{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:3T263RBRL6JPRNDNSAF7RTSHKT","short_pith_number":"pith:3T263RBR","canonical_record":{"source":{"id":"1511.08121","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-11-25T17:02:46Z","cross_cats_sorted":["physics.space-ph"],"title_canon_sha256":"4f30026c10f5eac26fa58788a6ed511a256ddcd5683b8d53fad82160d7acf687","abstract_canon_sha256":"bb9a45cfc0dfadad332220ce0ed49489ed7db21a07aed8b0f6d82ff23459ecbf"},"schema_version":"1.0"},"canonical_sha256":"dcf5edc4315f92f8b46d900bf8ce4754f5637d42d74d7132b79fa6c29105e47a","source":{"kind":"arxiv","id":"1511.08121","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.08121","created_at":"2026-05-18T01:17:07Z"},{"alias_kind":"arxiv_version","alias_value":"1511.08121v2","created_at":"2026-05-18T01:17:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.08121","created_at":"2026-05-18T01:17:07Z"},{"alias_kind":"pith_short_12","alias_value":"3T263RBRL6JP","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3T263RBRL6JPRNDN","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3T263RBR","created_at":"2026-05-18T12:29:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:3T263RBRL6JPRNDNSAF7RTSHKT","target":"record","payload":{"canonical_record":{"source":{"id":"1511.08121","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-11-25T17:02:46Z","cross_cats_sorted":["physics.space-ph"],"title_canon_sha256":"4f30026c10f5eac26fa58788a6ed511a256ddcd5683b8d53fad82160d7acf687","abstract_canon_sha256":"bb9a45cfc0dfadad332220ce0ed49489ed7db21a07aed8b0f6d82ff23459ecbf"},"schema_version":"1.0"},"canonical_sha256":"dcf5edc4315f92f8b46d900bf8ce4754f5637d42d74d7132b79fa6c29105e47a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:07.766010Z","signature_b64":"2r52IjPJJoPmq3AIe5uI7c5dIVDl9c8cgEj5wkMmyOkAnUGG4J9TgSlan9CPWW8a9DIX7LgIB6zr3TNCpHmVBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dcf5edc4315f92f8b46d900bf8ce4754f5637d42d74d7132b79fa6c29105e47a","last_reissued_at":"2026-05-18T01:17:07.765181Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:07.765181Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.08121","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":"2026-05-18T01:17:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kMFzvy7VmWCkHkPSszedFKAko5ucWkZInCwFR+yEG46gBrcMp/z1WMBcyYqnlfNkjb/cmpPCalAf5zSL47FFCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T01:38:27.582758Z"},"content_sha256":"c0b2a2f0249fd55d5d9318b3dffc5245f229427b781a39c22e5393835c9741b1","schema_version":"1.0","event_id":"sha256:c0b2a2f0249fd55d5d9318b3dffc5245f229427b781a39c22e5393835c9741b1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:3T263RBRL6JPRNDNSAF7RTSHKT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Circular orbit spacecraft control at the L4 point using Lyapunov functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.space-ph"],"primary_cat":"math.DS","authors_text":"Rachana Agrawal, Ravi N Banavar","submitted_at":"2015-11-25T17:02:46Z","abstract_excerpt":"The objective of this work is to demonstrate the utility of Lyapunov functions in control synthesis for the purpose of maintaining and stabilizing a spacecraft in a circular orbit around the L4 point in the circular restricted three body problem (CRTBP). Incorporating the requirements of a fixed radius orbit and a desired angular momentum, a Lyapunov function is constructed and the requisite analysis is performed to obtain a controller. Asymptotic stability is proved in a defined region around the L4 point using LaSalle's principle."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.08121","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":"2026-05-18T01:17:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E24nehZHQKurwzpQ+/rC3zeOCTGOsYiDVgj6i9I937ANRU6zDnNb05X81Nnt3FtshEklr77EW3y9gwcaqLrhCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T01:38:27.583486Z"},"content_sha256":"156baf3b764310319550797259f9cdb5388e90a71adac12020544ecbc5b189e6","schema_version":"1.0","event_id":"sha256:156baf3b764310319550797259f9cdb5388e90a71adac12020544ecbc5b189e6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3T263RBRL6JPRNDNSAF7RTSHKT/bundle.json","state_url":"https://