{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:3K2V4FEUH52PUFYAYTMIJKQG7A","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":"5221df0a95f91c097fa3f83d95b2e0623cd737a5a193ef51eadcbf20f4779c39","cross_cats_sorted":["math-ph","math.MP","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-03-21T19:29:23Z","title_canon_sha256":"b8d8fa1a38c7786bff7b1e023185caa8c62f11e8546f0ec4d080b8c7b56b1043"},"schema_version":"1.0","source":{"id":"1103.4117","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.4117","created_at":"2026-05-18T03:32:59Z"},{"alias_kind":"arxiv_version","alias_value":"1103.4117v5","created_at":"2026-05-18T03:32:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.4117","created_at":"2026-05-18T03:32:59Z"},{"alias_kind":"pith_short_12","alias_value":"3K2V4FEUH52P","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"3K2V4FEUH52PUFYA","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"3K2V4FEU","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:7cc825def0ee3568eb26b941e1a542fc8436ad0ebdb096a1d52df78e22767b39","target":"graph","created_at":"2026-05-18T03:32:59Z","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":"The paper is devoted to optimization of resonances associated with 1-D wave equations in inhomogeneous media. The medium's structure is represented by a nonnegative function B. The problem is to design for a given $\\alpha \\in \\R$ a medium that generates a resonance on the line $\\alpha + \\i \\R$ with a minimal possible modulus of the imaginary part. We consider an admissible family of mediums that arises in a problem of optimal design for photonic crystals. This admissible family is defined by the constraints $0\\leq b_1 \\leq B (x) \\leq b_2$ with certain constants $b_{1,2}$. The paper gives an ac","authors_text":"Illya M. Karabash","cross_cats":["math-ph","math.MP","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-03-21T19:29:23Z","title":"Optimization of quasi-normal eigenvalues for 1-D wave equations in inhomogeneous media; description of optimal structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.4117","kind":"arxiv","version":5},"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:d9c4f5d3d54d642122bf10eb15fa53f6ccbe3cc6d4c63eacfaa403df602c82e9","target":"record","created_at":"2026-05-18T03:32:59Z","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":"5221df0a95f91c097fa3f83d95b2e0623cd737a5a193ef51eadcbf20f4779c39","cross_cats_sorted":["math-ph","math.MP","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-03-21T19:29:23Z","title_canon_sha256":"b8d8fa1a38c7786bff7b1e023185caa8c62f11e8546f0ec4d080b8c7b56b1043"},"schema_version":"1.0","source":{"id":"1103.4117","kind":"arxiv","version":5}},"canonical_sha256":"dab55e14943f74fa1700c4d884aa06f83762f3034f41f5ec4f3379ea52eea6df","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dab55e14943f74fa1700c4d884aa06f83762f3034f41f5ec4f3379ea52eea6df","first_computed_at":"2026-05-18T03:32:59.097453Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:32:59.097453Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Jg2yZ6yftvftVBOpEaWZRnwWX/uwaWNQWQu3nKLjmJ+qE6cKA8xm6KnsGb0eiwz0TEhkn/Tu81Chh3FtjqqSCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:32:59.098245Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.4117","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d9c4f5d3d54d642122bf10eb15fa53f6ccbe3cc6d4c63eacfaa403df602c82e9","sha256:7cc825def0ee3568eb26b941e1a542fc8436ad0ebdb096a1d52df78e22767b39"],"state_sha256":"dfc948fd20d9bbbb2c3120ea331b4e8ef798923f8ea484b25246049c50879ef7"}