{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:CU2AMYI7SQUFVIU5P7ZQHGAWIW","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":"127d694b21a5828266cabc38b33ec695ae94eaa00049add6c393630358135ada","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-06-02T13:03:06Z","title_canon_sha256":"6f1905466c051dc1cdebcf81230d9d28dc0d573d0d9c16814256f166e7d67a1c"},"schema_version":"1.0","source":{"id":"1506.00866","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.00866","created_at":"2026-05-18T01:59:34Z"},{"alias_kind":"arxiv_version","alias_value":"1506.00866v1","created_at":"2026-05-18T01:59:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.00866","created_at":"2026-05-18T01:59:34Z"},{"alias_kind":"pith_short_12","alias_value":"CU2AMYI7SQUF","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"CU2AMYI7SQUFVIU5","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"CU2AMYI7","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:8fdd9c8c329935806983933cb600b6b5757e00cdfe2d8bd45f4dae6545899e11","target":"graph","created_at":"2026-05-18T01:59:34Z","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":"Localized surface plasmons are charge density oscillations confined to metallic nanoparticles. Excitation of localized surface plasmons by an electromagnetic field at an incident wavelength where resonance occurs results in a strong light scattering and an enhancement of the local electromagnetic fields. This paper is devoted to the mathematical modeling of plasmonic nanoparticles. Its aim is threefold: (i) to mathematically define the notion of plasmonic resonance and to analyze the shift and broadening of the plasmon resonance with changes in size and shape of the nanoparticles; (ii) to stud","authors_text":"Habib Ammari, Hai Zhang, Matias Ruiz, Pierre Millien","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-06-02T13:03:06Z","title":"Mathematical analysis of plasmonic nanoparticles: the scalar case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.00866","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":"sha256:0428eaae740e24e9b739481cd20d5790b196ba4e5c3631a2eb5c4a5a5caccec8","target":"record","created_at":"2026-05-18T01:59:34Z","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":"127d694b21a5828266cabc38b33ec695ae94eaa00049add6c393630358135ada","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-06-02T13:03:06Z","title_canon_sha256":"6f1905466c051dc1cdebcf81230d9d28dc0d573d0d9c16814256f166e7d67a1c"},"schema_version":"1.0","source":{"id":"1506.00866","kind":"arxiv","version":1}},"canonical_sha256":"153406611f94285aa29d7ff303981645b7177adc57f1735e692e6a97a978def6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"153406611f94285aa29d7ff303981645b7177adc57f1735e692e6a97a978def6","first_computed_at":"2026-05-18T01:59:34.254380Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:59:34.254380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GspXJzY5j2JMELSqN1+ohmT8ck3Bn3S9LtnMPUzMdgpo7PK4e/KzDqtygKMW34F5xfg6eTIITrFtil3V1oUwCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:59:34.255037Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.00866","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0428eaae740e24e9b739481cd20d5790b196ba4e5c3631a2eb5c4a5a5caccec8","sha256:8fdd9c8c329935806983933cb600b6b5757e00cdfe2d8bd45f4dae6545899e11"],"state_sha256":"128702c84047535e183edcf56bffaebe9ac7ff2f47b8ad73e7e80e6111eac4e2"}