{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:VS3OIUS4LTUTOP5MTJWJ3RYEC3","short_pith_number":"pith:VS3OIUS4","canonical_record":{"source":{"id":"1506.01084","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2015-06-02T23:18:59Z","cross_cats_sorted":["astro-ph.IM","math.NA","nlin.CD","physics.comp-ph"],"title_canon_sha256":"1bb40ae25e425e94343951f2fbc9d19a47eb106fbbd0df1c82e1d93f5ecfb968","abstract_canon_sha256":"119bb695932f857c4b9f3da0ae5e27777955f6a0cd99180f2fa14c988fc6f879"},"schema_version":"1.0"},"canonical_sha256":"acb6e4525c5ce9373fac9a6c9dc70416d7a930c4e9305ca3feea990971b737fc","source":{"kind":"arxiv","id":"1506.01084","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.01084","created_at":"2026-05-18T01:36:53Z"},{"alias_kind":"arxiv_version","alias_value":"1506.01084v1","created_at":"2026-05-18T01:36:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.01084","created_at":"2026-05-18T01:36:53Z"},{"alias_kind":"pith_short_12","alias_value":"VS3OIUS4LTUT","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"VS3OIUS4LTUTOP5M","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"VS3OIUS4","created_at":"2026-05-18T12:29:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:VS3OIUS4LTUTOP5MTJWJ3RYEC3","target":"record","payload":{"canonical_record":{"source":{"id":"1506.01084","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2015-06-02T23:18:59Z","cross_cats_sorted":["astro-ph.IM","math.NA","nlin.CD","physics.comp-ph"],"title_canon_sha256":"1bb40ae25e425e94343951f2fbc9d19a47eb106fbbd0df1c82e1d93f5ecfb968","abstract_canon_sha256":"119bb695932f857c4b9f3da0ae5e27777955f6a0cd99180f2fa14c988fc6f879"},"schema_version":"1.0"},"canonical_sha256":"acb6e4525c5ce9373fac9a6c9dc70416d7a930c4e9305ca3feea990971b737fc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:53.119713Z","signature_b64":"BRx65EoB6KY7OcDKVXNJZeUaPuiy64yBncteHZ+HWvT06blCObBju59e9omJcSdrNhFul0MJLE9kC1lNtlpZDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"acb6e4525c5ce9373fac9a6c9dc70416d7a930c4e9305ca3feea990971b737fc","last_reissued_at":"2026-05-18T01:36:53.119246Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:53.119246Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.01084","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:36:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rqvl0u4ZJS2dEgnSW8xN/+i9sLhBs7Y/CitFWLn5XWbbb20HJVrDERI18Ss7d6yeKbYCZ+YY/QlsDSt9Tq+hAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T21:15:28.028584Z"},"content_sha256":"3e18d93c7e72f80dcd07fd9dab299f2ac782d84500cc996ea1c08d0eb4360b1b","schema_version":"1.0","event_id":"sha256:3e18d93c7e72f80dcd07fd9dab299f2ac782d84500cc996ea1c08d0eb4360b1b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:VS3OIUS4LTUTOP5MTJWJ3RYEC3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"WHFast: A fast and unbiased implementation of a symplectic Wisdom-Holman integrator for long term gravitational simulations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.IM","math.NA","nlin.CD","physics.comp-ph"],"primary_cat":"astro-ph.EP","authors_text":"Daniel Tamayo, Hanno Rein","submitted_at":"2015-06-02T23:18:59Z","abstract_excerpt":"We present WHFast, a fast and accurate implementation of a Wisdom-Holman symplectic integrator for long-term orbit integrations of planetary systems. WHFast is significantly faster and conserves energy better than all other Wisdom-Holman integrators tested. We achieve this by significantly improving the Kepler-solver and ensuring numerical stability of coordinate transformations to and from Jacobi coordinates. These refinements allow us to remove the linear secular trend in the energy error that is present in other implementations. For small enough timesteps we achieve Brouwer's law, i.e. the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.01084","kind":"arxiv","version":1},"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":"2026-05-18T01:36:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+LUm5DBTWZSxky6AyI3xOszt4+ZD07CFgA/lt5u/NfD4NLmuyrBAfQhOuibwV7KV/ctMdZWAdoh8HfWl/Jl0Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T21:15:28.029279Z"},"content_sha256":"62b25b370b012f4390672d534a76ab1c844021523a10ee79017fa2ea7701b287","schema_version":"1.0","event_id":"sha256:62b25b370b012f4390672d534a76ab1c844021523a10ee79017fa2ea7701b287"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VS3OIUS4LTUTOP5MTJWJ3RYEC3/bundle.json","state