{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:QWFQ3MJ2YHPSGJPUQDZHK4X7IG","short_pith_number":"pith:QWFQ3MJ2","canonical_record":{"source":{"id":"1106.5115","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-06-25T09:05:24Z","cross_cats_sorted":[],"title_canon_sha256":"5a6370bc296e2bdbcc148d7e248a23bb9972b42bc8bdf6fb214e1f7338f13f2b","abstract_canon_sha256":"0c4232b8bb5201b959005b8265112141853ac9813f18ac5c6a29b6a601b48d9f"},"schema_version":"1.0"},"canonical_sha256":"858b0db13ac1df2325f480f27572ff41a26afba71a4e1c15a95339b5fdd5d120","source":{"kind":"arxiv","id":"1106.5115","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.5115","created_at":"2026-05-18T04:19:14Z"},{"alias_kind":"arxiv_version","alias_value":"1106.5115v1","created_at":"2026-05-18T04:19:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.5115","created_at":"2026-05-18T04:19:14Z"},{"alias_kind":"pith_short_12","alias_value":"QWFQ3MJ2YHPS","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"QWFQ3MJ2YHPSGJPU","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"QWFQ3MJ2","created_at":"2026-05-18T12:26:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:QWFQ3MJ2YHPSGJPUQDZHK4X7IG","target":"record","payload":{"canonical_record":{"source":{"id":"1106.5115","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-06-25T09:05:24Z","cross_cats_sorted":[],"title_canon_sha256":"5a6370bc296e2bdbcc148d7e248a23bb9972b42bc8bdf6fb214e1f7338f13f2b","abstract_canon_sha256":"0c4232b8bb5201b959005b8265112141853ac9813f18ac5c6a29b6a601b48d9f"},"schema_version":"1.0"},"canonical_sha256":"858b0db13ac1df2325f480f27572ff41a26afba71a4e1c15a95339b5fdd5d120","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:19:14.309043Z","signature_b64":"jOOvXAKFBN5Qj0A3eMai/rBLySVP0eBhULS/XSkuykDvsTHpja2Lge68b7DawWfvwtpDeKU48mGyCQvTfV+fDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"858b0db13ac1df2325f480f27572ff41a26afba71a4e1c15a95339b5fdd5d120","last_reissued_at":"2026-05-18T04:19:14.308635Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:19:14.308635Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1106.5115","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":"2026-05-18T04:19:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yQJNvSmMCI7IOQyOC4US5sw3ek+nzGTYP2k8iWMmvZFzZrQqTTvuzr3JTCIXrL7JN+VVmKW4lXWdKhqsOJwmAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T11:09:39.755593Z"},"content_sha256":"48da89ed7667440424c8b306c9d7ec6e61f450199de50e78daa19b8d35969e76","schema_version":"1.0","event_id":"sha256:48da89ed7667440424c8b306c9d7ec6e61f450199de50e78daa19b8d35969e76"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:QWFQ3MJ2YHPSGJPUQDZHK4X7IG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Conjugacy classes of trialitarian automorphisms and symmetric compositions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Jean-Pierre Tignol, Max-Albert Knus, Vladimir Chernousov","submitted_at":"2011-06-25T09:05:24Z","abstract_excerpt":"The trialitarian automorphisms considered in this paper are the outer automorphisms of order 3 of adjoint classical groups of type D_4 over arbitrary fields. A one-to-one correspondence is established between their conjugacy classes and similarity classes of symmetric compositions on 8-dimensional quadratic spaces. Using the known classification of symmetric compositions, we distinguish two conjugacy classes of trialitarian automorphisms over algebraically closed fields. For type I, the group of fixed points is of type G_2, whereas it is of type A_2 for trialitarian automorphisms of type II."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.5115","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":"2026-05-18T04:19:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j/ANGWTwxNJ0vkbI9ALnkZEvs2KuuwARFzBVThrn+FcBVitDgbK1DrrF2EKNMAS+N6sb9xH9QuOYuNqmrs1+DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T11:09:39.755934Z"},"content_sha256":"8b97e0bab722a50733c794684749b4e80c3e1a5084a6a966560b953241cb805e","schema_version":"1.0","event_id":"sha256:8b97e0bab722a50733c794684749b4e80c3e1a5084a6a966560b953241cb805e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QWFQ3MJ2YHPSGJPUQDZHK4X7IG/bundle.json","state_url":