{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:J7SYR5CQJQHB7Q6TIM4D2DTH2Z","short_pith_number":"pith:J7SYR5CQ","canonical_record":{"source":{"id":"1103.3171","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-03-16T13:51:30Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"2ec4fac24dce9c63ef156088d367c687e554db535e541f36dac80551f5462c06","abstract_canon_sha256":"e15c461d90c789b0562ab07a3367af58de0001562c98f0c4a1b0c77e744f59ac"},"schema_version":"1.0"},"canonical_sha256":"4fe588f4504c0e1fc3d343383d0e67d67b15acf10c8012c5ab977ffae2ccbd01","source":{"kind":"arxiv","id":"1103.3171","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.3171","created_at":"2026-05-18T04:26:44Z"},{"alias_kind":"arxiv_version","alias_value":"1103.3171v1","created_at":"2026-05-18T04:26:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.3171","created_at":"2026-05-18T04:26:44Z"},{"alias_kind":"pith_short_12","alias_value":"J7SYR5CQJQHB","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"J7SYR5CQJQHB7Q6T","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"J7SYR5CQ","created_at":"2026-05-18T12:26:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:J7SYR5CQJQHB7Q6TIM4D2DTH2Z","target":"record","payload":{"canonical_record":{"source":{"id":"1103.3171","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-03-16T13:51:30Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"2ec4fac24dce9c63ef156088d367c687e554db535e541f36dac80551f5462c06","abstract_canon_sha256":"e15c461d90c789b0562ab07a3367af58de0001562c98f0c4a1b0c77e744f59ac"},"schema_version":"1.0"},"canonical_sha256":"4fe588f4504c0e1fc3d343383d0e67d67b15acf10c8012c5ab977ffae2ccbd01","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:26:44.661514Z","signature_b64":"yu/EEHt3Y8T69KfToa9KqXNL3Dje8CnWyJsvDXMZ9oyrJTcvEJnOzTn1kcXFW0QN1XCTV+4ze8mkTAtoi35aDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4fe588f4504c0e1fc3d343383d0e67d67b15acf10c8012c5ab977ffae2ccbd01","last_reissued_at":"2026-05-18T04:26:44.660740Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:26:44.660740Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1103.3171","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":"2026-05-18T04:26:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2jHN3espvSgFeThX0/k7zHR5xPCj6POrWut4SAOKEifFJxxdasHIT7NyQx5JUr+zDqPV4WuWKBmPuWWoSCPqCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T09:50:41.359306Z"},"content_sha256":"e8ae29c6e84d4bc6ac898b77946af5a20654d08f5788c49f7142b9208a722ac9","schema_version":"1.0","event_id":"sha256:e8ae29c6e84d4bc6ac898b77946af5a20654d08f5788c49f7142b9208a722ac9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:J7SYR5CQJQHB7Q6TIM4D2DTH2Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Real characters in blocks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RT","authors_text":"Endre Szabo, Erzsebet Horvath, Laszlo Hethelyi","submitted_at":"2011-03-16T13:51:30Z","abstract_excerpt":"We consider real versions of Brauer's k(B) conjecture, Olsson's conjecture and Eaton's conjecture. We prove the real version of Eaton's conjecture for 2-blocks of groups with cyclic defect group and for the principal 2-blocks of groups with trivial real core. We also characterize G-classes, real and rational G-classes of the defect group of a block B."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.3171","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":"2026-05-18T04:26:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3L+Hx0MaB5GkN2Ies/3dBnl1APKugwz0BGpLoUuYhBPHjjxTEJF1m2ew+ZLRsm1/N3TjRbZt5c/qtoRB4tFGCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T09:50:41.359661Z"},"content_sha256":"8f4130d2070cfe9cd4c625217bb5b3bc0a7886f04e471fd9baf3f888f282ec91","schema_version":"1.0","event_id":"sha256:8f4130d2070cfe9cd4c625217bb5b3bc0a7886f04e471fd9baf3f888f282ec91"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J7SYR5CQJQHB7Q6TIM4D2DTH2Z/bundle.