{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:OY2E3KZKUXF2ZXUYNYRE6J7MKU","short_pith_number":"pith:OY2E3KZK","canonical_record":{"source":{"id":"1804.06920","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.IM","submitted_at":"2018-04-18T21:22:44Z","cross_cats_sorted":["astro-ph.GA"],"title_canon_sha256":"cf111a0fce610cbd343be8bf0bf6ac1fa12622ac98878c4ceb77cd58ffb599f8","abstract_canon_sha256":"554d6592facef47ea907af72768f49882e69fffd8fe3620ccea243e22f7bd773"},"schema_version":"1.0"},"canonical_sha256":"76344dab2aa5cbacde986e224f27ec552523b063eb261a67220462456da6a1fe","source":{"kind":"arxiv","id":"1804.06920","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.06920","created_at":"2026-05-17T23:55:59Z"},{"alias_kind":"arxiv_version","alias_value":"1804.06920v2","created_at":"2026-05-17T23:55:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.06920","created_at":"2026-05-17T23:55:59Z"},{"alias_kind":"pith_short_12","alias_value":"OY2E3KZKUXF2","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"OY2E3KZKUXF2ZXUY","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"OY2E3KZK","created_at":"2026-05-18T12:32:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:OY2E3KZKUXF2ZXUYNYRE6J7MKU","target":"record","payload":{"canonical_record":{"source":{"id":"1804.06920","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.IM","submitted_at":"2018-04-18T21:22:44Z","cross_cats_sorted":["astro-ph.GA"],"title_canon_sha256":"cf111a0fce610cbd343be8bf0bf6ac1fa12622ac98878c4ceb77cd58ffb599f8","abstract_canon_sha256":"554d6592facef47ea907af72768f49882e69fffd8fe3620ccea243e22f7bd773"},"schema_version":"1.0"},"canonical_sha256":"76344dab2aa5cbacde986e224f27ec552523b063eb261a67220462456da6a1fe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:59.084080Z","signature_b64":"DoXEQtIvF0Swwy//HM/xFgkMuDxY33qjpxY2skhbSemdC6kUFa188gt/ZHD+mBDrbcSlL5mdF2kyz8rAUvzgAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"76344dab2aa5cbacde986e224f27ec552523b063eb261a67220462456da6a1fe","last_reissued_at":"2026-05-17T23:55:59.083523Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:59.083523Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.06920","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":"2026-05-17T23:55:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/aN7dsOwQmdnWSl7PzFqn3HQHd36ZwemIalp/+0lHoK+BWZWPCxVT9+xaypbGNbXgswErObDfw1SG5QWffEfAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T12:07:39.151071Z"},"content_sha256":"e8c31d90eaee0bbf78d4adeaec483c44e998c16b0457e4962deeffda85dd6d2a","schema_version":"1.0","event_id":"sha256:e8c31d90eaee0bbf78d4adeaec483c44e998c16b0457e4962deeffda85dd6d2a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:OY2E3KZKUXF2ZXUYNYRE6J7MKU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Errors, chaos and the collisionless limit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.GA"],"primary_cat":"astro-ph.IM","authors_text":"Amr El-Zant, Mark Everitt, Summer Kassem","submitted_at":"2018-04-18T21:22:44Z","abstract_excerpt":"We simultaneously study the dynamics of the growth of errors and the question of the faithfulness of simulations of $N$-body systems. The errors are quantified through the numerical reversibility of small-$N$ spherical systems, and by comparing fixed-timestep runs with different stepsizes. The errors add randomly, before exponential divergence sets in, with exponentiation rate virtually independent of $N$, but scale saturating as $\\sim 1/\\sqrt{N}$, in line with theoretical estimates presented. In a third phase, the growth rate is initially driven by multiplicative enhancement of errors, as in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.06920","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":"2026-05-17T23:55:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HszPXCTVUdtDAUN15O2lRy2aIt1yzk2n64zQO5dr1eyuFEe9hQjq4ubXCFIg9FTDQeCeLYz0yEbBXil/dbFZBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T12:07:39.151559Z"},"content_sha256":"71a33b42e78cab2cc9eaaaa7bba5c7e5d100bb7778b38180623a976e2258995f","schema_version":"1.0","event_id":"sha256:71a33b42e78cab2cc9eaaaa7bba5c7e5d100bb7778b38180623a976e2258995f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OY2E3KZKUXF2ZXUYNYRE6J7MKU/bundle.json","state_url":"https://pith.science/pith/OY2E3KZKUXF2ZXUYNYRE6J7MKU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OY2E3KZKUXF2ZXUYNYRE6J7MKU/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":"2026-07-04T12:07:39Z","links":{"resolver":"https://pith.science/pith/OY2E3KZKUXF2ZXUYNYRE6J7MKU","bundle":"https://pith.science/pith/OY2E3KZKUXF2ZXUYNYRE6J7MKU/bundle.json","state":"https://pith.science/pith/OY2E3KZKUXF2ZXUYNYRE6J7MKU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OY2E3KZKUXF2ZXUYNYRE6J7MKU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:OY2E3KZKUXF2ZXUYNYRE6J7MKU","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":"554d6592facef47ea907af72768f49882e69fffd8fe3620ccea243e22f7bd773","cross_cats_sorted":["astro-ph.GA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.IM","submitted_at":"2018-04-18T21:22:44Z","title_canon_sha256":"cf111a0fce610cbd343be8bf0bf6ac1fa12622ac98878c4ceb77cd58ffb599f8"},"schema_version":"1.0","source":{"id":"1804.06920","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.06920","created_at":"2026-05-17T23:55:59Z"},{"alias_kind":"arxiv_version","alias_value":"1804.06920v2","created_at":"2026-05-17T23:55:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.06920","created_at":"2026-05-17T23:55:59Z"},{"alias_kind":"pith_short_12","alias_value":"OY2E3KZKUXF2","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"OY2E3KZKUXF2ZXUY","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"OY2E3KZK","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:71a33b42e78cab2cc9eaaaa7bba5c7e5d100bb7778b38180623a976e2258995f","target":"graph","created_at":"2026-05-17T23:55:59Z","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"},"paper":{"abstract_excerpt":"We simultaneously study the dynamics of the growth of errors and the question of the faithfulness of simulations of $N$-body systems. The errors are quantified through the numerical reversibility of small-$N$ spherical systems, and by comparing fixed-timestep runs with different stepsizes. The errors add randomly, before exponential divergence sets in, with exponentiation rate virtually independent of $N$, but scale saturating as $\\sim 1/\\sqrt{N}$, in line with theoretical estimates presented. In a third phase, the growth rate is initially driven by multiplicative enhancement of errors, as in ","authors_text":"Amr El-Zant, Mark Everitt, Summer Kassem","cross_cats":["astro-ph.GA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.IM","submitted_at":"2018-04-18T21:22:44Z","title":"Errors, chaos and the collisionless limit"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.06920","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:e8c31d90eaee0bbf78d4adeaec483c44e998c16b0457e4962deeffda85dd6d2a","target":"record","created_at":"2026-05-17T23:55:59Z","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":"554d6592facef47ea907af72768f49882e69fffd8fe3620ccea243e22f7bd773","cross_cats_sorted":["astro-ph.GA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.IM","submitted_at":"2018-04-18T21:22:44Z","title_canon_sha256":"cf111a0fce610cbd343be8bf0bf6ac1fa12622ac98878c4ceb77cd58ffb599f8"},"schema_version":"1.0","source":{"id":"1804.06920","kind":"arxiv","version":2}},"canonical_sha256":"76344dab2aa5cbacde986e224f27ec552523b063eb261a67220462456da6a1fe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"76344dab2aa5cbacde986e224f27ec552523b063eb261a67220462456da6a1fe","first_computed_at":"2026-05-17T23:55:59.083523Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:59.083523Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DoXEQtIvF0Swwy//HM/xFgkMuDxY33qjpxY2skhbSemdC6kUFa188gt/ZHD+mBDrbcSlL5mdF2kyz8rAUvzgAA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:59.084080Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.06920","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e8c31d90eaee0bbf78d4adeaec483c44e998c16b0457e4962deeffda85dd6d2a","sha256:71a33b42e78cab2cc9eaaaa7bba5c7e5d100bb7778b38180623a976e2258995f"],"state_sha256":"cf0dbd2ed0822588511588505ba468d6f4ef097deec91ff4a4e8609f45b8af85"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9ogxBhAj6jGA+bv1kazqMsDNuTWbn/B378+XhVDXar+ZPdZSwzqgBR7VszePf1eLOMsgSIUl0kT+bHxFv3PEBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T12:07:39.153453Z","bundle_sha256":"8ff5771242be09bf3f9c591474538e2bfd42858c596b395f3d67d0cce2e02016"}}