{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:M7AV75FZW6POJAVVMVQ7LMICDV","short_pith_number":"pith:M7AV75FZ","canonical_record":{"source":{"id":"1511.03054","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-11-10T10:37:08Z","cross_cats_sorted":[],"title_canon_sha256":"695d5a19c7fdae4bffaa28abeabf59d7d13f8771af102d0b09d34f4a0180a5b5","abstract_canon_sha256":"a39945040631224f6f155cf4df0f4c6dd9ed82b15f15967232fb45cc851ff1df"},"schema_version":"1.0"},"canonical_sha256":"67c15ff4b9b79ee482b56561f5b1021d79087f9a1e05e6afcdf18d90ff7130bc","source":{"kind":"arxiv","id":"1511.03054","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.03054","created_at":"2026-05-18T01:13:30Z"},{"alias_kind":"arxiv_version","alias_value":"1511.03054v2","created_at":"2026-05-18T01:13:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.03054","created_at":"2026-05-18T01:13:30Z"},{"alias_kind":"pith_short_12","alias_value":"M7AV75FZW6PO","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"M7AV75FZW6POJAVV","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"M7AV75FZ","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:M7AV75FZW6POJAVVMVQ7LMICDV","target":"record","payload":{"canonical_record":{"source":{"id":"1511.03054","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-11-10T10:37:08Z","cross_cats_sorted":[],"title_canon_sha256":"695d5a19c7fdae4bffaa28abeabf59d7d13f8771af102d0b09d34f4a0180a5b5","abstract_canon_sha256":"a39945040631224f6f155cf4df0f4c6dd9ed82b15f15967232fb45cc851ff1df"},"schema_version":"1.0"},"canonical_sha256":"67c15ff4b9b79ee482b56561f5b1021d79087f9a1e05e6afcdf18d90ff7130bc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:13:30.788376Z","signature_b64":"Jjo6l3wU0UyrBMGghPVUovwMvLsn4S2FBSNnQFHBm6tTVj5oXTN9jnhNKXFHmuw5skXtWSZ8g9xYrNHuPAwFCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"67c15ff4b9b79ee482b56561f5b1021d79087f9a1e05e6afcdf18d90ff7130bc","last_reissued_at":"2026-05-18T01:13:30.787885Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:13:30.787885Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.03054","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":"2026-05-18T01:13:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bYWFfw+/Hi+Ob2FwCisi1tukc6x6P7oYoyOs9d1KiGSOTKc2umHhKTTXyu3lF6hGo+vdrfRreN561a06n+hgAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T13:49:17.893277Z"},"content_sha256":"4b8809ebe8cfe93a3a9a019b0881c3c0f9ef2ccaccd200f19e5fe50516c83f88","schema_version":"1.0","event_id":"sha256:4b8809ebe8cfe93a3a9a019b0881c3c0f9ef2ccaccd200f19e5fe50516c83f88"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:M7AV75FZW6POJAVVMVQ7LMICDV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fast Sampling of Evolving Systems with Periodic Trajectories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"A.N. Gorban, I.Yu. Tyukin, J. Al Ameri, T.A. Tyukina, Yu.A. Korablev","submitted_at":"2015-11-10T10:37:08Z","abstract_excerpt":"We propose a novel method for fast and scalable evaluation of periodic solutions of systems of ordinary differential equations for a given set of parameter values and initial conditions. The equations governing the system dynamics are supposed to be of a special class, albeit admitting nonlinear parametrization and state nonlinearities. The method enables to represent a given periodic solution as sums of computable integrals and functions that are explicitly dependent on parameters of interest and initial conditions. This allows invoking parallel computational streams in order to increase spee"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.03054","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":"2026-05-18T01:13:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ROkJZzKQDbUmFF2LKrDvnnnnLsGZGsTKUqCoPLCL5H4GeMif4/qLOaAgrcaSR4jm0AnAPjtMm0PEZPsirsPgDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T13:49:17.893970Z"},"content_sha256":"10d78787e0d1830a0fbe349d413315f9b4fc55d1634b65f3fab9e7aabf83a2c0","schema_version":"1.0","event_id":"sha256:10d78787e0d1830a0fbe349d413315f9b4fc55d1634b65f3fab9e7aabf83a2c0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M7AV75FZW6POJAVVMVQ7LMICDV/bundle.json","state_url":"https://pith.science