{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:J4TR2L2SPT7ISK7TDSJERQOL56","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":"be702a46a9c2be30b866e0358587aa0b46948bd432b7f220d60fa6a928b849f8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-08-15T15:11:53Z","title_canon_sha256":"ccbe55502f0b079529e6be07be8709bc78e362b8cbdc427fd092cbf0f434b2b2"},"schema_version":"1.0","source":{"id":"1908.05576","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.05576","created_at":"2026-07-05T01:32:56Z"},{"alias_kind":"arxiv_version","alias_value":"1908.05576v1","created_at":"2026-07-05T01:32:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.05576","created_at":"2026-07-05T01:32:56Z"},{"alias_kind":"pith_short_12","alias_value":"J4TR2L2SPT7I","created_at":"2026-07-05T01:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"J4TR2L2SPT7ISK7T","created_at":"2026-07-05T01:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"J4TR2L2S","created_at":"2026-07-05T01:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:1e34acf63bf079562e94d8de08b682be3823e905e263eea13bfe26e91c87f6b6","target":"graph","created_at":"2026-07-05T01:32:56Z","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/1908.05576/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The singularity at a simultaneous binary collision is explored in the collinear 4-body problem. It is known that any attempt to remove the singularity via block regularisation will result in a regularised flow that is no more than $ C^{8/3} $ differentiable with respect to initial conditions. Through a blow-up of the singularity, this loss of differentiability is investigated and a new proof of the $ C^{8/3} $ regularity is provided. In the process, it is revealed that the collision manifold consists of two manifolds of normally hyperbolic saddle singularities which are connected by a manifold","authors_text":"Holger R. Dullin, Nathan Duignan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-08-15T15:11:53Z","title":"On the $ C^{8/3} $-Regularisation of Simultaneous Binary Collisions in the Collinear 4-Body Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.05576","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":"sha256:87db6d0decdf6aa378943ab7a45e70ee9dc26fa7cb58c6a1414a917c74daddb0","target":"record","created_at":"2026-07-05T01:32:56Z","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":"be702a46a9c2be30b866e0358587aa0b46948bd432b7f220d60fa6a928b849f8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-08-15T15:11:53Z","title_canon_sha256":"ccbe55502f0b079529e6be07be8709bc78e362b8cbdc427fd092cbf0f434b2b2"},"schema_version":"1.0","source":{"id":"1908.05576","kind":"arxiv","version":1}},"canonical_sha256":"4f271d2f527cfe892bf31c9248c1cbefbb2ca4615b9111d364eac1d79148699b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f271d2f527cfe892bf31c9248c1cbefbb2ca4615b9111d364eac1d79148699b","first_computed_at":"2026-07-05T01:32:56.458134Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:32:56.458134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Zm7icUf2n9ZnN+oqi3y6hA9znDCiaJnOFq2mhCu/sBJyMYclXyZXj5cDYxEYLHtNGrZR8AiWYD+bX4vZxqN3AQ==","signature_status":"signed_v1","signed_at":"2026-07-05T01:32:56.458528Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.05576","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:87db6d0decdf6aa378943ab7a45e70ee9dc26fa7cb58c6a1414a917c74daddb0","sha256:1e34acf63bf079562e94d8de08b682be3823e905e263eea13bfe26e91c87f6b6"],"state_sha256":"4a35f151cd9c979e4b106a61b8bcbf2f9f79ae206afe931ea094e3be76c7ef61"}