{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:SZ7GR7ZQYUILLODKG3FKXKGJMZ","short_pith_number":"pith:SZ7GR7ZQ","schema_version":"1.0","canonical_sha256":"967e68ff30c510b5b86a36caaba8c9664cd8e0a697d8818d02bb137e40dd9297","source":{"kind":"arxiv","id":"1606.08379","version":2},"attestation_state":"computed","paper":{"title":"Differential bundles and fibrations for tangent categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.CT","authors_text":"G.S.H. Cruttwell, J.R.B. Cockett","submitted_at":"2016-06-27T17:38:44Z","abstract_excerpt":"Tangent categories are categories equipped with a tangent functor: an endofunctor with certain natural transformations which make it behave like the tangent bundle functor on the category of smooth manifolds. They provide an abstract setting for differential geometry by axiomatizing key aspects of the subject which allow the basic theory of these geometric settings to be captured. Importantly, they have models not only in classical differential geometry and its extensions, but also in algebraic geometry, combinatorics, computer science, and physics.\n  This paper develops the theory of \"differe"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1606.08379","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2016-06-27T17:38:44Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"62d003be7d0971c3cfaa37711e3d0707897c8f519b4ec84f752b0949dd102e28","abstract_canon_sha256":"1f4dd6f5aed17944e44a2ae206958063fdc8522d8d6ec5369db63735ced80082"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:04.563735Z","signature_b64":"Ls6GmqVxPUbDyobNJLILl8qCwzRvm9pFcGD7GykvyTOb6Kx6jwtX2E75+eVfR4kdb0xkAta2xyanKNK1DGCMAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"967e68ff30c510b5b86a36caaba8c9664cd8e0a697d8818d02bb137e40dd9297","last_reissued_at":"2026-05-18T00:49:04.563180Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:04.563180Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Differential bundles and fibrations for tangent categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.CT","authors_text":"G.S.H. Cruttwell, J.R.B. Cockett","submitted_at":"2016-06-27T17:38:44Z","abstract_excerpt":"Tangent categories are categories equipped with a tangent functor: an endofunctor with certain natural transformations which make it behave like the tangent bundle functor on the category of smooth manifolds. They provide an abstract setting for differential geometry by axiomatizing key aspects of the subject which allow the basic theory of these geometric settings to be captured. Importantly, they have models not only in classical differential geometry and its extensions, but also in algebraic geometry, combinatorics, computer science, and physics.\n  This paper develops the theory of \"differe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.08379","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1606.08379","created_at":"2026-05-18T00:49:04.563259+00:00"},{"alias_kind":"arxiv_version","alias_value":"1606.08379v2","created_at":"2026-05-18T00:49:04.563259+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.08379","created_at":"2026-05-18T00:49:04.563259+00:00"},{"alias_kind":"pith_short_12","alias_value":"SZ7GR7ZQYUIL","created_at":"2026-05-18T12:30:44.179134+00:00"},{"alias_kind":"pith_short_16","alias_value":"SZ7GR7ZQYUILLODK","created_at":"2026-05-18T12:30:44.179134+00:00"},{"alias_kind":"pith_short_8","alias_value":"SZ7GR7ZQ","created_at":"2026-05-18T12:30:44.179134+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SZ7GR7ZQYUILLODKG3FKXKGJMZ","json":"https://pith.science/pith/SZ7GR7ZQYUILLODKG3FKXKGJMZ.json","graph_json":"https://pith.science/api/pith-number/SZ7GR7ZQYUILLODKG3FKXKGJMZ/graph.json","events_json":"https://pith.science/api/pith-number/SZ7GR7ZQYUILLODKG3FKXKGJMZ/events.json","paper":"https://pith.science/paper/SZ7GR7ZQ"},"agent_actions":{"view_html":"https://pith.science/pith/SZ7GR7ZQYUILLODKG3FKXKGJMZ","download_json":"https://pith.science/pith/SZ7GR7ZQYUILLODKG3FKXKGJMZ.json","view_paper":"https://pith.science/paper/SZ7GR7ZQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1606.08379&json=true","fetch_graph":"https://pith.science/api/pith-number/SZ7GR7ZQYUILLODKG3FKXKGJMZ/graph.json","fetch_events":"https://pith.science/api/pith-number/SZ7GR7ZQYUILLODKG3FKXKGJMZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SZ7GR7ZQYUILLODKG3FKXKGJMZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SZ7GR7ZQYUILLODKG3FKXKGJMZ/action/storage_attestation","attest_author":"https://pith.science/pith/SZ7GR7ZQYUILLODKG3FKXKGJMZ/action/author_attestation","sign_citation":"https://pith.science/pith/SZ7GR7ZQYUILLODKG3FKXKGJMZ/action/citation_signature","submit_replication":"https://pith.science/pith/SZ7GR7ZQYUILLODKG3FKXKGJMZ/action/replication_record"}},"created_at":"2026-05-18T00:49:04.563259+00:00","updated_at":"2026-05-18T00:49:04.563259+00:00"}