{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:NF72IYNCVKKB6OY6WNX7LNG4KV","short_pith_number":"pith:NF72IYNC","canonical_record":{"source":{"id":"1904.01549","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-04-02T17:05:49Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"e8604def3c14f51c41dbc8c83db41b48f27d394bbe2b1db6aee7639380537790","abstract_canon_sha256":"60736fab14ce178ee794213e4a0d7f26e882e4281b5c627b05f28a718a40594f"},"schema_version":"1.0"},"canonical_sha256":"697fa461a2aa941f3b1eb36ff5b4dc55618ada799c52e2f4ebb7daa1b8c855b6","source":{"kind":"arxiv","id":"1904.01549","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.01549","created_at":"2026-05-17T23:40:11Z"},{"alias_kind":"arxiv_version","alias_value":"1904.01549v2","created_at":"2026-05-17T23:40:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.01549","created_at":"2026-05-17T23:40:11Z"},{"alias_kind":"pith_short_12","alias_value":"NF72IYNCVKKB","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"NF72IYNCVKKB6OY6","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"NF72IYNC","created_at":"2026-05-18T12:33:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:NF72IYNCVKKB6OY6WNX7LNG4KV","target":"record","payload":{"canonical_record":{"source":{"id":"1904.01549","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-04-02T17:05:49Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"e8604def3c14f51c41dbc8c83db41b48f27d394bbe2b1db6aee7639380537790","abstract_canon_sha256":"60736fab14ce178ee794213e4a0d7f26e882e4281b5c627b05f28a718a40594f"},"schema_version":"1.0"},"canonical_sha256":"697fa461a2aa941f3b1eb36ff5b4dc55618ada799c52e2f4ebb7daa1b8c855b6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:11.047874Z","signature_b64":"eO76weRSMGr/fW3fv1USB3OKjLP6/ONVSa1Z3TyAm6TsHDn0Brozuas6Jja+o77uQxzSbim0e7hPYIkSTv+eAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"697fa461a2aa941f3b1eb36ff5b4dc55618ada799c52e2f4ebb7daa1b8c855b6","last_reissued_at":"2026-05-17T23:40:11.047365Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:11.047365Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.01549","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":"2026-05-17T23:40:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MAtJRJHbI+L7IRCiW6VSfZ4DMr24UkQmu+5Kks02G5BTxZX/LR49uC6jQfhvWrgibqNlvVF5Un7csdN2WSkVBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T04:21:36.084559Z"},"content_sha256":"d2f0a66a995c79a34ad5548d145abc9ca19c4293eca426cc16fc5c3eae7d3d6f","schema_version":"1.0","event_id":"sha256:d2f0a66a995c79a34ad5548d145abc9ca19c4293eca426cc16fc5c3eae7d3d6f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:NF72IYNCVKKB6OY6WNX7LNG4KV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Pushouts and e-Projective Semimodules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.RA","authors_text":"Jawad Abuhlail, Rangga Ganzar Noegraha","submitted_at":"2019-04-02T17:05:49Z","abstract_excerpt":"Projective modules play an important role in the study of the category of modules over rings and in the characterization of various classes of rings. Several characterizations of projective objects which are equivalent for modules over rings are not necessarily equivalent for semimodules over an arbitrary semiring. We study several of these notions, in particular the e-projective semimodules introduced by the first author using his new notion of exact sequences of semimodules. As pushouts of semimodules play an important role in some of our proofs, we investigate them and give a constructive p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.01549","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":"2026-05-17T23:40:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0wR122ZcLqDrdvLeorMumYauFtj54frrsefNDwGl69ZAH5HXsWsNBmeAWVMrGQegE5k94esd10kLcY2EOAaeAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T04:21:36.084931Z"},"content_sha256":"d2d94b901be998ea79f11bcc93eb5246d1c25e467b173d53568b8843237a17ad","schema_version":"1.0","event_id":"sha256:d2d94b901be998ea79f11bcc93eb5246d1c25e467b173d53568b8843237a17ad"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NF72IYNCVKKB6OY6WNX7LNG4KV/bundle.json","state_url