{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:A3B7U5URRMKQXWSWID5AWCY3KY","short_pith_number":"pith:A3B7U5UR","canonical_record":{"source":{"id":"1512.02920","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-09T16:11:25Z","cross_cats_sorted":[],"title_canon_sha256":"0279c59099da85a5cda5375623cf400cf13492f3271f2e69e3e0c5a2c5457904","abstract_canon_sha256":"30cbaea1fc36b5264ed2536053809db38211114c5bb486ace2440fc3df41f98b"},"schema_version":"1.0"},"canonical_sha256":"06c3fa76918b150bda5640fa0b0b1b56175111779104330c0a2f38a5153d6171","source":{"kind":"arxiv","id":"1512.02920","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.02920","created_at":"2026-05-18T00:34:52Z"},{"alias_kind":"arxiv_version","alias_value":"1512.02920v2","created_at":"2026-05-18T00:34:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.02920","created_at":"2026-05-18T00:34:52Z"},{"alias_kind":"pith_short_12","alias_value":"A3B7U5URRMKQ","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"A3B7U5URRMKQXWSW","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"A3B7U5UR","created_at":"2026-05-18T12:29:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:A3B7U5URRMKQXWSWID5AWCY3KY","target":"record","payload":{"canonical_record":{"source":{"id":"1512.02920","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-09T16:11:25Z","cross_cats_sorted":[],"title_canon_sha256":"0279c59099da85a5cda5375623cf400cf13492f3271f2e69e3e0c5a2c5457904","abstract_canon_sha256":"30cbaea1fc36b5264ed2536053809db38211114c5bb486ace2440fc3df41f98b"},"schema_version":"1.0"},"canonical_sha256":"06c3fa76918b150bda5640fa0b0b1b56175111779104330c0a2f38a5153d6171","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:52.971775Z","signature_b64":"1ef1Eq7xM2g9l9npJLNkxT8ZbLUeYgVKfDgY+L+nU/7M8m+dKvvq7YZVlUWslCTtInlKCdofiO32EiAG7XEnBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"06c3fa76918b150bda5640fa0b0b1b56175111779104330c0a2f38a5153d6171","last_reissued_at":"2026-05-18T00:34:52.971104Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:52.971104Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.02920","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":"2026-05-18T00:34:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kaY5ysA/Vb/IE143cKohN6sved9UqHJAede0jrVPy1Pumc4zGyV2a1dp0/j3nyXRRn+xkGIK+ZXoPTGHq/wxDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T16:35:07.380995Z"},"content_sha256":"21f0331bf67d4defe2cd498f2fe644760997a4214cd37a3de27f1fc83218399f","schema_version":"1.0","event_id":"sha256:21f0331bf67d4defe2cd498f2fe644760997a4214cd37a3de27f1fc83218399f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:A3B7U5URRMKQXWSWID5AWCY3KY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Oscillating behaviour of the spectrum for a plasmonic problem in a domain with a rounded corner","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Lucas Chesnel, Sergei A. Nazarov, Xavier Claeys","submitted_at":"2015-12-09T16:11:25Z","abstract_excerpt":"We investigate the eigenvalue problem $-\\text{div}(\\sigma \\nabla u) = \\lambda u\\ (\\mathscr{P})$ in a 2D domain $\\Omega$ divided into two regions $\\Omega_{\\pm}$. We are interested in situations where $\\sigma$ takes positive values on $\\Omega_{+}$ and negative ones on $\\Omega_{-}$. Such problems appear in time harmonic electromagnetics in the modeling of plasmonic technologies. In a recent work [15], we highlighted an unusual instability phenomenon for the source term problem associated with $(\\mathscr{P})$: for certain configurations, when the interface between the subdomains $\\Omega_{\\pm}$ pre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02920","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":"2026-05-18T00:34:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cRBqikyupLDENDDtnZlMtdxiUWsW7WVZFc5pcEJs3sPNvfCuato7eg+Woq/HA/ftLRwFgl2/puWCw5Eo45glBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T16:35:07.381711Z"},"content_sha256":"2fb5a3095f80cb4a1c8af820a193148d31f6b50c6fcccac4f7d25ede9fa56db6","schema_version":"1.0","event_id":"sha256:2fb5a3095f80cb4a1c8af820a193148d31f6b50c6fcccac4f7d25ede9fa56db6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A3B7U5URRMKQXWSWID5AWCY3KY/bundle.json","state_url":"