{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:VE3MLPM264LMGGTKLIHCCFSXJK","short_pith_number":"pith:VE3MLPM2","canonical_record":{"source":{"id":"2310.19428","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2023-10-30T10:37:34Z","cross_cats_sorted":[],"title_canon_sha256":"61b84cc2d5444acb1d3142b35e5c757c9871365e2627ccbbad7851b03e3e7d47","abstract_canon_sha256":"07524153e45180736d3eff943f29adf86a956439f7b9004c5a2c4080f225ecdb"},"schema_version":"1.0"},"canonical_sha256":"a936c5bd9af716c31a6a5a0e2116574aa4281214e01aa140ba8a1c56a27826a0","source":{"kind":"arxiv","id":"2310.19428","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2310.19428","created_at":"2026-07-05T10:04:10Z"},{"alias_kind":"arxiv_version","alias_value":"2310.19428v3","created_at":"2026-07-05T10:04:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.19428","created_at":"2026-07-05T10:04:10Z"},{"alias_kind":"pith_short_12","alias_value":"VE3MLPM264LM","created_at":"2026-07-05T10:04:10Z"},{"alias_kind":"pith_short_16","alias_value":"VE3MLPM264LMGGTK","created_at":"2026-07-05T10:04:10Z"},{"alias_kind":"pith_short_8","alias_value":"VE3MLPM2","created_at":"2026-07-05T10:04:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:VE3MLPM264LMGGTKLIHCCFSXJK","target":"record","payload":{"canonical_record":{"source":{"id":"2310.19428","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2023-10-30T10:37:34Z","cross_cats_sorted":[],"title_canon_sha256":"61b84cc2d5444acb1d3142b35e5c757c9871365e2627ccbbad7851b03e3e7d47","abstract_canon_sha256":"07524153e45180736d3eff943f29adf86a956439f7b9004c5a2c4080f225ecdb"},"schema_version":"1.0"},"canonical_sha256":"a936c5bd9af716c31a6a5a0e2116574aa4281214e01aa140ba8a1c56a27826a0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:04:10.675276Z","signature_b64":"+TmiUhngTSX20pgZsVeY976AHJL0LFajxfQ7InwJYl+ORKCC+j9vqxTBtu0e8I6xhSwpkihS2lUVBefj4pYQDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a936c5bd9af716c31a6a5a0e2116574aa4281214e01aa140ba8a1c56a27826a0","last_reissued_at":"2026-07-05T10:04:10.674593Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:04:10.674593Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2310.19428","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:04:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JU2wF4MwJawgH33HVf8H3uOm5MLpWh4hghOVND8e6F1WsbmlRT96z/7SN8S3Waub67nUDFLrPKFff9PBfPiRCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T10:39:59.484817Z"},"content_sha256":"c5c1034f2b00383b7e6d187a1bc00e8ef890f4b240c37884746ed2ccea5971a7","schema_version":"1.0","event_id":"sha256:c5c1034f2b00383b7e6d187a1bc00e8ef890f4b240c37884746ed2ccea5971a7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:VE3MLPM264LMGGTKLIHCCFSXJK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Double categories of relations relative to factorisation systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Hayato Nasu, Keisuke Hoshino","submitted_at":"2023-10-30T10:37:34Z","abstract_excerpt":"We relativise double categories of relations to stable orthogonal factorisation systems. Furthermore, we present the characterisation of the relative double categories of relations in two ways. The first utilises a generalised comprehension scheme, and the second focuses on a specific class of vertical arrows defined solely double-categorically. We organise diverse classes of double categories of relations and correlate them with significant classes of factorisation systems. Our framework embraces double categories of spans and double categories of relations on regular categories, which we met"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.19428","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2310.19428/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T10:04:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"weio+nbxWfP1xUFM5bLHo45LhCDm7n0qjCNskedoNfwgmgy46WYrh0Nn76dNYPLUcMtSlYHgZw5SeZ/7gM0KBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T10:39:59.485314Z"},"content_sha256":"5e475ba82ca0ce65ad9313ff95e90499acc6a290565c41285e9e0a839d469558","schema_version":"1.0","event_id":"sha256:5e475ba82ca0ce65ad9313ff95e90499acc6a290565c41285e9e0a839d469558"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VE3MLPM264LMGGTKLIHCCFSXJK/bundle.json","state_url":"https://pith.science/pith/VE3MLPM264LMGGTKLIHCCFSXJK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VE3MLPM264LMGGTKLIHCCFSXJK/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":"2026-08-12T10:39:59Z","links":{"resolver":"https://pith.science/pith/VE3MLPM264LMGGTKLIHCCFSXJK","bundle":"https://pith.science/pith/VE3MLPM264LMGGTKLIHCCFSXJK/bundle.json","state":"https://pith.science/pith/VE3MLPM264LMGGTKLIHCCFSXJK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VE3MLPM264LMGGTKLIHCCFSXJK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:VE3MLPM264LMGGTKLIHCCFSXJK","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":"07524153e45180736d3eff943f29adf86a956439f7b9004c5a2c4080f225ecdb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2023-10-30T10:37:34Z","title_canon_sha256":"61b84cc2d5444acb1d3142b35e5c757c9871365e2627ccbbad7851b03e3e7d47"},"schema_version":"1.0","source":{"id":"2310.19428","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2310.19428","created_at":"2026-07-05T10:04:10Z"},{"alias_kind":"arxiv_version","alias_value":"2310.19428v3","created_at":"2026-07-05T10:04:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.19428","created_at":"2026-07-05T10:04:10Z"},{"alias_kind":"pith_short_12","alias_value":"VE3MLPM264LM","created_at":"2026-07-05T10:04:10Z"},{"alias_kind":"pith_short_16","alias_value":"VE3MLPM264LMGGTK","created_at":"2026-07-05T10:04:10Z"},{"alias_kind":"pith_short_8","alias_value":"VE3MLPM2","created_at":"2026-07-05T10:04:10Z"}],"graph_snapshots":[{"event_id":"sha256:5e475ba82ca0ce65ad9313ff95e90499acc6a290565c41285e9e0a839d469558","target":"graph","created_at":"2026-07-05T10:04:10Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2310.19428/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We relativise double categories of relations to stable orthogonal factorisation systems. Furthermore, we present the characterisation of the relative double categories of relations in two ways. The first utilises a generalised comprehension scheme, and the second focuses on a specific class of vertical arrows defined solely double-categorically. We organise diverse classes of double categories of relations and correlate them with significant classes of factorisation systems. Our framework embraces double categories of spans and double categories of relations on regular categories, which we met","authors_text":"Hayato Nasu, Keisuke Hoshino","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2023-10-30T10:37:34Z","title":"Double categories of relations relative to factorisation systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.19428","kind":"arxiv","version":3},"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:c5c1034f2b00383b7e6d187a1bc00e8ef890f4b240c37884746ed2ccea5971a7","target":"record","created_at":"2026-07-05T10:04:10Z","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":"07524153e45180736d3eff943f29adf86a956439f7b9004c5a2c4080f225ecdb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2023-10-30T10:37:34Z","title_canon_sha256":"61b84cc2d5444acb1d3142b35e5c757c9871365e2627ccbbad7851b03e3e7d47"},"schema_version":"1.0","source":{"id":"2310.19428","kind":"arxiv","version":3}},"canonical_sha256":"a936c5bd9af716c31a6a5a0e2116574aa4281214e01aa140ba8a1c56a27826a0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a936c5bd9af716c31a6a5a0e2116574aa4281214e01aa140ba8a1c56a27826a0","first_computed_at":"2026-07-05T10:04:10.674593Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:04:10.674593Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+TmiUhngTSX20pgZsVeY976AHJL0LFajxfQ7InwJYl+ORKCC+j9vqxTBtu0e8I6xhSwpkihS2lUVBefj4pYQDw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:04:10.675276Z","signed_message":"canonical_sha256_bytes"},"source_id":"2310.19428","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c5c1034f2b00383b7e6d187a1bc00e8ef890f4b240c37884746ed2ccea5971a7","sha256:5e475ba82ca0ce65ad9313ff95e90499acc6a290565c41285e9e0a839d469558"],"state_sha256":"4ccca0e7c2a3c33ae68e605efebbe6003ada70d53658bd0f11c7399c9ad96535"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PU/lEXq5Fmfk5y1X8MpvljWMjr9ZfQ9WfQHsjzfiJANr6Avm999+ShBm4Bjuv+TSrToWMBny1xkm26gwQz1fCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T10:39:59.490741Z","bundle_sha256":"53be812948c6995471f0980241b6374c24e1780ba19c44eed6ad50c2a436dbf5"}}