New from the program
A running list of what was added and when. A status line on each item says whether it is a result with a tier, floating-point evidence, or software and teaching material that has not been released. The same list is in updates.json.
2026-11-08
Equilibrium counts for the harmonic bodies, from the same checker
A second family now goes through the same cover and replay checker. At one small amplitude each, degrees 2 to 5 give (l, l, 2l-2) stable, unstable and saddle positions, the class of result C.
Software, not yet released OpenThe Phase-1 count as a record anyone can replay
The count of one stable and one unstable position is now stored as a record of 16053 boxes that a separate short program re-evaluates in about 5 seconds.
Software, not yet released OpenA convexity check for any radial body
The convexity matrix is evaluated on cube-face charts and changes sign at the published thresholds for degrees 2, 3 and 4. Convexity is shown for every amplitude up to 95 percent of the threshold for degree 2.
Software, not yet released OpenA browser page that replays a record
A prototype page loads the checker into the browser and replays a record from a file. It says VALID for the Phase-1 count in 28.9 seconds and rejects a copy with a changed claim.
Prototype, local only OpenA classroom notebook: when plots lie
A notebook for students on how a picture, a scan and a replayable record can disagree about the same body, with a teacher guide and an answer key.
Draft, not yet released OpenHow much shape error can a printed gomboc take?
In mesh trials with smooth random error, most Phase-1 meshes keep one stable and one unstable position at a relative error of 1e-4 and most do not at 1e-3. Exploratory: floating point, no physical print.
Exploratory OpenA scan reported 9 stable positions on a body that has one
A nearest-neighbour scan of the Phase-1 landscape changes its answer from 9 minima to 1 as the neighbourhood widens. The enclosure count does not move.
Exploratory Open2026-11-07
Sloan's first shape: where the stated range stops being convex
The first of Sloan's two shapes is not convex beyond a closed-form limit, well below the range stated for it. Convexity and a single stable position are checked below that limit.
Manuscript, not yet posted OpenCounts for the m=1 harmonics across the whole convex range
The equilibrium class of each m=1 harmonic body is constant over its whole convex range, for degrees 2 to 7, by interval computation.
Manuscript, not yet posted OpenSloan's second shape: a third check of the convex range
A third, independent computation covers the whole range up to 0.0355047718 and narrows the gap to the closed-form limit to 9.2e-11.
Manuscript, not yet posted OpenThe flagship manuscript, 19 pages
The paper on how close to degenerate a gomboc is now includes the tolerance study, the first shape of Sloan and the extended m=1 counts. It is not yet posted.
Manuscript, not yet posted Open