{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:A77ACZD7TAYWCNAL2VUI4BQKZS","short_pith_number":"pith:A77ACZD7","canonical_record":{"source":{"id":"1604.08409","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-28T13:31:40Z","cross_cats_sorted":[],"title_canon_sha256":"d8f4f41c0e84fc730ac60db456238988706cd07d117306799d4840e000500849","abstract_canon_sha256":"8ed5308a5c44f1cc95a3e55cf6123dfa0875fd9ca474375e8ba9af883646f03f"},"schema_version":"1.0"},"canonical_sha256":"07fe01647f983161340bd5688e060acca6bfc892a7e92141eecbe4baaecd9c3f","source":{"kind":"arxiv","id":"1604.08409","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.08409","created_at":"2026-05-18T01:16:04Z"},{"alias_kind":"arxiv_version","alias_value":"1604.08409v1","created_at":"2026-05-18T01:16:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.08409","created_at":"2026-05-18T01:16:04Z"},{"alias_kind":"pith_short_12","alias_value":"A77ACZD7TAYW","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"A77ACZD7TAYWCNAL","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"A77ACZD7","created_at":"2026-05-18T12:30:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:A77ACZD7TAYWCNAL2VUI4BQKZS","target":"record","payload":{"canonical_record":{"source":{"id":"1604.08409","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-28T13:31:40Z","cross_cats_sorted":[],"title_canon_sha256":"d8f4f41c0e84fc730ac60db456238988706cd07d117306799d4840e000500849","abstract_canon_sha256":"8ed5308a5c44f1cc95a3e55cf6123dfa0875fd9ca474375e8ba9af883646f03f"},"schema_version":"1.0"},"canonical_sha256":"07fe01647f983161340bd5688e060acca6bfc892a7e92141eecbe4baaecd9c3f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:04.078402Z","signature_b64":"dZlOwjhdZmOF9VdPiT10aqM5YLWNcnVSAPn7fhXwdWsZAPiqP5xccQkYMCQjyuQnqWupj23CgvVgTkcwk0ixBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"07fe01647f983161340bd5688e060acca6bfc892a7e92141eecbe4baaecd9c3f","last_reissued_at":"2026-05-18T01:16:04.077712Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:04.077712Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.08409","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":"2026-05-18T01:16:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pQIXj/3l2YK2tN9Ug8prfGejzIn5r2ftBw5jEFmuh1kjMc6/+2JUVAXFvYiHfU4TW4oQmG4VwsurPk0FsthpDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T22:56:54.608688Z"},"content_sha256":"5b2719476ed26ec59c5a872f68811a34e8e038c42afbda92efdc41261860f260","schema_version":"1.0","event_id":"sha256:5b2719476ed26ec59c5a872f68811a34e8e038c42afbda92efdc41261860f260"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:A77ACZD7TAYWCNAL2VUI4BQKZS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Effective medium theory for acoustic waves in bubbly fluids near Minnaert resonant frequency","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Habib Ammari, Hai Zhang","submitted_at":"2016-04-28T13:31:40Z","abstract_excerpt":"We derive an effective medium theory for acoustic wave propagation in bubbly fluid near Minnaert resonant frequency. We start with a multiple scattering formulation of the scattering problem of an incident wave by a large number of identical small bubbles in a homogeneous fluid. Under certain conditions on the configuration of the bubbles, we justify the point interaction approximation and establish an effective medium theory for the bubbly fluid as the number of bubbles tends to infinity. The convergence rate is also derived. As a consequence, we show that near and below the Minnaert resonant"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.08409","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":"2026-05-18T01:16:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rNgkF/RN8VdwKhkSTf4hlGcd/vOinYznHszg30efPNRT+qa7dfeSe1njHfZ8SmqtwyC9BXLqPYFw60z3MuwNDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T22:56:54.609040Z"},"content_sha256":"81e65e319fe4fdb7a2bd412c7d7897a8b0e0c6f81a66bd2b8cb0870f25f5acb0","schema_version":"1.0","event_id":"sha256:81e65e319fe4fdb7a2bd412c7d7897a8b0e0c6f81a66bd2b8cb0870f25f5acb0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A77ACZD7TAYWCNAL2VUI4BQKZS/bundle.json","state_url