{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:GK5DAQZW64AOP27IDLTSNPVD7G","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":"f4c624e3cf07c9d884eb45d8b29f3ec2acc3ea29dbb77848c3f6ebc124b978b2","cross_cats_sorted":["math.AT"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CT","submitted_at":"2021-01-19T19:03:02Z","title_canon_sha256":"31d34f82ac6ba8dcbcfb5173c82ea88efa1fb7905983c9b523b7c09e5f51e64a"},"schema_version":"1.0","source":{"id":"2101.07819","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2101.07819","created_at":"2026-06-05T01:15:10Z"},{"alias_kind":"arxiv_version","alias_value":"2101.07819v5","created_at":"2026-06-05T01:15:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2101.07819","created_at":"2026-06-05T01:15:10Z"},{"alias_kind":"pith_short_12","alias_value":"GK5DAQZW64AO","created_at":"2026-06-05T01:15:10Z"},{"alias_kind":"pith_short_16","alias_value":"GK5DAQZW64AOP27I","created_at":"2026-06-05T01:15:10Z"},{"alias_kind":"pith_short_8","alias_value":"GK5DAQZW","created_at":"2026-06-05T01:15:10Z"}],"graph_snapshots":[{"event_id":"sha256:be8df7d0a282ffc4d3336b24b2996f653b101b0935f2a8fa8a7d6c1127a09ba9","target":"graph","created_at":"2026-06-05T01:15:10Z","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/2101.07819/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We make precise the analogy between Goodwillie's calculus of functors in homotopy theory and the differential calculus of smooth manifolds by introducing a higher-categorical framework of which both theories are examples. That framework is an extension to infinity-categories of the tangent categories of Cockett and Cruttwell (introduced originally by Rosick\\'y). The basic data of a tangent infinity-category consist of an endofunctor, that plays the role of the tangent bundle construction, together with various natural transformations that mimic structure possessed by the ordinary tangent bundl","authors_text":"Kristine Bauer, Matthew Burke, Michael Ching","cross_cats":["math.AT"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CT","submitted_at":"2021-01-19T19:03:02Z","title":"Tangent $\\infty$-categories and Goodwillie calculus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2101.07819","kind":"arxiv","version":5},"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:d1bcc27aa8852f4df068bb351043823d0b1e00273712e90d6fba06782a674662","target":"record","created_at":"2026-06-05T01:15:10Z","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":"f4c624e3cf07c9d884eb45d8b29f3ec2acc3ea29dbb77848c3f6ebc124b978b2","cross_cats_sorted":["math.AT"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CT","submitted_at":"2021-01-19T19:03:02Z","title_canon_sha256":"31d34f82ac6ba8dcbcfb5173c82ea88efa1fb7905983c9b523b7c09e5f51e64a"},"schema_version":"1.0","source":{"id":"2101.07819","kind":"arxiv","version":5}},"canonical_sha256":"32ba304336f700e7ebe81ae726bea3f9b96da46e18ab331bbbea0140f7efa081","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"32ba304336f700e7ebe81ae726bea3f9b96da46e18ab331bbbea0140f7efa081","first_computed_at":"2026-06-05T01:15:10.816643Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-05T01:15:10.816643Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xzNfpSeB0mtWgKPBaiXsgXNQtLFQKLj699yPvb5hoNWKHoRSASHPu0PYaAr68r9wmfFP2hJHiYCBvQyG5vq3Aw==","signature_status":"signed_v1","signed_at":"2026-06-05T01:15:10.817049Z","signed_message":"canonical_sha256_bytes"},"source_id":"2101.07819","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d1bcc27aa8852f4df068bb351043823d0b1e00273712e90d6fba06782a674662","sha256:be8df7d0a282ffc4d3336b24b2996f653b101b0935f2a8fa8a7d6c1127a09ba9"],"state_sha256":"564511667c736967e1ba7a5c894ed5c12e9b0ce2322bd3bf89e4a936299ee3fc"}