{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:3RBYT4UA22GOTG7DI5W3AZB72W","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":"6a1ebf09940c3f7ceade29bbe1e480a25576df4987890687cd9e84f970008f7c","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-04-24T10:59:24Z","title_canon_sha256":"5cd849d9872a702fb4a9e62f331e54a2678b14904b3a7d0796a3d1dfe7b578a6"},"schema_version":"1.0","source":{"id":"1804.08952","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.08952","created_at":"2026-05-17T23:45:38Z"},{"alias_kind":"arxiv_version","alias_value":"1804.08952v1","created_at":"2026-05-17T23:45:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.08952","created_at":"2026-05-17T23:45:38Z"},{"alias_kind":"pith_short_12","alias_value":"3RBYT4UA22GO","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"3RBYT4UA22GOTG7D","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"3RBYT4UA","created_at":"2026-05-18T12:32:02Z"}],"graph_snapshots":[{"event_id":"sha256:30416d9e0a2f10cf22eb131885b836897e9ec71e292db451920065fe39659710","target":"graph","created_at":"2026-05-17T23:45:38Z","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 study the essential spectrum of operator pencils associated with anisotropic Maxwell equations, with permittivity $\\varepsilon$, permeability $\\mu$ and conductivity $\\sigma$, on finitely connected unbounded domains. The main result is that the essential spectrum of the Maxwell pencil is the union of two sets: namely, the spectrum of the pencil $\\mathrm{div}((\\omega\\varepsilon + i \\sigma) \\nabla\\,\\cdot\\,)$, and the essential spectrum of the Maxwell pencil with constant coefficients. We expect the analysis to be of more general interest and to open avenues to investigation of other questions ","authors_text":"Giovanni S. Alberti, Ian Wood, Malcolm Brown, Marco Marletta","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-04-24T10:59:24Z","title":"Essential spectrum for Maxwell's equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.08952","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":"sha256:087aedecdc94c4a9a71ece795835622541248a7e139b80ed7510f7043e268a20","target":"record","created_at":"2026-05-17T23:45:38Z","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":"6a1ebf09940c3f7ceade29bbe1e480a25576df4987890687cd9e84f970008f7c","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-04-24T10:59:24Z","title_canon_sha256":"5cd849d9872a702fb4a9e62f331e54a2678b14904b3a7d0796a3d1dfe7b578a6"},"schema_version":"1.0","source":{"id":"1804.08952","kind":"arxiv","version":1}},"canonical_sha256":"dc4389f280d68ce99be3476db0643fd5a7ab03a0d7933895a5d538e97d1743b7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dc4389f280d68ce99be3476db0643fd5a7ab03a0d7933895a5d538e97d1743b7","first_computed_at":"2026-05-17T23:45:38.601787Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:38.601787Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gu5+lg3msBxj2GxTlWUv63SZ/QHsWx0GYdrqSCGzbJjjfLNZo/4bnpWwaMeVGswDxZiX+TLP71L/4IqhZoBABQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:38.602255Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.08952","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:087aedecdc94c4a9a71ece795835622541248a7e139b80ed7510f7043e268a20","sha256:30416d9e0a2f10cf22eb131885b836897e9ec71e292db451920065fe39659710"],"state_sha256":"a8fdbe8f48b52534da7696bae64ded1869a35e5277985f5cc9ec3b01ae4a164e"}