{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:TVIWW2PFFWGTGI2MNLHWITLVRQ","short_pith_number":"pith:TVIWW2PF","canonical_record":{"source":{"id":"1711.03472","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-11-09T16:58:48Z","cross_cats_sorted":[],"title_canon_sha256":"a5346b393de99ca4fa773f64a5b2f14037fe7348233932c76ed81777fde2e349","abstract_canon_sha256":"b640e81758daef75d76838bc37b6c6d1e686db1b1259fb6015dcc351f4179590"},"schema_version":"1.0"},"canonical_sha256":"9d516b69e52d8d33234c6acf644d758c1c6150f24e7c63bcec2d5590cae18fdc","source":{"kind":"arxiv","id":"1711.03472","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.03472","created_at":"2026-05-18T00:30:55Z"},{"alias_kind":"arxiv_version","alias_value":"1711.03472v1","created_at":"2026-05-18T00:30:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.03472","created_at":"2026-05-18T00:30:55Z"},{"alias_kind":"pith_short_12","alias_value":"TVIWW2PFFWGT","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"TVIWW2PFFWGTGI2M","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"TVIWW2PF","created_at":"2026-05-18T12:31:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:TVIWW2PFFWGTGI2MNLHWITLVRQ","target":"record","payload":{"canonical_record":{"source":{"id":"1711.03472","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-11-09T16:58:48Z","cross_cats_sorted":[],"title_canon_sha256":"a5346b393de99ca4fa773f64a5b2f14037fe7348233932c76ed81777fde2e349","abstract_canon_sha256":"b640e81758daef75d76838bc37b6c6d1e686db1b1259fb6015dcc351f4179590"},"schema_version":"1.0"},"canonical_sha256":"9d516b69e52d8d33234c6acf644d758c1c6150f24e7c63bcec2d5590cae18fdc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:30:55.996255Z","signature_b64":"3eIFFY0fPa1MQDc5RYp9fCJdUaZQeGZY3kI65SMvcPcFhpKLXLNm5t+p46oYrK2MePW3RLanuOD6gCQfCvcyAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9d516b69e52d8d33234c6acf644d758c1c6150f24e7c63bcec2d5590cae18fdc","last_reissued_at":"2026-05-18T00:30:55.995540Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:30:55.995540Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.03472","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":"2026-05-18T00:30:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o0oHpRTLXnyHoWueiar7KCiaQQSLttrSDrUKPSKEF9cLC6IbicdMVuOnWxDCFhzC8g/cQeiuIH6BNen+rt+0Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T10:24:50.501156Z"},"content_sha256":"6814698e60bfd1fbb2144db404109d56b636b29d208ce2194e1e2392aaabd407","schema_version":"1.0","event_id":"sha256:6814698e60bfd1fbb2144db404109d56b636b29d208ce2194e1e2392aaabd407"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:TVIWW2PFFWGTGI2MNLHWITLVRQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On categories of slices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Dylan Wilson","submitted_at":"2017-11-09T16:58:48Z","abstract_excerpt":"In this paper we give an algebraic description of the category of $n$-slices for an arbitrary group $G$, in the sense of Hill-Hopkins-Ravenel. Specifically, given a finite group $G$ and an integer $n$, we construct an explicit $G$-spectrum $W$ (called an isotropic slice $n$-sphere) with the following properties: (i) the $n$-slice of a $G$-spectrum $X$ is equivalent to the data of a certain quotient of the Mackey functor $\\underline{[W,X]}$ as a module over the endomorphism Green functor $\\underline{[W,W]}$; (ii) the category of $n$-slices is equivalent to the full subcategory of right modules "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.03472","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":""},"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":"2026-05-18T00:30:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GDs64vwOPzkNJrCFwn9ztEn/iG/pyJMEvZmd1fFs8gZErALfBlU1dLrhzW1G8Trkruw5eW39JSa5agMiBIdoBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T10:24:50.501516Z"},"content_sha256":"5eed6bc83df4ec43e65e9ee8e0506fccce4e33868e3b35ee0b6166055ea701d3","schema_version":"1.0","event_id":"sha256:5eed6bc83df4ec43e65e9ee8e0506fccce4e33868e3b35ee0b6166055ea701d3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TVIWW2PFFWGTGI2MNLHWITLVRQ/bundle.json","