{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:ZKJOCJ7UUGQH757T4MZN66NO2R","short_pith_number":"pith:ZKJOCJ7U","canonical_record":{"source":{"id":"1312.4326","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-12-16T12:01:08Z","cross_cats_sorted":["math.RA","math.RT"],"title_canon_sha256":"82c2d178490d0ac2ceaa3bfcd4d9e93016b6975fa679443271e24549ca8534f7","abstract_canon_sha256":"b0a1760fbce7c0bd9d912da5d654767ad566e5aa2554ccf58b54a2e772f735f4"},"schema_version":"1.0"},"canonical_sha256":"ca92e127f4a1a07ff7f3e332df79aed46e3cc53b4709a0b3cdca6989ee53b547","source":{"kind":"arxiv","id":"1312.4326","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.4326","created_at":"2026-05-18T00:33:53Z"},{"alias_kind":"arxiv_version","alias_value":"1312.4326v1","created_at":"2026-05-18T00:33:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.4326","created_at":"2026-05-18T00:33:53Z"},{"alias_kind":"pith_short_12","alias_value":"ZKJOCJ7UUGQH","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZKJOCJ7UUGQH757T","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZKJOCJ7U","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:ZKJOCJ7UUGQH757T4MZN66NO2R","target":"record","payload":{"canonical_record":{"source":{"id":"1312.4326","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-12-16T12:01:08Z","cross_cats_sorted":["math.RA","math.RT"],"title_canon_sha256":"82c2d178490d0ac2ceaa3bfcd4d9e93016b6975fa679443271e24549ca8534f7","abstract_canon_sha256":"b0a1760fbce7c0bd9d912da5d654767ad566e5aa2554ccf58b54a2e772f735f4"},"schema_version":"1.0"},"canonical_sha256":"ca92e127f4a1a07ff7f3e332df79aed46e3cc53b4709a0b3cdca6989ee53b547","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:53.580821Z","signature_b64":"XKVZ5pDCya71jAllg6OBt3XQZE3ER5YvsuvqQEHtc6Mz+P6F9SrXmlc94imo80z64kV1WTM3c5hOanGCMbR8CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ca92e127f4a1a07ff7f3e332df79aed46e3cc53b4709a0b3cdca6989ee53b547","last_reissued_at":"2026-05-18T00:33:53.580369Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:53.580369Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.4326","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":"2026-05-18T00:33:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uQtbWaZlyMxu7Uol/yG0nyrUlLxGJzxSsAkxFor6vggZScn0pxsU4xGyg4TfONOuXsZutn80TEf6lnXALXwSDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T12:57:00.895732Z"},"content_sha256":"b4b013177309dc18a7edddd87b1cfdf284b2c537822423b579aa569fd0188d96","schema_version":"1.0","event_id":"sha256:b4b013177309dc18a7edddd87b1cfdf284b2c537822423b579aa569fd0188d96"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:ZKJOCJ7UUGQH757T4MZN66NO2R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Maximal finite abelian subgroups of E8","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA","math.RT"],"primary_cat":"math.GR","authors_text":"Alberto Elduque, Cristina Draper","submitted_at":"2013-12-16T12:01:08Z","abstract_excerpt":"The maximal finite abelian subgroups, up to conjugation, of the simple algebraic group of type E8 over an algebraically closed field of characteristic 0 are computed. This is equivalent to the determination of the fine gradings on the simple Lie algebra of type E8 with trivial neutral homogeneous component."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.4326","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":"2026-05-18T00:33:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pToz735skjuzJicx3BDlT4as2MLxQnODKSmgFJcNmNXzPhWf1aV24NvbS0RHLSQEYXA15mX6Yae6r0GrX9Y2Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T12:57:00.896453Z"},"content_sha256":"444521336d6de5d2e1b1e0c8a799491b624654b7b6db269e61a3c5f653123c10","schema_version":"1.0","event_id":"sha256:444521336d6de5d2e1b1e0c8a799491b624654b7b6db269e61a3c5f653123c10"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZKJOCJ7UUGQH757T4MZN66NO2R/bundle.json","state_url":"https://pith