{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:MGP2CIWRLQZA6VXO3NBN7I5NST","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":"e12aa8e5dd71d4506c37ff8939261b5e62db98e253794f4a540fd82384542d4b","cross_cats_sorted":["math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-04-06T17:15:42Z","title_canon_sha256":"64f5be663feed6a64dad14fdc38b07fc72580fb05b9bcebfb0ab2711257e1090"},"schema_version":"1.0","source":{"id":"1204.1518","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.1518","created_at":"2026-05-18T03:12:35Z"},{"alias_kind":"arxiv_version","alias_value":"1204.1518v2","created_at":"2026-05-18T03:12:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.1518","created_at":"2026-05-18T03:12:35Z"},{"alias_kind":"pith_short_12","alias_value":"MGP2CIWRLQZA","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MGP2CIWRLQZA6VXO","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MGP2CIWR","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:7da8b249e8ab2148dcdc01ff2e3f24884b1147974286fe731cff8fdcce7b61f6","target":"graph","created_at":"2026-05-18T03:12:35Z","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 is devoted to the study of the behavior of the unique solution $u_\\delta \\in H^{1}_{0}(\\Omega)$, as $\\delta \\to 0$, to the equation \\begin{equation*} \\dive(\\epss_\\delta A \\nabla u_{\\delta}) + k^2 \\epss_0 \\Sigma u_{\\delta} = \\epss_0 f \\mbox{in} \\Omega, \\end{equation*} where $\\Omega$ is a smooth connected bounded open subset of $\\mR^d$ with $d=2$ or 3, $f \\in L^2(\\Omega)$, $k$ is a non-negative constant, $A$ is a uniformly elliptic matrix-valued function, $\\Sigma$ is a real function bounded above and below by positive constants, and $\\epss_\\delta$ is a complex function whose {\\bf the ","authors_text":"Hoai-Minh Nguyen","cross_cats":["math.AP","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-04-06T17:15:42Z","title":"Asymptotic behavior of solutions to the Helmholtz equations with sign changing coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.1518","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":"sha256:8e6fbb3e4dd043795f3fb75b6395b6a3810ebc5b040f791bfd4e395366142c05","target":"record","created_at":"2026-05-18T03:12:35Z","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":"e12aa8e5dd71d4506c37ff8939261b5e62db98e253794f4a540fd82384542d4b","cross_cats_sorted":["math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-04-06T17:15:42Z","title_canon_sha256":"64f5be663feed6a64dad14fdc38b07fc72580fb05b9bcebfb0ab2711257e1090"},"schema_version":"1.0","source":{"id":"1204.1518","kind":"arxiv","version":2}},"canonical_sha256":"619fa122d15c320f56eedb42dfa3ad94fd31c5f01709f36d3ac7bda1bf903de1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"619fa122d15c320f56eedb42dfa3ad94fd31c5f01709f36d3ac7bda1bf903de1","first_computed_at":"2026-05-18T03:12:35.219597Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:12:35.219597Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BOudP6pcuIB9b2JZXMwxtQK1PPl1ltiRSJLWEfQsnyr1sSIVnObSCdX0d8PHRSZHKuCZwyi5hi1f7aNgJ26KCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:12:35.220405Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.1518","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8e6fbb3e4dd043795f3fb75b6395b6a3810ebc5b040f791bfd4e395366142c05","sha256:7da8b249e8ab2148dcdc01ff2e3f24884b1147974286fe731cff8fdcce7b61f6"],"state_sha256":"1403e06767a7b12fbd5cfc8dce5907e81d6dbffc1f32eb9d4df9148bdd97a0e9"}