kaal:claim:7598518-031

Claim. A threshold arm that accepts too few candidates fills the shortfall uniformly from rejected candidates, and an arm whose minimum over generations of the seed-mean fill-free share falls below 0.98 in a family has its tests there invalidated.

Type. design · Support. stated

Holds when

• The gate binds every threshold arm, including the single verifier and the equal-weight pool.
• Validator compute is not equal across arms, so an equal candidate budget does not mean equal assessment cost.

Source quote

A threshold arm that accepts too few fills the shortfall uniformly from rejected candidates, and an arm whose minimum over generations of the seed-mean fill-free share, min(accepted, N)/N with N = 2, 000 training rows per generation, falls below amin = 0. 98 in a family has its tests there invalidated.

From. Wulf A. Kaal, Can Reputation Prevent Model Collapse? A Preregistered Test of Reputation-Weighted Data Filtering (2026). Full text.

Cite as. Wulf A. Kaal, Can Reputation Prevent Model Collapse? A Preregistered Test of Reputation-Weighted Data Filtering (2026). SSRN: https://ssrn.com/abstract=7598518

Verify. sha256 of source PDF cd22d148b2b55c2e27f087dcaa61cdf44ad7022b400b355c31a9cd7e43a31749 at https://wulfkaal.com/papers/7598518.pdf

Content hash. a0c84f24724d0fa26876dcdd5365845f2e493ba447116b75ece128a8619d6898