.science/pith/ZKJOCJ7UUGQH757T4MZN66NO2R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZKJOCJ7UUGQH757T4MZN66NO2R/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":"2026-05-31T12:57:00Z","links":{"resolver":"https://pith.science/pith/ZKJOCJ7UUGQH757T4MZN66NO2R","bundle":"https://pith.science/pith/ZKJOCJ7UUGQH757T4MZN66NO2R/bundle.json","state":"https://pith.science/pith/ZKJOCJ7UUGQH757T4MZN66NO2R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZKJOCJ7UUGQH757T4MZN66NO2R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ZKJOCJ7UUGQH757T4MZN66NO2R","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":"b0a1760fbce7c0bd9d912da5d654767ad566e5aa2554ccf58b54a2e772f735f4","cross_cats_sorted":["math.RA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-12-16T12:01:08Z","title_canon_sha256":"82c2d178490d0ac2ceaa3bfcd4d9e93016b6975fa679443271e24549ca8534f7"},"schema_version":"1.0","source":{"id":"1312.4326","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.4326","created_at":"2026-05-18T00:33:53Z"},{"alias_kind":"arxiv_version","alias_value":"1312.4326v1","created_at":"2026-05-18T00:33:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.4326","created_at":"2026-05-18T00:33:53Z"},{"alias_kind":"pith_short_12","alias_value":"ZKJOCJ7UUGQH","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZKJOCJ7UUGQH757T","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZKJOCJ7U","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:444521336d6de5d2e1b1e0c8a799491b624654b7b6db269e61a3c5f653123c10","target":"graph","created_at":"2026-05-18T00:33:53Z","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":"The maximal finite abelian subgroups, up to conjugation, of the simple algebraic group of type E8 over an algebraically closed field of characteristic 0 are computed. This is equivalent to the determination of the fine gradings on the simple Lie algebra of type E8 with trivial neutral homogeneous component.","authors_text":"Alberto Elduque, Cristina Draper","cross_cats":["math.RA","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-12-16T12:01:08Z","title":"Maximal finite abelian subgroups of E8"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.4326","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:b4b013177309dc18a7edddd87b1cfdf284b2c537822423b579aa569fd0188d96","target":"record","created_at":"2026-05-18T00:33:53Z","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":"b0a1760fbce7c0bd9d912da5d654767ad566e5aa2554ccf58b54a2e772f735f4","cross_cats_sorted":["math.RA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-12-16T12:01:08Z","title_canon_sha256":"82c2d178490d0ac2ceaa3bfcd4d9e93016b6975fa679443271e24549ca8534f7"},"schema_version":"1.0","source":{"id":"1312.4326","kind":"arxiv","version":1}},"canonical_sha256":"ca92e127f4a1a07ff7f3e332df79aed46e3cc53b4709a0b3cdca6989ee53b547","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ca92e127f4a1a07ff7f3e332df79aed46e3cc53b4709a0b3cdca6989ee53b547","first_computed_at":"2026-05-18T00:33:53.580369Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:53.580369Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XKVZ5pDCya71jAllg6OBt3XQZE3ER5YvsuvqQEHtc6Mz+P6F9SrXmlc94imo80z64kV1WTM3c5hOanGCMbR8CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:53.580821Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.4326","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b4b013177309dc18a7edddd87b1cfdf284b2c537822423b579aa569fd0188d96","sha256:444521336d6de5d2e1b1e0c8a799491b624654b7b6db269e61a3c5f653123c10"],"state_sha256":"66fdbac34abb3a4a8224a9cf7c2cbbbbc3231d0bc43902d831d707fe16bebcca"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H5RE+tkK2ZW40wkCTiJsJsyVI9BdYxnAVaK3MSCcOpvT4LnUyt4m7ngGQki7IevIbuDJSex/Fmvc+1vHzRKQCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T12:57:00.900547Z","bundle_sha256":"d77336ca3bff6f5fbaa39ff3f456f024b12cb0fe264608dcf85f84cb65d86871"}}