":"https://pith.science/pith/NF72IYNCVKKB6OY6WNX7LNG4KV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NF72IYNCVKKB6OY6WNX7LNG4KV/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":"2026-06-12T04:21:36Z","links":{"resolver":"https://pith.science/pith/NF72IYNCVKKB6OY6WNX7LNG4KV","bundle":"https://pith.science/pith/NF72IYNCVKKB6OY6WNX7LNG4KV/bundle.json","state":"https://pith.science/pith/NF72IYNCVKKB6OY6WNX7LNG4KV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NF72IYNCVKKB6OY6WNX7LNG4KV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:NF72IYNCVKKB6OY6WNX7LNG4KV","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":"60736fab14ce178ee794213e4a0d7f26e882e4281b5c627b05f28a718a40594f","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-04-02T17:05:49Z","title_canon_sha256":"e8604def3c14f51c41dbc8c83db41b48f27d394bbe2b1db6aee7639380537790"},"schema_version":"1.0","source":{"id":"1904.01549","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.01549","created_at":"2026-05-17T23:40:11Z"},{"alias_kind":"arxiv_version","alias_value":"1904.01549v2","created_at":"2026-05-17T23:40:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.01549","created_at":"2026-05-17T23:40:11Z"},{"alias_kind":"pith_short_12","alias_value":"NF72IYNCVKKB","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"NF72IYNCVKKB6OY6","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"NF72IYNC","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:d2d94b901be998ea79f11bcc93eb5246d1c25e467b173d53568b8843237a17ad","target":"graph","created_at":"2026-05-17T23:40:11Z","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":"Projective modules play an important role in the study of the category of modules over rings and in the characterization of various classes of rings. Several characterizations of projective objects which are equivalent for modules over rings are not necessarily equivalent for semimodules over an arbitrary semiring. We study several of these notions, in particular the e-projective semimodules introduced by the first author using his new notion of exact sequences of semimodules. As pushouts of semimodules play an important role in some of our proofs, we investigate them and give a constructive p","authors_text":"Jawad Abuhlail, Rangga Ganzar Noegraha","cross_cats":["math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-04-02T17:05:49Z","title":"Pushouts and e-Projective Semimodules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.01549","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:d2f0a66a995c79a34ad5548d145abc9ca19c4293eca426cc16fc5c3eae7d3d6f","target":"record","created_at":"2026-05-17T23:40:11Z","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":"60736fab14ce178ee794213e4a0d7f26e882e4281b5c627b05f28a718a40594f","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-04-02T17:05:49Z","title_canon_sha256":"e8604def3c14f51c41dbc8c83db41b48f27d394bbe2b1db6aee7639380537790"},"schema_version":"1.0","source":{"id":"1904.01549","kind":"arxiv","version":2}},"canonical_sha256":"697fa461a2aa941f3b1eb36ff5b4dc55618ada799c52e2f4ebb7daa1b8c855b6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"697fa461a2aa941f3b1eb36ff5b4dc55618ada799c52e2f4ebb7daa1b8c855b6","first_computed_at":"2026-05-17T23:40:11.047365Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:11.047365Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eO76weRSMGr/fW3fv1USB3OKjLP6/ONVSa1Z3TyAm6TsHDn0Brozuas6Jja+o77uQxzSbim0e7hPYIkSTv+eAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:11.047874Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.01549","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d2f0a66a995c79a34ad5548d145abc9ca19c4293eca426cc16fc5c3eae7d3d6f","sha256:d2d94b901be998ea79f11bcc93eb5246d1c25e467b173d53568b8843237a17ad"],"state_sha256":"1546dd3fcae72aef9ecb2f0493c122b9761a32238060d80feeeabcb4b1cd74be"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p9YX+1M2G245b6+s/MjTty2vkFK/yy7u1y1cXPLxS57Bi13v+YqJfc5JP6Oyo35O3C6/XPAH5NJ6TnItd+Y7DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T04:21:36.087036Z","bundle_sha256":"e37441baa5aa37b25cc8f8710c68ab9d2ed0353d9a0bff8dba146cbb5a8478f3"}}