{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:436GWS5CSDLMZ5KVUMSD43E57Y","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":"1b1c32e68f0ca6d359a40417d17356f346172b608db87348163b72344c41d340","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-10T13:06:21Z","title_canon_sha256":"15f7aefe5cc4d20723f78c9f2c0911c1b7e28594102cb31736426258e0aba1aa"},"schema_version":"1.0","source":{"id":"1504.02665","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.02665","created_at":"2026-05-18T01:01:52Z"},{"alias_kind":"arxiv_version","alias_value":"1504.02665v3","created_at":"2026-05-18T01:01:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.02665","created_at":"2026-05-18T01:01:52Z"},{"alias_kind":"pith_short_12","alias_value":"436GWS5CSDLM","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"436GWS5CSDLMZ5KV","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"436GWS5C","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:bbe5922cbe6f68d097f5a6aa895a81aad5b6e59948024f01857bc19db99c287c","target":"graph","created_at":"2026-05-18T01:01:52Z","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 are concerned with the acoustic scattering problem, at a frequency $\\kappa$, by many small obstacles of arbitrary shapes with impedance boundary condition. These scatterers are assumed to be included in a bounded domain $\\Omega$ in $\\mathbb{R}^3$ which is embedded in an acoustic background characterized by an eventually locally varying index of refraction. The collection of the scatterers $D_m, \\; m=1,...,M$ is modeled by four parameters: their number $M$, their maximum radius $a$, their minimum distance $d$ and the surface impedances $\\lambda_m, \\; m=1,...,M$. We consider the parameters $M","authors_text":"Durga Prasad Challa, Mourad Sini","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-10T13:06:21Z","title":"Multiscale analysis of the acoustic scattering by many scatterers of impedance type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.02665","kind":"arxiv","version":3},"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:d61876fd4986b737cc7a23c4795061bda07993c23756066ab30b4d59c277dbb7","target":"record","created_at":"2026-05-18T01:01:52Z","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":"1b1c32e68f0ca6d359a40417d17356f346172b608db87348163b72344c41d340","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-10T13:06:21Z","title_canon_sha256":"15f7aefe5cc4d20723f78c9f2c0911c1b7e28594102cb31736426258e0aba1aa"},"schema_version":"1.0","source":{"id":"1504.02665","kind":"arxiv","version":3}},"canonical_sha256":"e6fc6b4ba290d6ccf555a3243e6c9dfe392d07e40e5044814c4e07d16826cfb3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e6fc6b4ba290d6ccf555a3243e6c9dfe392d07e40e5044814c4e07d16826cfb3","first_computed_at":"2026-05-18T01:01:52.378662Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:01:52.378662Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gIdsKspWbLy0RR3srUteDzFmkEbBWr48ba0TyovAlS7wrjQFZKp0HQj2CLDi9rLKt/XpQA4B8zPij9Fo9Os4Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:01:52.379843Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.02665","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d61876fd4986b737cc7a23c4795061bda07993c23756066ab30b4d59c277dbb7","sha256:bbe5922cbe6f68d097f5a6aa895a81aad5b6e59948024f01857bc19db99c287c"],"state_sha256":"fd18de3a6f5f0a3de1fa92b4c9f19a2167108a34b0ee9465b99cdb0df50a87f6"}