{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:BPBF4IP46RUH3ZT2JT3WNBLGZK","short_pith_number":"pith:BPBF4IP4","canonical_record":{"source":{"id":"2407.11703","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-07-16T13:21:54Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"e3257e3ebb9b9d6dcc567a88007efc5ff23d4bb0eddf16e7a4e64a3ddf95f59c","abstract_canon_sha256":"6dc83e71cd6d8d591695ec0b950bc200829d3db3a8c22bed28d034a90906c9ac"},"schema_version":"1.0"},"canonical_sha256":"0bc25e21fcf4687de67a4cf7668566ca9d0586d2c9bc515fe8ddb34aa2fd60bc","source":{"kind":"arxiv","id":"2407.11703","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.11703","created_at":"2026-05-20T00:02:46Z"},{"alias_kind":"arxiv_version","alias_value":"2407.11703v1","created_at":"2026-05-20T00:02:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.11703","created_at":"2026-05-20T00:02:46Z"},{"alias_kind":"pith_short_12","alias_value":"BPBF4IP46RUH","created_at":"2026-05-20T00:02:46Z"},{"alias_kind":"pith_short_16","alias_value":"BPBF4IP46RUH3ZT2","created_at":"2026-05-20T00:02:46Z"},{"alias_kind":"pith_short_8","alias_value":"BPBF4IP4","created_at":"2026-05-20T00:02:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:BPBF4IP46RUH3ZT2JT3WNBLGZK","target":"record","payload":{"canonical_record":{"source":{"id":"2407.11703","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-07-16T13:21:54Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"e3257e3ebb9b9d6dcc567a88007efc5ff23d4bb0eddf16e7a4e64a3ddf95f59c","abstract_canon_sha256":"6dc83e71cd6d8d591695ec0b950bc200829d3db3a8c22bed28d034a90906c9ac"},"schema_version":"1.0"},"canonical_sha256":"0bc25e21fcf4687de67a4cf7668566ca9d0586d2c9bc515fe8ddb34aa2fd60bc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:02:46.477413Z","signature_b64":"8hYIOeSpTS5mkf3ZbhrHH3b1QSUUkKqJM6OSJY9C7SyBxlmLR43mfxrNebqYATiSTzCjgIMpfJnEYqyOxCAvBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0bc25e21fcf4687de67a4cf7668566ca9d0586d2c9bc515fe8ddb34aa2fd60bc","last_reissued_at":"2026-05-20T00:02:46.476784Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:02:46.476784Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2407.11703","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-20T00:02:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XjLch8SWA9IctEwImQUYqhE6g6KFjAdTgqchjwBFlixmrN5UBcB287n00CGKDD+azzRUAFv1ioCjwvHprvfhCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T03:02:13.246119Z"},"content_sha256":"c3adadf0b97a9069f91672db6d55a58bea6e7b5166059226224f99a67ac53ff2","schema_version":"1.0","event_id":"sha256:c3adadf0b97a9069f91672db6d55a58bea6e7b5166059226224f99a67ac53ff2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:BPBF4IP46RUH3ZT2JT3WNBLGZK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Numerical Eigenvalue Optimization by Shape-Variations for Maxwell's Eigenvalue Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"math.OC","authors_text":"Christine Herter, Sebastian Sch\\\"ops, Winnifried Wollner","submitted_at":"2024-07-16T13:21:54Z","abstract_excerpt":"In this paper we consider the free-form optimization of eigenvalues in electromagnetic systems by means of shape-variations with respect to small deformations. The objective is to optimize a particular eigenvalue to a target value. We introduce the mixed variational formulation of the Maxwell eigenvalue problem introduced by Kikuchi (1987) in function spaces of (H(\\operatorname{curl}; \\Omega)) and (H^1(\\Omega)). To handle this formulation, suitable transformations of these spaces are utilized, e.g., of Piola-type for the space of (H(\\operatorname{curl}; \\Omega)). This allows for a formulation "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.11703","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2407.11703/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-05-20T00:02:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UQugKqNOxVMqa0IPjPNzmuC9lIOg6BYadOAV3KD5Rx11FhGVGraBUIQoxpneaL0ZScMzY+MbLynQZefTKG5rDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T03:02:13.246509Z"},"content_sha256":"ddc42c13900491882284468b847acacb9aec65a93bec79533b9068f51f597aac","schema_version":"1.0","event_id":"sha256:ddc42c13900491882284468b847acacb9aec65a93bec79533b9068f51f597aac"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BPBF4IP46RUH3ZT2JT3WNBLGZK/bundle.json","state_url":"https