{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:CLMSVKGXROXQCPPXEX4HYJMP7G","short_pith_number":"pith:CLMSVKGX","canonical_record":{"source":{"id":"1409.3804","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2014-09-11T10:03:32Z","cross_cats_sorted":[],"title_canon_sha256":"62db9f68fec6db2a8a90a3abae87aec973fbb7b5af8015998fd08d0096502f47","abstract_canon_sha256":"3179c9a518b8d209b356487afee225796e309bf2b8943204449773d60b3d4515"},"schema_version":"1.0"},"canonical_sha256":"12d92aa8d78baf013df725f87c258ff994766f35622091822b542d29c1ca656d","source":{"kind":"arxiv","id":"1409.3804","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.3804","created_at":"2026-05-18T02:42:54Z"},{"alias_kind":"arxiv_version","alias_value":"1409.3804v1","created_at":"2026-05-18T02:42:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.3804","created_at":"2026-05-18T02:42:54Z"},{"alias_kind":"pith_short_12","alias_value":"CLMSVKGXROXQ","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"CLMSVKGXROXQCPPX","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"CLMSVKGX","created_at":"2026-05-18T12:28:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:CLMSVKGXROXQCPPXEX4HYJMP7G","target":"record","payload":{"canonical_record":{"source":{"id":"1409.3804","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2014-09-11T10:03:32Z","cross_cats_sorted":[],"title_canon_sha256":"62db9f68fec6db2a8a90a3abae87aec973fbb7b5af8015998fd08d0096502f47","abstract_canon_sha256":"3179c9a518b8d209b356487afee225796e309bf2b8943204449773d60b3d4515"},"schema_version":"1.0"},"canonical_sha256":"12d92aa8d78baf013df725f87c258ff994766f35622091822b542d29c1ca656d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:42:54.645063Z","signature_b64":"9abKOCpwkc6NWPe6ng7apc7Tn/aJYmPzMQzpMKW3nby0kWMewuM1LRZh3CRbXuLbjFXpzj9GOWxGBILIRzIlDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"12d92aa8d78baf013df725f87c258ff994766f35622091822b542d29c1ca656d","last_reissued_at":"2026-05-18T02:42:54.644710Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:42:54.644710Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.3804","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":"2026-05-18T02:42:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QkDgHAJaqFNMyWy3RTfRFCV3BbT/Ci3UjWscKG5VCofHZ+nf/6ORnuBACv4d++CoaqCBboYke3AdmZ/1npbyDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T01:01:23.668583Z"},"content_sha256":"80e73878e263ce23e9eca9aacfdb1b6fc882ba675222bbbecaadf29ae7397757","schema_version":"1.0","event_id":"sha256:80e73878e263ce23e9eca9aacfdb1b6fc882ba675222bbbecaadf29ae7397757"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:CLMSVKGXROXQCPPXEX4HYJMP7G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Coproducts of Monads on Set","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Ji\\v{r}\\'i Ad\\'amek, Nathan Bowler, Paul B. Levy, Stefan Milius","submitted_at":"2014-09-11T10:03:32Z","abstract_excerpt":"Coproducts of monads on Set have arisen in both the study of computational effects and universal algebra.\n  We describe coproducts of consistent monads on Set by an initial algebra formula, and prove also the converse: if the coproduct exists, so do the required initial algebras. That formula was, in the case of ideal monads, also used by Ghani and Uustalu. We deduce that coproduct embeddings of consistent monads are injective; and that a coproduct of injective monad morphisms is injective.\n  Two consistent monads have a coproduct iff either they have arbitrarily large common fixpoints, or one"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.3804","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":"2026-05-18T02:42:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8faohBEsoMHlARARsrhvOOw1f4JFuooA5VKunaPQ5bViiot6dQXi7p1PrZlg28RjVeVF0PPmC1eoR+l/uwMcAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T01:01:23.668918Z"},"content_sha256":"0fd4be5038c16d8391d764c327e3cab569d6a1e1606052e0095c40f7c290361f","schema_version":"1.0","event_id":"sha256:0fd4be5038c16d8391d764c327e3cab569d6a1e1606052e0095c40f7c290361f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CLMSVKGXROXQCPPXEX4HYJMP7G/bundle.json","state_url":"https://pith.science/pith/CLMSVKGXROXQCPPXEX4HYJMP7G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CLMSVKGXROXQCPPXEX4HYJMP7G/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":"2026-06-09T01:01:23Z","links":{"resolver":"https://pith.science/pith/CLMSVKGXROXQCPPXEX4HYJMP7G","bundle":"https://pith.science/pith/CLMSVKGXROXQCPPXEX4HYJMP7G/bundle.json","state":"https://pith.science/pith/CLMSVKGXROXQCPPXEX4HYJMP7G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CLMSVKGXROXQCPPXEX4HYJMP7G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:CLMSVKGXROXQCPPXEX4HYJMP7G","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":"3179c9a518b8d209b356487afee225796e309bf2b8943204449773d60b3d4515","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2014-09-11T10:03:32Z","title_canon_sha256":"62db9f68fec6db2a8a90a3abae87aec973fbb7b5af8015998fd08d0096502f47"},"schema_version":"1.0","source":{"id":"1409.3804","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.3804","created_at":"2026-05-18T02:42:54Z"},{"alias_kind":"arxiv_version","alias_value":"1409.3804v1","created_at":"2026-05-18T02:42:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.3804","created_at":"2026-05-18T02:42:54Z"},{"alias_kind":"pith_short_12","alias_value":"CLMSVKGXROXQ","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"CLMSVKGXROXQCPPX","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"CLMSVKGX","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:0fd4be5038c16d8391d764c327e3cab569d6a1e1606052e0095c40f7c290361f","target":"graph","created_at":"2026-05-18T02:42:54Z","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":"Coproducts of monads on Set have arisen in both the study of computational effects and universal algebra.\n  We describe coproducts of consistent monads on Set by an initial algebra formula, and prove also the converse: if the coproduct exists, so do the required initial algebras. That formula was, in the case of ideal monads, also used by Ghani and Uustalu. We deduce that coproduct embeddings of consistent monads are injective; and that a coproduct of injective monad morphisms is injective.\n  Two consistent monads have a coproduct iff either they have arbitrarily large common fixpoints, or one","authors_text":"Ji\\v{r}\\'i Ad\\'amek, Nathan Bowler, Paul B. Levy, Stefan Milius","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2014-09-11T10:03:32Z","title":"Coproducts of Monads on Set"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.3804","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":"sha256:80e73878e263ce23e9eca9aacfdb1b6fc882ba675222bbbecaadf29ae7397757","target":"record","created_at":"2026-05-18T02:42:54Z","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":"3179c9a518b8d209b356487afee225796e309bf2b8943204449773d60b3d4515","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2014-09-11T10:03:32Z","title_canon_sha256":"62db9f68fec6db2a8a90a3abae87aec973fbb7b5af8015998fd08d0096502f47"},"schema_version":"1.0","source":{"id":"1409.3804","kind":"arxiv","version":1}},"canonical_sha256":"12d92aa8d78baf013df725f87c258ff994766f35622091822b542d29c1ca656d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"12d92aa8d78baf013df725f87c258ff994766f35622091822b542d29c1ca656d","first_computed_at":"2026-05-18T02:42:54.644710Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:42:54.644710Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9abKOCpwkc6NWPe6ng7apc7Tn/aJYmPzMQzpMKW3nby0kWMewuM1LRZh3CRbXuLbjFXpzj9GOWxGBILIRzIlDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:42:54.645063Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.3804","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:80e73878e263ce23e9eca9aacfdb1b6fc882ba675222bbbecaadf29ae7397757","sha256:0fd4be5038c16d8391d764c327e3cab569d6a1e1606052e0095c40f7c290361f"],"state_sha256":"3976c30d3347a0f23492464f03d4bdfc1134a9de2c852f2e13a0a87f037b87ce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IqxGxuoQHqPgWIc9mImjK5jr1X4skjaR7KlHKGwMYTJ0a0MOOJpB0YZJ8uOw7sI3jaVCKi/hQihl3vhFtQNyBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T01:01:23.670902Z","bundle_sha256":"38a3dbc3c96bc787520f7e831446b402dec14f10efd32eae2cbf0d5ee87c1986"}}