{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:4G37DZUYI737NBHP5G7LTSXEO3","short_pith_number":"pith:4G37DZUY","canonical_record":{"source":{"id":"1608.06467","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-08-23T11:17:13Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"b92e479e85696d00b2a7b08b85ec65894cf8c205b8e2af29315dbb8d42812451","abstract_canon_sha256":"643c61b8ef6eb1f130a995240388942e4828dd5f3c5b1e6183b9799ccae5ea68"},"schema_version":"1.0"},"canonical_sha256":"e1b7f1e69847f7f684efe9beb9cae476eb7e2245775e85c0d08064d0414fdda9","source":{"kind":"arxiv","id":"1608.06467","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.06467","created_at":"2026-05-18T00:09:53Z"},{"alias_kind":"arxiv_version","alias_value":"1608.06467v2","created_at":"2026-05-18T00:09:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.06467","created_at":"2026-05-18T00:09:53Z"},{"alias_kind":"pith_short_12","alias_value":"4G37DZUYI737","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4G37DZUYI737NBHP","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4G37DZUY","created_at":"2026-05-18T12:29:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:4G37DZUYI737NBHP5G7LTSXEO3","target":"record","payload":{"canonical_record":{"source":{"id":"1608.06467","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-08-23T11:17:13Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"b92e479e85696d00b2a7b08b85ec65894cf8c205b8e2af29315dbb8d42812451","abstract_canon_sha256":"643c61b8ef6eb1f130a995240388942e4828dd5f3c5b1e6183b9799ccae5ea68"},"schema_version":"1.0"},"canonical_sha256":"e1b7f1e69847f7f684efe9beb9cae476eb7e2245775e85c0d08064d0414fdda9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:53.321264Z","signature_b64":"xYiZMXoCGLuC0vx2y6sX3GeWt0Pv1OJw4cd51VJHTHl25dJLOaalyCFwqFPMqf7AplbKAuVzzTITnNDbh96JBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e1b7f1e69847f7f684efe9beb9cae476eb7e2245775e85c0d08064d0414fdda9","last_reissued_at":"2026-05-18T00:09:53.320574Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:53.320574Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.06467","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:09:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d9LtmmWQ8yXUXCc2VnnUnjF11NvTuDcz5WlDSDNBC373FpSo/4UG5w3NzTiNyqaR2cBaaJNWPhalzYiOaZtQCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T08:31:14.979383Z"},"content_sha256":"99f9288b81299a4fc38a17674ba55de2051060fdfe0787c63b86670346c880ef","schema_version":"1.0","event_id":"sha256:99f9288b81299a4fc38a17674ba55de2051060fdfe0787c63b86670346c880ef"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:4G37DZUYI737NBHP5G7LTSXEO3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the isometry group of $RCD^*(K,N)$-spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.DG","authors_text":"Jaime Santos-Rodr\\'iguez, Luis Guijarro","submitted_at":"2016-08-23T11:17:13Z","abstract_excerpt":"We prove that the group of isometries of a metric measure space that satisfies the Riemannian curvature condition, $RCD^*(K,N),$ is in fact a Lie group. We obtain an optimal upper bound on its dimension and classify the spaces where this maximal dimension is achieved."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.06467","kind":"arxiv","version":2},"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":"2026-05-18T00:09:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PIOTfM1fRR1Lb3MvNGsm91gJQCno+V551PFqcMl4FdJuBoiVA19fPWC0qcO8x8aKVOB7A9y8UKmqLDS7exlMCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T08:31:14.979730Z"},"content_sha256":"a6f3178c8554179fa6aad5b11f1c86534ca98f304246e7c3e709bc3a9f664213","schema_version":"1.0","event_id":"sha256:a6f3178c8554179fa6aad5b11f1c86534ca98f304246e7c3e709bc3a9f664213"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4G37DZUYI737NBHP5G7LTSXEO3/bundle.json","state_url":"https