{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:BNLXYQ4ZJCCLEQWJXV5NQZ5GKN","short_pith_number":"pith:BNLXYQ4Z","canonical_record":{"source":{"id":"1407.1845","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-07-07T20:00:11Z","cross_cats_sorted":[],"title_canon_sha256":"f6280ff92542bb4882d9e06165472fa612be770c47072142e779f1146a926357","abstract_canon_sha256":"703369a7766234b497b0a964b657bda95bc684666a084bf7250658d7c5865dde"},"schema_version":"1.0"},"canonical_sha256":"0b577c43994884b242c9bd7ad867a6534ef4aca8c371faf2b4d307ae52b2bee5","source":{"kind":"arxiv","id":"1407.1845","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.1845","created_at":"2026-05-18T02:39:48Z"},{"alias_kind":"arxiv_version","alias_value":"1407.1845v2","created_at":"2026-05-18T02:39:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.1845","created_at":"2026-05-18T02:39:48Z"},{"alias_kind":"pith_short_12","alias_value":"BNLXYQ4ZJCCL","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"BNLXYQ4ZJCCLEQWJ","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"BNLXYQ4Z","created_at":"2026-05-18T12:28:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:BNLXYQ4ZJCCLEQWJXV5NQZ5GKN","target":"record","payload":{"canonical_record":{"source":{"id":"1407.1845","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-07-07T20:00:11Z","cross_cats_sorted":[],"title_canon_sha256":"f6280ff92542bb4882d9e06165472fa612be770c47072142e779f1146a926357","abstract_canon_sha256":"703369a7766234b497b0a964b657bda95bc684666a084bf7250658d7c5865dde"},"schema_version":"1.0"},"canonical_sha256":"0b577c43994884b242c9bd7ad867a6534ef4aca8c371faf2b4d307ae52b2bee5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:39:48.018678Z","signature_b64":"j215izhrKQMeD3WjXIR4KT3FSKQy9rnTDCY2rFywMMqNCvpgUALResbahCfavxtYIPoGaWkyPxlAnC+Lu8VuCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0b577c43994884b242c9bd7ad867a6534ef4aca8c371faf2b4d307ae52b2bee5","last_reissued_at":"2026-05-18T02:39:48.018165Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:39:48.018165Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.1845","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":"2026-05-18T02:39:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KQbHyQzIbq7ukzOd7ajQRrpHdraHIMGVAvLXevx5DLY4ZQRYT5aqP2XssT9Jmb0YZADeyDplzCobyYcYtfSEDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T12:33:00.500674Z"},"content_sha256":"bf46957336bd8f0a950d155cfe94c9316981ecc741baed810486dc8840a49ad7","schema_version":"1.0","event_id":"sha256:bf46957336bd8f0a950d155cfe94c9316981ecc741baed810486dc8840a49ad7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:BNLXYQ4ZJCCLEQWJXV5NQZ5GKN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Vertices of simple modules of symmetric groups labelled by hook partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Eugenio Giannelli, Susanne Danz","submitted_at":"2014-07-07T20:00:11Z","abstract_excerpt":"In this article we study the vertices of simple modules for the symmetric groups in prime characteristic $p$. In particular, we complete the classification of the vertices of simple $S_n$-modules labelled by hook partitions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.1845","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":"2026-05-18T02:39:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QqHfaUQ6hDoQ8hXkPfb7m2zLlmjNsWBZJty2WXW3fY2/wPJheCfrWBwi649Bql1bet4DVNzFy+ncLtTxim9iBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T12:33:00.501077Z"},"content_sha256":"14661548fe094bb7f4aa730c4734131955cd042d020d685d3c29104eea89efe2","schema_version":"1.0","event_id":"sha256:14661548fe094bb7f4aa730c4734131955cd042d020d685d3c29104eea89efe2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BNLXYQ4ZJCCLEQWJXV5NQZ5GKN/bundle.json","state_url":"https://pith.science/pith/BNLXYQ4ZJCCLEQWJXV5NQZ5GKN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BNLXYQ4ZJCCLEQWJXV5NQZ5GKN/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":"2026-06-02T12:33:00Z","links":{"resolver":"https://pith.science/pith/BNLXYQ4ZJCCLEQWJXV5NQZ5GKN","bundle":"https://pith.science/pith/BNLXYQ4ZJCCLEQWJXV5NQZ5GKN/bundle.json","state":"https://pith.science/pith/BNLXYQ4ZJCCLEQWJXV5NQZ5GKN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BNLXYQ4ZJCCLEQWJXV5NQZ5GKN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:BNLXYQ4ZJCCLEQWJXV5NQZ5GKN","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":"703369a7766234b497b0a964b657bda95bc684666a084bf7250658d7c5865dde","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-07-07T20:00:11Z","title_canon_sha256":"f6280ff92542bb4882d9e06165472fa612be770c47072142e779f1146a926357"},"schema_version":"1.0","source":{"id":"1407.1845","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.1845","created_at":"2026-05-18T02:39:48Z"},{"alias_kind":"arxiv_version","alias_value":"1407.1845v2","created_at":"2026-05-18T02:39:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.1845","created_at":"2026-05-18T02:39:48Z"},{"alias_kind":"pith_short_12","alias_value":"BNLXYQ4ZJCCL","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"BNLXYQ4ZJCCLEQWJ","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"BNLXYQ4Z","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:14661548fe094bb7f4aa730c4734131955cd042d020d685d3c29104eea89efe2","target":"graph","created_at":"2026-05-18T02:39:48Z","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 article we study the vertices of simple modules for the symmetric groups in prime characteristic $p$. In particular, we complete the classification of the vertices of simple $S_n$-modules labelled by hook partitions.","authors_text":"Eugenio Giannelli, Susanne Danz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-07-07T20:00:11Z","title":"Vertices of simple modules of symmetric groups labelled by hook partitions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.1845","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:bf46957336bd8f0a950d155cfe94c9316981ecc741baed810486dc8840a49ad7","target":"record","created_at":"2026-05-18T02:39:48Z","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":"703369a7766234b497b0a964b657bda95bc684666a084bf7250658d7c5865dde","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-07-07T20:00:11Z","title_canon_sha256":"f6280ff92542bb4882d9e06165472fa612be770c47072142e779f1146a926357"},"schema_version":"1.0","source":{"id":"1407.1845","kind":"arxiv","version":2}},"canonical_sha256":"0b577c43994884b242c9bd7ad867a6534ef4aca8c371faf2b4d307ae52b2bee5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0b577c43994884b242c9bd7ad867a6534ef4aca8c371faf2b4d307ae52b2bee5","first_computed_at":"2026-05-18T02:39:48.018165Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:48.018165Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j215izhrKQMeD3WjXIR4KT3FSKQy9rnTDCY2rFywMMqNCvpgUALResbahCfavxtYIPoGaWkyPxlAnC+Lu8VuCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:48.018678Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.1845","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bf46957336bd8f0a950d155cfe94c9316981ecc741baed810486dc8840a49ad7","sha256:14661548fe094bb7f4aa730c4734131955cd042d020d685d3c29104eea89efe2"],"state_sha256":"32adbf52c9253dc5ef3af0ab35e063810e68b2b8ac03648b62bd7c17ea6a38c9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SEU1jcXGF0dbz0irq1jMoLiGW3ldUd69qnHiJbzLZwP+avWkVddkJNZDdUl9v+lBDcd0RB7stEY1G/VFCfJQDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T12:33:00.503800Z","bundle_sha256":"dd3f4cac930bb7ebb25bcc4d947661748d9a7234e39e2fd9ff4a485d6e3a8d82"}}