{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:DH6356WPON3OA2GQILR7OBA4J2","short_pith_number":"pith:DH6356WP","canonical_record":{"source":{"id":"1610.02252","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-10-07T12:36:47Z","cross_cats_sorted":["nlin.CD"],"title_canon_sha256":"6027423e6c8563b79f77efd35b19a090dc491bbbc7abe7b6c2c78b601ca5193c","abstract_canon_sha256":"a2c1dc94020cd61a242f1abc7c2645d0251298fb1db6cfe7dc069cd122f9671e"},"schema_version":"1.0"},"canonical_sha256":"19fdbefacf7376e068d042e3f7041c4ead4b66455da08cc380934d6163bd1c73","source":{"kind":"arxiv","id":"1610.02252","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.02252","created_at":"2026-05-18T00:37:36Z"},{"alias_kind":"arxiv_version","alias_value":"1610.02252v1","created_at":"2026-05-18T00:37:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.02252","created_at":"2026-05-18T00:37:36Z"},{"alias_kind":"pith_short_12","alias_value":"DH6356WPON3O","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DH6356WPON3OA2GQ","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DH6356WP","created_at":"2026-05-18T12:30:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:DH6356WPON3OA2GQILR7OBA4J2","target":"record","payload":{"canonical_record":{"source":{"id":"1610.02252","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-10-07T12:36:47Z","cross_cats_sorted":["nlin.CD"],"title_canon_sha256":"6027423e6c8563b79f77efd35b19a090dc491bbbc7abe7b6c2c78b601ca5193c","abstract_canon_sha256":"a2c1dc94020cd61a242f1abc7c2645d0251298fb1db6cfe7dc069cd122f9671e"},"schema_version":"1.0"},"canonical_sha256":"19fdbefacf7376e068d042e3f7041c4ead4b66455da08cc380934d6163bd1c73","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:37:36.632891Z","signature_b64":"CuBMO/1cxROuklPLnQoJUd0XduXd/3CGt2k6DrJB951lNA2k9yc1ZU/fVQbwSFBC+awBuHSMuTtxmHv5SRDtDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"19fdbefacf7376e068d042e3f7041c4ead4b66455da08cc380934d6163bd1c73","last_reissued_at":"2026-05-18T00:37:36.632232Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:37:36.632232Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.02252","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":"2026-05-18T00:37:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HT7dyMjH6A86cclpfL1kpR7cstBGfRYHnxdGE0moQcs0rY8GWfZEJ5zq45DM0AC0fpNLBAyTUtuOWT89pcppAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T00:03:14.370712Z"},"content_sha256":"a3aaccc4d06bdfbb7d2ec6144059ee45b89b7bcdc73cdbd0b49c071480911b43","schema_version":"1.0","event_id":"sha256:a3aaccc4d06bdfbb7d2ec6144059ee45b89b7bcdc73cdbd0b49c071480911b43"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:DH6356WPON3OA2GQILR7OBA4J2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonlinear model identification and spectral submanifolds for multi-degree-of-freedom mechanical vibrations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.CD"],"primary_cat":"math.DS","authors_text":"David Ehrhardt, George Haller, Robert Szalai","submitted_at":"2016-10-07T12:36:47Z","abstract_excerpt":"In a nonlinear oscillatory system, spectral submanifolds (SSMs) are the smoothest invariant manifolds tangent to linear modal subspaces of an equilibrium. Amplitude-frequency plots of the dynamics on SSMs provide the classic backbone curves sought in experimental nonlinear model identification. We develop here a methodology to compute analytically both the shape of SSMs and their corresponding backbone curves from a data-assimilating model fitted to experimental vibration signals. Using examples of both synthetic and real experimental data, we demonstrate that this approach reproduces backbone"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.02252","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":"2026-05-18T00:37:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QNpQqJgszOn+1YPnAXn3nUfpsd8FIyX1q4+Aqo2N7QC20aB6RrW7JtScTCzRL6YJIpFyC2nPa3h5zldTEsPUDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T00:03:14.371058Z"},"content_sha256":"24e80ade2b3a34d90cfae677fd730b7289dc4a0c34f8f59d65406b52101290ed","schema_version":"1.0","event_id":"sha256:24e80ade2b3a34d90cfae677fd730b7289dc4a0c34f8f59d65406b52101290ed"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DH6356WPON3OA2GQILR7OBA4J2/bundle.json","state_url":"https