{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:PGGAFDE6PO6F6M7BGPSWI4IDKG","short_pith_number":"pith:PGGAFDE6","canonical_record":{"source":{"id":"1711.02444","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-11-07T12:52:00Z","cross_cats_sorted":["math.GR","math.RT"],"title_canon_sha256":"170cba3187caf30283322382298ac3d1c3976ca98f29db721519c59a03316f5e","abstract_canon_sha256":"ef33e1c600aba544a26b2719fb19294300b6237f12791be0362ecac901adf0af"},"schema_version":"1.0"},"canonical_sha256":"798c028c9e7bbc5f33e133e564710351a83f31701556e005435671743fb2e9a2","source":{"kind":"arxiv","id":"1711.02444","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.02444","created_at":"2026-05-17T23:51:39Z"},{"alias_kind":"arxiv_version","alias_value":"1711.02444v1","created_at":"2026-05-17T23:51:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.02444","created_at":"2026-05-17T23:51:39Z"},{"alias_kind":"pith_short_12","alias_value":"PGGAFDE6PO6F","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PGGAFDE6PO6F6M7B","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PGGAFDE6","created_at":"2026-05-18T12:31:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:PGGAFDE6PO6F6M7BGPSWI4IDKG","target":"record","payload":{"canonical_record":{"source":{"id":"1711.02444","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-11-07T12:52:00Z","cross_cats_sorted":["math.GR","math.RT"],"title_canon_sha256":"170cba3187caf30283322382298ac3d1c3976ca98f29db721519c59a03316f5e","abstract_canon_sha256":"ef33e1c600aba544a26b2719fb19294300b6237f12791be0362ecac901adf0af"},"schema_version":"1.0"},"canonical_sha256":"798c028c9e7bbc5f33e133e564710351a83f31701556e005435671743fb2e9a2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:39.823594Z","signature_b64":"ukQ3aYruWcsBH63vvlkfOk2uJSyfkevFEaJWT2i6ZDA2UcaCnvPgZWI8H9Fg4jo0x03vN6fVCs+MpGa6fKhvDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"798c028c9e7bbc5f33e133e564710351a83f31701556e005435671743fb2e9a2","last_reissued_at":"2026-05-17T23:51:39.822915Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:39.822915Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.02444","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":"2026-05-17T23:51:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+JGZvtAZxhZ813oyAjIFf+ad0ACb549g9m0oTsf8vQbQLkyFtrwDZYVaeRdzJgnYgstosEQTpAgt7fq04MmhAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T20:29:04.587354Z"},"content_sha256":"ec0b8f2a62806c7b411863d0a3ed04269c8261e80b26680dbf0e877dfa3ac743","schema_version":"1.0","event_id":"sha256:ec0b8f2a62806c7b411863d0a3ed04269c8261e80b26680dbf0e877dfa3ac743"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:PGGAFDE6PO6F6M7BGPSWI4IDKG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A remark on the invariant theory of real Lie groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.RT"],"primary_cat":"math.DG","authors_text":"A. Gordillo, J. Navarro, P. Sancho","submitted_at":"2017-11-07T12:52:00Z","abstract_excerpt":"We present a simple remark that assures that the invariant theory of certain real Lie groups coincides with that of the underlying affine, real algebraic groups. In particular, this result applies to the non-compact orthogonal or symplectic Lie groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.02444","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":"2026-05-17T23:51:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vqrA6dqmatW3RFupyFcj1VklNh9p475w4O/B+QI97lnxuPqqQph39ZGNCWAe/Cy4PS/UN13DY4IUVYJ46bHpDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T20:29:04.588017Z"},"content_sha256":"1bf6152592c5361377a6a0aa1ee660c07fe3ed095984c6b557856df1f3a41e63","schema_version":"1.0","event_id":"sha256:1bf6152592c5361377a6a0aa1ee660c07fe3ed095984c6b557856df1f3a41e63"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PGGAFDE6PO6F6M7BGPSWI4IDKG/bundle.json","state_url":"https