{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:AD3SJX44FDC7YREK7LWUQYG2MN","short_pith_number":"pith:AD3SJX44","canonical_record":{"source":{"id":"1608.07956","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-08-29T09:06:50Z","cross_cats_sorted":[],"title_canon_sha256":"de801d9db7f0d636a1d966d54350d4b3f41b0f7ebb2da29505809b1dead13ed0","abstract_canon_sha256":"20499505c5519c90eee7c05d2b534f7cbd3ce0b18e1dc29f4c49e55b1c5e48ab"},"schema_version":"1.0"},"canonical_sha256":"00f724df9c28c5fc448afaed4860da637b151a47a041e320bf8c432dbf0b1c9f","source":{"kind":"arxiv","id":"1608.07956","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.07956","created_at":"2026-05-18T00:26:12Z"},{"alias_kind":"arxiv_version","alias_value":"1608.07956v2","created_at":"2026-05-18T00:26:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.07956","created_at":"2026-05-18T00:26:12Z"},{"alias_kind":"pith_short_12","alias_value":"AD3SJX44FDC7","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"AD3SJX44FDC7YREK","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"AD3SJX44","created_at":"2026-05-18T12:30:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:AD3SJX44FDC7YREK7LWUQYG2MN","target":"record","payload":{"canonical_record":{"source":{"id":"1608.07956","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-08-29T09:06:50Z","cross_cats_sorted":[],"title_canon_sha256":"de801d9db7f0d636a1d966d54350d4b3f41b0f7ebb2da29505809b1dead13ed0","abstract_canon_sha256":"20499505c5519c90eee7c05d2b534f7cbd3ce0b18e1dc29f4c49e55b1c5e48ab"},"schema_version":"1.0"},"canonical_sha256":"00f724df9c28c5fc448afaed4860da637b151a47a041e320bf8c432dbf0b1c9f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:12.988808Z","signature_b64":"nuf1xpY3cIXB9Y00VWph6puPxcQpzOQdzY3cWlMtk9A6pn0xsnHXrLJTa2krPx/M2PIu0IVPLZPyzRTDwTRnAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"00f724df9c28c5fc448afaed4860da637b151a47a041e320bf8c432dbf0b1c9f","last_reissued_at":"2026-05-18T00:26:12.988285Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:12.988285Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.07956","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":"2026-05-18T00:26:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0PKvUiw5Z9KYeZKzFS/eycYeZZf2FW8+W+aU4360ropDi/MxLhAiE9EsJiePI/TOVwTdHpFngWrSZ6AOjtkOCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T08:52:06.359154Z"},"content_sha256":"033d5cd6cbec57899659c942c26a195e35220bd6188d537bfe7eb8c0a60bd815","schema_version":"1.0","event_id":"sha256:033d5cd6cbec57899659c942c26a195e35220bd6188d537bfe7eb8c0a60bd815"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:AD3SJX44FDC7YREK7LWUQYG2MN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spatial double choreographies of the Newtonian $2n$-body problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Guowei Yu","submitted_at":"2016-08-29T09:06:50Z","abstract_excerpt":"In this paper, for the spatial Newtonian $2n$-body problem with equal masses, by proving the minimizers of the action functional under certain symmetric, topological and monotone constraints are collision-free, we found a family of spatial double choreographies, which have the common feature that half of the masses are circling around the $z$-axis clockwise along a spatial loop, while the motions of the other half masses are given by a rotation of the first half around the $x$-axis by $\\pi$. Both loops are simple, without any self-intersection, and symmetric with respect to the $xz$-plane and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.07956","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":"2026-05-18T00:26:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NIWp2iisX34ACU7xjUQfNxmpix0TWunmRwO0KyV3T1VbRwmsXc5x7oyBeKDQ7PPO1fIo3n3Gn5tKAHkb+XbcBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T08:52:06.359850Z"},"content_sha256":"77023f379377cda0f311bf435686a39c7ee5f639f82da5d6cf3848c07db4277f","schema_version":"1.0","event_id":"sha256:77023f379377cda0f311bf435686a39c7ee5f639f82da5d6cf3848c07db4277f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AD3SJX44FDC7YREK7LWUQYG2MN/bundle.json","state_url":