{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:ZAWE2MQTFJZLWZSW5JJ7QPNBAA","short_pith_number":"pith:ZAWE2MQT","canonical_record":{"source":{"id":"1301.0193","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-01-02T09:03:28Z","cross_cats_sorted":["math.CO","math.GR"],"title_canon_sha256":"571265a003dbca8d8f9346ab46a29b9d968b8ba7fa235d66dfff3addef56e909","abstract_canon_sha256":"a39716ac0f383b1da534d3cbc692b46f2525de457fd9dd93a8341f32e7f431b1"},"schema_version":"1.0"},"canonical_sha256":"c82c4d32132a72bb6656ea53f83da100016afa5485d3d7f5133ad6b35893d4f1","source":{"kind":"arxiv","id":"1301.0193","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.0193","created_at":"2026-05-18T02:49:31Z"},{"alias_kind":"arxiv_version","alias_value":"1301.0193v2","created_at":"2026-05-18T02:49:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.0193","created_at":"2026-05-18T02:49:31Z"},{"alias_kind":"pith_short_12","alias_value":"ZAWE2MQTFJZL","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZAWE2MQTFJZLWZSW","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZAWE2MQT","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:ZAWE2MQTFJZLWZSW5JJ7QPNBAA","target":"record","payload":{"canonical_record":{"source":{"id":"1301.0193","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-01-02T09:03:28Z","cross_cats_sorted":["math.CO","math.GR"],"title_canon_sha256":"571265a003dbca8d8f9346ab46a29b9d968b8ba7fa235d66dfff3addef56e909","abstract_canon_sha256":"a39716ac0f383b1da534d3cbc692b46f2525de457fd9dd93a8341f32e7f431b1"},"schema_version":"1.0"},"canonical_sha256":"c82c4d32132a72bb6656ea53f83da100016afa5485d3d7f5133ad6b35893d4f1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:31.863340Z","signature_b64":"M9U+wVQxOAxdgiaYZ6GLXkYBafyVD6hfNiUtpnGVJRNpfX8eHrIXi2kl7A2goRRPwR97XmPH1a2T4E27WdU4DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c82c4d32132a72bb6656ea53f83da100016afa5485d3d7f5133ad6b35893d4f1","last_reissued_at":"2026-05-18T02:49:31.862892Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:31.862892Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.0193","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:49:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DCmfNRnaZHgnsEZT1jZbxKhGoZaSo5TKokaRr3ybDKKI243jSWPBu8+1s2x0W5XdFOLvkOxzAEx7VzssYlhqAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T09:25:26.579630Z"},"content_sha256":"814859f484ac054e8e12e466e2dda83439205f67def0e4b1b9f71c3222a5ec66","schema_version":"1.0","event_id":"sha256:814859f484ac054e8e12e466e2dda83439205f67def0e4b1b9f71c3222a5ec66"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:ZAWE2MQTFJZLWZSW5JJ7QPNBAA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Homotopy equivalences between p-subgroup categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.GR"],"primary_cat":"math.AT","authors_text":"Jesper M{\\o}ller, Matthew Gelvin","submitted_at":"2013-01-02T09:03:28Z","abstract_excerpt":"Let p be a prime number and G a finite group of order divisible by p. Quillen showed that the Brown poset of nonidentity p-subgroups of G is homotopy equivalent to its subposet of nonidentity elementary abelian subgroups. We show here that a similar statement holds for the fusion category of nonidentity p-subgroups of G. Other categories of p-subgroups of G are also considered."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.0193","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:49:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sjwKScSek3AnXWJDeqabbrdkynwp4k+pczVqkCEoiclmhL6WIcJvZhp21Ff7K4CXSPSj3s1Sz9rAsUqx3hxuBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T09:25:26.580163Z"},"content_sha256":"b846d10ac35a37b803243894035cf0134d528433ba863b809bb9ee5ff2505cbf","schema_version":"1.0","event_id":"sha256:b846d10ac35a37b803243894035cf0134d528433ba863b809bb9ee5ff2505cbf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZAWE2MQTFJZLWZSW5JJ7QPNBAA/bundle.json","state_url":"https://pith.science/pith/ZAWE2MQTFJZLWZSW5JJ7QPNBAA