{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:JGXS675J3O7ONFYADNXJHTGVG7","short_pith_number":"pith:JGXS675J","canonical_record":{"source":{"id":"0911.3387","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-11-17T19:58:56Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"d64c1245cc3bc094799d3a2d897dfb9a714448f0a6a4be01deaa2347c7014a97","abstract_canon_sha256":"7855e761f734797240132d6e9f9fa001cf2899f33e14622069a11dc05702c580"},"schema_version":"1.0"},"canonical_sha256":"49af2f7fa9dbbee697001b6e93ccd537ea5e858cf6fadf650036c49ec9177712","source":{"kind":"arxiv","id":"0911.3387","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.3387","created_at":"2026-05-18T02:34:04Z"},{"alias_kind":"arxiv_version","alias_value":"0911.3387v1","created_at":"2026-05-18T02:34:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.3387","created_at":"2026-05-18T02:34:04Z"},{"alias_kind":"pith_short_12","alias_value":"JGXS675J3O7O","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"JGXS675J3O7ONFYA","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"JGXS675J","created_at":"2026-05-18T12:26:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:JGXS675J3O7ONFYADNXJHTGVG7","target":"record","payload":{"canonical_record":{"source":{"id":"0911.3387","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-11-17T19:58:56Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"d64c1245cc3bc094799d3a2d897dfb9a714448f0a6a4be01deaa2347c7014a97","abstract_canon_sha256":"7855e761f734797240132d6e9f9fa001cf2899f33e14622069a11dc05702c580"},"schema_version":"1.0"},"canonical_sha256":"49af2f7fa9dbbee697001b6e93ccd537ea5e858cf6fadf650036c49ec9177712","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:34:04.856957Z","signature_b64":"TuIn3QVTH4u1m9bWrAO0wazf9DEpBey83PYuFwtPjdJwCh83BqgnB22TqABPaNSXuk3F2BPDGTUmQZxpTD3zBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"49af2f7fa9dbbee697001b6e93ccd537ea5e858cf6fadf650036c49ec9177712","last_reissued_at":"2026-05-18T02:34:04.856261Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:34:04.856261Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0911.3387","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":"2026-05-18T02:34:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/CJpMTHwtt+3M/ypDtGQQUGWoLXua5BSKNJES2djzlFgjV+3ZVEBcCu+UjHif8C147M86BE+T1k9O4PwH6CmCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T19:18:19.640112Z"},"content_sha256":"96dc428ae29e219c2e191cdc904b456894b80292a0049865c1f17d20bb65d5df","schema_version":"1.0","event_id":"sha256:96dc428ae29e219c2e191cdc904b456894b80292a0049865c1f17d20bb65d5df"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:JGXS675J3O7ONFYADNXJHTGVG7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Composition algebras and the two faces of $G_{2}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Luis J. Boya, R. Campoamor-Stursberg","submitted_at":"2009-11-17T19:58:56Z","abstract_excerpt":"We consider composition and division algebras over the real numbers: We note two r\\^oles for the group $G_{2}$: as automorphism group of the octonions and as the isotropy group of a generic 3-form in 7 dimensions. We show why they are equivalent, by means of a regular metric. We express in some diagrams the relation between some pertinent groups, most of them related to the octonions. Some applications to physics are also discussed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.3387","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":"2026-05-18T02:34:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"radAZBumaioAFFpwGTQo25jRIsUIeKuHgrL0lekYp1HvfCHVEANRejkRIU2Nn0QiQ3BVfAnjO6+AAchJgAwpBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T19:18:19.640783Z"},"content_sha256":"cf3026fb95e542d33ad8886b0bd92826ec20ec74f3cb63260f9454c0ebc3efd0","schema_version":"1.0","event_id":"sha256:cf3026fb95e542d33ad8886b0bd92826ec20ec74f3cb63260f9454c0ebc3efd0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JGXS675J3O7ONFYADNXJHTGVG7/bundle.json","state_url":