{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:2CQY2XOMQVGQP3TQX5N52F3YFU","short_pith_number":"pith:2CQY2XOM","canonical_record":{"source":{"id":"1305.6573","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-05-28T17:59:29Z","cross_cats_sorted":[],"title_canon_sha256":"f31c57ca57b4f0bdff30bb01594a92280066b62715cc197bf208c642cb30315c","abstract_canon_sha256":"55611965c82922ea9d674203fb0800bb72accdb698a988775d16c1ac773e2900"},"schema_version":"1.0"},"canonical_sha256":"d0a18d5dcc854d07ee70bf5bdd17782d1687b000df65b8fa6f0d8aa7fcb50c48","source":{"kind":"arxiv","id":"1305.6573","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.6573","created_at":"2026-05-18T03:24:40Z"},{"alias_kind":"arxiv_version","alias_value":"1305.6573v1","created_at":"2026-05-18T03:24:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.6573","created_at":"2026-05-18T03:24:40Z"},{"alias_kind":"pith_short_12","alias_value":"2CQY2XOMQVGQ","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"2CQY2XOMQVGQP3TQ","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"2CQY2XOM","created_at":"2026-05-18T12:27:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:2CQY2XOMQVGQP3TQX5N52F3YFU","target":"record","payload":{"canonical_record":{"source":{"id":"1305.6573","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-05-28T17:59:29Z","cross_cats_sorted":[],"title_canon_sha256":"f31c57ca57b4f0bdff30bb01594a92280066b62715cc197bf208c642cb30315c","abstract_canon_sha256":"55611965c82922ea9d674203fb0800bb72accdb698a988775d16c1ac773e2900"},"schema_version":"1.0"},"canonical_sha256":"d0a18d5dcc854d07ee70bf5bdd17782d1687b000df65b8fa6f0d8aa7fcb50c48","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:24:40.402125Z","signature_b64":"NbOXfT7bQSpkJv88VIkO/3/gaQPe961mz6RydiLWqsmUCguRTm5GjvtvS2brwBnDismWqhD24LPDtkiTCUMcDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d0a18d5dcc854d07ee70bf5bdd17782d1687b000df65b8fa6f0d8aa7fcb50c48","last_reissued_at":"2026-05-18T03:24:40.401631Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:24:40.401631Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.6573","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":"2026-05-18T03:24:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+Q+MJnKD7gMyRpNk1OHremXEpdgt79kfp+nOoopVDf3SOTa+35Fgw3z2UB9q9xPpfcrsfM6rz2Gb7Kdw8MuTDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T19:38:29.168656Z"},"content_sha256":"16e1ad48476534a527b0aa16d52df1a82a65ae6974ecadff7f117c424c12f823","schema_version":"1.0","event_id":"sha256:16e1ad48476534a527b0aa16d52df1a82a65ae6974ecadff7f117c424c12f823"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:2CQY2XOMQVGQP3TQX5N52F3YFU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Subgroups of p-divisible groups and centralizers in symmetric groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Nathaniel Stapleton","submitted_at":"2013-05-28T17:59:29Z","abstract_excerpt":"For cohomology theories closely related to Morava E-theory, we provide an algebro-geometric interpretation of the cohomology of groups that arise as centralizers of tuples of commuting elements inside of symmetric groups. The interpretation is given in terms of the connected components of the scheme that classifies subgroup schemes of a particular p-divisible group."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6573","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":"2026-05-18T03:24:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BPshLOzA3eQw6BIzkVxBv/t3q3ySw6zMIjq+HuzwrCqb856MNtxq4FABfuu0nICLngO3hW4/1GjM/T82EdytDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T19:38:29.168996Z"},"content_sha256":"b13caa130b09d7f82d3fedb256dd7e0cb2d12a1dce8ff86e318f723225688785","schema_version":"1.0","event_id":"sha256:b13caa130b09d7f82d3fedb256dd7e0cb2d12a1dce8ff86e318f723225688785"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2CQY2XOMQVGQP3TQX5N52F3YFU/bundle.json","state_url":"https://pith.science/