{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:R36G34DP7BE7L6Z2XQXEXC6IFP","short_pith_number":"pith:R36G34DP","canonical_record":{"source":{"id":"1812.11222","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2018-12-28T21:25:59Z","cross_cats_sorted":[],"title_canon_sha256":"de1614911ab788f575c1c10cd6f9addf5018029360936d4f76278c18d5ab41ff","abstract_canon_sha256":"ca9e2fcd49d137a795265774f2c7adfbf9de17a8aca024626479e82af6dbe53c"},"schema_version":"1.0"},"canonical_sha256":"8efc6df06ff849f5fb3abc2e4b8bc82bde079bd53db960aeba1436d9ce70a49e","source":{"kind":"arxiv","id":"1812.11222","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.11222","created_at":"2026-05-17T23:49:39Z"},{"alias_kind":"arxiv_version","alias_value":"1812.11222v2","created_at":"2026-05-17T23:49:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.11222","created_at":"2026-05-17T23:49:39Z"},{"alias_kind":"pith_short_12","alias_value":"R36G34DP7BE7","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"R36G34DP7BE7L6Z2","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"R36G34DP","created_at":"2026-05-18T12:32:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:R36G34DP7BE7L6Z2XQXEXC6IFP","target":"record","payload":{"canonical_record":{"source":{"id":"1812.11222","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2018-12-28T21:25:59Z","cross_cats_sorted":[],"title_canon_sha256":"de1614911ab788f575c1c10cd6f9addf5018029360936d4f76278c18d5ab41ff","abstract_canon_sha256":"ca9e2fcd49d137a795265774f2c7adfbf9de17a8aca024626479e82af6dbe53c"},"schema_version":"1.0"},"canonical_sha256":"8efc6df06ff849f5fb3abc2e4b8bc82bde079bd53db960aeba1436d9ce70a49e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:39.827514Z","signature_b64":"pPU8S24dyMeN3bUrshA3u3Z/U9LfBpfpZxxpNxVWJrARudNg2uacNRO0kOIn3VnrkaZMAzZtrhM72fUtKH8mBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8efc6df06ff849f5fb3abc2e4b8bc82bde079bd53db960aeba1436d9ce70a49e","last_reissued_at":"2026-05-17T23:49:39.826862Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:39.826862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.11222","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":"2026-05-17T23:49:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HYhMeALAcPr91rRnspoFHf5nCnJhI5qglagHl/vcOYrSp9sVNHa2WX6Cw7yiTqRpz3dzQJfxDDq7hTXMe43LCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T01:40:18.722923Z"},"content_sha256":"ec57953764322ca6a1daf56b6fe0f506e59d55fccc402feb140a0fc67beb7d5d","schema_version":"1.0","event_id":"sha256:ec57953764322ca6a1daf56b6fe0f506e59d55fccc402feb140a0fc67beb7d5d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:R36G34DP7BE7L6Z2XQXEXC6IFP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Order-enriched solid functors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Lurdes Sousa, Walter Tholen","submitted_at":"2018-12-28T21:25:59Z","abstract_excerpt":"Order-enriched solid functors, as presented in this paper in two versions, enjoy many of the strong properties of their ordinary counterparts, including the transfer of the existence of weighted (co)limits from their codomains to their domains. The ordinary version of the notion first appeared in Trnkov\\'a's work on automata theory of the 1970s and was subsequently studied by others under various names, before being put into a general enriched context by Anghel. Our focus in this paper is on differentiating the order-enriched notion from the ordinary one, mostly in terms of the functor's behav"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.11222","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":"2026-05-17T23:49:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U1qxBwMhPtD4DqoGbvGo0V5GrTcLxLs5Ep/UxUMzt8F/1vw0dkMj66Dhn5lP/vgJ5yrSI0EmdfxTwLlGX7fXBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T01:40:18.723267Z"},"content_sha256":"01a0f3c26472f856ae1dedd85c972ca5a85f701aee4112372b20ed1916aa77d4","schema_version":"1.0","event_id":"sha256:01a0f3c26472f856ae1dedd85c972ca5a85f701aee4112372b20ed1916aa77d4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/R36G34DP7BE7L6Z2XQXEXC6IFP/bundle.json","state_url":"https