://pith.science/pith/DH6356WPON3OA2GQILR7OBA4J2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DH6356WPON3OA2GQILR7OBA4J2/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":"2026-06-03T00:03:14Z","links":{"resolver":"https://pith.science/pith/DH6356WPON3OA2GQILR7OBA4J2","bundle":"https://pith.science/pith/DH6356WPON3OA2GQILR7OBA4J2/bundle.json","state":"https://pith.science/pith/DH6356WPON3OA2GQILR7OBA4J2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DH6356WPON3OA2GQILR7OBA4J2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:DH6356WPON3OA2GQILR7OBA4J2","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":"a2c1dc94020cd61a242f1abc7c2645d0251298fb1db6cfe7dc069cd122f9671e","cross_cats_sorted":["nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-10-07T12:36:47Z","title_canon_sha256":"6027423e6c8563b79f77efd35b19a090dc491bbbc7abe7b6c2c78b601ca5193c"},"schema_version":"1.0","source":{"id":"1610.02252","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.02252","created_at":"2026-05-18T00:37:36Z"},{"alias_kind":"arxiv_version","alias_value":"1610.02252v1","created_at":"2026-05-18T00:37:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.02252","created_at":"2026-05-18T00:37:36Z"},{"alias_kind":"pith_short_12","alias_value":"DH6356WPON3O","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DH6356WPON3OA2GQ","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DH6356WP","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:24e80ade2b3a34d90cfae677fd730b7289dc4a0c34f8f59d65406b52101290ed","target":"graph","created_at":"2026-05-18T00:37:36Z","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":"In a nonlinear oscillatory system, spectral submanifolds (SSMs) are the smoothest invariant manifolds tangent to linear modal subspaces of an equilibrium. Amplitude-frequency plots of the dynamics on SSMs provide the classic backbone curves sought in experimental nonlinear model identification. We develop here a methodology to compute analytically both the shape of SSMs and their corresponding backbone curves from a data-assimilating model fitted to experimental vibration signals. Using examples of both synthetic and real experimental data, we demonstrate that this approach reproduces backbone","authors_text":"David Ehrhardt, George Haller, Robert Szalai","cross_cats":["nlin.CD"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-10-07T12:36:47Z","title":"Nonlinear model identification and spectral submanifolds for multi-degree-of-freedom mechanical vibrations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.02252","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:a3aaccc4d06bdfbb7d2ec6144059ee45b89b7bcdc73cdbd0b49c071480911b43","target":"record","created_at":"2026-05-18T00:37:36Z","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":"a2c1dc94020cd61a242f1abc7c2645d0251298fb1db6cfe7dc069cd122f9671e","cross_cats_sorted":["nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-10-07T12:36:47Z","title_canon_sha256":"6027423e6c8563b79f77efd35b19a090dc491bbbc7abe7b6c2c78b601ca5193c"},"schema_version":"1.0","source":{"id":"1610.02252","kind":"arxiv","version":1}},"canonical_sha256":"19fdbefacf7376e068d042e3f7041c4ead4b66455da08cc380934d6163bd1c73","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"19fdbefacf7376e068d042e3f7041c4ead4b66455da08cc380934d6163bd1c73","first_computed_at":"2026-05-18T00:37:36.632232Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:37:36.632232Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CuBMO/1cxROuklPLnQoJUd0XduXd/3CGt2k6DrJB951lNA2k9yc1ZU/fVQbwSFBC+awBuHSMuTtxmHv5SRDtDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:37:36.632891Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.02252","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a3aaccc4d06bdfbb7d2ec6144059ee45b89b7bcdc73cdbd0b49c071480911b43","sha256:24e80ade2b3a34d90cfae677fd730b7289dc4a0c34f8f59d65406b52101290ed"],"state_sha256":"4926e1feb586cebe21886a93859930564bb5d2f5f2bee13540b98039893bbc77"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"roO3asKbDkWzD94lqPA6+x9f+sm0tdAhY22LM1pi1BlZ+l0vteis7YTLNE130T08V8JlL8RZ6+svDAUGKPUXBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T00:03:14.373074Z","bundle_sha256":"c76c393a9369cdddb15009fe85fbefeec6fb4c948496080eb7b2e59b12d281a7"}}