pith/2CQY2XOMQVGQP3TQX5N52F3YFU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2CQY2XOMQVGQP3TQX5N52F3YFU/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":"2026-07-02T19:38:29Z","links":{"resolver":"https://pith.science/pith/2CQY2XOMQVGQP3TQX5N52F3YFU","bundle":"https://pith.science/pith/2CQY2XOMQVGQP3TQX5N52F3YFU/bundle.json","state":"https://pith.science/pith/2CQY2XOMQVGQP3TQX5N52F3YFU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2CQY2XOMQVGQP3TQX5N52F3YFU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:2CQY2XOMQVGQP3TQX5N52F3YFU","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":"55611965c82922ea9d674203fb0800bb72accdb698a988775d16c1ac773e2900","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-05-28T17:59:29Z","title_canon_sha256":"f31c57ca57b4f0bdff30bb01594a92280066b62715cc197bf208c642cb30315c"},"schema_version":"1.0","source":{"id":"1305.6573","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.6573","created_at":"2026-05-18T03:24:40Z"},{"alias_kind":"arxiv_version","alias_value":"1305.6573v1","created_at":"2026-05-18T03:24:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.6573","created_at":"2026-05-18T03:24:40Z"},{"alias_kind":"pith_short_12","alias_value":"2CQY2XOMQVGQ","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"2CQY2XOMQVGQP3TQ","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"2CQY2XOM","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:b13caa130b09d7f82d3fedb256dd7e0cb2d12a1dce8ff86e318f723225688785","target":"graph","created_at":"2026-05-18T03:24:40Z","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"},"paper":{"abstract_excerpt":"For cohomology theories closely related to Morava E-theory, we provide an algebro-geometric interpretation of the cohomology of groups that arise as centralizers of tuples of commuting elements inside of symmetric groups. The interpretation is given in terms of the connected components of the scheme that classifies subgroup schemes of a particular p-divisible group.","authors_text":"Nathaniel Stapleton","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-05-28T17:59:29Z","title":"Subgroups of p-divisible groups and centralizers in symmetric groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6573","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":"sha256:16e1ad48476534a527b0aa16d52df1a82a65ae6974ecadff7f117c424c12f823","target":"record","created_at":"2026-05-18T03:24:40Z","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":"55611965c82922ea9d674203fb0800bb72accdb698a988775d16c1ac773e2900","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-05-28T17:59:29Z","title_canon_sha256":"f31c57ca57b4f0bdff30bb01594a92280066b62715cc197bf208c642cb30315c"},"schema_version":"1.0","source":{"id":"1305.6573","kind":"arxiv","version":1}},"canonical_sha256":"d0a18d5dcc854d07ee70bf5bdd17782d1687b000df65b8fa6f0d8aa7fcb50c48","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d0a18d5dcc854d07ee70bf5bdd17782d1687b000df65b8fa6f0d8aa7fcb50c48","first_computed_at":"2026-05-18T03:24:40.401631Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:24:40.401631Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NbOXfT7bQSpkJv88VIkO/3/gaQPe961mz6RydiLWqsmUCguRTm5GjvtvS2brwBnDismWqhD24LPDtkiTCUMcDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:24:40.402125Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.6573","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:16e1ad48476534a527b0aa16d52df1a82a65ae6974ecadff7f117c424c12f823","sha256:b13caa130b09d7f82d3fedb256dd7e0cb2d12a1dce8ff86e318f723225688785"],"state_sha256":"451f54ce4a2bd085dbf3e44ab8e2b82bcfe46ddc1b225d1d500920d89f7d6b27"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xysI6AI3yHaMsEDZGGHQkUPuJHK3uCzVoohsZursjxBT8cbyX/Ps8TzWb+H0lDplRv6M8LIoV4xa1XgcRvg4Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T19:38:29.170892Z","bundle_sha256":"3006094c6a1bad086ea7497aa134d0e3fab015a418e08c4f73eacfb6e4861aa6"}}