{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:QSSKXTNBMTAD7DOYY4GLYWTS2C","short_pith_number":"pith:QSSKXTNB","canonical_record":{"source":{"id":"1109.1439","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-09-07T12:47:02Z","cross_cats_sorted":[],"title_canon_sha256":"82ac63feddf3acedbc07df1d98d9917b72e4f4816e45e81eceb19b34d28e4b25","abstract_canon_sha256":"f302ecb5fc07384808a688abb91f67f1c2608e3db750debf37af3e97de25cb2d"},"schema_version":"1.0"},"canonical_sha256":"84a4abcda164c03f8dd8c70cbc5a72d0ae3c5e14c6d96602868bbbfb3ab3c80d","source":{"kind":"arxiv","id":"1109.1439","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.1439","created_at":"2026-05-18T04:13:54Z"},{"alias_kind":"arxiv_version","alias_value":"1109.1439v2","created_at":"2026-05-18T04:13:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.1439","created_at":"2026-05-18T04:13:54Z"},{"alias_kind":"pith_short_12","alias_value":"QSSKXTNBMTAD","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"QSSKXTNBMTAD7DOY","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"QSSKXTNB","created_at":"2026-05-18T12:26:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:QSSKXTNBMTAD7DOYY4GLYWTS2C","target":"record","payload":{"canonical_record":{"source":{"id":"1109.1439","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-09-07T12:47:02Z","cross_cats_sorted":[],"title_canon_sha256":"82ac63feddf3acedbc07df1d98d9917b72e4f4816e45e81eceb19b34d28e4b25","abstract_canon_sha256":"f302ecb5fc07384808a688abb91f67f1c2608e3db750debf37af3e97de25cb2d"},"schema_version":"1.0"},"canonical_sha256":"84a4abcda164c03f8dd8c70cbc5a72d0ae3c5e14c6d96602868bbbfb3ab3c80d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:13:54.910420Z","signature_b64":"G07CgB+8QE1TiKN4soQpP4Tk+aq4JXMa459y9RsjT3acijygYQD4L0aUeXOgslOZpzg34/6YtlkHrY43GxD2DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"84a4abcda164c03f8dd8c70cbc5a72d0ae3c5e14c6d96602868bbbfb3ab3c80d","last_reissued_at":"2026-05-18T04:13:54.909948Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:13:54.909948Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.1439","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":"2026-05-18T04:13:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7xVfBqJd8u1/7dIUX90ycYzkDVHQNm8J4+AYt8gAU5jXnNqwMf98YqLhaj6kMHrMmGkp//6JXn/UjcI5WxCTCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T13:15:38.051200Z"},"content_sha256":"cfbcb25fd4e5d14facb29bab7c87725b2ce1c2d507e263b71b88e26dec12d721","schema_version":"1.0","event_id":"sha256:cfbcb25fd4e5d14facb29bab7c87725b2ce1c2d507e263b71b88e26dec12d721"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:QSSKXTNBMTAD7DOYY4GLYWTS2C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lyapunov Orbits at L2 and Transversal Intersections of Invariant Manifolds in the Jupiter-Sun Planar Restricted Circular Three Body Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Maciej J. Capinski","submitted_at":"2011-09-07T12:47:02Z","abstract_excerpt":"We present a computer assisted proof of existence of a family of Lyapunov orbits which stretches from L2 up to half the distance to the smaller primary in the Jupiter-Sun planar restricted circular three body problem. We then focus on a small family of Lyapunov orbits with energies close to comet Oterma and show that their associated invariant manifolds intersect transversally. Our computer assisted proof provides explicit bounds on the location and on the angle of intersection."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.1439","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":"2026-05-18T04:13:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"czCQuz/LLv91Ngu5O8HY8NC5d78Yz/MSk7agVd26qNf/TpebnedbUy53Q9OCZFuYksNAxEACeg8rn0hxQ58aDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T13:15:38.051567Z"},"content_sha256":"d40c75ac9c1abe120aa1fcf9c70515c4860d752b05471e319cd837d7b631632f","schema_version":"1.0","event_id":"sha256:d40c75ac9c1abe120aa1fcf9c70515c4860d752b05471e319cd837d7b631632f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QSSKXTNBMTAD7DOYY4GLYWTS2C/bundle.json","state_url