD4Pa5IwDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:36.057143Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.02491","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:af42301f530514695206d85020ae88d28bc8dd1d10cd6873c9f0ef52222b7d2c","sha256:b9bc62f305bb920db46880f9bb0864198b1108b246e643635e5415bb754f9ec4"],"state_sha256":"2d4b08db01d863352a9bb82a2c6563703c27be434c6e59ecd3c5e6558e29471b"}