{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:UKLNAPMNYEUZGM375F7PV5KWQ7","short_pith_number":"pith:UKLNAPMN","canonical_record":{"source":{"id":"1209.5173","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-09-24T07:33:19Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"4fa96f933973daea30a1d051c22533242c193f8fb184a6736d0db159ce328436","abstract_canon_sha256":"e2193e8508a49628f94e52008031774acb0ecf13bf5e2bd16304d199f587df90"},"schema_version":"1.0"},"canonical_sha256":"a296d03d8dc12993337fe97efaf55687ca4c98096ff321d163293801ebb7182e","source":{"kind":"arxiv","id":"1209.5173","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.5173","created_at":"2026-05-18T03:44:58Z"},{"alias_kind":"arxiv_version","alias_value":"1209.5173v1","created_at":"2026-05-18T03:44:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.5173","created_at":"2026-05-18T03:44:58Z"},{"alias_kind":"pith_short_12","alias_value":"UKLNAPMNYEUZ","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"UKLNAPMNYEUZGM37","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"UKLNAPMN","created_at":"2026-05-18T12:27:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:UKLNAPMNYEUZGM375F7PV5KWQ7","target":"record","payload":{"canonical_record":{"source":{"id":"1209.5173","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-09-24T07:33:19Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"4fa96f933973daea30a1d051c22533242c193f8fb184a6736d0db159ce328436","abstract_canon_sha256":"e2193e8508a49628f94e52008031774acb0ecf13bf5e2bd16304d199f587df90"},"schema_version":"1.0"},"canonical_sha256":"a296d03d8dc12993337fe97efaf55687ca4c98096ff321d163293801ebb7182e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:44:58.995091Z","signature_b64":"4Or7WNvVr0/9jYRxBEmf12/VjBagkMTBwil0Of3yXZbHwfkrvSqCb+e3ujKOzwXzGNBkmwh6XZpnS7g3p0TkBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a296d03d8dc12993337fe97efaf55687ca4c98096ff321d163293801ebb7182e","last_reissued_at":"2026-05-18T03:44:58.994295Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:44:58.994295Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.5173","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":"2026-05-18T03:44:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ux3wNGWAsTeaUAMoxGKgxZu/W78iQY5uJKJdaJYlp85yfDkf+gV4vTsNVuZ4+as3zBbhrjT4GNkolCc3FasHCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T08:21:02.331698Z"},"content_sha256":"720318f9ea389a21fe3ba9bf9b73a3ea2236a62c0d40d363ecb725e22b4e3660","schema_version":"1.0","event_id":"sha256:720318f9ea389a21fe3ba9bf9b73a3ea2236a62c0d40d363ecb725e22b4e3660"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:UKLNAPMNYEUZGM375F7PV5KWQ7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Parametric Instability Caused by Step Size Variation in Runge-Kutta-Nystr\\\"om Methods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Robert Pich\\'e","submitted_at":"2012-09-24T07:33:19Z","abstract_excerpt":"The parametric instability arising when ordinary differential equations (ODEs) are numerically integrated with Runge-Kutta-Nystr\\\"om (RKN) methods with varying step sizes is investigated. It is shown that when linear constant coefficient ODEs are integrated with RKN methods that are based on A-stable Runge-Kutta methods, the solution is nonincreasing in some norm for all positive step sizes, constant or varying. Perturbation methods are used to quantify the critical step sizes associated with parametric instability."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.5173","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":"2026-05-18T03:44:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Aj8vGpjB2CW7Q3V2kFI+mMMSpQR0CLnYOdH3kONMeZoYotDw7DO250ptvWcw35nokhYfx4iChpW+Ch9IhxQ+Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T08:21:02.332048Z"},"content_sha256":"e631cc0bd9f660fb41a5a6444b647013d97229f9bbeaa8bf098860ec88c4969a","schema_version":"1.0","event_id":"sha256:e631cc0bd9f660fb41a5a6444b647013d97229f9bbeaa8bf098860ec88c4969a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UKLNAPMNYEUZGM375F7PV5KWQ7/bundle.json","state_url":"https://