://pith.science/pith/PGGAFDE6PO6F6M7BGPSWI4IDKG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PGGAFDE6PO6F6M7BGPSWI4IDKG/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":"2026-06-08T20:29:04Z","links":{"resolver":"https://pith.science/pith/PGGAFDE6PO6F6M7BGPSWI4IDKG","bundle":"https://pith.science/pith/PGGAFDE6PO6F6M7BGPSWI4IDKG/bundle.json","state":"https://pith.science/pith/PGGAFDE6PO6F6M7BGPSWI4IDKG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PGGAFDE6PO6F6M7BGPSWI4IDKG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:PGGAFDE6PO6F6M7BGPSWI4IDKG","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":"ef33e1c600aba544a26b2719fb19294300b6237f12791be0362ecac901adf0af","cross_cats_sorted":["math.GR","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-11-07T12:52:00Z","title_canon_sha256":"170cba3187caf30283322382298ac3d1c3976ca98f29db721519c59a03316f5e"},"schema_version":"1.0","source":{"id":"1711.02444","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.02444","created_at":"2026-05-17T23:51:39Z"},{"alias_kind":"arxiv_version","alias_value":"1711.02444v1","created_at":"2026-05-17T23:51:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.02444","created_at":"2026-05-17T23:51:39Z"},{"alias_kind":"pith_short_12","alias_value":"PGGAFDE6PO6F","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PGGAFDE6PO6F6M7B","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PGGAFDE6","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:1bf6152592c5361377a6a0aa1ee660c07fe3ed095984c6b557856df1f3a41e63","target":"graph","created_at":"2026-05-17T23:51:39Z","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 present a simple remark that assures that the invariant theory of certain real Lie groups coincides with that of the underlying affine, real algebraic groups. In particular, this result applies to the non-compact orthogonal or symplectic Lie groups.","authors_text":"A. Gordillo, J. Navarro, P. Sancho","cross_cats":["math.GR","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-11-07T12:52:00Z","title":"A remark on the invariant theory of real Lie groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.02444","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:ec0b8f2a62806c7b411863d0a3ed04269c8261e80b26680dbf0e877dfa3ac743","target":"record","created_at":"2026-05-17T23:51:39Z","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":"ef33e1c600aba544a26b2719fb19294300b6237f12791be0362ecac901adf0af","cross_cats_sorted":["math.GR","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-11-07T12:52:00Z","title_canon_sha256":"170cba3187caf30283322382298ac3d1c3976ca98f29db721519c59a03316f5e"},"schema_version":"1.0","source":{"id":"1711.02444","kind":"arxiv","version":1}},"canonical_sha256":"798c028c9e7bbc5f33e133e564710351a83f31701556e005435671743fb2e9a2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"798c028c9e7bbc5f33e133e564710351a83f31701556e005435671743fb2e9a2","first_computed_at":"2026-05-17T23:51:39.822915Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:39.822915Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ukQ3aYruWcsBH63vvlkfOk2uJSyfkevFEaJWT2i6ZDA2UcaCnvPgZWI8H9Fg4jo0x03vN6fVCs+MpGa6fKhvDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:39.823594Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.02444","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ec0b8f2a62806c7b411863d0a3ed04269c8261e80b26680dbf0e877dfa3ac743","sha256:1bf6152592c5361377a6a0aa1ee660c07fe3ed095984c6b557856df1f3a41e63"],"state_sha256":"0b30975514871b681c04073af41d1bf363adf42190d120f5330a97f1d35ee3b9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q6axLXivgxM9bZy6IDg+PhIk5Dr5OS6LxNXQeCOQ2JzxEbgolJvDfaVLllebeBEauzZGdDIZcy4NKK8rTTIEDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T20:29:04.592086Z","bundle_sha256":"007cd3acf15eb26387979c8090240f5c1dc6e03e6a2e605278c1284c52ef0b9a"}}