{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:UKXAXLJQSELGPOP27RCB2RBG3G","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":"1c18813cf20c39341d2a77687ce3f257570d99e8453d5c7ee0abdb2f307961b1","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2020-09-16T19:19:59Z","title_canon_sha256":"eeb958fec85438c11980b2bfbc5e36654afd6aee1d9602a8f280ec58b04b89ca"},"schema_version":"1.0","source":{"id":"2009.07901","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2009.07901","created_at":"2026-07-05T01:35:59Z"},{"alias_kind":"arxiv_version","alias_value":"2009.07901v1","created_at":"2026-07-05T01:35:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2009.07901","created_at":"2026-07-05T01:35:59Z"},{"alias_kind":"pith_short_12","alias_value":"UKXAXLJQSELG","created_at":"2026-07-05T01:35:59Z"},{"alias_kind":"pith_short_16","alias_value":"UKXAXLJQSELGPOP2","created_at":"2026-07-05T01:35:59Z"},{"alias_kind":"pith_short_8","alias_value":"UKXAXLJQ","created_at":"2026-07-05T01:35:59Z"}],"graph_snapshots":[{"event_id":"sha256:4f1aa48328303df607b44ed582d51c9adcee4ef8503553f6bbbed8f89bea3186","target":"graph","created_at":"2026-07-05T01:35:59Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2009.07901/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We take into account the Coulomb (N + 1)-body problem with N = 12, 24, 60. One of the particles has positive charge Q > 0, and the remaining N have all the same negative charge q < 0. These particles move under the Coulomb force, and the positive charge is assumed to be at rest at the center of mass. Imposing a symmetry constraint, given by the symmetry group of the Platonic polyhedra, we were able to compute periodic orbits, using a shooting method and continuation with respect to the value Q of the positive charge.\n  In the setting of the classical N -body problem, the existence of such orbi","authors_text":"\\`Angel Jorba, Marco Fenucci","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2020-09-16T19:19:59Z","title":"Braids with the symmetries of Platonic polyhedra in the Coulomb (N+1)-body problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.07901","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":"sha256:82923dcdadcda3744b7e01095c30c6f812e41fa3a7ad513b819f69317b921b85","target":"record","created_at":"2026-07-05T01:35:59Z","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":"1c18813cf20c39341d2a77687ce3f257570d99e8453d5c7ee0abdb2f307961b1","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2020-09-16T19:19:59Z","title_canon_sha256":"eeb958fec85438c11980b2bfbc5e36654afd6aee1d9602a8f280ec58b04b89ca"},"schema_version":"1.0","source":{"id":"2009.07901","kind":"arxiv","version":1}},"canonical_sha256":"a2ae0bad30911667b9fafc441d4426d9b67f569f67ac0920048fd30ccbf9fb19","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a2ae0bad30911667b9fafc441d4426d9b67f569f67ac0920048fd30ccbf9fb19","first_computed_at":"2026-07-05T01:35:59.447021Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:35:59.447021Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F+dI/+fIsIfe53goHIGae6wMRIvp02ltEan0bzTW31RaY4is/QLoRwH4hzBNi3327sHmmwO14kZBtxd6BDBoDg==","signature_status":"signed_v1","signed_at":"2026-07-05T01:35:59.447416Z","signed_message":"canonical_sha256_bytes"},"source_id":"2009.07901","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:82923dcdadcda3744b7e01095c30c6f812e41fa3a7ad513b819f69317b921b85","sha256:4f1aa48328303df607b44ed582d51c9adcee4ef8503553f6bbbed8f89bea3186"],"state_sha256":"f51a1517b5559abe3a88f53c12731ae912c5f0080a01a028560f556a82706b09"}