{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:P4UXV63LV6MIGP6ENRH2AEYJOQ","short_pith_number":"pith:P4UXV63L","canonical_record":{"source":{"id":"1702.07525","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-02-24T10:21:56Z","cross_cats_sorted":[],"title_canon_sha256":"f8dd9dbee9873065d46e84e2d6fbd38e6e1a24ecfe8dc489ddb3057489da48b1","abstract_canon_sha256":"143dcbe79ab576e92f24165f5748c86c3d8d10ea27e5eeca1850f30257fe72f5"},"schema_version":"1.0"},"canonical_sha256":"7f297afb6baf98833fc46c4fa0130974347a2eb2a5cb032dddec2628614061a3","source":{"kind":"arxiv","id":"1702.07525","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.07525","created_at":"2026-05-18T00:50:03Z"},{"alias_kind":"arxiv_version","alias_value":"1702.07525v1","created_at":"2026-05-18T00:50:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.07525","created_at":"2026-05-18T00:50:03Z"},{"alias_kind":"pith_short_12","alias_value":"P4UXV63LV6MI","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"P4UXV63LV6MIGP6E","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"P4UXV63L","created_at":"2026-05-18T12:31:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:P4UXV63LV6MIGP6ENRH2AEYJOQ","target":"record","payload":{"canonical_record":{"source":{"id":"1702.07525","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-02-24T10:21:56Z","cross_cats_sorted":[],"title_canon_sha256":"f8dd9dbee9873065d46e84e2d6fbd38e6e1a24ecfe8dc489ddb3057489da48b1","abstract_canon_sha256":"143dcbe79ab576e92f24165f5748c86c3d8d10ea27e5eeca1850f30257fe72f5"},"schema_version":"1.0"},"canonical_sha256":"7f297afb6baf98833fc46c4fa0130974347a2eb2a5cb032dddec2628614061a3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:50:03.038139Z","signature_b64":"+nzEGWWI9R1Gs9vCYRnbaky1+i7lkCZFAbRdllet2mEWe4UUQrO5wdfKeCLbgEORkGz4hcFw9Ob0ykBLjKQ/Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7f297afb6baf98833fc46c4fa0130974347a2eb2a5cb032dddec2628614061a3","last_reissued_at":"2026-05-18T00:50:03.037160Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:50:03.037160Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.07525","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":"2026-05-18T00:50:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ptuftX6+exteIzNUQvGkv8ktPi0WYi+W6xNkMwuiuqWrAJsUag/+mTEnoe7gMrsW6s8XXT/slYNG1Nh3GnxPDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T17:47:27.564331Z"},"content_sha256":"e41b3b72c652320c7343d806f9e9a21250009c340253b57ac9db5b4531445642","schema_version":"1.0","event_id":"sha256:e41b3b72c652320c7343d806f9e9a21250009c340253b57ac9db5b4531445642"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:P4UXV63LV6MIGP6ENRH2AEYJOQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A convex analysis approach to multi-material topology optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Christian Clason, Karl Kunisch","submitted_at":"2017-02-24T10:21:56Z","abstract_excerpt":"This work is concerned with optimal control of partial differential equations where the control enters the state equation as a coefficient and should take on values only from a given discrete set of values corresponding to available materials. A \"multi-bang\" framework based on convex analysis is proposed where the desired piecewise constant structure is incorporated using a convex penalty term. Together with a suitable tracking term, this allows formulating the problem of optimizing the topology of the distribution of material parameters as minimizing a convex functional subject to a (nonlinea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.07525","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":""},"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":"2026-05-18T00:50:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gp0CzhA+OIRyXW1+wmp+YUfQNWJw4PPhC7l9HzkQSejf0S3ii8tu9wf7cu2P6HG6id7joFO4H8Eag2b1E/KbAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T17:47:27.564891Z"},"content_sha256":"0b0c0ba7c235a7400d6cef3620ffe7d755dd7af8b2eaca9fe6cadbb81438ee39","schema_version":"1.0","event_id":"sha256:0b0c0ba7c235a7400d6cef3620ffe7d755dd7af8b2eaca9fe6cadbb81438ee39"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P4UXV63LV6MIGP6ENRH2