Four Pre-registered Tests of Emergent Second-Order Modulation in a Minimal Plasticity Testbed: Negative Results and a Failed Learner Control

The testbed note validated audit statistics against planted second-order modulation, in which a relation’s strength multiplicatively modulates the plasticity of another relation. The conjecture’s own question is whether such modulation can emerge without being planted. This note reports four pre-registered experiments (E1–E4, 60 confirmation systems each, new environments every time) in which a modulation matrix M is learned by an online analytic meta-gradient. E1: learned M grew but equally in a time-shuffled-credit control; adaptation loss was worse than with M = 0 in 60/60 systems while overall loss was better, and a uniform gain reproduced most of that benefit. E2 (optimal gain differs between regimes): learned M beat the best uniform gain in 17/60 systems and produced no gain contrast. E3 (positive control with an explicit context relation): the same learner again produced no gain contrast, so E1–E2 cannot be read as evidence about emergence in either direction. E4 (block-averaged Adam learner, the last pre-committed revision): the control gate failed more severely and the planned second stage was not run. In this engine, under these learners, no useful context-dependent modulation was obtained from internal relation states or even from an explicit context. Design lessons: a time-shuffled-credit control is not a null; an adaptive optimiser can amplify gradient noise into dense harmful structure; a positive control for the learner must precede any emergence claim. Unpublished draft, not peer reviewed; synthetic systems only; it neither supports nor refutes the conjecture. Companion to doi:10.5281/zenodo.23373288, doi:10.5281/zenodo.23006539 and doi:10.5281/zenodo.23192515. The bundle reproduces every quoted number with verify_paper4.py (45 checks). AI use: simulations were written and executed by an AI coding model under written specifications and audited by a second AI system; the author is responsible for all content.