https://pith.science/pith/A3B7U5URRMKQXWSWID5AWCY3KY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A3B7U5URRMKQXWSWID5AWCY3KY/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":"2026-05-26T16:35:07Z","links":{"resolver":"https://pith.science/pith/A3B7U5URRMKQXWSWID5AWCY3KY","bundle":"https://pith.science/pith/A3B7U5URRMKQXWSWID5AWCY3KY/bundle.json","state":"https://pith.science/pith/A3B7U5URRMKQXWSWID5AWCY3KY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A3B7U5URRMKQXWSWID5AWCY3KY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:A3B7U5URRMKQXWSWID5AWCY3KY","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":"30cbaea1fc36b5264ed2536053809db38211114c5bb486ace2440fc3df41f98b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-09T16:11:25Z","title_canon_sha256":"0279c59099da85a5cda5375623cf400cf13492f3271f2e69e3e0c5a2c5457904"},"schema_version":"1.0","source":{"id":"1512.02920","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.02920","created_at":"2026-05-18T00:34:52Z"},{"alias_kind":"arxiv_version","alias_value":"1512.02920v2","created_at":"2026-05-18T00:34:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.02920","created_at":"2026-05-18T00:34:52Z"},{"alias_kind":"pith_short_12","alias_value":"A3B7U5URRMKQ","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"A3B7U5URRMKQXWSW","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"A3B7U5UR","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:2fb5a3095f80cb4a1c8af820a193148d31f6b50c6fcccac4f7d25ede9fa56db6","target":"graph","created_at":"2026-05-18T00:34:52Z","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 investigate the eigenvalue problem $-\\text{div}(\\sigma \\nabla u) = \\lambda u\\ (\\mathscr{P})$ in a 2D domain $\\Omega$ divided into two regions $\\Omega_{\\pm}$. We are interested in situations where $\\sigma$ takes positive values on $\\Omega_{+}$ and negative ones on $\\Omega_{-}$. Such problems appear in time harmonic electromagnetics in the modeling of plasmonic technologies. In a recent work [15], we highlighted an unusual instability phenomenon for the source term problem associated with $(\\mathscr{P})$: for certain configurations, when the interface between the subdomains $\\Omega_{\\pm}$ pre","authors_text":"Lucas Chesnel, Sergei A. Nazarov, Xavier Claeys","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-09T16:11:25Z","title":"Oscillating behaviour of the spectrum for a plasmonic problem in a domain with a rounded corner"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02920","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":"sha256:21f0331bf67d4defe2cd498f2fe644760997a4214cd37a3de27f1fc83218399f","target":"record","created_at":"2026-05-18T00:34:52Z","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":"30cbaea1fc36b5264ed2536053809db38211114c5bb486ace2440fc3df41f98b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-09T16:11:25Z","title_canon_sha256":"0279c59099da85a5cda5375623cf400cf13492f3271f2e69e3e0c5a2c5457904"},"schema_version":"1.0","source":{"id":"1512.02920","kind":"arxiv","version":2}},"canonical_sha256":"06c3fa76918b150bda5640fa0b0b1b56175111779104330c0a2f38a5153d6171","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"06c3fa76918b150bda5640fa0b0b1b56175111779104330c0a2f38a5153d6171","first_computed_at":"2026-05-18T00:34:52.971104Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:52.971104Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1ef1Eq7xM2g9l9npJLNkxT8ZbLUeYgVKfDgY+L+nU/7M8m+dKvvq7YZVlUWslCTtInlKCdofiO32EiAG7XEnBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:52.971775Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.02920","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:21f0331bf67d4defe2cd498f2fe644760997a4214cd37a3de27f1fc83218399f","sha256:2fb5a3095f80cb4a1c8af820a193148d31f6b50c6fcccac4f7d25ede9fa56db6"],"state_sha256":"d0722935dec1a352485394bef7a9af3b30eae2cc44208690c985c1db9e123a2a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KzPj6iiTfRY2KIHgehV4fRro80/eY6ODD0AaRiLOZPwWkWT3F7Q30RlI2O8dal2v3n5p5GY8BrGVGRGEn0Z1BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T16:35:07.385395Z","bundle_sha256":"e410254e1bdfc6b888158d680091fb8e86d3e3672e4c05afe39c96dd5e4a5929"}}