pith.science/pith/3T263RBRL6JPRNDNSAF7RTSHKT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3T263RBRL6JPRNDNSAF7RTSHKT/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":"2026-05-26T01:38:27Z","links":{"resolver":"https://pith.science/pith/3T263RBRL6JPRNDNSAF7RTSHKT","bundle":"https://pith.science/pith/3T263RBRL6JPRNDNSAF7RTSHKT/bundle.json","state":"https://pith.science/pith/3T263RBRL6JPRNDNSAF7RTSHKT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3T263RBRL6JPRNDNSAF7RTSHKT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:3T263RBRL6JPRNDNSAF7RTSHKT","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":"bb9a45cfc0dfadad332220ce0ed49489ed7db21a07aed8b0f6d82ff23459ecbf","cross_cats_sorted":["physics.space-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-11-25T17:02:46Z","title_canon_sha256":"4f30026c10f5eac26fa58788a6ed511a256ddcd5683b8d53fad82160d7acf687"},"schema_version":"1.0","source":{"id":"1511.08121","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.08121","created_at":"2026-05-18T01:17:07Z"},{"alias_kind":"arxiv_version","alias_value":"1511.08121v2","created_at":"2026-05-18T01:17:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.08121","created_at":"2026-05-18T01:17:07Z"},{"alias_kind":"pith_short_12","alias_value":"3T263RBRL6JP","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3T263RBRL6JPRNDN","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3T263RBR","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:156baf3b764310319550797259f9cdb5388e90a71adac12020544ecbc5b189e6","target":"graph","created_at":"2026-05-18T01:17:07Z","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":"The objective of this work is to demonstrate the utility of Lyapunov functions in control synthesis for the purpose of maintaining and stabilizing a spacecraft in a circular orbit around the L4 point in the circular restricted three body problem (CRTBP). Incorporating the requirements of a fixed radius orbit and a desired angular momentum, a Lyapunov function is constructed and the requisite analysis is performed to obtain a controller. Asymptotic stability is proved in a defined region around the L4 point using LaSalle's principle.","authors_text":"Rachana Agrawal, Ravi N Banavar","cross_cats":["physics.space-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-11-25T17:02:46Z","title":"Circular orbit spacecraft control at the L4 point using Lyapunov functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.08121","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:c0b2a2f0249fd55d5d9318b3dffc5245f229427b781a39c22e5393835c9741b1","target":"record","created_at":"2026-05-18T01:17:07Z","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":"bb9a45cfc0dfadad332220ce0ed49489ed7db21a07aed8b0f6d82ff23459ecbf","cross_cats_sorted":["physics.space-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-11-25T17:02:46Z","title_canon_sha256":"4f30026c10f5eac26fa58788a6ed511a256ddcd5683b8d53fad82160d7acf687"},"schema_version":"1.0","source":{"id":"1511.08121","kind":"arxiv","version":2}},"canonical_sha256":"dcf5edc4315f92f8b46d900bf8ce4754f5637d42d74d7132b79fa6c29105e47a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dcf5edc4315f92f8b46d900bf8ce4754f5637d42d74d7132b79fa6c29105e47a","first_computed_at":"2026-05-18T01:17:07.765181Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:07.765181Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2r52IjPJJoPmq3AIe5uI7c5dIVDl9c8cgEj5wkMmyOkAnUGG4J9TgSlan9CPWW8a9DIX7LgIB6zr3TNCpHmVBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:07.766010Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.08121","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c0b2a2f0249fd55d5d9318b3dffc5245f229427b781a39c22e5393835c9741b1","sha256:156baf3b764310319550797259f9cdb5388e90a71adac12020544ecbc5b189e6"],"state_sha256":"60ad96f1730fc9f4453e22c6ed62e578f271220316417f0a42a928344d507a45"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hoFsgdr+vzQhqsE5ubOzeBBe7QzlqQjMLWgthpho7wsk4L+qd/6S45CzQm8v2aTOB2ed4DzSKX6w0BpqUU0aDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T01:38:27.587266Z","bundle_sha256":"88d43ea5a8e2d87048677abe4d8767d7c3fb70d2cb860bc41a526bb1d210fd92"}}