{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:SMYQMMJYBNQS7SDZLGTSYHAICH","short_pith_number":"pith:SMYQMMJY","canonical_record":{"source":{"id":"1610.03819","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-10-12T18:43:51Z","cross_cats_sorted":["cs.CV","math.ST","stat.TH"],"title_canon_sha256":"638b5c15babe077a65251f2b861c6e6d49b238c6436a3d36c5384fac3cf12525","abstract_canon_sha256":"913178b1b3559eb833953b23e53e729ca79cec540534df4b6922a2b90eedadd9"},"schema_version":"1.0"},"canonical_sha256":"93310631380b612fc87959a72c1c0811e6838b46bae6b4cc357dc5225fa68fbe","source":{"kind":"arxiv","id":"1610.03819","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.03819","created_at":"2026-05-18T00:39:13Z"},{"alias_kind":"arxiv_version","alias_value":"1610.03819v2","created_at":"2026-05-18T00:39:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.03819","created_at":"2026-05-18T00:39:13Z"},{"alias_kind":"pith_short_12","alias_value":"SMYQMMJYBNQS","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SMYQMMJYBNQS7SDZ","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SMYQMMJY","created_at":"2026-05-18T12:30:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:SMYQMMJYBNQS7SDZLGTSYHAICH","target":"record","payload":{"canonical_record":{"source":{"id":"1610.03819","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-10-12T18:43:51Z","cross_cats_sorted":["cs.CV","math.ST","stat.TH"],"title_canon_sha256":"638b5c15babe077a65251f2b861c6e6d49b238c6436a3d36c5384fac3cf12525","abstract_canon_sha256":"913178b1b3559eb833953b23e53e729ca79cec540534df4b6922a2b90eedadd9"},"schema_version":"1.0"},"canonical_sha256":"93310631380b612fc87959a72c1c0811e6838b46bae6b4cc357dc5225fa68fbe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:13.157799Z","signature_b64":"LF9qswigZOuJWDAytykNvS8qaWBFHauc6xvYMIBRxpNI4o1YwNtjWrF0c6u9rcezxWDTZRpcnJfocKJM/u9/DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"93310631380b612fc87959a72c1c0811e6838b46bae6b4cc357dc5225fa68fbe","last_reissued_at":"2026-05-18T00:39:13.156961Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:13.156961Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.03819","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":"2026-05-18T00:39:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3gi/pS8XeNgg4uF30xhjy0dmWM4ODF/PwcNVEhy5VjBMSL8GdzbD3iOkZY12JfEklZ9+Sc9zbyrMcMqXlQP8Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T01:25:50.686508Z"},"content_sha256":"0616c6b53df4788ce11c019bb1986ff0be504a180a2d8daaf43bc904008afa6f","schema_version":"1.0","event_id":"sha256:0616c6b53df4788ce11c019bb1986ff0be504a180a2d8daaf43bc904008afa6f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:SMYQMMJYBNQS7SDZLGTSYHAICH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Recursive Diffeomorphism-Based Regression for Shape Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CV","math.ST","stat.TH"],"primary_cat":"math.NA","authors_text":"Haizhao Yang, Ingrid Daubechies, Jieren Xu","submitted_at":"2016-10-12T18:43:51Z","abstract_excerpt":"This paper proposes a recursive diffeomorphism based regression method for one-dimensional generalized mode decomposition problem that aims at extracting generalized modes $\\alpha_k(t)s_k(2\\pi N_k\\phi_k(t))$ from their superposition $\\sum_{k=1}^K \\alpha_k(t)s_k(2\\pi N_k\\phi_k(t))$. First, a one-dimensional synchrosqueezed transform is applied to estimate instantaneous information, e.g., $\\alpha_k(t)$ and $N_k\\phi_k(t)$. Second, a novel approach based on diffeomorphisms and nonparametric regression is proposed to estimate wave shape functions $s_k(t)$. These two methods lead to a framework