_url":"https://pith.science/pith/VS3OIUS4LTUTOP5MTJWJ3RYEC3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VS3OIUS4LTUTOP5MTJWJ3RYEC3/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":"2026-06-06T21:15:28Z","links":{"resolver":"https://pith.science/pith/VS3OIUS4LTUTOP5MTJWJ3RYEC3","bundle":"https://pith.science/pith/VS3OIUS4LTUTOP5MTJWJ3RYEC3/bundle.json","state":"https://pith.science/pith/VS3OIUS4LTUTOP5MTJWJ3RYEC3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VS3OIUS4LTUTOP5MTJWJ3RYEC3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:VS3OIUS4LTUTOP5MTJWJ3RYEC3","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":"119bb695932f857c4b9f3da0ae5e27777955f6a0cd99180f2fa14c988fc6f879","cross_cats_sorted":["astro-ph.IM","math.NA","nlin.CD","physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2015-06-02T23:18:59Z","title_canon_sha256":"1bb40ae25e425e94343951f2fbc9d19a47eb106fbbd0df1c82e1d93f5ecfb968"},"schema_version":"1.0","source":{"id":"1506.01084","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.01084","created_at":"2026-05-18T01:36:53Z"},{"alias_kind":"arxiv_version","alias_value":"1506.01084v1","created_at":"2026-05-18T01:36:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.01084","created_at":"2026-05-18T01:36:53Z"},{"alias_kind":"pith_short_12","alias_value":"VS3OIUS4LTUT","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"VS3OIUS4LTUTOP5M","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"VS3OIUS4","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:62b25b370b012f4390672d534a76ab1c844021523a10ee79017fa2ea7701b287","target":"graph","created_at":"2026-05-18T01:36:53Z","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 WHFast, a fast and accurate implementation of a Wisdom-Holman symplectic integrator for long-term orbit integrations of planetary systems. WHFast is significantly faster and conserves energy better than all other Wisdom-Holman integrators tested. We achieve this by significantly improving the Kepler-solver and ensuring numerical stability of coordinate transformations to and from Jacobi coordinates. These refinements allow us to remove the linear secular trend in the energy error that is present in other implementations. For small enough timesteps we achieve Brouwer's law, i.e. the ","authors_text":"Daniel Tamayo, Hanno Rein","cross_cats":["astro-ph.IM","math.NA","nlin.CD","physics.comp-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2015-06-02T23:18:59Z","title":"WHFast: A fast and unbiased implementation of a symplectic Wisdom-Holman integrator for long term gravitational simulations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.01084","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":"sha256:3e18d93c7e72f80dcd07fd9dab299f2ac782d84500cc996ea1c08d0eb4360b1b","target":"record","created_at":"2026-05-18T01:36:53Z","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":"119bb695932f857c4b9f3da0ae5e27777955f6a0cd99180f2fa14c988fc6f879","cross_cats_sorted":["astro-ph.IM","math.NA","nlin.CD","physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2015-06-02T23:18:59Z","title_canon_sha256":"1bb40ae25e425e94343951f2fbc9d19a47eb106fbbd0df1c82e1d93f5ecfb968"},"schema_version":"1.0","source":{"id":"1506.01084","kind":"arxiv","version":1}},"canonical_sha256":"acb6e4525c5ce9373fac9a6c9dc70416d7a930c4e9305ca3feea990971b737fc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"acb6e4525c5ce9373fac9a6c9dc70416d7a930c4e9305ca3feea990971b737fc","first_computed_at":"2026-05-18T01:36:53.119246Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:53.119246Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BRx65EoB6KY7OcDKVXNJZeUaPuiy64yBncteHZ+HWvT06blCObBju59e9omJcSdrNhFul0MJLE9kC1lNtlpZDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:53.119713Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.01084","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3e18d93c7e72f80dcd07fd9dab299f2ac782d84500cc996ea1c08d0eb4360b1b","sha256:62b25b370b012f4390672d534a76ab1c844021523a10ee79017fa2ea7701b287"],"state_sha256":"d239f8bfec4354adeb7b59aa7ed8c01516ad1c37d676fa0554c65c754a4e5595"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fXwzCzcCekQUmjA8CHVZ7HBp6hj0TOAJXehkjtYvRY9jaDWwJ0TXNBLnfMfz2pKM3ti3YHDyV3v6eaiyfBuxBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T21:15:28.032904Z","bundle_sha256":"966a480074965417dcfd9f758b19e6fbd7ed0f6256cdddab06d3544dffb12102"}}