{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:EUCB67HRUPEEHTLP7H3CBAUV5Z","short_pith_number":"pith:EUCB67HR","canonical_record":{"source":{"id":"1604.04604","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-04-15T19:08:07Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"29f3a1426692f56616e821038e79c4b681afc5e6bdbf5d051e50f1777341e2ac","abstract_canon_sha256":"b2fc4f59b1ef866b04cb2c736d50e140b5029cd27fcad9ec4a40c826d467b242"},"schema_version":"1.0"},"canonical_sha256":"25041f7cf1a3c843cd6ff9f6208295ee577e804e3a069a00d0dd06bab4ab0a9b","source":{"kind":"arxiv","id":"1604.04604","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.04604","created_at":"2026-05-18T00:53:17Z"},{"alias_kind":"arxiv_version","alias_value":"1604.04604v2","created_at":"2026-05-18T00:53:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.04604","created_at":"2026-05-18T00:53:17Z"},{"alias_kind":"pith_short_12","alias_value":"EUCB67HRUPEE","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"EUCB67HRUPEEHTLP","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"EUCB67HR","created_at":"2026-05-18T12:30:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:EUCB67HRUPEEHTLP7H3CBAUV5Z","target":"record","payload":{"canonical_record":{"source":{"id":"1604.04604","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-04-15T19:08:07Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"29f3a1426692f56616e821038e79c4b681afc5e6bdbf5d051e50f1777341e2ac","abstract_canon_sha256":"b2fc4f59b1ef866b04cb2c736d50e140b5029cd27fcad9ec4a40c826d467b242"},"schema_version":"1.0"},"canonical_sha256":"25041f7cf1a3c843cd6ff9f6208295ee577e804e3a069a00d0dd06bab4ab0a9b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:17.545591Z","signature_b64":"x4LLoYBT/lbbEJtudUga7iPuABfjJxfFW8xhMM4pM77nJ5CXg8rXcjWvALtXRPjShTDsCoKZ+kfnZ52BxDDADw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"25041f7cf1a3c843cd6ff9f6208295ee577e804e3a069a00d0dd06bab4ab0a9b","last_reissued_at":"2026-05-18T00:53:17.544803Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:17.544803Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.04604","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":"2026-05-18T00:53:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"txzJRqKGBBmI2xqXp5oe7gS7CeYy2xPxffkYF8cADAHgCiEpmbESAsquJu4MGJ1i374Fcsn2ivFyLm/8yg3IDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T19:29:33.127153Z"},"content_sha256":"6f60732f56ad42eb6f36b0e22003187e8872c34c74323734967e31986183571a","schema_version":"1.0","event_id":"sha256:6f60732f56ad42eb6f36b0e22003187e8872c34c74323734967e31986183571a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:EUCB67HRUPEEHTLP7H3CBAUV5Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mathematical Analysis of Ultrafast Ultrasound Imaging","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.NA","authors_text":"Francisco Romero, Giovanni S. Alberti, Habib Ammari, Timoth\\'ee Wintz","submitted_at":"2016-04-15T19:08:07Z","abstract_excerpt":"This paper provides a mathematical analysis of ultrafast ultrasound imaging. This newly emerging modality for biomedical imaging uses plane waves instead of focused waves in order to achieve very high frame rates. We derive the point spread function of the system in the Born approximation for wave propagation and study its properties. We consider dynamic data for blood flow imaging, and introduce a suitable random model for blood cells. We show that a singular value decomposition method can successfully remove the clutter signal by using the different spatial coherence of tissue and blood