{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:VPQXZ7IJEZJXK2PWA244QPONTI","short_pith_number":"pith:VPQXZ7IJ","canonical_record":{"source":{"id":"1011.1835","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2010-11-08T16:06:49Z","cross_cats_sorted":["math-ph","math.DG","math.MP"],"title_canon_sha256":"c32adbf64ede5b7e70d542a277a33f85b7b8a5f21a8bb0c1dca06a79ed4126de","abstract_canon_sha256":"d3f150a0569e72065d1335f05ca1b3274bb9da953b654c3628c0716feaddab41"},"schema_version":"1.0"},"canonical_sha256":"abe17cfd0926537569f606b9c83dcd9a2d80c6eb2b2ab6f23fa83ac6b5ce6c1c","source":{"kind":"arxiv","id":"1011.1835","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.1835","created_at":"2026-05-18T03:51:48Z"},{"alias_kind":"arxiv_version","alias_value":"1011.1835v1","created_at":"2026-05-18T03:51:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.1835","created_at":"2026-05-18T03:51:48Z"},{"alias_kind":"pith_short_12","alias_value":"VPQXZ7IJEZJX","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"VPQXZ7IJEZJXK2PW","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"VPQXZ7IJ","created_at":"2026-05-18T12:26:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:VPQXZ7IJEZJXK2PWA244QPONTI","target":"record","payload":{"canonical_record":{"source":{"id":"1011.1835","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2010-11-08T16:06:49Z","cross_cats_sorted":["math-ph","math.DG","math.MP"],"title_canon_sha256":"c32adbf64ede5b7e70d542a277a33f85b7b8a5f21a8bb0c1dca06a79ed4126de","abstract_canon_sha256":"d3f150a0569e72065d1335f05ca1b3274bb9da953b654c3628c0716feaddab41"},"schema_version":"1.0"},"canonical_sha256":"abe17cfd0926537569f606b9c83dcd9a2d80c6eb2b2ab6f23fa83ac6b5ce6c1c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:51:48.908508Z","signature_b64":"XuoGFDG4GfWjIQfUEZJ6Szyf3wVKaKWuDpnStSJJMWBYu0jxX2VWs1aGJtYzxwTA5iROqfprL5Sa09aRCZBfAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"abe17cfd0926537569f606b9c83dcd9a2d80c6eb2b2ab6f23fa83ac6b5ce6c1c","last_reissued_at":"2026-05-18T03:51:48.908017Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:51:48.908017Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.1835","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":"2026-05-18T03:51:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DpdCPJgSfKqbce/DeXgGVUBDZ1fjxpvU4afQSGU0LbAZrrypL/1YF1tJRdNR4aDQi8O67Bx5ChLXUWYRhJwaBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T17:11:14.613998Z"},"content_sha256":"eda2c01f5bd6a51a504f0d126d616f94f258b4782d4dbb07cd01bf2951f37fc6","schema_version":"1.0","event_id":"sha256:eda2c01f5bd6a51a504f0d126d616f94f258b4782d4dbb07cd01bf2951f37fc6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:VPQXZ7IJEZJXK2PWA244QPONTI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Geodesic Flows and Neumann Systems on Stiefel Varieties. Geometry and Integrability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DG","math.MP"],"primary_cat":"nlin.SI","authors_text":"Bozidar Jovanovic, Yuri N. Fedorov","submitted_at":"2010-11-08T16:06:49Z","abstract_excerpt":"We study integrable geodesic flows on Stiefel varieties $V_{n,r}=SO(n)/SO(n-r)$ given by the Euclidean, normal (standard), Manakov-type, and Einstein metrics. We also consider natural generalizations of the Neumann systems on $V_{n,r}$ with the above metrics and proves their integrability in the non-commutative sense by presenting compatible Poisson brackets on $(T^*V_{n,r})/SO(r)$. Various reductions of the latter systems are described, in particular, the generalized Neumann system on an oriented Grassmannian $G_{n,r}$ and on a sphere $S^{n-1}$ in presence of Yang-Mills fields or a magnetic