{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:C33YWLILWRKQR5YF2BGXXBSRJV","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":"6525aec7dd52d649ca55b70f2747bcd530ebd543b28155e3e794d2549baf7b90","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-12-13T19:28:02Z","title_canon_sha256":"0792929d7cab01785299a90f5b2bb288e051f39f8a9e28997121ea2bca2c78c3"},"schema_version":"1.0","source":{"id":"1312.3915","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.3915","created_at":"2026-05-18T03:04:47Z"},{"alias_kind":"arxiv_version","alias_value":"1312.3915v1","created_at":"2026-05-18T03:04:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.3915","created_at":"2026-05-18T03:04:47Z"},{"alias_kind":"pith_short_12","alias_value":"C33YWLILWRKQ","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"C33YWLILWRKQR5YF","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"C33YWLIL","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:72a1cf6069563c2dd0585d1985aa6f5869bc17ba5d8896120a5f3a0e1b14af17","target":"graph","created_at":"2026-05-18T03:04:47Z","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 consider shape optimization problems of the form $$\\min\\big\\{J(\\Omega)\\ :\\ \\Omega\\subset X,\\ m(\\Omega)\\le c\\big\\},$$ where $X$ is a metric measure space and $J$ is a suitable shape functional. We adapt the notions of $\\gamma$-convergence and weak $\\gamma$-convergence to this new general abstract setting to prove the existence of an optimal domain. Several examples are pointed out and discussed.","authors_text":"Bozhidar Velichkov, Giuseppe Buttazzo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-12-13T19:28:02Z","title":"Shape optimization problems on metric measure spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.3915","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:f82e80ad66d9f3e1d3038d74c752cf3955e43d921d170564367cdc73c1dfebe3","target":"record","created_at":"2026-05-18T03:04:47Z","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":"6525aec7dd52d649ca55b70f2747bcd530ebd543b28155e3e794d2549baf7b90","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-12-13T19:28:02Z","title_canon_sha256":"0792929d7cab01785299a90f5b2bb288e051f39f8a9e28997121ea2bca2c78c3"},"schema_version":"1.0","source":{"id":"1312.3915","kind":"arxiv","version":1}},"canonical_sha256":"16f78b2d0bb45508f705d04d7b86514d5b3b873f0e1af2a9fc1d4d2bf4fefea4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"16f78b2d0bb45508f705d04d7b86514d5b3b873f0e1af2a9fc1d4d2bf4fefea4","first_computed_at":"2026-05-18T03:04:47.125383Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:04:47.125383Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YPgu1as/RqbUSW1mV8u9OelcIKh4fvkpIg1XStOQUilJyefMokup1CL5i2nV911rCz0BU1lRzlUZ2XyBI4f5BA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:04:47.125995Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.3915","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f82e80ad66d9f3e1d3038d74c752cf3955e43d921d170564367cdc73c1dfebe3","sha256:72a1cf6069563c2dd0585d1985aa6f5869bc17ba5d8896120a5f3a0e1b14af17"],"state_sha256":"3fca3ab7553322506529d81cd7540fb2beb99f1388111361cdb3af13db8a5408"}