{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:J6VFF624CHZRHLVO6KPHYBHVUV","short_pith_number":"pith:J6VFF624","canonical_record":{"source":{"id":"0905.4602","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2009-05-28T10:21:19Z","cross_cats_sorted":["math.NA","math.ST","stat.TH"],"title_canon_sha256":"84a94d4eed61a1d20a60fa26f52458008198787c0752fb90b4681febdaedc22a","abstract_canon_sha256":"62b17c48b081d8de48b467dcf437bb4af6eac32d083222d3a2b983f4952591be"},"schema_version":"1.0"},"canonical_sha256":"4faa52fb5c11f313aeaef29e7c04f5a5598031e3edfb69ab7f449d074b23d711","source":{"kind":"arxiv","id":"0905.4602","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0905.4602","created_at":"2026-05-18T03:44:36Z"},{"alias_kind":"arxiv_version","alias_value":"0905.4602v2","created_at":"2026-05-18T03:44:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.4602","created_at":"2026-05-18T03:44:36Z"},{"alias_kind":"pith_short_12","alias_value":"J6VFF624CHZR","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"J6VFF624CHZRHLVO","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"J6VFF624","created_at":"2026-05-18T12:26:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:J6VFF624CHZRHLVO6KPHYBHVUV","target":"record","payload":{"canonical_record":{"source":{"id":"0905.4602","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2009-05-28T10:21:19Z","cross_cats_sorted":["math.NA","math.ST","stat.TH"],"title_canon_sha256":"84a94d4eed61a1d20a60fa26f52458008198787c0752fb90b4681febdaedc22a","abstract_canon_sha256":"62b17c48b081d8de48b467dcf437bb4af6eac32d083222d3a2b983f4952591be"},"schema_version":"1.0"},"canonical_sha256":"4faa52fb5c11f313aeaef29e7c04f5a5598031e3edfb69ab7f449d074b23d711","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:44:36.612265Z","signature_b64":"uGkTDcPhMiAAOAXSPmr7NGp361ZEyk90tWHmYp65Bx8XD7evVx9kj+xbxv2YEVEUxYEcyNKnAvXX5QIyKRNhDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4faa52fb5c11f313aeaef29e7c04f5a5598031e3edfb69ab7f449d074b23d711","last_reissued_at":"2026-05-18T03:44:36.611625Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:44:36.611625Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0905.4602","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":"2026-05-18T03:44:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n8bM5vvdYR0hTItb7j4gohsdy9D9T+lOqIeWZsWjwigg877qdhluiF6gjNKVxGinUyYUPXudVZOS1G6PocrYDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T18:11:32.820119Z"},"content_sha256":"860aff9753819676d822ce02c3c2d18c7302ca89ac5f89e90aba326d1cfa9e59","schema_version":"1.0","event_id":"sha256:860aff9753819676d822ce02c3c2d18c7302ca89ac5f89e90aba326d1cfa9e59"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:J6VFF624CHZRHLVO6KPHYBHVUV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A black box method for solving the complex exponentials approximation problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA","math.ST","stat.TH"],"primary_cat":"stat.CO","authors_text":"Piero Barone","submitted_at":"2009-05-28T10:21:19Z","abstract_excerpt":"A common problem, arising in many different applied contexts, consists in estimating the number of exponentially damped sinusoids whose weighted sum best fits a finite set of noisy data and in estimating their parameters. Many different methods exist to this purpose. The best of them are based on approximate Maximum Likelihood estimators, assuming to know the number of damped sinusoids, which can then be estimated by an order selection procedure. As the problem can be severely ill posed, a stochastic perturbation method is proposed which provides better results than Maximum Likelihood based