{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:NUTQFZJDQN5J7ILSYO4BX2MPFE","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":"dde76360d19b05b9d43d7a8fc03b2705964c2848bfe59db76b4c3b41c37d3823","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-04-16T09:07:50Z","title_canon_sha256":"e5310c93a7863f06e3adf11e03c36c1fc44c88a175dda8a51ccc0098e0fcfcb7"},"schema_version":"1.0","source":{"id":"1304.4369","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.4369","created_at":"2026-05-18T03:27:53Z"},{"alias_kind":"arxiv_version","alias_value":"1304.4369v1","created_at":"2026-05-18T03:27:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.4369","created_at":"2026-05-18T03:27:53Z"},{"alias_kind":"pith_short_12","alias_value":"NUTQFZJDQN5J","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"NUTQFZJDQN5J7ILS","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"NUTQFZJD","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:d8cba1be6149e0a778d2ed400688987cb9281b7807676920227ca0030cdeef95","target":"graph","created_at":"2026-05-18T03:27:53Z","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 present some new problems in spectral optimization. The first one consists in determining the best domain for the Dirichlet energy (or for the first eigenvalue) of the {\\it metric Laplacian}, and we consider in particular Riemannian or Finsler manifolds, Carnot-Carath\\'eodory spaces, Gaussian spaces. The second one deals with the optimal shape of a graph when the minimization cost is of spectral type. The third one is the optimization problem for a Schr\\\"odinger potential in suitable classes.","authors_text":"Bozhidar Velichkov, Giuseppe Buttazzo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-04-16T09:07:50Z","title":"Some New Problems in Spectral Optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.4369","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":"sha256:2ec8d202592b76797f5e9fa2fa40e7cacfc863c426308c2f94308386a955b176","target":"record","created_at":"2026-05-18T03:27:53Z","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":"dde76360d19b05b9d43d7a8fc03b2705964c2848bfe59db76b4c3b41c37d3823","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-04-16T09:07:50Z","title_canon_sha256":"e5310c93a7863f06e3adf11e03c36c1fc44c88a175dda8a51ccc0098e0fcfcb7"},"schema_version":"1.0","source":{"id":"1304.4369","kind":"arxiv","version":1}},"canonical_sha256":"6d2702e523837a9fa172c3b81be98f2936e82dff569e75582d75ee8a29e8436a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6d2702e523837a9fa172c3b81be98f2936e82dff569e75582d75ee8a29e8436a","first_computed_at":"2026-05-18T03:27:53.283373Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:27:53.283373Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"X9WBskvAitzxLxcZkzxqE5accwsIKK6umHHAz3u+qy5r1doqmRCDNQ08GpFt6tP6PgxHyH2YTb/wwtuHa9syBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:27:53.283936Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.4369","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ec8d202592b76797f5e9fa2fa40e7cacfc863c426308c2f94308386a955b176","sha256:d8cba1be6149e0a778d2ed400688987cb9281b7807676920227ca0030cdeef95"],"state_sha256":"454d698e0b43b5a3575872bf61690cf91626bc8310d6ccc2fa4c803fec1e147b"}