{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:5AFYMVHUERSGMSAJIDBBD6RSNS","short_pith_number":"pith:5AFYMVHU","canonical_record":{"source":{"id":"1502.01208","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2015-02-04T14:41:56Z","cross_cats_sorted":[],"title_canon_sha256":"6b17a123240e74f7b97a4eb86317205a40aea015922d9ae66dd8eae7fc9514e4","abstract_canon_sha256":"cb83a4e711085ad8c4a67ffff2187a63392b7156c7f02e2f9efbc5f42206aca8"},"schema_version":"1.0"},"canonical_sha256":"e80b8654f4246466480940c211fa326c9d19ece9df38b20f2f29aa9601e62504","source":{"kind":"arxiv","id":"1502.01208","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.01208","created_at":"2026-05-18T01:30:51Z"},{"alias_kind":"arxiv_version","alias_value":"1502.01208v2","created_at":"2026-05-18T01:30:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.01208","created_at":"2026-05-18T01:30:51Z"},{"alias_kind":"pith_short_12","alias_value":"5AFYMVHUERSG","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"5AFYMVHUERSGMSAJ","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"5AFYMVHU","created_at":"2026-05-18T12:29:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:5AFYMVHUERSGMSAJIDBBD6RSNS","target":"record","payload":{"canonical_record":{"source":{"id":"1502.01208","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2015-02-04T14:41:56Z","cross_cats_sorted":[],"title_canon_sha256":"6b17a123240e74f7b97a4eb86317205a40aea015922d9ae66dd8eae7fc9514e4","abstract_canon_sha256":"cb83a4e711085ad8c4a67ffff2187a63392b7156c7f02e2f9efbc5f42206aca8"},"schema_version":"1.0"},"canonical_sha256":"e80b8654f4246466480940c211fa326c9d19ece9df38b20f2f29aa9601e62504","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:51.095109Z","signature_b64":"6IpHNqfUGxfeNRZcgDH9p+PsyoWCwns4lKV2Qw67LEthJ3R1Huz9LduGOwiq/Sam0zR1WW4YwQ58sqCFzlg4DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e80b8654f4246466480940c211fa326c9d19ece9df38b20f2f29aa9601e62504","last_reissued_at":"2026-05-18T01:30:51.094672Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:51.094672Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.01208","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":"2026-05-18T01:30:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TyL4YLnODS79Sx9yzAoXEVOnmuT29yYFkYd4ZoPo7tegaGrh2DL+w7m2UEhZJV7I5/aGLlK5x0PZ2e8vAtL+Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T17:19:36.156697Z"},"content_sha256":"020cbd752b261deb17e4c84c1bfcc126cd70900c8cd295327fbfd15e12926566","schema_version":"1.0","event_id":"sha256:020cbd752b261deb17e4c84c1bfcc126cd70900c8cd295327fbfd15e12926566"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:5AFYMVHUERSGMSAJIDBBD6RSNS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A moment-equation-copula-closure method for nonlinear vibrational systems subjected to correlated noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.CD","authors_text":"Han Kyul Joo, Themistoklis P. Sapsis","submitted_at":"2015-02-04T14:41:56Z","abstract_excerpt":"We develop a moment equation closure minimization method for the inexpensive approximation of the steady state statistical structure of nonlinear systems whose potential functions have bimodal shapes and which are subjected to correlated excitations. Our approach relies on the derivation of moment equations that describe the dynamics governing the two-time statistics. These are combined with a non-Gaussian pdf representation for the joint response-excitation statistics that has i) single time statistical structure consistent with the analytical solutions of the Fokker-Planck equation, and ii) "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.01208","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":"2026-05-18T01:30:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lH7bILXFmvI0RyCHhxrEwFAiYXKCK0GotE9y5nd+TWx+ebTNmOuRggInJVYNHruUXsdtWeGXOOorX8HdSScjBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T17:19:36.157034Z"},"content_sha256":"269b281236b4d8c5366f2ee24e6b632279e6aecd17ad6a7f2892bb4cf5fd58a1","schema_version":"1.0","event_id":"sha256:269b281236b4d8c5366f2ee24e6b632279e6aecd17ad6a7f2892bb4cf5fd58a1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5AFYMVHUERSGMSAJIDBBD6RSNS/bundle.json","state_url