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZAWE2MQTFJZLWZSW5JJ7QPNBAA/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":"2026-06-07T09:25:26Z","links":{"resolver":"https://pith.science/pith/ZAWE2MQTFJZLWZSW5JJ7QPNBAA","bundle":"https://pith.science/pith/ZAWE2MQTFJZLWZSW5JJ7QPNBAA/bundle.json","state":"https://pith.science/pith/ZAWE2MQTFJZLWZSW5JJ7QPNBAA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZAWE2MQTFJZLWZSW5JJ7QPNBAA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ZAWE2MQTFJZLWZSW5JJ7QPNBAA","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":"a39716ac0f383b1da534d3cbc692b46f2525de457fd9dd93a8341f32e7f431b1","cross_cats_sorted":["math.CO","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-01-02T09:03:28Z","title_canon_sha256":"571265a003dbca8d8f9346ab46a29b9d968b8ba7fa235d66dfff3addef56e909"},"schema_version":"1.0","source":{"id":"1301.0193","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.0193","created_at":"2026-05-18T02:49:31Z"},{"alias_kind":"arxiv_version","alias_value":"1301.0193v2","created_at":"2026-05-18T02:49:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.0193","created_at":"2026-05-18T02:49:31Z"},{"alias_kind":"pith_short_12","alias_value":"ZAWE2MQTFJZL","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZAWE2MQTFJZLWZSW","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZAWE2MQT","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:b846d10ac35a37b803243894035cf0134d528433ba863b809bb9ee5ff2505cbf","target":"graph","created_at":"2026-05-18T02:49:31Z","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":"Let p be a prime number and G a finite group of order divisible by p. Quillen showed that the Brown poset of nonidentity p-subgroups of G is homotopy equivalent to its subposet of nonidentity elementary abelian subgroups. We show here that a similar statement holds for the fusion category of nonidentity p-subgroups of G. Other categories of p-subgroups of G are also considered.","authors_text":"Jesper M{\\o}ller, Matthew Gelvin","cross_cats":["math.CO","math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-01-02T09:03:28Z","title":"Homotopy equivalences between p-subgroup categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.0193","kind":"arxiv","version":2},"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":"sha256:814859f484ac054e8e12e466e2dda83439205f67def0e4b1b9f71c3222a5ec66","target":"record","created_at":"2026-05-18T02:49:31Z","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":"a39716ac0f383b1da534d3cbc692b46f2525de457fd9dd93a8341f32e7f431b1","cross_cats_sorted":["math.CO","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-01-02T09:03:28Z","title_canon_sha256":"571265a003dbca8d8f9346ab46a29b9d968b8ba7fa235d66dfff3addef56e909"},"schema_version":"1.0","source":{"id":"1301.0193","kind":"arxiv","version":2}},"canonical_sha256":"c82c4d32132a72bb6656ea53f83da100016afa5485d3d7f5133ad6b35893d4f1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c82c4d32132a72bb6656ea53f83da100016afa5485d3d7f5133ad6b35893d4f1","first_computed_at":"2026-05-18T02:49:31.862892Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:49:31.862892Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M9U+wVQxOAxdgiaYZ6GLXkYBafyVD6hfNiUtpnGVJRNpfX8eHrIXi2kl7A2goRRPwR97XmPH1a2T4E27WdU4DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:49:31.863340Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.0193","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:814859f484ac054e8e12e466e2dda83439205f67def0e4b1b9f71c3222a5ec66","sha256:b846d10ac35a37b803243894035cf0134d528433ba863b809bb9ee5ff2505cbf"],"state_sha256":"bcfd854d38c3cd85ab5b2c3f753530718c1e931c6e64616ddd2334398d39a467"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eO6PVWduap31W44Pqqceui56i4s/BhY2ALxxV2GBzzcBivMQi89pL2XpX8cZy4VHpV0jOneEMdE+Q0ndh+W+Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T09:25:26.582826Z","bundle_sha256":"8b6441bdee017beba9b425950c27f613c9de8e9f7e79eda992d139c9474e1329"}}