{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:IK6SE6QQPUTQL6KXJ3VCAJA62S","short_pith_number":"pith:IK6SE6QQ","canonical_record":{"source":{"id":"1910.05617","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2019-10-12T18:26:00Z","cross_cats_sorted":[],"title_canon_sha256":"53444207ccf42946a4a5e0443d106d1cc57846f7c0e23041a4ba8810f60efda9","abstract_canon_sha256":"3069702067540b5bee733170600d079d3f37042655805d0b04c65f7df058896c"},"schema_version":"1.0"},"canonical_sha256":"42bd227a107d2705f9574eea20241ed49a4bbd6d7c00497f81c1fccd0b4e7090","source":{"kind":"arxiv","id":"1910.05617","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1910.05617","created_at":"2026-07-05T00:11:40Z"},{"alias_kind":"arxiv_version","alias_value":"1910.05617v1","created_at":"2026-07-05T00:11:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1910.05617","created_at":"2026-07-05T00:11:40Z"},{"alias_kind":"pith_short_12","alias_value":"IK6SE6QQPUTQ","created_at":"2026-07-05T00:11:40Z"},{"alias_kind":"pith_short_16","alias_value":"IK6SE6QQPUTQL6KX","created_at":"2026-07-05T00:11:40Z"},{"alias_kind":"pith_short_8","alias_value":"IK6SE6QQ","created_at":"2026-07-05T00:11:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:IK6SE6QQPUTQL6KXJ3VCAJA62S","target":"record","payload":{"canonical_record":{"source":{"id":"1910.05617","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2019-10-12T18:26:00Z","cross_cats_sorted":[],"title_canon_sha256":"53444207ccf42946a4a5e0443d106d1cc57846f7c0e23041a4ba8810f60efda9","abstract_canon_sha256":"3069702067540b5bee733170600d079d3f37042655805d0b04c65f7df058896c"},"schema_version":"1.0"},"canonical_sha256":"42bd227a107d2705f9574eea20241ed49a4bbd6d7c00497f81c1fccd0b4e7090","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:11:40.263170Z","signature_b64":"phLCANPh8CWJWhlT10sUZnQkg+8nL+CmiqN02mq/XT/kMT9VJg/e6mKNr42/V5mdBUjRKQOoa/KJs7YyUTVGBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"42bd227a107d2705f9574eea20241ed49a4bbd6d7c00497f81c1fccd0b4e7090","last_reissued_at":"2026-07-05T00:11:40.262667Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:11:40.262667Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1910.05617","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":"2026-07-05T00:11:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Soen/COc4cqZCacpqpPo41Mj7HXJLMsjCZxS6zO8qR5j726qw4XLgJbCW007cxpNyyVshmqCyY1sgPNoqaRUBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T19:41:41.314230Z"},"content_sha256":"96da35bac7c56f2248d484ae548a4c519adfc0101becd624c37c382e639f918f","schema_version":"1.0","event_id":"sha256:96da35bac7c56f2248d484ae548a4c519adfc0101becd624c37c382e639f918f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:IK6SE6QQPUTQL6KXJ3VCAJA62S","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tangent Categories from the Coalgebras of Differential Categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Jean-Simon Pacaud Lemay, Robin Cockett, Rory B. B. Lucyshyn-Wright","submitted_at":"2019-10-12T18:26:00Z","abstract_excerpt":"Following the pattern from linear logic, the coKleisli category of a differential category is a Cartesian differential category. What then is the coEilenberg-Moore category of a differential category? The answer is a tangent category! A key example arises from the opposite of the category of Abelian groups with the free exponential modality. The coEilenberg-Moore category, in this case, is the opposite of the category of commutative rings. That the latter is a tangent category captures a fundamental aspect of both algebraic geometry and Synthetic Differential Geometry. The general result appli"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.05617","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1910.05617/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":"2026-07-05T00:11:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QrYvfaFw2wejRXRiU8kb+PYe39yrTu6YRB6pp4X6loKhUKDfvg99oY5IP//sZZxNF+u9o88+939wPBjkh6HYAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T19:41:41.314558Z"},"content_sha256":"060a9f94ba3538cea9ec484008793eebbdadda8dfe01198251f9fc62d2c2294e","schema_version":"1.0","event_id":"sha256:060a9f94ba3538cea9ec484008793eebbdadda8dfe01198251f9fc62d2c2294e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IK6SE6QQPUTQL6KXJ3VCAJA62S/bundle.json","state_url":"https://pith.science/pith