sign"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.04604","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":"2026-05-18T00:53:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yE1BaxkGJMxYKfdoomJfuR2mHqMjMZBBJob9+5b9qYr3iy13JgtSxLaWk0lF7V1t+aCLI0YEnvBoXMIydJA5DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T19:29:33.127526Z"},"content_sha256":"57674968e00adb1a532077b6090a4401c27bda2983f06e6c37b2e9b9619bbd74","schema_version":"1.0","event_id":"sha256:57674968e00adb1a532077b6090a4401c27bda2983f06e6c37b2e9b9619bbd74"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EUCB67HRUPEEHTLP7H3CBAUV5Z/bundle.json","state_url":"https://pith.science/pith/EUCB67HRUPEEHTLP7H3CBAUV5Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EUCB67HRUPEEHTLP7H3CBAUV5Z/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":"2026-06-02T19:29:33Z","links":{"resolver":"https://pith.science/pith/EUCB67HRUPEEHTLP7H3CBAUV5Z","bundle":"https://pith.science/pith/EUCB67HRUPEEHTLP7H3CBAUV5Z/bundle.json","state":"https://pith.science/pith/EUCB67HRUPEEHTLP7H3CBAUV5Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EUCB67HRUPEEHTLP7H3CBAUV5Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:EUCB67HRUPEEHTLP7H3CBAUV5Z","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":"b2fc4f59b1ef866b04cb2c736d50e140b5029cd27fcad9ec4a40c826d467b242","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-04-15T19:08:07Z","title_canon_sha256":"29f3a1426692f56616e821038e79c4b681afc5e6bdbf5d051e50f1777341e2ac"},"schema_version":"1.0","source":{"id":"1604.04604","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.04604","created_at":"2026-05-18T00:53:17Z"},{"alias_kind":"arxiv_version","alias_value":"1604.04604v2","created_at":"2026-05-18T00:53:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.04604","created_at":"2026-05-18T00:53:17Z"},{"alias_kind":"pith_short_12","alias_value":"EUCB67HRUPEE","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"EUCB67HRUPEEHTLP","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"EUCB67HR","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:57674968e00adb1a532077b6090a4401c27bda2983f06e6c37b2e9b9619bbd74","target":"graph","created_at":"2026-05-18T00:53:17Z","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 provides a mathematical analysis of ultrafast ultrasound imaging. This newly emerging modality for biomedical imaging uses plane waves instead of focused waves in order to achieve very high frame rates. We derive the point spread function of the system in the Born approximation for wave propagation and study its properties. We consider dynamic data for blood flow imaging, and introduce a suitable random model for blood cells. We show that a singular value decomposition method can successfully remove the clutter signal by using the different spatial coherence of tissue and blood sign","authors_text":"Francisco Romero, Giovanni S. Alberti, Habib Ammari, Timoth\\'ee Wintz","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-04-15T19:08:07Z","title":"Mathematical Analysis of Ultrafast Ultrasound Imaging"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.04604","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":"sha256:6f60732f56ad42eb6f36b0e22003187e8872c34c74323734967e31986183571a","target":"record","created_at":"2026-05-18T00:53:17Z","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":"b2fc4f59b1ef866b04cb2c736d50e140b5029cd27fcad9ec4a40c826d467b242","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-04-15T19:08:07Z","title_canon_sha256":"29f3a1426692f56616e821038e79c4b681afc5e6bdbf5d051e50f1777341e2ac"},"schema_version":"1.0","source":{"id":"1604.04604","kind":"arxiv","version":2}},"canonical_sha256":"25041f7cf1a3c843cd6ff9f6208295ee577e804e3a069a00d0dd06bab4ab0a9b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"25041f7cf1a3c843cd6ff9f6208295ee577e804e3a069a00d0dd06bab4ab0a9b","first_computed_at":"2026-05-18T00:53:17.544803Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:17.544803Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"x4LLoYBT/lbbEJtudUga7iPuABfjJxfFW8xhMM4pM77nJ5CXg8rXcjWvALtXRPjShTDsCoKZ+kfnZ52BxDDADw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:17.545591Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.04604","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6f60732f56ad42eb6f36b0e22003187e8872c34c74323734967e31986183571a","sha256:57674968e00adb1a532077b6090a4401c27bda2983f06e6c37b2e9b9619bbd74"],"state_sha256":"9b16f9d9ad713a711ec3b055f85fcc75b308de3db3172f4e055a6be15db7c45a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Nr1dxBAiXINS32pv1E3dmckCgW/dM4Xu3Xp134hltI58oMx28b0M9HYfXNmUhpjgWRx+PNcYFivy0nI8A1LsAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T19:29:33.129864Z","bundle_sha256":"cb4844a95515d9e27b1112634c8af6b596be59cb6afbeb9704f99537fd6769e2"}}