/pith/M7AV75FZW6POJAVVMVQ7LMICDV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M7AV75FZW6POJAVVMVQ7LMICDV/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":"2026-05-27T13:49:17Z","links":{"resolver":"https://pith.science/pith/M7AV75FZW6POJAVVMVQ7LMICDV","bundle":"https://pith.science/pith/M7AV75FZW6POJAVVMVQ7LMICDV/bundle.json","state":"https://pith.science/pith/M7AV75FZW6POJAVVMVQ7LMICDV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M7AV75FZW6POJAVVMVQ7LMICDV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:M7AV75FZW6POJAVVMVQ7LMICDV","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":"a39945040631224f6f155cf4df0f4c6dd9ed82b15f15967232fb45cc851ff1df","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-11-10T10:37:08Z","title_canon_sha256":"695d5a19c7fdae4bffaa28abeabf59d7d13f8771af102d0b09d34f4a0180a5b5"},"schema_version":"1.0","source":{"id":"1511.03054","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.03054","created_at":"2026-05-18T01:13:30Z"},{"alias_kind":"arxiv_version","alias_value":"1511.03054v2","created_at":"2026-05-18T01:13:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.03054","created_at":"2026-05-18T01:13:30Z"},{"alias_kind":"pith_short_12","alias_value":"M7AV75FZW6PO","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"M7AV75FZW6POJAVV","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"M7AV75FZ","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:10d78787e0d1830a0fbe349d413315f9b4fc55d1634b65f3fab9e7aabf83a2c0","target":"graph","created_at":"2026-05-18T01:13:30Z","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 propose a novel method for fast and scalable evaluation of periodic solutions of systems of ordinary differential equations for a given set of parameter values and initial conditions. The equations governing the system dynamics are supposed to be of a special class, albeit admitting nonlinear parametrization and state nonlinearities. The method enables to represent a given periodic solution as sums of computable integrals and functions that are explicitly dependent on parameters of interest and initial conditions. This allows invoking parallel computational streams in order to increase spee","authors_text":"A.N. Gorban, I.Yu. Tyukin, J. Al Ameri, T.A. Tyukina, Yu.A. Korablev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-11-10T10:37:08Z","title":"Fast Sampling of Evolving Systems with Periodic Trajectories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.03054","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":"sha256:4b8809ebe8cfe93a3a9a019b0881c3c0f9ef2ccaccd200f19e5fe50516c83f88","target":"record","created_at":"2026-05-18T01:13:30Z","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":"a39945040631224f6f155cf4df0f4c6dd9ed82b15f15967232fb45cc851ff1df","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-11-10T10:37:08Z","title_canon_sha256":"695d5a19c7fdae4bffaa28abeabf59d7d13f8771af102d0b09d34f4a0180a5b5"},"schema_version":"1.0","source":{"id":"1511.03054","kind":"arxiv","version":2}},"canonical_sha256":"67c15ff4b9b79ee482b56561f5b1021d79087f9a1e05e6afcdf18d90ff7130bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"67c15ff4b9b79ee482b56561f5b1021d79087f9a1e05e6afcdf18d90ff7130bc","first_computed_at":"2026-05-18T01:13:30.787885Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:13:30.787885Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Jjo6l3wU0UyrBMGghPVUovwMvLsn4S2FBSNnQFHBm6tTVj5oXTN9jnhNKXFHmuw5skXtWSZ8g9xYrNHuPAwFCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:13:30.788376Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.03054","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4b8809ebe8cfe93a3a9a019b0881c3c0f9ef2ccaccd200f19e5fe50516c83f88","sha256:10d78787e0d1830a0fbe349d413315f9b4fc55d1634b65f3fab9e7aabf83a2c0"],"state_sha256":"b53b403b371fcf08e65654d1c9e82d459a159bf5e840480fdc3e9ffac44a3072"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g9J/x49Own3WlSfg9HNa3w/HPfeRYM7mdo77f/xAS5Sx29QkFeNObsdmj2QLNKFMQpuwV1JZ7S8X/wUKviX6Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T13:49:17.897491Z","bundle_sha256":"087e189146c862577b436480628d77c7a958032e81a09f618568774a53fa068b"}}