{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:HCNRAATT4NAHWLKA2YAJ42CFLP","short_pith_number":"pith:HCNRAATT","canonical_record":{"source":{"id":"0804.2763","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2008-04-17T10:50:56Z","cross_cats_sorted":[],"title_canon_sha256":"206147f7d00542752471d8ca3023097b35cc4206b4e10f127020f2dfea802929","abstract_canon_sha256":"f83a1ecffb51ab86fe7846ec6d8d0209ea281f004977ca5a6c457138d2b0febd"},"schema_version":"1.0"},"canonical_sha256":"389b100273e3407b2d40d6009e68455bd88b6ac84833bd806789254ee7d99b47","source":{"kind":"arxiv","id":"0804.2763","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0804.2763","created_at":"2026-05-18T02:26:45Z"},{"alias_kind":"arxiv_version","alias_value":"0804.2763v2","created_at":"2026-05-18T02:26:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0804.2763","created_at":"2026-05-18T02:26:45Z"},{"alias_kind":"pith_short_12","alias_value":"HCNRAATT4NAH","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"HCNRAATT4NAHWLKA","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"HCNRAATT","created_at":"2026-05-18T12:25:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:HCNRAATT4NAHWLKA2YAJ42CFLP","target":"record","payload":{"canonical_record":{"source":{"id":"0804.2763","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2008-04-17T10:50:56Z","cross_cats_sorted":[],"title_canon_sha256":"206147f7d00542752471d8ca3023097b35cc4206b4e10f127020f2dfea802929","abstract_canon_sha256":"f83a1ecffb51ab86fe7846ec6d8d0209ea281f004977ca5a6c457138d2b0febd"},"schema_version":"1.0"},"canonical_sha256":"389b100273e3407b2d40d6009e68455bd88b6ac84833bd806789254ee7d99b47","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:26:45.830979Z","signature_b64":"v57V9VKvmzUhwgUCGgH+sV5KIvO7hPEg7wlByMZS9TzoVHbFNMrc8yapAkUixVNt09+VE75b8i+CunvAqS0+Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"389b100273e3407b2d40d6009e68455bd88b6ac84833bd806789254ee7d99b47","last_reissued_at":"2026-05-18T02:26:45.830555Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:26:45.830555Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0804.2763","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":"2026-05-18T02:26:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BL+f/i5wCscxDp94nNiR5rKYM4+nkUNokhHfAt8JcNChE81DIko6QxpdSDrp0vttlM3VDm6BpzTjG/4DH5+MDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T11:21:48.229385Z"},"content_sha256":"e2b2d5804d5a80420e72f0def33a4adfcaf6c093f677e91630a4a919ac9a447d","schema_version":"1.0","event_id":"sha256:e2b2d5804d5a80420e72f0def33a4adfcaf6c093f677e91630a4a919ac9a447d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:HCNRAATT4NAHWLKA2YAJ42CFLP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Oliver's p-group conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"David J. Green, L\\'aszl\\'o H\\'ethelyi, Markus Lilienthal","submitted_at":"2008-04-17T10:50:56Z","abstract_excerpt":"Let S be a p-group for an odd prime p. Bob Oliver conjectures that a certain characteristic subgroup X(S) always contains the Thompson subgroup J(S). We obtain a reformulation of the conjecture as a statement about modular representations of p-groups. Using this we verify Oliver's conjecture for groups where S/X(S) has nilpotence class at most two."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0804.2763","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":"2026-05-18T02:26:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6yBzMpZYsiPEA76O0SI508ctkPBjbaFxwHQKOwn6vsy8Wcjv4lvgljcH/OzFjKF5mJ8/OqH9w5F0x7apUkofAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T11:21:48.230083Z"},"content_sha256":"ebb9b92441cdacc3214fdb7bcb6c1aefc5b4f5ceabe50cd4ce3597a555c53bb0","schema_version":"1.0","event_id":"sha256:ebb9b92441cdacc3214fdb7bcb6c1aefc5b4f5ceabe50cd4ce3597a555c53bb0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HCNRAATT4NAHWLKA2YAJ42CFLP/bundle.json","state_url":"https