for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.03819","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":"2026-05-18T00:39:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1xUvZEgdNkrwWzP5cRJXtWxW7xiorWw17694YDAs+ILQUatFYm/PQKsiOSThDbbTScp7+6uJn60ZQeRvaHvBCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T01:25:50.687340Z"},"content_sha256":"61d2c3030dcc76ec24b9d2cf8a88ae443c1915872e80c9f7eb3b2e1a111dc9e3","schema_version":"1.0","event_id":"sha256:61d2c3030dcc76ec24b9d2cf8a88ae443c1915872e80c9f7eb3b2e1a111dc9e3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SMYQMMJYBNQS7SDZLGTSYHAICH/bundle.json","state_url":"https://pith.science/pith/SMYQMMJYBNQS7SDZLGTSYHAICH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SMYQMMJYBNQS7SDZLGTSYHAICH/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":"2026-06-10T01:25:50Z","links":{"resolver":"https://pith.science/pith/SMYQMMJYBNQS7SDZLGTSYHAICH","bundle":"https://pith.science/pith/SMYQMMJYBNQS7SDZLGTSYHAICH/bundle.json","state":"https://pith.science/pith/SMYQMMJYBNQS7SDZLGTSYHAICH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SMYQMMJYBNQS7SDZLGTSYHAICH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:SMYQMMJYBNQS7SDZLGTSYHAICH","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":"913178b1b3559eb833953b23e53e729ca79cec540534df4b6922a2b90eedadd9","cross_cats_sorted":["cs.CV","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-10-12T18:43:51Z","title_canon_sha256":"638b5c15babe077a65251f2b861c6e6d49b238c6436a3d36c5384fac3cf12525"},"schema_version":"1.0","source":{"id":"1610.03819","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.03819","created_at":"2026-05-18T00:39:13Z"},{"alias_kind":"arxiv_version","alias_value":"1610.03819v2","created_at":"2026-05-18T00:39:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.03819","created_at":"2026-05-18T00:39:13Z"},{"alias_kind":"pith_short_12","alias_value":"SMYQMMJYBNQS","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SMYQMMJYBNQS7SDZ","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SMYQMMJY","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:61d2c3030dcc76ec24b9d2cf8a88ae443c1915872e80c9f7eb3b2e1a111dc9e3","target":"graph","created_at":"2026-05-18T00:39:13Z","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":"This paper proposes a recursive diffeomorphism based regression method for one-dimensional generalized mode decomposition problem that aims at extracting generalized modes $\\alpha_k(t)s_k(2\\pi N_k\\phi_k(t))$ from their superposition $\\sum_{k=1}^K \\alpha_k(t)s_k(2\\pi N_k\\phi_k(t))$. First, a one-dimensional synchrosqueezed transform is applied to estimate instantaneous information, e.g., $\\alpha_k(t)$ and $N_k\\phi_k(t)$. Second, a novel approach based on diffeomorphisms and nonparametric regression is proposed to estimate wave shape functions $s_k(t)$. These two methods lead to a framework for ","authors_text":"Haizhao Yang, Ingrid Daubechies, Jieren Xu","cross_cats":["cs.CV","math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-10-12T18:43:51Z","title":"Recursive Diffeomorphism-Based Regression for Shape Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.03819","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":"sha256:0616c6b53df4788ce11c019bb1986ff0be504a180a2d8daaf43bc904008afa6f","target":"record","created_at":"2026-05-18T00:39:13Z","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":"913178b1b3559eb833953b23e53e729ca79cec540534df4b6922a2b90eedadd9","cross_cats_sorted":["cs.CV","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-10-12T18:43:51Z","title_canon_sha256":"638b5c15babe077a65251f2b861c6e6d49b238c6436a3d36c5384fac3cf12525"},"schema_version":"1.0","source":{"id":"1610.03819","kind":"arxiv","version":2}},"canonical_sha256":"93310631380b612fc87959a72c1c0811e6838b46bae6b4cc357dc5225fa68fbe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"93310631380b612fc87959a72c1c0811e6838b46bae6b4cc357dc5225fa68fbe","first_computed_at":"2026-05-18T00:39:13.156961Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:39:13.156961Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LF9qswigZOuJWDAytykNvS8qaWBFHauc6xvYMIBRxpNI4o1YwNtjWrF0c6u9rcezxWDTZRpcnJfocKJM/u9/DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:39:13.157799Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.03819","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0616c6b53df4788ce11c019bb1986ff0be504a180a2d8daaf43bc904008afa6f","sha256:61d2c3030dcc76ec24b9d2cf8a88ae443c1915872e80c9f7eb3b2e1a111dc9e3"],"state_sha256":"dd517a00f2b413ed8ebbe247775e25ca4c6ed124a113b288b6613d215745a076"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6CoPFo7dgdgPSrnmecs66Cf0KB/ght/VxnmSmvDRlZXrZm2/DLkN5wid+4XTLLIzPqJDjfPmE2px7OfqnFgVCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T01:25:50.692057Z","bundle_sha256":"89d2526d343a1685700adeb89c7f5924cd42674774750df5d50b8d797218b97e"}}