"https://pith.science/pith/QWFQ3MJ2YHPSGJPUQDZHK4X7IG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QWFQ3MJ2YHPSGJPUQDZHK4X7IG/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":"2026-06-05T11:09:39Z","links":{"resolver":"https://pith.science/pith/QWFQ3MJ2YHPSGJPUQDZHK4X7IG","bundle":"https://pith.science/pith/QWFQ3MJ2YHPSGJPUQDZHK4X7IG/bundle.json","state":"https://pith.science/pith/QWFQ3MJ2YHPSGJPUQDZHK4X7IG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QWFQ3MJ2YHPSGJPUQDZHK4X7IG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:QWFQ3MJ2YHPSGJPUQDZHK4X7IG","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":"0c4232b8bb5201b959005b8265112141853ac9813f18ac5c6a29b6a601b48d9f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-06-25T09:05:24Z","title_canon_sha256":"5a6370bc296e2bdbcc148d7e248a23bb9972b42bc8bdf6fb214e1f7338f13f2b"},"schema_version":"1.0","source":{"id":"1106.5115","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.5115","created_at":"2026-05-18T04:19:14Z"},{"alias_kind":"arxiv_version","alias_value":"1106.5115v1","created_at":"2026-05-18T04:19:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.5115","created_at":"2026-05-18T04:19:14Z"},{"alias_kind":"pith_short_12","alias_value":"QWFQ3MJ2YHPS","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"QWFQ3MJ2YHPSGJPU","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"QWFQ3MJ2","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:8b97e0bab722a50733c794684749b4e80c3e1a5084a6a966560b953241cb805e","target":"graph","created_at":"2026-05-18T04:19:14Z","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 trialitarian automorphisms considered in this paper are the outer automorphisms of order 3 of adjoint classical groups of type D_4 over arbitrary fields. A one-to-one correspondence is established between their conjugacy classes and similarity classes of symmetric compositions on 8-dimensional quadratic spaces. Using the known classification of symmetric compositions, we distinguish two conjugacy classes of trialitarian automorphisms over algebraically closed fields. For type I, the group of fixed points is of type G_2, whereas it is of type A_2 for trialitarian automorphisms of type II.","authors_text":"Jean-Pierre Tignol, Max-Albert Knus, Vladimir Chernousov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-06-25T09:05:24Z","title":"Conjugacy classes of trialitarian automorphisms and symmetric compositions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.5115","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":"sha256:48da89ed7667440424c8b306c9d7ec6e61f450199de50e78daa19b8d35969e76","target":"record","created_at":"2026-05-18T04:19:14Z","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":"0c4232b8bb5201b959005b8265112141853ac9813f18ac5c6a29b6a601b48d9f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-06-25T09:05:24Z","title_canon_sha256":"5a6370bc296e2bdbcc148d7e248a23bb9972b42bc8bdf6fb214e1f7338f13f2b"},"schema_version":"1.0","source":{"id":"1106.5115","kind":"arxiv","version":1}},"canonical_sha256":"858b0db13ac1df2325f480f27572ff41a26afba71a4e1c15a95339b5fdd5d120","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"858b0db13ac1df2325f480f27572ff41a26afba71a4e1c15a95339b5fdd5d120","first_computed_at":"2026-05-18T04:19:14.308635Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:19:14.308635Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jOOvXAKFBN5Qj0A3eMai/rBLySVP0eBhULS/XSkuykDvsTHpja2Lge68b7DawWfvwtpDeKU48mGyCQvTfV+fDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:19:14.309043Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.5115","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:48da89ed7667440424c8b306c9d7ec6e61f450199de50e78daa19b8d35969e76","sha256:8b97e0bab722a50733c794684749b4e80c3e1a5084a6a966560b953241cb805e"],"state_sha256":"90b3ae830867df7561c40733659b46b9b0186ec9fd7a3c5b931632a16c59a27d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zisMzqmnW7rBvlUDVRPR46CtVFdDZ5YnhKUvuudRTCevD693g2jogtn0wj87c5Tbm8RrQS2K9t4J33+Emyi9Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T11:09:39.757876Z","bundle_sha256":"724f138fed716c210ae2bc71c40d65678400bba1f40783d8fcac7d34f0416d6b"}}