://pith.science/pith/HCNRAATT4NAHWLKA2YAJ42CFLP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HCNRAATT4NAHWLKA2YAJ42CFLP/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":"2026-05-31T11:21:48Z","links":{"resolver":"https://pith.science/pith/HCNRAATT4NAHWLKA2YAJ42CFLP","bundle":"https://pith.science/pith/HCNRAATT4NAHWLKA2YAJ42CFLP/bundle.json","state":"https://pith.science/pith/HCNRAATT4NAHWLKA2YAJ42CFLP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HCNRAATT4NAHWLKA2YAJ42CFLP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:HCNRAATT4NAHWLKA2YAJ42CFLP","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":"f83a1ecffb51ab86fe7846ec6d8d0209ea281f004977ca5a6c457138d2b0febd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2008-04-17T10:50:56Z","title_canon_sha256":"206147f7d00542752471d8ca3023097b35cc4206b4e10f127020f2dfea802929"},"schema_version":"1.0","source":{"id":"0804.2763","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0804.2763","created_at":"2026-05-18T02:26:45Z"},{"alias_kind":"arxiv_version","alias_value":"0804.2763v2","created_at":"2026-05-18T02:26:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0804.2763","created_at":"2026-05-18T02:26:45Z"},{"alias_kind":"pith_short_12","alias_value":"HCNRAATT4NAH","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"HCNRAATT4NAHWLKA","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"HCNRAATT","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:ebb9b92441cdacc3214fdb7bcb6c1aefc5b4f5ceabe50cd4ce3597a555c53bb0","target":"graph","created_at":"2026-05-18T02:26:45Z","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 S be a p-group for an odd prime p. Bob Oliver conjectures that a certain characteristic subgroup X(S) always contains the Thompson subgroup J(S). We obtain a reformulation of the conjecture as a statement about modular representations of p-groups. Using this we verify Oliver's conjecture for groups where S/X(S) has nilpotence class at most two.","authors_text":"David J. Green, L\\'aszl\\'o H\\'ethelyi, Markus Lilienthal","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2008-04-17T10:50:56Z","title":"On Oliver's p-group conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0804.2763","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:e2b2d5804d5a80420e72f0def33a4adfcaf6c093f677e91630a4a919ac9a447d","target":"record","created_at":"2026-05-18T02:26:45Z","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":"f83a1ecffb51ab86fe7846ec6d8d0209ea281f004977ca5a6c457138d2b0febd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2008-04-17T10:50:56Z","title_canon_sha256":"206147f7d00542752471d8ca3023097b35cc4206b4e10f127020f2dfea802929"},"schema_version":"1.0","source":{"id":"0804.2763","kind":"arxiv","version":2}},"canonical_sha256":"389b100273e3407b2d40d6009e68455bd88b6ac84833bd806789254ee7d99b47","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"389b100273e3407b2d40d6009e68455bd88b6ac84833bd806789254ee7d99b47","first_computed_at":"2026-05-18T02:26:45.830555Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:26:45.830555Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v57V9VKvmzUhwgUCGgH+sV5KIvO7hPEg7wlByMZS9TzoVHbFNMrc8yapAkUixVNt09+VE75b8i+CunvAqS0+Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:26:45.830979Z","signed_message":"canonical_sha256_bytes"},"source_id":"0804.2763","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e2b2d5804d5a80420e72f0def33a4adfcaf6c093f677e91630a4a919ac9a447d","sha256:ebb9b92441cdacc3214fdb7bcb6c1aefc5b4f5ceabe50cd4ce3597a555c53bb0"],"state_sha256":"a2d53a7946bd260ca2732d85a8d95e12764e15d9daf8161e3129807fb2092b66"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4P/DfZE9/O23iiil8pJAMvAKUHNi4ihfTOBi31drqWQ/dJg35tR23OsWnmxLX2Tf4Lf38WYM+ljFXUPpIJHrAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T11:21:48.233907Z","bundle_sha256":"eea91181a3b8ac2ff6e579d0ac11332de8b83a480a320c8b423bc5cb65c4da5e"}}