":"https://pith.science/pith/A77ACZD7TAYWCNAL2VUI4BQKZS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A77ACZD7TAYWCNAL2VUI4BQKZS/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":"2026-06-02T22:56:54Z","links":{"resolver":"https://pith.science/pith/A77ACZD7TAYWCNAL2VUI4BQKZS","bundle":"https://pith.science/pith/A77ACZD7TAYWCNAL2VUI4BQKZS/bundle.json","state":"https://pith.science/pith/A77ACZD7TAYWCNAL2VUI4BQKZS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A77ACZD7TAYWCNAL2VUI4BQKZS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:A77ACZD7TAYWCNAL2VUI4BQKZS","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":"8ed5308a5c44f1cc95a3e55cf6123dfa0875fd9ca474375e8ba9af883646f03f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-28T13:31:40Z","title_canon_sha256":"d8f4f41c0e84fc730ac60db456238988706cd07d117306799d4840e000500849"},"schema_version":"1.0","source":{"id":"1604.08409","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.08409","created_at":"2026-05-18T01:16:04Z"},{"alias_kind":"arxiv_version","alias_value":"1604.08409v1","created_at":"2026-05-18T01:16:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.08409","created_at":"2026-05-18T01:16:04Z"},{"alias_kind":"pith_short_12","alias_value":"A77ACZD7TAYW","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"A77ACZD7TAYWCNAL","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"A77ACZD7","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:81e65e319fe4fdb7a2bd412c7d7897a8b0e0c6f81a66bd2b8cb0870f25f5acb0","target":"graph","created_at":"2026-05-18T01:16:04Z","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 derive an effective medium theory for acoustic wave propagation in bubbly fluid near Minnaert resonant frequency. We start with a multiple scattering formulation of the scattering problem of an incident wave by a large number of identical small bubbles in a homogeneous fluid. Under certain conditions on the configuration of the bubbles, we justify the point interaction approximation and establish an effective medium theory for the bubbly fluid as the number of bubbles tends to infinity. The convergence rate is also derived. As a consequence, we show that near and below the Minnaert resonant","authors_text":"Habib Ammari, Hai Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-28T13:31:40Z","title":"Effective medium theory for acoustic waves in bubbly fluids near Minnaert resonant frequency"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.08409","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":"sha256:5b2719476ed26ec59c5a872f68811a34e8e038c42afbda92efdc41261860f260","target":"record","created_at":"2026-05-18T01:16:04Z","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":"8ed5308a5c44f1cc95a3e55cf6123dfa0875fd9ca474375e8ba9af883646f03f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-28T13:31:40Z","title_canon_sha256":"d8f4f41c0e84fc730ac60db456238988706cd07d117306799d4840e000500849"},"schema_version":"1.0","source":{"id":"1604.08409","kind":"arxiv","version":1}},"canonical_sha256":"07fe01647f983161340bd5688e060acca6bfc892a7e92141eecbe4baaecd9c3f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"07fe01647f983161340bd5688e060acca6bfc892a7e92141eecbe4baaecd9c3f","first_computed_at":"2026-05-18T01:16:04.077712Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:04.077712Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dZlOwjhdZmOF9VdPiT10aqM5YLWNcnVSAPn7fhXwdWsZAPiqP5xccQkYMCQjyuQnqWupj23CgvVgTkcwk0ixBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:04.078402Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.08409","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5b2719476ed26ec59c5a872f68811a34e8e038c42afbda92efdc41261860f260","sha256:81e65e319fe4fdb7a2bd412c7d7897a8b0e0c6f81a66bd2b8cb0870f25f5acb0"],"state_sha256":"a077d1a69d2eaa25bc81cc9f3125e21647194c94995f8d2aed27e95c3cb33927"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SgX6lc/qHqUIMkxjO7qls2NhFE8AkULgFgji42vK0W3xePcuFpftwuF3gA9VBAKmSapw/HjDczP7NndKfNTOAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T22:56:54.611151Z","bundle_sha256":"9d9846cf55b2a889e5c508f62dd00772d63c626ad62b7e98014406c69bc01e7a"}}