From one body to
an open regime.

The v1 incident.Catalog v1 (arXiv 2604.17120) claimed 13 verified mono-monostatic bodies. Peter Varkonyi, co-creator of the Gomboc, pushed back two weeks after the notification: under the Gauss-map identity, his R-critical-point argument forced the bodies to have exactly 2 equilibria for strictly convex shapes. v1's 9-21 basin count for the Sloan shape was therefore either mesh artifact or evidence that the strict-convexity precondition was failing. After a full analytical diagnostic, the second possibility resolved cleanly: Sloan's published bodies are not strictly convex at the parameters in his paper, and v1 had over-counted in their region by reading basins instead of curvature.

The honest v2 reframe. Catalog reduces from 13 verified bodies to 1 (Phase-1 survives cleanly; 9 radial members are polystatic; 3 fail the strict-convexity gate and are indeterminate). v2 was drafted around that retraction, integration-reviewed in the same session, and audited in a cold session the next day. The audit cleared. Title shifted to Sloan's Analytical Gomboc at Published Beta: A Strict-Convexity-Constrained Reanalysis. v2 was ready to ship.

The pushback that changed the finding.Before authorizing the arXiv replacement submit, the question came up: is there structure we haven't probed yet?A doubled-throttle adversarial probing pass tested whether shrinking the Fourier-perturbation coefficient inside the Sloan family could rescue strict convexity while preserving the two-R-critical-point structure. It did. At four interior points across the k=2 and k=3 sub-families, the shrunk shapes verify as mono-monostatic under the identity. The verified set isn't a single Phase-1 instance. It's an open regime in (beta, a_1) parameter space, inside three k-families.

What v2 actually says now.The retraction is from “13 bodies” to “an open regime in three k-families plus Phase-1 in the k=1 interior,” not from “13 bodies” to “1 body.” v1's optimizer happened to land on per-k boundary extrema that overshot the strict-convex regime; the interior of each family was already populated with verified mono-monostatic bodies, just not yet probed. v2 went up to 13 pages with a new regime-interior subsection, a 4-row interior-probe table, and the Varkonyi reply rewritten around the regime finding rather than the Sloan two-sided correction alone.

The methodology takeaway. A v1-to-v2 corrective cycle authored and audited in the same hands is the worst possible auditor of its own corrections. The doubled-throttle pass surfaced something both the same-session integration review and the cold-session adversarial audit had treated as load-bearing-under-scrutiny rather than something to probe. The standing question for any v2-after-an-incident is now: what structure haven't we probed yet?Asked once, the answer was: most of it.