The Vanishing Metric: The Thermal Cloak's Interior Claim Is Not Established — a Symmetry-Void Metric, and a Specificity Test on a Sound One
Year: 2026
Type: preprint
Abstract: The Tier 1 thermal cloak — a laminated aluminium highway and polymer moat around a spherical cavity in a background block, developed in the Aldred Industries research and development programme — carries one surviving claim from its simulation campaign. Its exterior claim was killed in simulation (imaged-face distortion RTD 27.057 / 27.061 / 27.512 at meshes n = 30/45/60 against a pre-registered pass line of RTD < 0.70). Its interior claim survived: a cavity temperature ratio (cloak / bare) of 0.189 / 0.114 / 0.196 against a pre-registered interior line of ≤ 0.50. This paper examines the surviving claim and finds, first, that it is NOT ESTABLISHED: the quantity it is a ratio of — cavity wall-mean temperature minus cavity-centre temperature — is identically zero in the continuum for every configuration of the problem, by the problem's own symmetry (reflection z → −z composed with T → 40 − T), so every recorded value of the metric is a discretisation artefact and the recorded ratios are quotients of artefacts, at one recorded mesh of solver residue at the 10^-10 K scale. The pass recorded on that metric stands as a grading act and is not disturbed as one; it cannot be cited as evidence for an interior effect. Second, on a replacement quantity that exists in the continuum — the axial temperature drop across the cavity, defined and registered before its first computation — the cloak's suppression is real and consistent in simulation (ratio to bare 0.207 / 0.239 / 0.207 at n = 30/40/60) but is NOT SPECIFIC to the laminated cloak geometry: a plain solid aluminium shell of the same inner and outer radii suppresses further at every mesh tested (0.110 / 0.172 / 0.101) while carrying less total heat flux than the cloak at every mesh. Ablation attributes the suppression to the conductive plates, not to the insulating moat, whose own contribution to the replacement metric is small and unresolved. Every figure in the paper is SIMULATED, NOT MEASURED. Consequence: the next design tier inherits nothing from the cloak geometry on the cavity axis, and the interior question, if asked again, must be asked of a quantity that exists — a decentred cavity, or the axial metric under a revised protocol with lines registered in advance. Keywords: thermal cloak; simulation validation; metric validity; symmetry; conduction; pre-registration; falsification; Aldred Industries. ---
Author: Aldred, William Alexander
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225322720