state_url":"https://pith.science/pith/TVIWW2PFFWGTGI2MNLHWITLVRQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TVIWW2PFFWGTGI2MNLHWITLVRQ/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":"2026-06-24T10:24:50Z","links":{"resolver":"https://pith.science/pith/TVIWW2PFFWGTGI2MNLHWITLVRQ","bundle":"https://pith.science/pith/TVIWW2PFFWGTGI2MNLHWITLVRQ/bundle.json","state":"https://pith.science/pith/TVIWW2PFFWGTGI2MNLHWITLVRQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TVIWW2PFFWGTGI2MNLHWITLVRQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:TVIWW2PFFWGTGI2MNLHWITLVRQ","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":"b640e81758daef75d76838bc37b6c6d1e686db1b1259fb6015dcc351f4179590","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-11-09T16:58:48Z","title_canon_sha256":"a5346b393de99ca4fa773f64a5b2f14037fe7348233932c76ed81777fde2e349"},"schema_version":"1.0","source":{"id":"1711.03472","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.03472","created_at":"2026-05-18T00:30:55Z"},{"alias_kind":"arxiv_version","alias_value":"1711.03472v1","created_at":"2026-05-18T00:30:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.03472","created_at":"2026-05-18T00:30:55Z"},{"alias_kind":"pith_short_12","alias_value":"TVIWW2PFFWGT","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"TVIWW2PFFWGTGI2M","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"TVIWW2PF","created_at":"2026-05-18T12:31:46Z"}],"graph_snapshots":[{"event_id":"sha256:5eed6bc83df4ec43e65e9ee8e0506fccce4e33868e3b35ee0b6166055ea701d3","target":"graph","created_at":"2026-05-18T00:30:55Z","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":"In this paper we give an algebraic description of the category of $n$-slices for an arbitrary group $G$, in the sense of Hill-Hopkins-Ravenel. Specifically, given a finite group $G$ and an integer $n$, we construct an explicit $G$-spectrum $W$ (called an isotropic slice $n$-sphere) with the following properties: (i) the $n$-slice of a $G$-spectrum $X$ is equivalent to the data of a certain quotient of the Mackey functor $\\underline{[W,X]}$ as a module over the endomorphism Green functor $\\underline{[W,W]}$; (ii) the category of $n$-slices is equivalent to the full subcategory of right modules ","authors_text":"Dylan Wilson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-11-09T16:58:48Z","title":"On categories of slices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.03472","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":"sha256:6814698e60bfd1fbb2144db404109d56b636b29d208ce2194e1e2392aaabd407","target":"record","created_at":"2026-05-18T00:30:55Z","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":"b640e81758daef75d76838bc37b6c6d1e686db1b1259fb6015dcc351f4179590","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-11-09T16:58:48Z","title_canon_sha256":"a5346b393de99ca4fa773f64a5b2f14037fe7348233932c76ed81777fde2e349"},"schema_version":"1.0","source":{"id":"1711.03472","kind":"arxiv","version":1}},"canonical_sha256":"9d516b69e52d8d33234c6acf644d758c1c6150f24e7c63bcec2d5590cae18fdc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9d516b69e52d8d33234c6acf644d758c1c6150f24e7c63bcec2d5590cae18fdc","first_computed_at":"2026-05-18T00:30:55.995540Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:30:55.995540Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3eIFFY0fPa1MQDc5RYp9fCJdUaZQeGZY3kI65SMvcPcFhpKLXLNm5t+p46oYrK2MePW3RLanuOD6gCQfCvcyAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:30:55.996255Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.03472","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6814698e60bfd1fbb2144db404109d56b636b29d208ce2194e1e2392aaabd407","sha256:5eed6bc83df4ec43e65e9ee8e0506fccce4e33868e3b35ee0b6166055ea701d3"],"state_sha256":"2af32b0ab66f97fefeb1dab93103cb68babc675a2c2ff15f9eff22931e953168"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"smO+7mM1EudoJoAmQodgqo67qqCJbIHj2dmumSJ3S7X3dheEhgE7tO61ZuPfdyS2dT6WHy2meeE+sZGNcwD2BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T10:24:50.503443Z","bundle_sha256":"ea0f82612db8d3326a3baf1b00335104b1523c051af5b084a89f97ad5192febe"}}