":"https://pith.science/pith/QSSKXTNBMTAD7DOYY4GLYWTS2C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QSSKXTNBMTAD7DOYY4GLYWTS2C/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":"2026-06-23T13:15:38Z","links":{"resolver":"https://pith.science/pith/QSSKXTNBMTAD7DOYY4GLYWTS2C","bundle":"https://pith.science/pith/QSSKXTNBMTAD7DOYY4GLYWTS2C/bundle.json","state":"https://pith.science/pith/QSSKXTNBMTAD7DOYY4GLYWTS2C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QSSKXTNBMTAD7DOYY4GLYWTS2C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:QSSKXTNBMTAD7DOYY4GLYWTS2C","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":"f302ecb5fc07384808a688abb91f67f1c2608e3db750debf37af3e97de25cb2d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-09-07T12:47:02Z","title_canon_sha256":"82ac63feddf3acedbc07df1d98d9917b72e4f4816e45e81eceb19b34d28e4b25"},"schema_version":"1.0","source":{"id":"1109.1439","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.1439","created_at":"2026-05-18T04:13:54Z"},{"alias_kind":"arxiv_version","alias_value":"1109.1439v2","created_at":"2026-05-18T04:13:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.1439","created_at":"2026-05-18T04:13:54Z"},{"alias_kind":"pith_short_12","alias_value":"QSSKXTNBMTAD","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"QSSKXTNBMTAD7DOY","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"QSSKXTNB","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:d40c75ac9c1abe120aa1fcf9c70515c4860d752b05471e319cd837d7b631632f","target":"graph","created_at":"2026-05-18T04:13:54Z","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 present a computer assisted proof of existence of a family of Lyapunov orbits which stretches from L2 up to half the distance to the smaller primary in the Jupiter-Sun planar restricted circular three body problem. We then focus on a small family of Lyapunov orbits with energies close to comet Oterma and show that their associated invariant manifolds intersect transversally. Our computer assisted proof provides explicit bounds on the location and on the angle of intersection.","authors_text":"Maciej J. Capinski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-09-07T12:47:02Z","title":"Lyapunov Orbits at L2 and Transversal Intersections of Invariant Manifolds in the Jupiter-Sun Planar Restricted Circular Three Body Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.1439","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:cfbcb25fd4e5d14facb29bab7c87725b2ce1c2d507e263b71b88e26dec12d721","target":"record","created_at":"2026-05-18T04:13:54Z","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":"f302ecb5fc07384808a688abb91f67f1c2608e3db750debf37af3e97de25cb2d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-09-07T12:47:02Z","title_canon_sha256":"82ac63feddf3acedbc07df1d98d9917b72e4f4816e45e81eceb19b34d28e4b25"},"schema_version":"1.0","source":{"id":"1109.1439","kind":"arxiv","version":2}},"canonical_sha256":"84a4abcda164c03f8dd8c70cbc5a72d0ae3c5e14c6d96602868bbbfb3ab3c80d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"84a4abcda164c03f8dd8c70cbc5a72d0ae3c5e14c6d96602868bbbfb3ab3c80d","first_computed_at":"2026-05-18T04:13:54.909948Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:13:54.909948Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G07CgB+8QE1TiKN4soQpP4Tk+aq4JXMa459y9RsjT3acijygYQD4L0aUeXOgslOZpzg34/6YtlkHrY43GxD2DA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:13:54.910420Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.1439","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cfbcb25fd4e5d14facb29bab7c87725b2ce1c2d507e263b71b88e26dec12d721","sha256:d40c75ac9c1abe120aa1fcf9c70515c4860d752b05471e319cd837d7b631632f"],"state_sha256":"d2021b4d795b869d71be890dd85f0f5044cb1a99c1be3f0d30a04315eeba15f9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dLKUSBML3zwYrnD/DWfM4G16ugZgNCG5/Lzdo78l0MjAUXCpNjDg9M5UFoP4K6TnAdHJSbFcDmrcQFxepAd4AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T13:15:38.053647Z","bundle_sha256":"a42a51f06d8297bba30bc243f1b5e3e1f48bccbac9bc845f27955b7d62151639"}}