me"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.4602","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":"2026-05-18T03:44:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EAh9PGfJTJHPes58vjqk9H/rgRfE3S6E8Z9s4FbAzMS4CTkn3c+TRmuUKq7e28Ymz+vrpVc0YVAPlCWaXSlIDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T18:11:32.820852Z"},"content_sha256":"d4852a90ac21a1e0e6b3e9f57e6f43b39c83ac5b895c689ff9c1560beafe2b0d","schema_version":"1.0","event_id":"sha256:d4852a90ac21a1e0e6b3e9f57e6f43b39c83ac5b895c689ff9c1560beafe2b0d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J6VFF624CHZRHLVO6KPHYBHVUV/bundle.json","state_url":"https://pith.science/pith/J6VFF624CHZRHLVO6KPHYBHVUV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J6VFF624CHZRHLVO6KPHYBHVUV/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":"2026-06-08T18:11:32Z","links":{"resolver":"https://pith.science/pith/J6VFF624CHZRHLVO6KPHYBHVUV","bundle":"https://pith.science/pith/J6VFF624CHZRHLVO6KPHYBHVUV/bundle.json","state":"https://pith.science/pith/J6VFF624CHZRHLVO6KPHYBHVUV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J6VFF624CHZRHLVO6KPHYBHVUV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:J6VFF624CHZRHLVO6KPHYBHVUV","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":"62b17c48b081d8de48b467dcf437bb4af6eac32d083222d3a2b983f4952591be","cross_cats_sorted":["math.NA","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2009-05-28T10:21:19Z","title_canon_sha256":"84a94d4eed61a1d20a60fa26f52458008198787c0752fb90b4681febdaedc22a"},"schema_version":"1.0","source":{"id":"0905.4602","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0905.4602","created_at":"2026-05-18T03:44:36Z"},{"alias_kind":"arxiv_version","alias_value":"0905.4602v2","created_at":"2026-05-18T03:44:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.4602","created_at":"2026-05-18T03:44:36Z"},{"alias_kind":"pith_short_12","alias_value":"J6VFF624CHZR","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"J6VFF624CHZRHLVO","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"J6VFF624","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:d4852a90ac21a1e0e6b3e9f57e6f43b39c83ac5b895c689ff9c1560beafe2b0d","target":"graph","created_at":"2026-05-18T03:44:36Z","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":"A common problem, arising in many different applied contexts, consists in estimating the number of exponentially damped sinusoids whose weighted sum best fits a finite set of noisy data and in estimating their parameters. Many different methods exist to this purpose. The best of them are based on approximate Maximum Likelihood estimators, assuming to know the number of damped sinusoids, which can then be estimated by an order selection procedure. As the problem can be severely ill posed, a stochastic perturbation method is proposed which provides better results than Maximum Likelihood based me","authors_text":"Piero Barone","cross_cats":["math.NA","math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2009-05-28T10:21:19Z","title":"A black box method for solving the complex exponentials approximation problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.4602","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":"sha256:860aff9753819676d822ce02c3c2d18c7302ca89ac5f89e90aba326d1cfa9e59","target":"record","created_at":"2026-05-18T03:44:36Z","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":"62b17c48b081d8de48b467dcf437bb4af6eac32d083222d3a2b983f4952591be","cross_cats_sorted":["math.NA","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2009-05-28T10:21:19Z","title_canon_sha256":"84a94d4eed61a1d20a60fa26f52458008198787c0752fb90b4681febdaedc22a"},"schema_version":"1.0","source":{"id":"0905.4602","kind":"arxiv","version":2}},"canonical_sha256":"4faa52fb5c11f313aeaef29e7c04f5a5598031e3edfb69ab7f449d074b23d711","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4faa52fb5c11f313aeaef29e7c04f5a5598031e3edfb69ab7f449d074b23d711","first_computed_at":"2026-05-18T03:44:36.611625Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:44:36.611625Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uGkTDcPhMiAAOAXSPmr7NGp361ZEyk90tWHmYp65Bx8XD7evVx9kj+xbxv2YEVEUxYEcyNKnAvXX5QIyKRNhDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:44:36.612265Z","signed_message":"canonical_sha256_bytes"},"source_id":"0905.4602","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:860aff9753819676d822ce02c3c2d18c7302ca89ac5f89e90aba326d1cfa9e59","sha256:d4852a90ac21a1e0e6b3e9f57e6f43b39c83ac5b895c689ff9c1560beafe2b0d"],"state_sha256":"ba64935e6b21691d0f01be41b7aa49eb4c38b3bc05ec96086c8352a32d68fdda"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ll09nghJ29G0k21fVc1wrLd/gGPO+NfCYHNxTuZBUnHOp9OsyiNtBu3EI1uDMUz7k9auWkhFkRmWpl7coy1dDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T18:11:32.824712Z","bundle_sha256":"f3d54bae1e5970ea929594e7f0154b95dd2fe9f6c541e6c28b4a1f20ad7d69be"}}