pith.science/pith/UKLNAPMNYEUZGM375F7PV5KWQ7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UKLNAPMNYEUZGM375F7PV5KWQ7/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":"2026-06-20T08:21:02Z","links":{"resolver":"https://pith.science/pith/UKLNAPMNYEUZGM375F7PV5KWQ7","bundle":"https://pith.science/pith/UKLNAPMNYEUZGM375F7PV5KWQ7/bundle.json","state":"https://pith.science/pith/UKLNAPMNYEUZGM375F7PV5KWQ7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UKLNAPMNYEUZGM375F7PV5KWQ7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:UKLNAPMNYEUZGM375F7PV5KWQ7","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":"e2193e8508a49628f94e52008031774acb0ecf13bf5e2bd16304d199f587df90","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-09-24T07:33:19Z","title_canon_sha256":"4fa96f933973daea30a1d051c22533242c193f8fb184a6736d0db159ce328436"},"schema_version":"1.0","source":{"id":"1209.5173","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.5173","created_at":"2026-05-18T03:44:58Z"},{"alias_kind":"arxiv_version","alias_value":"1209.5173v1","created_at":"2026-05-18T03:44:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.5173","created_at":"2026-05-18T03:44:58Z"},{"alias_kind":"pith_short_12","alias_value":"UKLNAPMNYEUZ","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"UKLNAPMNYEUZGM37","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"UKLNAPMN","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:e631cc0bd9f660fb41a5a6444b647013d97229f9bbeaa8bf098860ec88c4969a","target":"graph","created_at":"2026-05-18T03:44:58Z","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":"The parametric instability arising when ordinary differential equations (ODEs) are numerically integrated with Runge-Kutta-Nystr\\\"om (RKN) methods with varying step sizes is investigated. It is shown that when linear constant coefficient ODEs are integrated with RKN methods that are based on A-stable Runge-Kutta methods, the solution is nonincreasing in some norm for all positive step sizes, constant or varying. Perturbation methods are used to quantify the critical step sizes associated with parametric instability.","authors_text":"Robert Pich\\'e","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-09-24T07:33:19Z","title":"On the Parametric Instability Caused by Step Size Variation in Runge-Kutta-Nystr\\\"om Methods"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.5173","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":"sha256:720318f9ea389a21fe3ba9bf9b73a3ea2236a62c0d40d363ecb725e22b4e3660","target":"record","created_at":"2026-05-18T03:44:58Z","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":"e2193e8508a49628f94e52008031774acb0ecf13bf5e2bd16304d199f587df90","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-09-24T07:33:19Z","title_canon_sha256":"4fa96f933973daea30a1d051c22533242c193f8fb184a6736d0db159ce328436"},"schema_version":"1.0","source":{"id":"1209.5173","kind":"arxiv","version":1}},"canonical_sha256":"a296d03d8dc12993337fe97efaf55687ca4c98096ff321d163293801ebb7182e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a296d03d8dc12993337fe97efaf55687ca4c98096ff321d163293801ebb7182e","first_computed_at":"2026-05-18T03:44:58.994295Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:44:58.994295Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4Or7WNvVr0/9jYRxBEmf12/VjBagkMTBwil0Of3yXZbHwfkrvSqCb+e3ujKOzwXzGNBkmwh6XZpnS7g3p0TkBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:44:58.995091Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.5173","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:720318f9ea389a21fe3ba9bf9b73a3ea2236a62c0d40d363ecb725e22b4e3660","sha256:e631cc0bd9f660fb41a5a6444b647013d97229f9bbeaa8bf098860ec88c4969a"],"state_sha256":"76e257ec6d2d596232760f4a39e987406492f48ec384f21129d3ac1079e38306"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zK0vKGOahflmQroreH7fDfqOtYJoKgVt/ju8EmJiHh6tHLx8buyc3ijNBWylBKVg/hXkKSz0dbMfwkWE8JGJBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T08:21:02.334071Z","bundle_sha256":"a4f37066025eb77be00579af94f6eaabdf2cf66ae0a7b990f795413cc9889f25"}}