"https://pith.science/pith/JGXS675J3O7ONFYADNXJHTGVG7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JGXS675J3O7ONFYADNXJHTGVG7/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":"2026-05-28T19:18:19Z","links":{"resolver":"https://pith.science/pith/JGXS675J3O7ONFYADNXJHTGVG7","bundle":"https://pith.science/pith/JGXS675J3O7ONFYADNXJHTGVG7/bundle.json","state":"https://pith.science/pith/JGXS675J3O7ONFYADNXJHTGVG7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JGXS675J3O7ONFYADNXJHTGVG7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:JGXS675J3O7ONFYADNXJHTGVG7","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":"7855e761f734797240132d6e9f9fa001cf2899f33e14622069a11dc05702c580","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-11-17T19:58:56Z","title_canon_sha256":"d64c1245cc3bc094799d3a2d897dfb9a714448f0a6a4be01deaa2347c7014a97"},"schema_version":"1.0","source":{"id":"0911.3387","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.3387","created_at":"2026-05-18T02:34:04Z"},{"alias_kind":"arxiv_version","alias_value":"0911.3387v1","created_at":"2026-05-18T02:34:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.3387","created_at":"2026-05-18T02:34:04Z"},{"alias_kind":"pith_short_12","alias_value":"JGXS675J3O7O","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"JGXS675J3O7ONFYA","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"JGXS675J","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:cf3026fb95e542d33ad8886b0bd92826ec20ec74f3cb63260f9454c0ebc3efd0","target":"graph","created_at":"2026-05-18T02:34:04Z","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 composition and division algebras over the real numbers: We note two r\\^oles for the group $G_{2}$: as automorphism group of the octonions and as the isotropy group of a generic 3-form in 7 dimensions. We show why they are equivalent, by means of a regular metric. We express in some diagrams the relation between some pertinent groups, most of them related to the octonions. Some applications to physics are also discussed.","authors_text":"Luis J. Boya, R. Campoamor-Stursberg","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-11-17T19:58:56Z","title":"Composition algebras and the two faces of $G_{2}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.3387","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":"sha256:96dc428ae29e219c2e191cdc904b456894b80292a0049865c1f17d20bb65d5df","target":"record","created_at":"2026-05-18T02:34:04Z","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":"7855e761f734797240132d6e9f9fa001cf2899f33e14622069a11dc05702c580","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-11-17T19:58:56Z","title_canon_sha256":"d64c1245cc3bc094799d3a2d897dfb9a714448f0a6a4be01deaa2347c7014a97"},"schema_version":"1.0","source":{"id":"0911.3387","kind":"arxiv","version":1}},"canonical_sha256":"49af2f7fa9dbbee697001b6e93ccd537ea5e858cf6fadf650036c49ec9177712","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"49af2f7fa9dbbee697001b6e93ccd537ea5e858cf6fadf650036c49ec9177712","first_computed_at":"2026-05-18T02:34:04.856261Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:34:04.856261Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TuIn3QVTH4u1m9bWrAO0wazf9DEpBey83PYuFwtPjdJwCh83BqgnB22TqABPaNSXuk3F2BPDGTUmQZxpTD3zBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:34:04.856957Z","signed_message":"canonical_sha256_bytes"},"source_id":"0911.3387","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:96dc428ae29e219c2e191cdc904b456894b80292a0049865c1f17d20bb65d5df","sha256:cf3026fb95e542d33ad8886b0bd92826ec20ec74f3cb63260f9454c0ebc3efd0"],"state_sha256":"e6b8c9fe83ae3cb476ce909bde74b9aa6588141c25dac053faf563487bd77f7c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RhNht2g4J3ir8ftOAf5gUBTRmTBJd94hSyN3Q7dIsGXZklvPTNcwFdSzfVx/kF+yeGb2nFgZqnOfWSnN7PKhDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T19:18:19.644260Z","bundle_sha256":"ade3033f89232b5f6b7a915c6e360b6d97cec7e5cb534a272a93496a25e7cb09"}}