"https://pith.science/pith/AD3SJX44FDC7YREK7LWUQYG2MN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AD3SJX44FDC7YREK7LWUQYG2MN/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":"2026-05-27T08:52:06Z","links":{"resolver":"https://pith.science/pith/AD3SJX44FDC7YREK7LWUQYG2MN","bundle":"https://pith.science/pith/AD3SJX44FDC7YREK7LWUQYG2MN/bundle.json","state":"https://pith.science/pith/AD3SJX44FDC7YREK7LWUQYG2MN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AD3SJX44FDC7YREK7LWUQYG2MN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:AD3SJX44FDC7YREK7LWUQYG2MN","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":"20499505c5519c90eee7c05d2b534f7cbd3ce0b18e1dc29f4c49e55b1c5e48ab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-08-29T09:06:50Z","title_canon_sha256":"de801d9db7f0d636a1d966d54350d4b3f41b0f7ebb2da29505809b1dead13ed0"},"schema_version":"1.0","source":{"id":"1608.07956","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.07956","created_at":"2026-05-18T00:26:12Z"},{"alias_kind":"arxiv_version","alias_value":"1608.07956v2","created_at":"2026-05-18T00:26:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.07956","created_at":"2026-05-18T00:26:12Z"},{"alias_kind":"pith_short_12","alias_value":"AD3SJX44FDC7","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"AD3SJX44FDC7YREK","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"AD3SJX44","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:77023f379377cda0f311bf435686a39c7ee5f639f82da5d6cf3848c07db4277f","target":"graph","created_at":"2026-05-18T00:26:12Z","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 paper, for the spatial Newtonian $2n$-body problem with equal masses, by proving the minimizers of the action functional under certain symmetric, topological and monotone constraints are collision-free, we found a family of spatial double choreographies, which have the common feature that half of the masses are circling around the $z$-axis clockwise along a spatial loop, while the motions of the other half masses are given by a rotation of the first half around the $x$-axis by $\\pi$. Both loops are simple, without any self-intersection, and symmetric with respect to the $xz$-plane and ","authors_text":"Guowei Yu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-08-29T09:06:50Z","title":"Spatial double choreographies of the Newtonian $2n$-body problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.07956","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":"sha256:033d5cd6cbec57899659c942c26a195e35220bd6188d537bfe7eb8c0a60bd815","target":"record","created_at":"2026-05-18T00:26:12Z","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":"20499505c5519c90eee7c05d2b534f7cbd3ce0b18e1dc29f4c49e55b1c5e48ab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-08-29T09:06:50Z","title_canon_sha256":"de801d9db7f0d636a1d966d54350d4b3f41b0f7ebb2da29505809b1dead13ed0"},"schema_version":"1.0","source":{"id":"1608.07956","kind":"arxiv","version":2}},"canonical_sha256":"00f724df9c28c5fc448afaed4860da637b151a47a041e320bf8c432dbf0b1c9f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"00f724df9c28c5fc448afaed4860da637b151a47a041e320bf8c432dbf0b1c9f","first_computed_at":"2026-05-18T00:26:12.988285Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:12.988285Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nuf1xpY3cIXB9Y00VWph6puPxcQpzOQdzY3cWlMtk9A6pn0xsnHXrLJTa2krPx/M2PIu0IVPLZPyzRTDwTRnAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:12.988808Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.07956","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:033d5cd6cbec57899659c942c26a195e35220bd6188d537bfe7eb8c0a60bd815","sha256:77023f379377cda0f311bf435686a39c7ee5f639f82da5d6cf3848c07db4277f"],"state_sha256":"a26ecdb83ee8eca23dc471a414c7d0e195205f92f9c3ecee7514942fb516ee3d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9j7CYaRP2Pl9+0smKGQvIlvGji58HIMJLibaL+lqihU9ANKyR8xlkFFQYp+tjRuxfTaeNzrelv6GQDarvcLyDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T08:52:06.363573Z","bundle_sha256":"6da22ac051fef442726314ad51b07961e2f48f62ec36b006040ddc50a91b7f56"}}