{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:3JQWKI62GFZJ2B3HWH657WN4XB","short_pith_number":"pith:3JQWKI62","schema_version":"1.0","canonical_sha256":"da616523da31729d0767b1fddfd9bcb873427c52a723d2a2b8f80b5e6363ad19","source":{"kind":"arxiv","id":"1601.00419","version":1},"attestation_state":"computed","paper":{"title":"Optimal Reliability for Components under Thermomechanical Cyclic Loading","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Hanno Gottschalk, Laura Bittner","submitted_at":"2016-01-04T09:30:15Z","abstract_excerpt":"We consider the existence of optimal shapes in the context of the thermomechanical system of partial differential equations (PDE) using the recent approach based on elliptic regularity theory. We give an extended and improved definition of the set of admissible shapes based on a class of sufficiently differentiable deformation maps applied to a baseline shape. The obtained set of admissible shapes again allows one to prove a uniform Schauder estimate for the elasticity PDE. In order to deal with thermal stress, a related uniform Schauder estimate is also given for the heat equation. Special em"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1601.00419","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-01-04T09:30:15Z","cross_cats_sorted":[],"title_canon_sha256":"49553b1a6f83d3b14c4444e487aae3229498b6f344f6a3d0adbbe80ee87e9977","abstract_canon_sha256":"14ba8a00f1878c580f3c5549bec2f2221bc7f2751e8de302011f326e07eca588"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:27.498939Z","signature_b64":"5KKwv4Zc8/Ruwn8H/JcGSfYunrsryxeQVL/zvp6ZOfqf36j9u/x5RKL59DGVIE6B7/qbKCJu4sfHllnh/Cd5AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"da616523da31729d0767b1fddfd9bcb873427c52a723d2a2b8f80b5e6363ad19","last_reissued_at":"2026-05-18T01:23:27.498276Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:27.498276Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Optimal Reliability for Components under Thermomechanical Cyclic Loading","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Hanno Gottschalk, Laura Bittner","submitted_at":"2016-01-04T09:30:15Z","abstract_excerpt":"We consider the existence of optimal shapes in the context of the thermomechanical system of partial differential equations (PDE) using the recent approach based on elliptic regularity theory. We give an extended and improved definition of the set of admissible shapes based on a class of sufficiently differentiable deformation maps applied to a baseline shape. The obtained set of admissible shapes again allows one to prove a uniform Schauder estimate for the elasticity PDE. In order to deal with thermal stress, a related uniform Schauder estimate is also given for the heat equation. Special em"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.00419","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1601.00419","created_at":"2026-05-18T01:23:27.498390+00:00"},{"alias_kind":"arxiv_version","alias_value":"1601.00419v1","created_at":"2026-05-18T01:23:27.498390+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.00419","created_at":"2026-05-18T01:23:27.498390+00:00"},{"alias_kind":"pith_short_12","alias_value":"3JQWKI62GFZJ","created_at":"2026-05-18T12:29:55.572404+00:00"},{"alias_kind":"pith_short_16","alias_value":"3JQWKI62GFZJ2B3H","created_at":"2026-05-18T12:29:55.572404+00:00"},{"alias_kind":"pith_short_8","alias_value":"3JQWKI62","created_at":"2026-05-18T12:29:55.572404+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3JQWKI62GFZJ2B3HWH657WN4XB","json":"https://pith.science/pith/3JQWKI62GFZJ2B3HWH657WN4XB.json","graph_json":"https://pith.science/api/pith-number/3JQWKI62GFZJ2B3HWH657WN4XB/graph.json","events_json":"https://pith.science/api/pith-number/3JQWKI62GFZJ2B3HWH657WN4XB/events.json","paper":"https://pith.science/paper/3JQWKI62"},"agent_actions":{"view_html":"https://pith.science/pith/3JQWKI62GFZJ2B3HWH657WN4XB","download_json":"https://pith.science/pith/3JQWKI62GFZJ2B3HWH657WN4XB.json","view_paper":"https://pith.science/paper/3JQWKI62","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1601.00419&json=true","fetch_graph":"https://pith.science/api/pith-number/3JQWKI62GFZJ2B3HWH657WN4XB/graph.json","fetch_events":"https://pith.science/api/pith-number/3JQWKI62GFZJ2B3HWH657WN4XB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3JQWKI62GFZJ2B3HWH657WN4XB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3JQWKI62GFZJ2B3HWH657WN4XB/action/storage_attestation","attest_author":"https://pith.science/pith/3JQWKI62GFZJ2B3HWH657WN4XB/action/author_attestation","sign_citation":"https://pith.science/pith/3JQWKI62GFZJ2B3HWH657WN4XB/action/citation_signature","submit_replication":"https://pith.science/pith/3JQWKI62GFZJ2B3HWH657WN4XB/action/replication_record"}},"created_at":"2026-05-18T01:23:27.498390+00:00","updated_at":"2026-05-18T01:23:27.498390+00:00"}