{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:ZDP5VVJYQP7YV5TUQG54BTEIGL","short_pith_number":"pith:ZDP5VVJY","canonical_record":{"source":{"id":"1402.6395","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-02-26T02:20:41Z","cross_cats_sorted":[],"title_canon_sha256":"f63fcb760bb727c69e9ed80698c23f8ee34a4c3bf3497353b8fb996da541b7f7","abstract_canon_sha256":"3f7f2a280caccfceb8dd90618e7ac861d50f03f7520039d25c7a2b2ba2848072"},"schema_version":"1.0"},"canonical_sha256":"c8dfdad53883ff8af67481bbc0cc8832fb3fd2c0452ab686b1b70965adcb4576","source":{"kind":"arxiv","id":"1402.6395","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.6395","created_at":"2026-05-18T02:57:44Z"},{"alias_kind":"arxiv_version","alias_value":"1402.6395v1","created_at":"2026-05-18T02:57:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.6395","created_at":"2026-05-18T02:57:44Z"},{"alias_kind":"pith_short_12","alias_value":"ZDP5VVJYQP7Y","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZDP5VVJYQP7YV5TU","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZDP5VVJY","created_at":"2026-05-18T12:28:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:ZDP5VVJYQP7YV5TUQG54BTEIGL","target":"record","payload":{"canonical_record":{"source":{"id":"1402.6395","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-02-26T02:20:41Z","cross_cats_sorted":[],"title_canon_sha256":"f63fcb760bb727c69e9ed80698c23f8ee34a4c3bf3497353b8fb996da541b7f7","abstract_canon_sha256":"3f7f2a280caccfceb8dd90618e7ac861d50f03f7520039d25c7a2b2ba2848072"},"schema_version":"1.0"},"canonical_sha256":"c8dfdad53883ff8af67481bbc0cc8832fb3fd2c0452ab686b1b70965adcb4576","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:57:44.607878Z","signature_b64":"nG1gjIx+NCVrMj8q0aGv95PWsvjkKw5fg5QtmO4G1eODL5Mqnyckot3SzmZOj/JYh8cd16IEPKG+dAsEIc3PCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c8dfdad53883ff8af67481bbc0cc8832fb3fd2c0452ab686b1b70965adcb4576","last_reissued_at":"2026-05-18T02:57:44.607442Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:57:44.607442Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1402.6395","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":"2026-05-18T02:57:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Iout+CYS8CtVfeQxgcbKLnt5Fg/aN3cvjJDBPRf1dFE2Mys8cBRcGxevXs/4lJAAHaFNpV3CoBOf27+W4KdZBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T12:58:00.780053Z"},"content_sha256":"35de55cabd3a3bfcb5bc519e056dcc9836afd68cf8930e6841305ca92457798f","schema_version":"1.0","event_id":"sha256:35de55cabd3a3bfcb5bc519e056dcc9836afd68cf8930e6841305ca92457798f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:ZDP5VVJYQP7YV5TUQG54BTEIGL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Determining Aschbacher classes using characters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Sebastian Jambor","submitted_at":"2014-02-26T02:20:41Z","abstract_excerpt":"Let $\\Delta\\colon G \\to \\mathrm{GL}(n, K)$ be an absolutely irreducible representation of an arbitrary group $G$ over an arbitrary field $K$; let $\\chi\\colon G \\to K\\colon g \\mapsto \\mathrm{tr}(\\Delta(g))$ be its character. In this paper, we assume knowledge of $\\chi$ only, and study which properties of $\\Delta$ can be inferred. We prove criteria to decide whether $\\Delta$ preserves a form, is realizable over a subfield, or acts imprimitively on $K^{n \\times 1}$. If $K$ is finite, this allows us to decide whether the image of $\\Delta$ belongs to certain Aschbacher classes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.6395","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":"2026-05-18T02:57:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a9hlzxZQnVcT3jVSKpXzm6IeTFcQPAroT5rm/iYTnvzDg/wHtUE/01JwPdvdAXwhUTPaLchrMLYmQyUmYDkfBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T12:58:00.780420Z"},"content_sha256":"584268f21d7cd1ffca02fc434994e4525e7dd73ae3261482a92408135a403457","schema_version":"1.0","event_id":"sha256:584268f21d7cd1ffca02fc434994e4525e7dd73ae3261482a92408135a403457"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZDP5VVJYQP7YV5TUQG54BTEIGL/bundle.json","state_url":"https://pith.science/pith/ZDP5VVJYQP7YV5TUQG54BTEIGL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZDP5VVJYQP7YV5TUQG54BTEIGL/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":"2026-05-28T12:58:00Z","links":{"resolver":"https://pith.science/pith/ZDP5VVJYQP7YV5TUQG54BTEIGL","bundle":"https://pith.science/pith/ZDP5VVJYQP7YV5TUQG54BTEIGL/bundle.json","state":"https://pith.science/pith/ZDP5VVJYQP7YV5TUQG54BTEIGL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZDP5VVJYQP7YV5TUQG54BTEIGL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ZDP5VVJYQP7YV5TUQG54BTEIGL","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":"3f7f2a280caccfceb8dd90618e7ac861d50f03f7520039d25c7a2b2ba2848072","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-02-26T02:20:41Z","title_canon_sha256":"f63fcb760bb727c69e9ed80698c23f8ee34a4c3bf3497353b8fb996da541b7f7"},"schema_version":"1.0","source":{"id":"1402.6395","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.6395","created_at":"2026-05-18T02:57:44Z"},{"alias_kind":"arxiv_version","alias_value":"1402.6395v1","created_at":"2026-05-18T02:57:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.6395","created_at":"2026-05-18T02:57:44Z"},{"alias_kind":"pith_short_12","alias_value":"ZDP5VVJYQP7Y","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZDP5VVJYQP7YV5TU","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZDP5VVJY","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:584268f21d7cd1ffca02fc434994e4525e7dd73ae3261482a92408135a403457","target":"graph","created_at":"2026-05-18T02:57:44Z","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":"Let $\\Delta\\colon G \\to \\mathrm{GL}(n, K)$ be an absolutely irreducible representation of an arbitrary group $G$ over an arbitrary field $K$; let $\\chi\\colon G \\to K\\colon g \\mapsto \\mathrm{tr}(\\Delta(g))$ be its character. In this paper, we assume knowledge of $\\chi$ only, and study which properties of $\\Delta$ can be inferred. We prove criteria to decide whether $\\Delta$ preserves a form, is realizable over a subfield, or acts imprimitively on $K^{n \\times 1}$. If $K$ is finite, this allows us to decide whether the image of $\\Delta$ belongs to certain Aschbacher classes.","authors_text":"Sebastian Jambor","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-02-26T02:20:41Z","title":"Determining Aschbacher classes using characters"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.6395","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":"sha256:35de55cabd3a3bfcb5bc519e056dcc9836afd68cf8930e6841305ca92457798f","target":"record","created_at":"2026-05-18T02:57:44Z","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":"3f7f2a280caccfceb8dd90618e7ac861d50f03f7520039d25c7a2b2ba2848072","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-02-26T02:20:41Z","title_canon_sha256":"f63fcb760bb727c69e9ed80698c23f8ee34a4c3bf3497353b8fb996da541b7f7"},"schema_version":"1.0","source":{"id":"1402.6395","kind":"arxiv","version":1}},"canonical_sha256":"c8dfdad53883ff8af67481bbc0cc8832fb3fd2c0452ab686b1b70965adcb4576","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c8dfdad53883ff8af67481bbc0cc8832fb3fd2c0452ab686b1b70965adcb4576","first_computed_at":"2026-05-18T02:57:44.607442Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:57:44.607442Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nG1gjIx+NCVrMj8q0aGv95PWsvjkKw5fg5QtmO4G1eODL5Mqnyckot3SzmZOj/JYh8cd16IEPKG+dAsEIc3PCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:57:44.607878Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.6395","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:35de55cabd3a3bfcb5bc519e056dcc9836afd68cf8930e6841305ca92457798f","sha256:584268f21d7cd1ffca02fc434994e4525e7dd73ae3261482a92408135a403457"],"state_sha256":"e78809727427222ed3ca88332bbd8cad38bd96d2556d745785ac1e5134340a7f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Yan4B+Ij6vocMy58OysPm2/I+C9kmb1Y6TepFk7W1qCGEuT+NRNBWBR+2UGsiP8+7ZQnH8uyY19QKm+qPRHSAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T12:58:00.782353Z","bundle_sha256":"84c9f740faec273caa16a32e8f8d650792eef9d0f06adc4d596ea6e1a70f0d40"}}