://pith.science/pith/BPBF4IP46RUH3ZT2JT3WNBLGZK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BPBF4IP46RUH3ZT2JT3WNBLGZK/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":"2026-05-28T03:02:13Z","links":{"resolver":"https://pith.science/pith/BPBF4IP46RUH3ZT2JT3WNBLGZK","bundle":"https://pith.science/pith/BPBF4IP46RUH3ZT2JT3WNBLGZK/bundle.json","state":"https://pith.science/pith/BPBF4IP46RUH3ZT2JT3WNBLGZK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BPBF4IP46RUH3ZT2JT3WNBLGZK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:BPBF4IP46RUH3ZT2JT3WNBLGZK","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":"6dc83e71cd6d8d591695ec0b950bc200829d3db3a8c22bed28d034a90906c9ac","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-07-16T13:21:54Z","title_canon_sha256":"e3257e3ebb9b9d6dcc567a88007efc5ff23d4bb0eddf16e7a4e64a3ddf95f59c"},"schema_version":"1.0","source":{"id":"2407.11703","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.11703","created_at":"2026-05-20T00:02:46Z"},{"alias_kind":"arxiv_version","alias_value":"2407.11703v1","created_at":"2026-05-20T00:02:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.11703","created_at":"2026-05-20T00:02:46Z"},{"alias_kind":"pith_short_12","alias_value":"BPBF4IP46RUH","created_at":"2026-05-20T00:02:46Z"},{"alias_kind":"pith_short_16","alias_value":"BPBF4IP46RUH3ZT2","created_at":"2026-05-20T00:02:46Z"},{"alias_kind":"pith_short_8","alias_value":"BPBF4IP4","created_at":"2026-05-20T00:02:46Z"}],"graph_snapshots":[{"event_id":"sha256:ddc42c13900491882284468b847acacb9aec65a93bec79533b9068f51f597aac","target":"graph","created_at":"2026-05-20T00:02:46Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2407.11703/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we consider the free-form optimization of eigenvalues in electromagnetic systems by means of shape-variations with respect to small deformations. The objective is to optimize a particular eigenvalue to a target value. We introduce the mixed variational formulation of the Maxwell eigenvalue problem introduced by Kikuchi (1987) in function spaces of (H(\\operatorname{curl}; \\Omega)) and (H^1(\\Omega)). To handle this formulation, suitable transformations of these spaces are utilized, e.g., of Piola-type for the space of (H(\\operatorname{curl}; \\Omega)). This allows for a formulation ","authors_text":"Christine Herter, Sebastian Sch\\\"ops, Winnifried Wollner","cross_cats":["cs.NA","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-07-16T13:21:54Z","title":"Numerical Eigenvalue Optimization by Shape-Variations for Maxwell's Eigenvalue Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.11703","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:c3adadf0b97a9069f91672db6d55a58bea6e7b5166059226224f99a67ac53ff2","target":"record","created_at":"2026-05-20T00:02:46Z","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":"6dc83e71cd6d8d591695ec0b950bc200829d3db3a8c22bed28d034a90906c9ac","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-07-16T13:21:54Z","title_canon_sha256":"e3257e3ebb9b9d6dcc567a88007efc5ff23d4bb0eddf16e7a4e64a3ddf95f59c"},"schema_version":"1.0","source":{"id":"2407.11703","kind":"arxiv","version":1}},"canonical_sha256":"0bc25e21fcf4687de67a4cf7668566ca9d0586d2c9bc515fe8ddb34aa2fd60bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0bc25e21fcf4687de67a4cf7668566ca9d0586d2c9bc515fe8ddb34aa2fd60bc","first_computed_at":"2026-05-20T00:02:46.476784Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:02:46.476784Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8hYIOeSpTS5mkf3ZbhrHH3b1QSUUkKqJM6OSJY9C7SyBxlmLR43mfxrNebqYATiSTzCjgIMpfJnEYqyOxCAvBA==","signature_status":"signed_v1","signed_at":"2026-05-20T00:02:46.477413Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.11703","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c3adadf0b97a9069f91672db6d55a58bea6e7b5166059226224f99a67ac53ff2","sha256:ddc42c13900491882284468b847acacb9aec65a93bec79533b9068f51f597aac"],"state_sha256":"9bda9ffa9350993f7c12909b77a484e75ee58282dad27cc06b5da6863912b7c1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8HYiBJwdFI3asv/y0RVJhlVZ9NZWbxKRtq55QZ+XmiJPa+z4QtpPJuUZAf8novfRYKgQBDanRPxuETy6gXqnBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T03:02:13.248588Z","bundle_sha256":"22cc5cef26f5b73eaa2d1205551e04aa65cde4e42c2f1a8644b5b4f7561db3a2"}}