AEYJOQ/bundle.json","state_url":"https://pith.science/pith/P4UXV63LV6MIGP6ENRH2AEYJOQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P4UXV63LV6MIGP6ENRH2AEYJOQ/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":"2026-06-02T17:47:27Z","links":{"resolver":"https://pith.science/pith/P4UXV63LV6MIGP6ENRH2AEYJOQ","bundle":"https://pith.science/pith/P4UXV63LV6MIGP6ENRH2AEYJOQ/bundle.json","state":"https://pith.science/pith/P4UXV63LV6MIGP6ENRH2AEYJOQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P4UXV63LV6MIGP6ENRH2AEYJOQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:P4UXV63LV6MIGP6ENRH2AEYJOQ","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":"143dcbe79ab576e92f24165f5748c86c3d8d10ea27e5eeca1850f30257fe72f5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-02-24T10:21:56Z","title_canon_sha256":"f8dd9dbee9873065d46e84e2d6fbd38e6e1a24ecfe8dc489ddb3057489da48b1"},"schema_version":"1.0","source":{"id":"1702.07525","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.07525","created_at":"2026-05-18T00:50:03Z"},{"alias_kind":"arxiv_version","alias_value":"1702.07525v1","created_at":"2026-05-18T00:50:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.07525","created_at":"2026-05-18T00:50:03Z"},{"alias_kind":"pith_short_12","alias_value":"P4UXV63LV6MI","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"P4UXV63LV6MIGP6E","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"P4UXV63L","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:0b0c0ba7c235a7400d6cef3620ffe7d755dd7af8b2eaca9fe6cadbb81438ee39","target":"graph","created_at":"2026-05-18T00:50:03Z","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":"This work is concerned with optimal control of partial differential equations where the control enters the state equation as a coefficient and should take on values only from a given discrete set of values corresponding to available materials. A \"multi-bang\" framework based on convex analysis is proposed where the desired piecewise constant structure is incorporated using a convex penalty term. Together with a suitable tracking term, this allows formulating the problem of optimizing the topology of the distribution of material parameters as minimizing a convex functional subject to a (nonlinea","authors_text":"Christian Clason, Karl Kunisch","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-02-24T10:21:56Z","title":"A convex analysis approach to multi-material topology optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.07525","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:e41b3b72c652320c7343d806f9e9a21250009c340253b57ac9db5b4531445642","target":"record","created_at":"2026-05-18T00:50:03Z","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":"143dcbe79ab576e92f24165f5748c86c3d8d10ea27e5eeca1850f30257fe72f5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-02-24T10:21:56Z","title_canon_sha256":"f8dd9dbee9873065d46e84e2d6fbd38e6e1a24ecfe8dc489ddb3057489da48b1"},"schema_version":"1.0","source":{"id":"1702.07525","kind":"arxiv","version":1}},"canonical_sha256":"7f297afb6baf98833fc46c4fa0130974347a2eb2a5cb032dddec2628614061a3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7f297afb6baf98833fc46c4fa0130974347a2eb2a5cb032dddec2628614061a3","first_computed_at":"2026-05-18T00:50:03.037160Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:03.037160Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+nzEGWWI9R1Gs9vCYRnbaky1+i7lkCZFAbRdllet2mEWe4UUQrO5wdfKeCLbgEORkGz4hcFw9Ob0ykBLjKQ/Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:03.038139Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.07525","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e41b3b72c652320c7343d806f9e9a21250009c340253b57ac9db5b4531445642","sha256:0b0c0ba7c235a7400d6cef3620ffe7d755dd7af8b2eaca9fe6cadbb81438ee39"],"state_sha256":"5692695741d5b50d3d4eee1bbfb950cd128c379b83dad86449bb6cf2b1243517"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"slVTyP38HmKPTIo5ReAMvaawp/eKCUZnMhw2Bq95OjSdmCtFcpHv5l2T8lU20aXfi48tA4nGta5bj1qHWGCsBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T17:47:27.568723Z","bundle_sha256":"c4f58bbe6c099d99c54e6b39863069962d8917c800489080e90fcc70b81f7470"}}