{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:ZUWV23AMKBZYY4J6FV5QD625PQ","short_pith_number":"pith:ZUWV23AM","canonical_record":{"source":{"id":"1311.2256","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-11-10T09:51:04Z","cross_cats_sorted":[],"title_canon_sha256":"470ce57888adb850149d89e7c33c21b8b06ea8ce8b9270a9bd3879d692173c02","abstract_canon_sha256":"aa65b08edcb393377f2bf3ec9016d59bcf8d49917075bcf0411ee850378b37c9"},"schema_version":"1.0"},"canonical_sha256":"cd2d5d6c0c50738c713e2d7b01fb5d7c0bcb3c4c53bbb206a6dcc170e08d406c","source":{"kind":"arxiv","id":"1311.2256","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.2256","created_at":"2026-05-18T03:07:33Z"},{"alias_kind":"arxiv_version","alias_value":"1311.2256v1","created_at":"2026-05-18T03:07:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.2256","created_at":"2026-05-18T03:07:33Z"},{"alias_kind":"pith_short_12","alias_value":"ZUWV23AMKBZY","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZUWV23AMKBZYY4J6","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZUWV23AM","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:ZUWV23AMKBZYY4J6FV5QD625PQ","target":"record","payload":{"canonical_record":{"source":{"id":"1311.2256","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-11-10T09:51:04Z","cross_cats_sorted":[],"title_canon_sha256":"470ce57888adb850149d89e7c33c21b8b06ea8ce8b9270a9bd3879d692173c02","abstract_canon_sha256":"aa65b08edcb393377f2bf3ec9016d59bcf8d49917075bcf0411ee850378b37c9"},"schema_version":"1.0"},"canonical_sha256":"cd2d5d6c0c50738c713e2d7b01fb5d7c0bcb3c4c53bbb206a6dcc170e08d406c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:07:33.147288Z","signature_b64":"0CQKMDwnufvHk38ZWkjVXmxroPBy0ofp/BKAfMRVa+X2ECZTB48kS1uOgsZ2eiXsV6RS6xpBysK/C0Q/PAPxBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cd2d5d6c0c50738c713e2d7b01fb5d7c0bcb3c4c53bbb206a6dcc170e08d406c","last_reissued_at":"2026-05-18T03:07:33.146588Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:07:33.146588Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.2256","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":"2026-05-18T03:07:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OpgbKAC82idXyXJbmqKqIGLCSD7XodTwD+j8JxMjcoYkKY306Ybm7c8sf5W58RLL3P0o8Bck5z5wRTFMwlWdDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T02:38:29.062246Z"},"content_sha256":"342983e2635c01bcf56ddee7a2af169380358942214d6bd55d509bf1218713d4","schema_version":"1.0","event_id":"sha256:342983e2635c01bcf56ddee7a2af169380358942214d6bd55d509bf1218713d4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:ZUWV23AMKBZYY4J6FV5QD625PQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stability of Hamiltonian relative equilibria in symmetric magnetically confined rigid bodies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Juan-Pablo Ortega, Lyudmila Grigoryeva, Stanislav Zub","submitted_at":"2013-11-10T09:51:04Z","abstract_excerpt":"This work studies the symmetries, the associated momentum map, and relative equilibria of a mechanical system consisting of a small axisymmetric magnetic body-dipole in an also axisymmetric external magnetic field that additionally exhibits a mirror symmetry; we call this system the ``orbitron\". We study the nonlinear stability of a branch of equatorial quasiorbital relative equilibria using the energy-momentum method and we provide sufficient conditions for their $\\mathbb{T}^2$--stability that complete partial stability relations already existing in the literature. These stability prescriptio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.2256","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":"2026-05-18T03:07:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jZk1Aa20MMOhX7V8CfK1qF13gP75MlEOPOYOHPjHF3ABrmNO8upo8udwpKvVk5D3qGgvAaD4uYyMfgYswIuSAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T02:38:29.063157Z"},"content_sha256":"a35b69dff43053dbd097fae8b29ba463856cb2ed7d874541355bd7355510db0f","schema_version":"1.0","event_id":"sha256:a35b69dff43053dbd097fae8b29ba463856cb2ed7d874541355bd7355510db0f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZUWV23AMKBZYY4J6FV5QD625PQ/bundle.json","state_url":"https://pith.science