json","state_url":"https://pith.science/pith/J7SYR5CQJQHB7Q6TIM4D2DTH2Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J7SYR5CQJQHB7Q6TIM4D2DTH2Z/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":"2026-06-22T09:50:41Z","links":{"resolver":"https://pith.science/pith/J7SYR5CQJQHB7Q6TIM4D2DTH2Z","bundle":"https://pith.science/pith/J7SYR5CQJQHB7Q6TIM4D2DTH2Z/bundle.json","state":"https://pith.science/pith/J7SYR5CQJQHB7Q6TIM4D2DTH2Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J7SYR5CQJQHB7Q6TIM4D2DTH2Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:J7SYR5CQJQHB7Q6TIM4D2DTH2Z","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":"e15c461d90c789b0562ab07a3367af58de0001562c98f0c4a1b0c77e744f59ac","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-03-16T13:51:30Z","title_canon_sha256":"2ec4fac24dce9c63ef156088d367c687e554db535e541f36dac80551f5462c06"},"schema_version":"1.0","source":{"id":"1103.3171","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.3171","created_at":"2026-05-18T04:26:44Z"},{"alias_kind":"arxiv_version","alias_value":"1103.3171v1","created_at":"2026-05-18T04:26:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.3171","created_at":"2026-05-18T04:26:44Z"},{"alias_kind":"pith_short_12","alias_value":"J7SYR5CQJQHB","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"J7SYR5CQJQHB7Q6T","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"J7SYR5CQ","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:8f4130d2070cfe9cd4c625217bb5b3bc0a7886f04e471fd9baf3f888f282ec91","target":"graph","created_at":"2026-05-18T04:26:44Z","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 consider real versions of Brauer's k(B) conjecture, Olsson's conjecture and Eaton's conjecture. We prove the real version of Eaton's conjecture for 2-blocks of groups with cyclic defect group and for the principal 2-blocks of groups with trivial real core. We also characterize G-classes, real and rational G-classes of the defect group of a block B.","authors_text":"Endre Szabo, Erzsebet Horvath, Laszlo Hethelyi","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-03-16T13:51:30Z","title":"Real characters in blocks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.3171","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:e8ae29c6e84d4bc6ac898b77946af5a20654d08f5788c49f7142b9208a722ac9","target":"record","created_at":"2026-05-18T04:26:44Z","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":"e15c461d90c789b0562ab07a3367af58de0001562c98f0c4a1b0c77e744f59ac","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-03-16T13:51:30Z","title_canon_sha256":"2ec4fac24dce9c63ef156088d367c687e554db535e541f36dac80551f5462c06"},"schema_version":"1.0","source":{"id":"1103.3171","kind":"arxiv","version":1}},"canonical_sha256":"4fe588f4504c0e1fc3d343383d0e67d67b15acf10c8012c5ab977ffae2ccbd01","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4fe588f4504c0e1fc3d343383d0e67d67b15acf10c8012c5ab977ffae2ccbd01","first_computed_at":"2026-05-18T04:26:44.660740Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:26:44.660740Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yu/EEHt3Y8T69KfToa9KqXNL3Dje8CnWyJsvDXMZ9oyrJTcvEJnOzTn1kcXFW0QN1XCTV+4ze8mkTAtoi35aDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:26:44.661514Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.3171","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e8ae29c6e84d4bc6ac898b77946af5a20654d08f5788c49f7142b9208a722ac9","sha256:8f4130d2070cfe9cd4c625217bb5b3bc0a7886f04e471fd9baf3f888f282ec91"],"state_sha256":"e3ba526936fae38f0c3596033d15a7339600cbae339a5e7ad212c5474f0252b7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n4WISYmJb07B26FnujNxljhIbvAq43/jGkoeJTALKt526GGcEBJlmvdge32D1rYvesbVNYc4zSq9yuOSkGURCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T09:50:41.361564Z","bundle_sha256":"d83feaf3a39c321a3f3288f429945a9e7e68b30efb778b043e83e8c54ff80f3c"}}