{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:TEFRSXYMEIJHDBTYJUEWJ6MZW7","short_pith_number":"pith:TEFRSXYM","canonical_record":{"source":{"id":"1411.3502","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-11-13T11:18:22Z","cross_cats_sorted":[],"title_canon_sha256":"4b80f070bb0731ba6f481757e870e4815273854b4351f634249542535219d3b4","abstract_canon_sha256":"913d5e3f0ac01b6fe34292de7da42f21a01a26ee086641397eca98943c8bbcfb"},"schema_version":"1.0"},"canonical_sha256":"990b195f0c22127186784d0964f999b7f00b8ad39fbab76807fe32b3dfa2a2d8","source":{"kind":"arxiv","id":"1411.3502","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.3502","created_at":"2026-05-18T02:37:43Z"},{"alias_kind":"arxiv_version","alias_value":"1411.3502v1","created_at":"2026-05-18T02:37:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.3502","created_at":"2026-05-18T02:37:43Z"},{"alias_kind":"pith_short_12","alias_value":"TEFRSXYMEIJH","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"TEFRSXYMEIJHDBTY","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"TEFRSXYM","created_at":"2026-05-18T12:28:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:TEFRSXYMEIJHDBTYJUEWJ6MZW7","target":"record","payload":{"canonical_record":{"source":{"id":"1411.3502","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-11-13T11:18:22Z","cross_cats_sorted":[],"title_canon_sha256":"4b80f070bb0731ba6f481757e870e4815273854b4351f634249542535219d3b4","abstract_canon_sha256":"913d5e3f0ac01b6fe34292de7da42f21a01a26ee086641397eca98943c8bbcfb"},"schema_version":"1.0"},"canonical_sha256":"990b195f0c22127186784d0964f999b7f00b8ad39fbab76807fe32b3dfa2a2d8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:37:43.607565Z","signature_b64":"n0URsBIC51keq0vQt7iO8zkjpQn5aa6kvBQumPVAC+c4C8GFJiMfIBAu93n6bwdhdy/zgA4muL0h5ux0tWfyCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"990b195f0c22127186784d0964f999b7f00b8ad39fbab76807fe32b3dfa2a2d8","last_reissued_at":"2026-05-18T02:37:43.607157Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:37:43.607157Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.3502","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":"2026-05-18T02:37:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XEXKjFRUAgTJQcPjFbLyQrAy60wIlcRbyR8CLTsZdt2zf6OrSCLxV+a4yBpuU7QK07CIAN62kFrDcFWOg956Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T02:25:44.784921Z"},"content_sha256":"01617e73eb33a3a186a3b2fa40759cf1ed8bc6438c7dac5c21dd8bdbabc75152","schema_version":"1.0","event_id":"sha256:01617e73eb33a3a186a3b2fa40759cf1ed8bc6438c7dac5c21dd8bdbabc75152"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:TEFRSXYMEIJHDBTYJUEWJ6MZW7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sylow subgroups of symmetric and alternating groups and the vertex of $S^{(kp-p,1^p)}$ in characteristic $p$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Eugenio Giannelli, Kay Jin Lim, Mark Wildon","submitted_at":"2014-11-13T11:18:22Z","abstract_excerpt":"We show that the Sylow $p$-subgroups of a symmetric group, respectively an alternating group, are characterized as the $p$-subgroups containing all elementary abelian $p$-subgroups up to conjugacy of the symmetric group, respectively the alternating group. We apply the characterization result for symmetric groups to compute the vertices of the hook Specht modules associated to the partition $(kp-p,1^p)$ under the assumption that $k \\equiv 1$ mod $p$ and $k \\not\\equiv 1$ mod $p^2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.3502","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":"2026-05-18T02:37:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B8NIulPHDW3JxO3xJhvkdTRhzCb1r6RwDF+7yGHxEwlqeGLqBEotFZuf1UgdAATLzIsDzlEVzuEQS8s1/ZSkBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T02:25:44.785271Z"},"content_sha256":"372790e8b2113235c46055050d87b5abe80d88cdcab72e1a34fd687f546ba0e2","schema_version":"1.0","event_id":"sha256:372790e8b2113235c46055050d87b5abe80d88cdcab72e1a34fd687f546ba0e2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TEFRSXYMEIJHDBTYJUEWJ6MZW7/bundle.json","state_url":"https