{"inputs":{"volumeFt3":2400,"bandLoFt3":1333,"bandHiFt3":2894,"slug":"1333-2894"},"result":{"band":{"loFt3":1333,"hiFt3":2894,"ratio":{"lengthOverHeight":2.2466601562500004,"widthOverHeight":1.2813671874999994},"maxPenalty":0.047238345894282885,"worstRangeFt3":[1333,2550]},"slug":"1333-2894","reference":{"volumeFt3":2114,"spec":{"widthFt":11.56036639819744,"lengthFt":20.269142859163097,"heightFt":9.02189981995106},"worstGapHz":20.912440374282816,"axialModeCount":14},"bolt":{"W/H>=1.0":0.28136718749999945,"W/H<=1.9":0.6186328125000005,"L/H>=1.1":1.1466601562500003,"L/H<=3.2":0.9533398437499998,"L>=1.05W":0.9012246093750009,"L<=2.6W":1.0848945312499985,"inBoltArea":true,"activeConstraints":[]},"atVolume":{"volumeFt3":2400,"spec":{"widthFt":12.059806841640183,"lengthFt":21.14482701562402,"heightFt":9.411671345486353},"worstGapHz":20.046380193456457,"optimalSpec":{"widthFt":13.57005632590148,"lengthFt":16.038102916465803,"heightFt":11.027488038824787},"optimalWorstGapHz":19.142137290950714,"penalty":0.047238345894280886},"verification":{"agrees":true,"forwardHz":20.912440374282816,"deltaHz":0}},"provenance":{"method":"The inverse room problem: hold the volume, search the shape. Minimises the widest gap between adjacent axial modes below 200 Hz, over the Bolt (1946, JASA) ratio area, by a compass search seeded on a feasible grid — derivative-free because the objective has genuine jump discontinuities where a mode crosses the 200 Hz window. Axial modes are n*c/(2L) per axis at c = 343 m/s. The volume is a given and never a free variable: unconstrained, the objective is monotone in volume and the answer degenerates to \"build a bigger room\". The published answer is a BAND recommendation, one shape covering a range of volumes, with the range derived from a covering number rather than chosen. Pure mathematics - nothing is fetched and nothing is recalled.","canonicalUrl":"https://makerportal.ai/lab/room-shape/1333-2894"},"license":"free-with-attribution"}