{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:LBF5PCJKOQQTYBJVJHD6KU4XX5","short_pith_number":"pith:LBF5PCJK","canonical_record":{"source":{"id":"1508.07589","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-08-30T15:31:28Z","cross_cats_sorted":[],"title_canon_sha256":"fb3106c2cf9f9512b2961534c36dbf5003c01d4907877ae8e7666b6d4277c2cc","abstract_canon_sha256":"269d100665cae135d2603a72e241d36b570a897e69b2faf1dbd7ef5984c3d796"},"schema_version":"1.0"},"canonical_sha256":"584bd7892a74213c053549c7e55397bf7b824583a9f068d619d875aa3c953549","source":{"kind":"arxiv","id":"1508.07589","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.07589","created_at":"2026-05-18T01:34:31Z"},{"alias_kind":"arxiv_version","alias_value":"1508.07589v1","created_at":"2026-05-18T01:34:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.07589","created_at":"2026-05-18T01:34:31Z"},{"alias_kind":"pith_short_12","alias_value":"LBF5PCJKOQQT","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LBF5PCJKOQQTYBJV","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LBF5PCJK","created_at":"2026-05-18T12:29:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:LBF5PCJKOQQTYBJVJHD6KU4XX5","target":"record","payload":{"canonical_record":{"source":{"id":"1508.07589","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-08-30T15:31:28Z","cross_cats_sorted":[],"title_canon_sha256":"fb3106c2cf9f9512b2961534c36dbf5003c01d4907877ae8e7666b6d4277c2cc","abstract_canon_sha256":"269d100665cae135d2603a72e241d36b570a897e69b2faf1dbd7ef5984c3d796"},"schema_version":"1.0"},"canonical_sha256":"584bd7892a74213c053549c7e55397bf7b824583a9f068d619d875aa3c953549","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:31.912784Z","signature_b64":"kV/Lhzy/SlRnt9FnaIYEosuY1SYOuWcsU8nwqpv1s4bDk9ceOfRebGcKJHdNnB7XUXZ4tV62vPMufEH6ccdyAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"584bd7892a74213c053549c7e55397bf7b824583a9f068d619d875aa3c953549","last_reissued_at":"2026-05-18T01:34:31.912119Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:31.912119Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.07589","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":"2026-05-18T01:34:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I35s0wagoY4F1isRABHi8ubuBCRLPneo81F0noAtjCHqOzaeXhIpFObsGbZ0Ukc/5Yyvkah9GTzGAG45uVByDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T08:49:38.559944Z"},"content_sha256":"c5fad98f73a8068bb87dde5e4bf77680a1c227f02f121ff5dcc27f6843eea349","schema_version":"1.0","event_id":"sha256:c5fad98f73a8068bb87dde5e4bf77680a1c227f02f121ff5dcc27f6843eea349"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:LBF5PCJKOQQTYBJVJHD6KU4XX5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"De Sitter's Theory of Galilean Satellites and the Related Quasi-periodic Orbits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Henk Broer, Lei Zhao","submitted_at":"2015-08-30T15:31:28Z","abstract_excerpt":"In this article, we investigate the mathematical part of De Sitter's theory on the Galilean satellites, and further extend this theory by showing the existence of some quasi-periodic librating orbits by applications of KAM theorems. After showing the existence of De Sitter's family of linearly stable periodic orbits in the Jupiter-Io-Europa-Ganymede model by averaging and reduction techniques in the Hamiltonian framework, we further discuss the possible extension of this theory to include a fourth satellite Callisto, and establish the existence of a set of positive measure of quasi-periodic li"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07589","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":"2026-05-18T01:34:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BCMiK/bEag/FHE1t/QGh1mB0oUhjNot9KMgiyL4j7HRpY7o6bDwMrw8pQi9KCuNzYnPn9E1n03knlOQoICEZDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T08:49:38.560294Z"},"content_sha256":"00451df664421814aee930aad8ddac29ac27b9e7fc5b1a29991532a53ff3a35d","schema_version":"1.0","event_id":"sha256:00451df664421814aee930aad8ddac29ac27b9e7fc5b1a29991532a53ff3a35d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LBF5PCJKOQQTYBJVJHD6KU4XX5/bundle.json","state_url":"https