://pith.science/pith/TEFRSXYMEIJHDBTYJUEWJ6MZW7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TEFRSXYMEIJHDBTYJUEWJ6MZW7/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":"2026-05-30T02:25:44Z","links":{"resolver":"https://pith.science/pith/TEFRSXYMEIJHDBTYJUEWJ6MZW7","bundle":"https://pith.science/pith/TEFRSXYMEIJHDBTYJUEWJ6MZW7/bundle.json","state":"https://pith.science/pith/TEFRSXYMEIJHDBTYJUEWJ6MZW7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TEFRSXYMEIJHDBTYJUEWJ6MZW7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:TEFRSXYMEIJHDBTYJUEWJ6MZW7","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":"913d5e3f0ac01b6fe34292de7da42f21a01a26ee086641397eca98943c8bbcfb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-11-13T11:18:22Z","title_canon_sha256":"4b80f070bb0731ba6f481757e870e4815273854b4351f634249542535219d3b4"},"schema_version":"1.0","source":{"id":"1411.3502","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.3502","created_at":"2026-05-18T02:37:43Z"},{"alias_kind":"arxiv_version","alias_value":"1411.3502v1","created_at":"2026-05-18T02:37:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.3502","created_at":"2026-05-18T02:37:43Z"},{"alias_kind":"pith_short_12","alias_value":"TEFRSXYMEIJH","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"TEFRSXYMEIJHDBTY","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"TEFRSXYM","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:372790e8b2113235c46055050d87b5abe80d88cdcab72e1a34fd687f546ba0e2","target":"graph","created_at":"2026-05-18T02:37:43Z","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 show that the Sylow $p$-subgroups of a symmetric group, respectively an alternating group, are characterized as the $p$-subgroups containing all elementary abelian $p$-subgroups up to conjugacy of the symmetric group, respectively the alternating group. We apply the characterization result for symmetric groups to compute the vertices of the hook Specht modules associated to the partition $(kp-p,1^p)$ under the assumption that $k \\equiv 1$ mod $p$ and $k \\not\\equiv 1$ mod $p^2$.","authors_text":"Eugenio Giannelli, Kay Jin Lim, Mark Wildon","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-11-13T11:18:22Z","title":"Sylow subgroups of symmetric and alternating groups and the vertex of $S^{(kp-p,1^p)}$ in characteristic $p$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.3502","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":"sha256:01617e73eb33a3a186a3b2fa40759cf1ed8bc6438c7dac5c21dd8bdbabc75152","target":"record","created_at":"2026-05-18T02:37:43Z","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":"913d5e3f0ac01b6fe34292de7da42f21a01a26ee086641397eca98943c8bbcfb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-11-13T11:18:22Z","title_canon_sha256":"4b80f070bb0731ba6f481757e870e4815273854b4351f634249542535219d3b4"},"schema_version":"1.0","source":{"id":"1411.3502","kind":"arxiv","version":1}},"canonical_sha256":"990b195f0c22127186784d0964f999b7f00b8ad39fbab76807fe32b3dfa2a2d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"990b195f0c22127186784d0964f999b7f00b8ad39fbab76807fe32b3dfa2a2d8","first_computed_at":"2026-05-18T02:37:43.607157Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:37:43.607157Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n0URsBIC51keq0vQt7iO8zkjpQn5aa6kvBQumPVAC+c4C8GFJiMfIBAu93n6bwdhdy/zgA4muL0h5ux0tWfyCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:37:43.607565Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.3502","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:01617e73eb33a3a186a3b2fa40759cf1ed8bc6438c7dac5c21dd8bdbabc75152","sha256:372790e8b2113235c46055050d87b5abe80d88cdcab72e1a34fd687f546ba0e2"],"state_sha256":"bc379bf5180d0bc9f91f70bda37d31db3c352cdae3f638cdcbec1098458ffe1b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9cSJcblkKMHisPqZSVbyqi2UG5zLYBWxJXgpW/BxNih6PbH1n7vfJIZpvdsPhXH1nxdqf5kHqhalQzCerYQxBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T02:25:44.787338Z","bundle_sha256":"901870be3e0a03d67c41ada8389e43588ccb9fd2b513001c47d112cf2da76107"}}