://pith.science/pith/4G37DZUYI737NBHP5G7LTSXEO3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4G37DZUYI737NBHP5G7LTSXEO3/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":"2026-06-12T08:31:14Z","links":{"resolver":"https://pith.science/pith/4G37DZUYI737NBHP5G7LTSXEO3","bundle":"https://pith.science/pith/4G37DZUYI737NBHP5G7LTSXEO3/bundle.json","state":"https://pith.science/pith/4G37DZUYI737NBHP5G7LTSXEO3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4G37DZUYI737NBHP5G7LTSXEO3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:4G37DZUYI737NBHP5G7LTSXEO3","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":"643c61b8ef6eb1f130a995240388942e4828dd5f3c5b1e6183b9799ccae5ea68","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-08-23T11:17:13Z","title_canon_sha256":"b92e479e85696d00b2a7b08b85ec65894cf8c205b8e2af29315dbb8d42812451"},"schema_version":"1.0","source":{"id":"1608.06467","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.06467","created_at":"2026-05-18T00:09:53Z"},{"alias_kind":"arxiv_version","alias_value":"1608.06467v2","created_at":"2026-05-18T00:09:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.06467","created_at":"2026-05-18T00:09:53Z"},{"alias_kind":"pith_short_12","alias_value":"4G37DZUYI737","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4G37DZUYI737NBHP","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4G37DZUY","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:a6f3178c8554179fa6aad5b11f1c86534ca98f304246e7c3e709bc3a9f664213","target":"graph","created_at":"2026-05-18T00:09:53Z","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":"We prove that the group of isometries of a metric measure space that satisfies the Riemannian curvature condition, $RCD^*(K,N),$ is in fact a Lie group. We obtain an optimal upper bound on its dimension and classify the spaces where this maximal dimension is achieved.","authors_text":"Jaime Santos-Rodr\\'iguez, Luis Guijarro","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-08-23T11:17:13Z","title":"On the isometry group of $RCD^*(K,N)$-spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.06467","kind":"arxiv","version":2},"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":"sha256:99f9288b81299a4fc38a17674ba55de2051060fdfe0787c63b86670346c880ef","target":"record","created_at":"2026-05-18T00:09:53Z","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":"643c61b8ef6eb1f130a995240388942e4828dd5f3c5b1e6183b9799ccae5ea68","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-08-23T11:17:13Z","title_canon_sha256":"b92e479e85696d00b2a7b08b85ec65894cf8c205b8e2af29315dbb8d42812451"},"schema_version":"1.0","source":{"id":"1608.06467","kind":"arxiv","version":2}},"canonical_sha256":"e1b7f1e69847f7f684efe9beb9cae476eb7e2245775e85c0d08064d0414fdda9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e1b7f1e69847f7f684efe9beb9cae476eb7e2245775e85c0d08064d0414fdda9","first_computed_at":"2026-05-18T00:09:53.320574Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:09:53.320574Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xYiZMXoCGLuC0vx2y6sX3GeWt0Pv1OJw4cd51VJHTHl25dJLOaalyCFwqFPMqf7AplbKAuVzzTITnNDbh96JBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:09:53.321264Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.06467","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:99f9288b81299a4fc38a17674ba55de2051060fdfe0787c63b86670346c880ef","sha256:a6f3178c8554179fa6aad5b11f1c86534ca98f304246e7c3e709bc3a9f664213"],"state_sha256":"0f7efbf4843bcf42e7beb527c2b96870335a02d43fed5ca9a9db38284833e49c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rTR1z+IXL5pJy83P47lg6b4i4fCnx09a7HNCkYy5THpNg7Kq6oI5KYXQy9da/RmRptIDxkBgnS84nfivFXQ0CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T08:31:14.981939Z","bundle_sha256":"15ed68dc6f6a2d8b6bf9001fa9cdf690a3d5c618b1869e99dec1fda29f87c61f"}}