":"https://pith.science/pith/5AFYMVHUERSGMSAJIDBBD6RSNS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5AFYMVHUERSGMSAJIDBBD6RSNS/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":"2026-06-22T17:19:36Z","links":{"resolver":"https://pith.science/pith/5AFYMVHUERSGMSAJIDBBD6RSNS","bundle":"https://pith.science/pith/5AFYMVHUERSGMSAJIDBBD6RSNS/bundle.json","state":"https://pith.science/pith/5AFYMVHUERSGMSAJIDBBD6RSNS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5AFYMVHUERSGMSAJIDBBD6RSNS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:5AFYMVHUERSGMSAJIDBBD6RSNS","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":"cb83a4e711085ad8c4a67ffff2187a63392b7156c7f02e2f9efbc5f42206aca8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2015-02-04T14:41:56Z","title_canon_sha256":"6b17a123240e74f7b97a4eb86317205a40aea015922d9ae66dd8eae7fc9514e4"},"schema_version":"1.0","source":{"id":"1502.01208","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.01208","created_at":"2026-05-18T01:30:51Z"},{"alias_kind":"arxiv_version","alias_value":"1502.01208v2","created_at":"2026-05-18T01:30:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.01208","created_at":"2026-05-18T01:30:51Z"},{"alias_kind":"pith_short_12","alias_value":"5AFYMVHUERSG","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"5AFYMVHUERSGMSAJ","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"5AFYMVHU","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:269b281236b4d8c5366f2ee24e6b632279e6aecd17ad6a7f2892bb4cf5fd58a1","target":"graph","created_at":"2026-05-18T01:30:51Z","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 develop a moment equation closure minimization method for the inexpensive approximation of the steady state statistical structure of nonlinear systems whose potential functions have bimodal shapes and which are subjected to correlated excitations. Our approach relies on the derivation of moment equations that describe the dynamics governing the two-time statistics. These are combined with a non-Gaussian pdf representation for the joint response-excitation statistics that has i) single time statistical structure consistent with the analytical solutions of the Fokker-Planck equation, and ii) ","authors_text":"Han Kyul Joo, Themistoklis P. Sapsis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2015-02-04T14:41:56Z","title":"A moment-equation-copula-closure method for nonlinear vibrational systems subjected to correlated noise"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.01208","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":"sha256:020cbd752b261deb17e4c84c1bfcc126cd70900c8cd295327fbfd15e12926566","target":"record","created_at":"2026-05-18T01:30:51Z","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":"cb83a4e711085ad8c4a67ffff2187a63392b7156c7f02e2f9efbc5f42206aca8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2015-02-04T14:41:56Z","title_canon_sha256":"6b17a123240e74f7b97a4eb86317205a40aea015922d9ae66dd8eae7fc9514e4"},"schema_version":"1.0","source":{"id":"1502.01208","kind":"arxiv","version":2}},"canonical_sha256":"e80b8654f4246466480940c211fa326c9d19ece9df38b20f2f29aa9601e62504","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e80b8654f4246466480940c211fa326c9d19ece9df38b20f2f29aa9601e62504","first_computed_at":"2026-05-18T01:30:51.094672Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:51.094672Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6IpHNqfUGxfeNRZcgDH9p+PsyoWCwns4lKV2Qw67LEthJ3R1Huz9LduGOwiq/Sam0zR1WW4YwQ58sqCFzlg4DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:51.095109Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.01208","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:020cbd752b261deb17e4c84c1bfcc126cd70900c8cd295327fbfd15e12926566","sha256:269b281236b4d8c5366f2ee24e6b632279e6aecd17ad6a7f2892bb4cf5fd58a1"],"state_sha256":"a2b282772de6315506d29ccc0d536828efd91b269aca7b211d074a0a9dacb752"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EVJCcSgzvN8F1uj0fhpgdfhBkkf31bMUQzHeMK3+3fUpungfunrc+qc34s73xDamoj59ZnapgGGkCYASVeCrBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T17:19:36.158871Z","bundle_sha256":"8cb3ba91e28ffefd9ef2964cb0a668fe1ab0edbf47d6a14fabf41cf7b3296346"}}