{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:VJTFW3JXXED76WAZIRKROEDW63","short_pith_number":"pith:VJTFW3JX","canonical_record":{"source":{"id":"1601.04136","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-01-16T08:22:05Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"895538cb9403d478886e858009369fc778d51bcf614bca6537fdcda31260127f","abstract_canon_sha256":"9c97cedfa0ebf5deccbce74d74e78fd3f734588d26296ec026b7b43f944dd82c"},"schema_version":"1.0"},"canonical_sha256":"aa665b6d37b907ff58194455171076f6e5448f2b9ea73d99e891e9aa7e7fa3bf","source":{"kind":"arxiv","id":"1601.04136","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.04136","created_at":"2026-05-18T01:04:37Z"},{"alias_kind":"arxiv_version","alias_value":"1601.04136v3","created_at":"2026-05-18T01:04:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.04136","created_at":"2026-05-18T01:04:37Z"},{"alias_kind":"pith_short_12","alias_value":"VJTFW3JXXED7","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VJTFW3JXXED76WAZ","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VJTFW3JX","created_at":"2026-05-18T12:30:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:VJTFW3JXXED76WAZIRKROEDW63","target":"record","payload":{"canonical_record":{"source":{"id":"1601.04136","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-01-16T08:22:05Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"895538cb9403d478886e858009369fc778d51bcf614bca6537fdcda31260127f","abstract_canon_sha256":"9c97cedfa0ebf5deccbce74d74e78fd3f734588d26296ec026b7b43f944dd82c"},"schema_version":"1.0"},"canonical_sha256":"aa665b6d37b907ff58194455171076f6e5448f2b9ea73d99e891e9aa7e7fa3bf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:37.654074Z","signature_b64":"C4m5Ot5GFkCwdXWpBIgx2N9S2o6CIz2UB8mfHalVN2T0hps0oYC/ZWMJzV/XnxE03YFogs33zV7eunfoL9tiAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aa665b6d37b907ff58194455171076f6e5448f2b9ea73d99e891e9aa7e7fa3bf","last_reissued_at":"2026-05-18T01:04:37.653533Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:37.653533Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.04136","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:04:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HUDKVHI0cAUQC5fDjJoRSacEi0SGHwdXKN9wCAQ1DBMr5ntKnTHEhwFYQvLxGkSoNiHHsNw+Iz9GKaLbaAYCBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T16:23:13.528730Z"},"content_sha256":"b7186e1fdbe85487a6d4d8fcd6d4cc3639fb04ea876f9806b35cc5cffafc2f4d","schema_version":"1.0","event_id":"sha256:b7186e1fdbe85487a6d4d8fcd6d4cc3639fb04ea876f9806b35cc5cffafc2f4d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:VJTFW3JXXED76WAZIRKROEDW63","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Shape optimisation for a class of semilinear variational inequalities with applications to damage models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.OC","authors_text":"Christian Heinemann, Kevin Sturm","submitted_at":"2016-01-16T08:22:05Z","abstract_excerpt":"The present contribution investigates shape optimisation problems for a class of semilinear elliptic variational inequalities with Neumann boundary conditions. Sensitivity estimates and material derivatives are firstly derived in an abstract operator setting where the operators are defined on polyhedral subsets of reflexive Banach spaces. The results are then refined for variational inequalities arising from minimisation problems for certain convex energy functionals considered over upper obstacle sets in $H^1$. One particularity is that we allow for dynamic obstacle functions which may arise "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.04136","kind":"arxiv","version":3},"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":"2026-05-18T01:04:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KN79IspHIUs9uN9TBc+OHkuT09L1amMlx2OElGps4st2mKABANizUynHA0aEbbdVGEpHYWhEPexqxxsMatorBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T16:23:13.529071Z"},"content_sha256":"3406ae3693e1669afe82f7c5816467e54cb48b6e30306371b5b36b24a536e96e","schema_version":"1.0","event_id":"sha256:3406ae3693e1669afe82f7c5816467e54cb48b6e30306371b5b36b24a536e96e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VJTFW3JXXED76WAZIRKROEDW63/bundle.json","state