://pith.science/pith/R36G34DP7BE7L6Z2XQXEXC6IFP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/R36G34DP7BE7L6Z2XQXEXC6IFP/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":"2026-06-20T01:40:18Z","links":{"resolver":"https://pith.science/pith/R36G34DP7BE7L6Z2XQXEXC6IFP","bundle":"https://pith.science/pith/R36G34DP7BE7L6Z2XQXEXC6IFP/bundle.json","state":"https://pith.science/pith/R36G34DP7BE7L6Z2XQXEXC6IFP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/R36G34DP7BE7L6Z2XQXEXC6IFP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:R36G34DP7BE7L6Z2XQXEXC6IFP","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":"ca9e2fcd49d137a795265774f2c7adfbf9de17a8aca024626479e82af6dbe53c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2018-12-28T21:25:59Z","title_canon_sha256":"de1614911ab788f575c1c10cd6f9addf5018029360936d4f76278c18d5ab41ff"},"schema_version":"1.0","source":{"id":"1812.11222","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.11222","created_at":"2026-05-17T23:49:39Z"},{"alias_kind":"arxiv_version","alias_value":"1812.11222v2","created_at":"2026-05-17T23:49:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.11222","created_at":"2026-05-17T23:49:39Z"},{"alias_kind":"pith_short_12","alias_value":"R36G34DP7BE7","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"R36G34DP7BE7L6Z2","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"R36G34DP","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:01a0f3c26472f856ae1dedd85c972ca5a85f701aee4112372b20ed1916aa77d4","target":"graph","created_at":"2026-05-17T23:49:39Z","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":"Order-enriched solid functors, as presented in this paper in two versions, enjoy many of the strong properties of their ordinary counterparts, including the transfer of the existence of weighted (co)limits from their codomains to their domains. The ordinary version of the notion first appeared in Trnkov\\'a's work on automata theory of the 1970s and was subsequently studied by others under various names, before being put into a general enriched context by Anghel. Our focus in this paper is on differentiating the order-enriched notion from the ordinary one, mostly in terms of the functor's behav","authors_text":"Lurdes Sousa, Walter Tholen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2018-12-28T21:25:59Z","title":"Order-enriched solid functors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.11222","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:ec57953764322ca6a1daf56b6fe0f506e59d55fccc402feb140a0fc67beb7d5d","target":"record","created_at":"2026-05-17T23:49:39Z","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":"ca9e2fcd49d137a795265774f2c7adfbf9de17a8aca024626479e82af6dbe53c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2018-12-28T21:25:59Z","title_canon_sha256":"de1614911ab788f575c1c10cd6f9addf5018029360936d4f76278c18d5ab41ff"},"schema_version":"1.0","source":{"id":"1812.11222","kind":"arxiv","version":2}},"canonical_sha256":"8efc6df06ff849f5fb3abc2e4b8bc82bde079bd53db960aeba1436d9ce70a49e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8efc6df06ff849f5fb3abc2e4b8bc82bde079bd53db960aeba1436d9ce70a49e","first_computed_at":"2026-05-17T23:49:39.826862Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:39.826862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pPU8S24dyMeN3bUrshA3u3Z/U9LfBpfpZxxpNxVWJrARudNg2uacNRO0kOIn3VnrkaZMAzZtrhM72fUtKH8mBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:39.827514Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.11222","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ec57953764322ca6a1daf56b6fe0f506e59d55fccc402feb140a0fc67beb7d5d","sha256:01a0f3c26472f856ae1dedd85c972ca5a85f701aee4112372b20ed1916aa77d4"],"state_sha256":"c000469cfeb1a035d17c5a79af9053e38ebb229899910f3463dacc3400210374"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HB9m/lDY+8/O7yozUhxskFtL5QgMP7l0HvXo20QT2jPSAv6HAxH02nutpZE6EkMjC0WwvAdDgyFIHlZJiAv0Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T01:40:18.725196Z","bundle_sha256":"64c2f536861536b680ca6f2c2bcfaf059884fba463a34d2fe1a7472a5664f37d"}}