{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:UPFB4QCBZ3HNED2DNYD7KUDNVW","short_pith_number":"pith:UPFB4QCB","canonical_record":{"source":{"id":"1305.6217","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-05-27T13:43:29Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"ebacaae978be05f9bb5c2d2801622c8f238781a9e2f38a3f15b6f4201747db85","abstract_canon_sha256":"763361917c556b6705da9e046375dca8639486b1edf6cc92047d5aed4652813b"},"schema_version":"1.0"},"canonical_sha256":"a3ca1e4041ceced20f436e07f5506dadbef1b7f3bb2429bfdf1450741b80cbd7","source":{"kind":"arxiv","id":"1305.6217","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.6217","created_at":"2026-05-17T23:53:17Z"},{"alias_kind":"arxiv_version","alias_value":"1305.6217v4","created_at":"2026-05-17T23:53:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.6217","created_at":"2026-05-17T23:53:17Z"},{"alias_kind":"pith_short_12","alias_value":"UPFB4QCBZ3HN","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"UPFB4QCBZ3HNED2D","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"UPFB4QCB","created_at":"2026-05-18T12:28:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:UPFB4QCBZ3HNED2DNYD7KUDNVW","target":"record","payload":{"canonical_record":{"source":{"id":"1305.6217","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-05-27T13:43:29Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"ebacaae978be05f9bb5c2d2801622c8f238781a9e2f38a3f15b6f4201747db85","abstract_canon_sha256":"763361917c556b6705da9e046375dca8639486b1edf6cc92047d5aed4652813b"},"schema_version":"1.0"},"canonical_sha256":"a3ca1e4041ceced20f436e07f5506dadbef1b7f3bb2429bfdf1450741b80cbd7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:17.485959Z","signature_b64":"TfWLXLbk1jyu0tVVCLqCFxe2jbvoMv1ylIPHwmK3zlY/ZqoUmjUhwwpnbtEZ3cgTsrELj+JFxe9qkoi0F6ReBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a3ca1e4041ceced20f436e07f5506dadbef1b7f3bb2429bfdf1450741b80cbd7","last_reissued_at":"2026-05-17T23:53:17.485243Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:17.485243Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.6217","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:53:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DriSktRMqOrdZtXBgabuoVNlUpTqOYd2pv6DQK+vfi1GODjiq2u+bip4t8/764b+iI4LlKwLAeXCoFbdtxVcCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T21:16:35.209204Z"},"content_sha256":"2bf83d12b6e0a51b4686f2d9d816db861ad96b901fb5c1893e10e144f24d1dbf","schema_version":"1.0","event_id":"sha256:2bf83d12b6e0a51b4686f2d9d816db861ad96b901fb5c1893e10e144f24d1dbf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:UPFB4QCBZ3HNED2DNYD7KUDNVW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Equivariant calculus of functors and Z/2-analyticity of real K-theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.AT","authors_text":"Emanuele Dotto","submitted_at":"2013-05-27T13:43:29Z","abstract_excerpt":"We define a theory of Goodwillie calculus for enriched functors from finite pointed simplicial G-sets to symmetric G-spectra, where G is a finite group. We extend a notion of G-linearity suggested by Blumberg to define stably excisive and rho-analytic homotopy functors, as well as a G-differential, in this equivariant context. A main result of the paper is that analytic functors with trivial derivatives send highly connected G-maps to G-equivalences. It is analogous to the classical result of Goodwillie that \"functors with zero derivative are locally constant\". As main example we show that Hes"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6217","kind":"arxiv","version":4},"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":"2026-05-17T23:53:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r7fdFq626Rr9h1cadI6X40LTFpdQNHesvujRa+Z71Vni+FnFnW7UAV/rU5eQ3CV/25oMloBuLlUN2FWNkbvLCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T21:16:35.209568Z"},"content_sha256":"cad47fd028d6a65ebb78a403bbfffe8469d8247c92a0714e3747d41fa80f01ba","schema_version":"1.0","event_id":"sha256:cad47fd028d6a65ebb78a403bbfffe8469d8247c92a0714e3747d41fa80f01ba"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UPFB4QCBZ3HNED2DNYD7KUDNVW/bundle.json","state_url":"https://pith.science/pith/UPFB4QCBZ3HNED2DNYD7KUDNVW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UPFB4QCBZ3HNED2DNYD7KUDNVW/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":"2026-06-01T21:16:35Z","links":{"resolver":"https://pith.science/pith/UPFB4QCBZ3HNED2DNYD7KUDNVW","bundle":"https://pith.science/pith/UPFB4QCBZ3HNED2DNYD7KUDNVW/bundle.json","state":"https://pith.science/pith/UPFB4QCBZ3HNED2DNYD7KUDNVW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UPFB4QCBZ3HNED2DNYD7KUDNVW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:UPFB4QCBZ3HNED2DNYD7KUDNVW","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":"763361917c556b6705da9e046375dca8639486b1edf6cc92047d5aed4652813b","cross_cats_sorted":["math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-05-27T13:43:29Z","title_canon_sha256":"ebacaae978be05f9bb5c2d2801622c8f238781a9e2f38a3f15b6f4201747db85"},"schema_version":"1.0","source":{"id":"1305.6217","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.6217","created_at":"2026-05-17T23:53:17Z"},{"alias_kind":"arxiv_version","alias_value":"1305.6217v4","created_at":"2026-05-17T23:53:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.6217","created_at":"2026-05-17T23:53:17Z"},{"alias_kind":"pith_short_12","alias_value":"UPFB4QCBZ3HN","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"UPFB4QCBZ3HNED2D","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"UPFB4QCB","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:cad47fd028d6a65ebb78a403bbfffe8469d8247c92a0714e3747d41fa80f01ba","target":"graph","created_at":"2026-05-17T23:53:17Z","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":"We define a theory of Goodwillie calculus for enriched functors from finite pointed simplicial G-sets to symmetric G-spectra, where G is a finite group. We extend a notion of G-linearity suggested by Blumberg to define stably excisive and rho-analytic homotopy functors, as well as a G-differential, in this equivariant context. A main result of the paper is that analytic functors with trivial derivatives send highly connected G-maps to G-equivalences. It is analogous to the classical result of Goodwillie that \"functors with zero derivative are locally constant\". As main example we show that Hes","authors_text":"Emanuele Dotto","cross_cats":["math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-05-27T13:43:29Z","title":"Equivariant calculus of functors and Z/2-analyticity of real K-theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6217","kind":"arxiv","version":4},"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":"sha256:2bf83d12b6e0a51b4686f2d9d816db861ad96b901fb5c1893e10e144f24d1dbf","target":"record","created_at":"2026-05-17T23:53:17Z","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":"763361917c556b6705da9e046375dca8639486b1edf6cc92047d5aed4652813b","cross_cats_sorted":["math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-05-27T13:43:29Z","title_canon_sha256":"ebacaae978be05f9bb5c2d2801622c8f238781a9e2f38a3f15b6f4201747db85"},"schema_version":"1.0","source":{"id":"1305.6217","kind":"arxiv","version":4}},"canonical_sha256":"a3ca1e4041ceced20f436e07f5506dadbef1b7f3bb2429bfdf1450741b80cbd7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a3ca1e4041ceced20f436e07f5506dadbef1b7f3bb2429bfdf1450741b80cbd7","first_computed_at":"2026-05-17T23:53:17.485243Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:17.485243Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TfWLXLbk1jyu0tVVCLqCFxe2jbvoMv1ylIPHwmK3zlY/ZqoUmjUhwwpnbtEZ3cgTsrELj+JFxe9qkoi0F6ReBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:17.485959Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.6217","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2bf83d12b6e0a51b4686f2d9d816db861ad96b901fb5c1893e10e144f24d1dbf","sha256:cad47fd028d6a65ebb78a403bbfffe8469d8247c92a0714e3747d41fa80f01ba"],"state_sha256":"5fb1ae125ba7ab0b658aa2a069f958c1d446f49142c1efdb68d268397f30d17f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9t1Qacg2NHjBXO3VzaFaC+3oEnaeDWAyJD9tnBeip2NCrI0TN8axPDB/QAhSlI8SC+ZqAmTgF9vqtdruXL/PCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T21:16:35.211984Z","bundle_sha256":"18f35b21157a1aabd9ae332c5dbbc7af50f3337f0b2d6d9aacd92fe4598c99f3"}}