://pith.science/pith/LBF5PCJKOQQTYBJVJHD6KU4XX5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LBF5PCJKOQQTYBJVJHD6KU4XX5/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":"2026-06-01T08:49:38Z","links":{"resolver":"https://pith.science/pith/LBF5PCJKOQQTYBJVJHD6KU4XX5","bundle":"https://pith.science/pith/LBF5PCJKOQQTYBJVJHD6KU4XX5/bundle.json","state":"https://pith.science/pith/LBF5PCJKOQQTYBJVJHD6KU4XX5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LBF5PCJKOQQTYBJVJHD6KU4XX5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:LBF5PCJKOQQTYBJVJHD6KU4XX5","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":"269d100665cae135d2603a72e241d36b570a897e69b2faf1dbd7ef5984c3d796","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-08-30T15:31:28Z","title_canon_sha256":"fb3106c2cf9f9512b2961534c36dbf5003c01d4907877ae8e7666b6d4277c2cc"},"schema_version":"1.0","source":{"id":"1508.07589","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.07589","created_at":"2026-05-18T01:34:31Z"},{"alias_kind":"arxiv_version","alias_value":"1508.07589v1","created_at":"2026-05-18T01:34:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.07589","created_at":"2026-05-18T01:34:31Z"},{"alias_kind":"pith_short_12","alias_value":"LBF5PCJKOQQT","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LBF5PCJKOQQTYBJV","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LBF5PCJK","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:00451df664421814aee930aad8ddac29ac27b9e7fc5b1a29991532a53ff3a35d","target":"graph","created_at":"2026-05-18T01:34:31Z","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":"In this article, we investigate the mathematical part of De Sitter's theory on the Galilean satellites, and further extend this theory by showing the existence of some quasi-periodic librating orbits by applications of KAM theorems. After showing the existence of De Sitter's family of linearly stable periodic orbits in the Jupiter-Io-Europa-Ganymede model by averaging and reduction techniques in the Hamiltonian framework, we further discuss the possible extension of this theory to include a fourth satellite Callisto, and establish the existence of a set of positive measure of quasi-periodic li","authors_text":"Henk Broer, Lei Zhao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-08-30T15:31:28Z","title":"De Sitter's Theory of Galilean Satellites and the Related Quasi-periodic Orbits"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07589","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:c5fad98f73a8068bb87dde5e4bf77680a1c227f02f121ff5dcc27f6843eea349","target":"record","created_at":"2026-05-18T01:34:31Z","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":"269d100665cae135d2603a72e241d36b570a897e69b2faf1dbd7ef5984c3d796","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-08-30T15:31:28Z","title_canon_sha256":"fb3106c2cf9f9512b2961534c36dbf5003c01d4907877ae8e7666b6d4277c2cc"},"schema_version":"1.0","source":{"id":"1508.07589","kind":"arxiv","version":1}},"canonical_sha256":"584bd7892a74213c053549c7e55397bf7b824583a9f068d619d875aa3c953549","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"584bd7892a74213c053549c7e55397bf7b824583a9f068d619d875aa3c953549","first_computed_at":"2026-05-18T01:34:31.912119Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:31.912119Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kV/Lhzy/SlRnt9FnaIYEosuY1SYOuWcsU8nwqpv1s4bDk9ceOfRebGcKJHdNnB7XUXZ4tV62vPMufEH6ccdyAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:31.912784Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.07589","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c5fad98f73a8068bb87dde5e4bf77680a1c227f02f121ff5dcc27f6843eea349","sha256:00451df664421814aee930aad8ddac29ac27b9e7fc5b1a29991532a53ff3a35d"],"state_sha256":"a0a3bad5d10f0aa46066f623b989eb438261740ef8919ab56dcba828525c836d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jIG8YOC1FLVwJ361Jl9P3TKbOsdgJtV0usg0S3P/kdGulLJcfUf8O97nQQCvrptt/PpUOU+FXVYgDPF+piqKDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T08:49:38.562600Z","bundle_sha256":"19d52f71e00bcf86ddf9050f08d4cce58f214e64daba38e57f62891dbbf81130"}}