/pith/ZUWV23AMKBZYY4J6FV5QD625PQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZUWV23AMKBZYY4J6FV5QD625PQ/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":"2026-06-01T02:38:29Z","links":{"resolver":"https://pith.science/pith/ZUWV23AMKBZYY4J6FV5QD625PQ","bundle":"https://pith.science/pith/ZUWV23AMKBZYY4J6FV5QD625PQ/bundle.json","state":"https://pith.science/pith/ZUWV23AMKBZYY4J6FV5QD625PQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZUWV23AMKBZYY4J6FV5QD625PQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ZUWV23AMKBZYY4J6FV5QD625PQ","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":"aa65b08edcb393377f2bf3ec9016d59bcf8d49917075bcf0411ee850378b37c9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-11-10T09:51:04Z","title_canon_sha256":"470ce57888adb850149d89e7c33c21b8b06ea8ce8b9270a9bd3879d692173c02"},"schema_version":"1.0","source":{"id":"1311.2256","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.2256","created_at":"2026-05-18T03:07:33Z"},{"alias_kind":"arxiv_version","alias_value":"1311.2256v1","created_at":"2026-05-18T03:07:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.2256","created_at":"2026-05-18T03:07:33Z"},{"alias_kind":"pith_short_12","alias_value":"ZUWV23AMKBZY","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZUWV23AMKBZYY4J6","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZUWV23AM","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:a35b69dff43053dbd097fae8b29ba463856cb2ed7d874541355bd7355510db0f","target":"graph","created_at":"2026-05-18T03:07:33Z","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":"This work studies the symmetries, the associated momentum map, and relative equilibria of a mechanical system consisting of a small axisymmetric magnetic body-dipole in an also axisymmetric external magnetic field that additionally exhibits a mirror symmetry; we call this system the ``orbitron\". We study the nonlinear stability of a branch of equatorial quasiorbital relative equilibria using the energy-momentum method and we provide sufficient conditions for their $\\mathbb{T}^2$--stability that complete partial stability relations already existing in the literature. These stability prescriptio","authors_text":"Juan-Pablo Ortega, Lyudmila Grigoryeva, Stanislav Zub","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-11-10T09:51:04Z","title":"Stability of Hamiltonian relative equilibria in symmetric magnetically confined rigid bodies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.2256","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":"sha256:342983e2635c01bcf56ddee7a2af169380358942214d6bd55d509bf1218713d4","target":"record","created_at":"2026-05-18T03:07:33Z","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":"aa65b08edcb393377f2bf3ec9016d59bcf8d49917075bcf0411ee850378b37c9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-11-10T09:51:04Z","title_canon_sha256":"470ce57888adb850149d89e7c33c21b8b06ea8ce8b9270a9bd3879d692173c02"},"schema_version":"1.0","source":{"id":"1311.2256","kind":"arxiv","version":1}},"canonical_sha256":"cd2d5d6c0c50738c713e2d7b01fb5d7c0bcb3c4c53bbb206a6dcc170e08d406c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cd2d5d6c0c50738c713e2d7b01fb5d7c0bcb3c4c53bbb206a6dcc170e08d406c","first_computed_at":"2026-05-18T03:07:33.146588Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:07:33.146588Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0CQKMDwnufvHk38ZWkjVXmxroPBy0ofp/BKAfMRVa+X2ECZTB48kS1uOgsZ2eiXsV6RS6xpBysK/C0Q/PAPxBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:07:33.147288Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.2256","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:342983e2635c01bcf56ddee7a2af169380358942214d6bd55d509bf1218713d4","sha256:a35b69dff43053dbd097fae8b29ba463856cb2ed7d874541355bd7355510db0f"],"state_sha256":"95661f4cdba2cd247f78776e6d436fcf6078820b26b07b361b105b1aecdeb56e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IZp/IGerDtXgy0+et3vn/LFgAKGXuDIeOvAM2tQTw4MuD4LL/wZVygZsiRTgMNHTOsHF++chyK09dszd3+71Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T02:38:29.066932Z","bundle_sha256":"e3557dc6f90110825ca087bb041fd7b82a929ad183038468ce2a3300f6a3d06b"}}