_url":"https://pith.science/pith/VJTFW3JXXED76WAZIRKROEDW63/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VJTFW3JXXED76WAZIRKROEDW63/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":"2026-06-01T16:23:13Z","links":{"resolver":"https://pith.science/pith/VJTFW3JXXED76WAZIRKROEDW63","bundle":"https://pith.science/pith/VJTFW3JXXED76WAZIRKROEDW63/bundle.json","state":"https://pith.science/pith/VJTFW3JXXED76WAZIRKROEDW63/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VJTFW3JXXED76WAZIRKROEDW63/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:VJTFW3JXXED76WAZIRKROEDW63","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":"9c97cedfa0ebf5deccbce74d74e78fd3f734588d26296ec026b7b43f944dd82c","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-01-16T08:22:05Z","title_canon_sha256":"895538cb9403d478886e858009369fc778d51bcf614bca6537fdcda31260127f"},"schema_version":"1.0","source":{"id":"1601.04136","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.04136","created_at":"2026-05-18T01:04:37Z"},{"alias_kind":"arxiv_version","alias_value":"1601.04136v3","created_at":"2026-05-18T01:04:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.04136","created_at":"2026-05-18T01:04:37Z"},{"alias_kind":"pith_short_12","alias_value":"VJTFW3JXXED7","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VJTFW3JXXED76WAZ","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VJTFW3JX","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:3406ae3693e1669afe82f7c5816467e54cb48b6e30306371b5b36b24a536e96e","target":"graph","created_at":"2026-05-18T01:04:37Z","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 present contribution investigates shape optimisation problems for a class of semilinear elliptic variational inequalities with Neumann boundary conditions. Sensitivity estimates and material derivatives are firstly derived in an abstract operator setting where the operators are defined on polyhedral subsets of reflexive Banach spaces. The results are then refined for variational inequalities arising from minimisation problems for certain convex energy functionals considered over upper obstacle sets in $H^1$. One particularity is that we allow for dynamic obstacle functions which may arise ","authors_text":"Christian Heinemann, Kevin Sturm","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-01-16T08:22:05Z","title":"Shape optimisation for a class of semilinear variational inequalities with applications to damage models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.04136","kind":"arxiv","version":3},"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:b7186e1fdbe85487a6d4d8fcd6d4cc3639fb04ea876f9806b35cc5cffafc2f4d","target":"record","created_at":"2026-05-18T01:04:37Z","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":"9c97cedfa0ebf5deccbce74d74e78fd3f734588d26296ec026b7b43f944dd82c","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-01-16T08:22:05Z","title_canon_sha256":"895538cb9403d478886e858009369fc778d51bcf614bca6537fdcda31260127f"},"schema_version":"1.0","source":{"id":"1601.04136","kind":"arxiv","version":3}},"canonical_sha256":"aa665b6d37b907ff58194455171076f6e5448f2b9ea73d99e891e9aa7e7fa3bf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aa665b6d37b907ff58194455171076f6e5448f2b9ea73d99e891e9aa7e7fa3bf","first_computed_at":"2026-05-18T01:04:37.653533Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:37.653533Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C4m5Ot5GFkCwdXWpBIgx2N9S2o6CIz2UB8mfHalVN2T0hps0oYC/ZWMJzV/XnxE03YFogs33zV7eunfoL9tiAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:37.654074Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.04136","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b7186e1fdbe85487a6d4d8fcd6d4cc3639fb04ea876f9806b35cc5cffafc2f4d","sha256:3406ae3693e1669afe82f7c5816467e54cb48b6e30306371b5b36b24a536e96e"],"state_sha256":"20ced4a179580605621e867fccd4fda92e6aebb9038329c2eab50b45371ea282"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GpBpx7O6U6XFha4HBYNNDvIVgNvCVb4xV8u67s+WtsuEryaVG46zxzM0ftJCpBUpL5T9DzPqWoQi8eNw7AynBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T16:23:13.530915Z","bundle_sha256":"44cf3afd383ad5b2fe18e00705f6935f4e85446ab5ce0eb6472c9a9831361f8a"}}