{"paper":{"title":"How to Cook a Soft-Boiled Egg Optimally: A Laplace-Transform Solution of a Two-Domain Heat Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","physics.class-ph"],"primary_cat":"math.AP","authors_text":"Matthew Lorig","submitted_at":"2026-06-20T17:27:19Z","abstract_excerpt":"We study the problem of cooking the yolk and albumen of a hen's egg to their respective optimal temperatures of $T_Y^* = 65^\\circ$C and $T_W^* = 85^\\circ$C, subject to the requirement that neither temperature ever exceed its target at any time during cooking, since temporary overshoot still overcooks the egg even if the final reading is correct. We model the egg as a two-domain sphere with distinct thermal diffusivities, and take the Laplace transform of the heat equation in each domain, reducing the problem to a $3 \\times 3$ linear system in the transform variable $s$ with hyperbolic-trigonom"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.22156","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.22156/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}