m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.1835","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":"2026-05-18T03:51:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5JVbaWYkuKgrymdLrzAltfG+/E1HJ5vyIyG3ZC2SR2p24YPHgwekqVgON8cjh+If4YnvU6gRrX8En4VLcpSHCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T17:11:14.614738Z"},"content_sha256":"155cb9769757eb2a51a4429ad7ab72f7f361c26964d10679f1e4af945e6ba4cd","schema_version":"1.0","event_id":"sha256:155cb9769757eb2a51a4429ad7ab72f7f361c26964d10679f1e4af945e6ba4cd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VPQXZ7IJEZJXK2PWA244QPONTI/bundle.json","state_url":"https://pith.science/pith/VPQXZ7IJEZJXK2PWA244QPONTI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VPQXZ7IJEZJXK2PWA244QPONTI/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":"2026-06-08T17:11:14Z","links":{"resolver":"https://pith.science/pith/VPQXZ7IJEZJXK2PWA244QPONTI","bundle":"https://pith.science/pith/VPQXZ7IJEZJXK2PWA244QPONTI/bundle.json","state":"https://pith.science/pith/VPQXZ7IJEZJXK2PWA244QPONTI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VPQXZ7IJEZJXK2PWA244QPONTI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:VPQXZ7IJEZJXK2PWA244QPONTI","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":"d3f150a0569e72065d1335f05ca1b3274bb9da953b654c3628c0716feaddab41","cross_cats_sorted":["math-ph","math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2010-11-08T16:06:49Z","title_canon_sha256":"c32adbf64ede5b7e70d542a277a33f85b7b8a5f21a8bb0c1dca06a79ed4126de"},"schema_version":"1.0","source":{"id":"1011.1835","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.1835","created_at":"2026-05-18T03:51:48Z"},{"alias_kind":"arxiv_version","alias_value":"1011.1835v1","created_at":"2026-05-18T03:51:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.1835","created_at":"2026-05-18T03:51:48Z"},{"alias_kind":"pith_short_12","alias_value":"VPQXZ7IJEZJX","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"VPQXZ7IJEZJXK2PW","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"VPQXZ7IJ","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:155cb9769757eb2a51a4429ad7ab72f7f361c26964d10679f1e4af945e6ba4cd","target":"graph","created_at":"2026-05-18T03:51:48Z","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 study integrable geodesic flows on Stiefel varieties $V_{n,r}=SO(n)/SO(n-r)$ given by the Euclidean, normal (standard), Manakov-type, and Einstein metrics. We also consider natural generalizations of the Neumann systems on $V_{n,r}$ with the above metrics and proves their integrability in the non-commutative sense by presenting compatible Poisson brackets on $(T^*V_{n,r})/SO(r)$. Various reductions of the latter systems are described, in particular, the generalized Neumann system on an oriented Grassmannian $G_{n,r}$ and on a sphere $S^{n-1}$ in presence of Yang-Mills fields or a magnetic m","authors_text":"Bozidar Jovanovic, Yuri N. Fedorov","cross_cats":["math-ph","math.DG","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2010-11-08T16:06:49Z","title":"Geodesic Flows and Neumann Systems on Stiefel Varieties. Geometry and Integrability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.1835","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:eda2c01f5bd6a51a504f0d126d616f94f258b4782d4dbb07cd01bf2951f37fc6","target":"record","created_at":"2026-05-18T03:51:48Z","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":"d3f150a0569e72065d1335f05ca1b3274bb9da953b654c3628c0716feaddab41","cross_cats_sorted":["math-ph","math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2010-11-08T16:06:49Z","title_canon_sha256":"c32adbf64ede5b7e70d542a277a33f85b7b8a5f21a8bb0c1dca06a79ed4126de"},"schema_version":"1.0","source":{"id":"1011.1835","kind":"arxiv","version":1}},"canonical_sha256":"abe17cfd0926537569f606b9c83dcd9a2d80c6eb2b2ab6f23fa83ac6b5ce6c1c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"abe17cfd0926537569f606b9c83dcd9a2d80c6eb2b2ab6f23fa83ac6b5ce6c1c","first_computed_at":"2026-05-18T03:51:48.908017Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:51:48.908017Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XuoGFDG4GfWjIQfUEZJ6Szyf3wVKaKWuDpnStSJJMWBYu0jxX2VWs1aGJtYzxwTA5iROqfprL5Sa09aRCZBfAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:51:48.908508Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.1835","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eda2c01f5bd6a51a504f0d126d616f94f258b4782d4dbb07cd01bf2951f37fc6","sha256:155cb9769757eb2a51a4429ad7ab72f7f361c26964d10679f1e4af945e6ba4cd"],"state_sha256":"17eb1888ce247fd7dfbdb886a8c81e9f8bc761b0434b7e80b141d23f2206a012"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Dw1AwDR+5kc0LyyOpHj+Op4I0bQrQgCYPoUCL+AM9RIpiVImQmlKQZx6bN6YQQs9il+FIFi79WOqC7B17Be7BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T17:11:14.622062Z","bundle_sha256":"10eeb5caa384795c2b02383aad1aabd838c003ceff1b3c7e537f8b81f2ebfc14"}}