/IK6SE6QQPUTQL6KXJ3VCAJA62S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IK6SE6QQPUTQL6KXJ3VCAJA62S/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":"2026-08-14T19:41:41Z","links":{"resolver":"https://pith.science/pith/IK6SE6QQPUTQL6KXJ3VCAJA62S","bundle":"https://pith.science/pith/IK6SE6QQPUTQL6KXJ3VCAJA62S/bundle.json","state":"https://pith.science/pith/IK6SE6QQPUTQL6KXJ3VCAJA62S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IK6SE6QQPUTQL6KXJ3VCAJA62S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:IK6SE6QQPUTQL6KXJ3VCAJA62S","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":"3069702067540b5bee733170600d079d3f37042655805d0b04c65f7df058896c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2019-10-12T18:26:00Z","title_canon_sha256":"53444207ccf42946a4a5e0443d106d1cc57846f7c0e23041a4ba8810f60efda9"},"schema_version":"1.0","source":{"id":"1910.05617","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1910.05617","created_at":"2026-07-05T00:11:40Z"},{"alias_kind":"arxiv_version","alias_value":"1910.05617v1","created_at":"2026-07-05T00:11:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1910.05617","created_at":"2026-07-05T00:11:40Z"},{"alias_kind":"pith_short_12","alias_value":"IK6SE6QQPUTQ","created_at":"2026-07-05T00:11:40Z"},{"alias_kind":"pith_short_16","alias_value":"IK6SE6QQPUTQL6KX","created_at":"2026-07-05T00:11:40Z"},{"alias_kind":"pith_short_8","alias_value":"IK6SE6QQ","created_at":"2026-07-05T00:11:40Z"}],"graph_snapshots":[{"event_id":"sha256:060a9f94ba3538cea9ec484008793eebbdadda8dfe01198251f9fc62d2c2294e","target":"graph","created_at":"2026-07-05T00:11:40Z","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/1910.05617/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Following the pattern from linear logic, the coKleisli category of a differential category is a Cartesian differential category. What then is the coEilenberg-Moore category of a differential category? The answer is a tangent category! A key example arises from the opposite of the category of Abelian groups with the free exponential modality. The coEilenberg-Moore category, in this case, is the opposite of the category of commutative rings. That the latter is a tangent category captures a fundamental aspect of both algebraic geometry and Synthetic Differential Geometry. The general result appli","authors_text":"Jean-Simon Pacaud Lemay, Robin Cockett, Rory B. B. Lucyshyn-Wright","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2019-10-12T18:26:00Z","title":"Tangent Categories from the Coalgebras of Differential Categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.05617","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":"sha256:96da35bac7c56f2248d484ae548a4c519adfc0101becd624c37c382e639f918f","target":"record","created_at":"2026-07-05T00:11:40Z","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":"3069702067540b5bee733170600d079d3f37042655805d0b04c65f7df058896c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2019-10-12T18:26:00Z","title_canon_sha256":"53444207ccf42946a4a5e0443d106d1cc57846f7c0e23041a4ba8810f60efda9"},"schema_version":"1.0","source":{"id":"1910.05617","kind":"arxiv","version":1}},"canonical_sha256":"42bd227a107d2705f9574eea20241ed49a4bbd6d7c00497f81c1fccd0b4e7090","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"42bd227a107d2705f9574eea20241ed49a4bbd6d7c00497f81c1fccd0b4e7090","first_computed_at":"2026-07-05T00:11:40.262667Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:11:40.262667Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"phLCANPh8CWJWhlT10sUZnQkg+8nL+CmiqN02mq/XT/kMT9VJg/e6mKNr42/V5mdBUjRKQOoa/KJs7YyUTVGBA==","signature_status":"signed_v1","signed_at":"2026-07-05T00:11:40.263170Z","signed_message":"canonical_sha256_bytes"},"source_id":"1910.05617","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:96da35bac7c56f2248d484ae548a4c519adfc0101becd624c37c382e639f918f","sha256:060a9f94ba3538cea9ec484008793eebbdadda8dfe01198251f9fc62d2c2294e"],"state_sha256":"a800d7140d163653fdfc0206113290337e1d5903d0370c29eae4c62f1d0a1495"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ELu5HXAm9h9bEoghy7XWkTRL334VEZGWG664YwtQl6/8mgOKYWOe/CSfH0+Wl3QLnms9532ae7v+9n4ZYW5NDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T19:41:41.322482Z","bundle_sha256":"3f1d5c94d40f20c9783b06ee7453baee81c16ee049b8a94b509645459932c385"}}