{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:G5W37KGUJINKRMMR5SLGXAULOL","short_pith_number":"pith:G5W37KGU","schema_version":"1.0","canonical_sha256":"376dbfa8d44a1aa8b191ec966b828b72c2094c777630883f9971bf58f06c7559","source":{"kind":"arxiv","id":"1710.04834","version":4},"attestation_state":"computed","paper":{"title":"Morse index for figure-eight choreographies of the planar equal mass three-body problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Hiroshi Fukuda, Hiroshi Ozaki, Toshiaki Fujiwara","submitted_at":"2017-10-13T08:25:02Z","abstract_excerpt":"We report on numerical calculations of Morse index for figure-eight choreographic solutions to a system of three identical bodies in a plane interacting through homogeneous potential, $-1/r^a$, or through Lennard-Jones-type (LJ) potential, $1/r^{12} - 1/r^6$, where $r$ is a distance between the bodies. The Morse index is a number of independent variational functions giving negative second variation $S^{(2)}$ of action functional $S$. We calculated three kinds of Morse indices, $N$, $N_c$ and $N_e$, in the domain of the periodic, the choreographic and the figure-eight choreographic function, re"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1710.04834","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-10-13T08:25:02Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"22a0185576951de8d516997070fa5f93df745791881a5cd78eea58bfee945164","abstract_canon_sha256":"fc29a541a1c88441a0648f96df724010c137d2285bcf6de4e4bd8c686d4a69cc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:58.764857Z","signature_b64":"K0q5WDy9OnWlBbW7TfC4TiZ2zfDVMURzfuBUxeI74s1/+Fky1+1nW4cIwv9rx+zUTQ/aDMFDjZJWvoz7MjwNCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"376dbfa8d44a1aa8b191ec966b828b72c2094c777630883f9971bf58f06c7559","last_reissued_at":"2026-05-17T23:56:58.764336Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:58.764336Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Morse index for figure-eight choreographies of the planar equal mass three-body problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Hiroshi Fukuda, Hiroshi Ozaki, Toshiaki Fujiwara","submitted_at":"2017-10-13T08:25:02Z","abstract_excerpt":"We report on numerical calculations of Morse index for figure-eight choreographic solutions to a system of three identical bodies in a plane interacting through homogeneous potential, $-1/r^a$, or through Lennard-Jones-type (LJ) potential, $1/r^{12} - 1/r^6$, where $r$ is a distance between the bodies. The Morse index is a number of independent variational functions giving negative second variation $S^{(2)}$ of action functional $S$. We calculated three kinds of Morse indices, $N$, $N_c$ and $N_e$, in the domain of the periodic, the choreographic and the figure-eight choreographic function, re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.04834","kind":"arxiv","version":4},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1710.04834","created_at":"2026-05-17T23:56:58.764422+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.04834v4","created_at":"2026-05-17T23:56:58.764422+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.04834","created_at":"2026-05-17T23:56:58.764422+00:00"},{"alias_kind":"pith_short_12","alias_value":"G5W37KGUJINK","created_at":"2026-05-18T12:31:15.632608+00:00"},{"alias_kind":"pith_short_16","alias_value":"G5W37KGUJINKRMMR","created_at":"2026-05-18T12:31:15.632608+00:00"},{"alias_kind":"pith_short_8","alias_value":"G5W37KGU","created_at":"2026-05-18T12:31:15.632608+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/G5W37KGUJINKRMMR5SLGXAULOL","json":"https://pith.science/pith/G5W37KGUJINKRMMR5SLGXAULOL.json","graph_json":"https://pith.science/api/pith-number/G5W37KGUJINKRMMR5SLGXAULOL/graph.json","events_json":"https://pith.science/api/pith-number/G5W37KGUJINKRMMR5SLGXAULOL/events.json","paper":"https://pith.science/paper/G5W37KGU"},"agent_actions":{"view_html":"https://pith.science/pith/G5W37KGUJINKRMMR5SLGXAULOL","download_json":"https://pith.science/pith/G5W37KGUJINKRMMR5SLGXAULOL.json","view_paper":"https://pith.science/paper/G5W37KGU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.04834&json=true","fetch_graph":"https://pith.science/api/pith-number/G5W37KGUJINKRMMR5SLGXAULOL/graph.json","fetch_events":"https://pith.science/api/pith-number/G5W37KGUJINKRMMR5SLGXAULOL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/G5W37KGUJINKRMMR5SLGXAULOL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/G5W37KGUJINKRMMR5SLGXAULOL/action/storage_attestation","attest_author":"https://pith.science/pith/G5W37KGUJINKRMMR5SLGXAULOL/action/author_attestation","sign_citation":"https://pith.science/pith/G5W37KGUJINKRMMR5SLGXAULOL/action/citation_signature","submit_replication":"https://pith.science/pith/G5W37KGUJINKRMMR5SLGXAULOL/action/replication_record"}},"created_at":"2026-05-17T23:56:58.764422+00:00","updated_at":"2026-05-17T23:56:58.764422+00:00"}