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Fourier Gap Sign Stabilizes Before the Sustained-Accuracy Landmark in Measured Failure Trajectories

Khaliq, Shamim
PhilArchive · Papers
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philosophy
We re-analyze time-resolved Fourier power gaps from a completed modular-addition experiment. The descriptive question is when the sign of the normalized power difference between an initialized scaffold mode and its strongest Fourier competitor becomes stable relative to a sustained-accuracy landmark. Two timing definitions are kept separate: sign stability through the analysis-grok checkpoint, and sign stability through the remainder of the logged trajectory. All 10 N=79 runs and 8 of 10 N=127 runs had strict short-horizon scaffold persistence; the remaining 2 N=127 runs and all 7 measured N=257 runs were non-strict. In the two measured N=127 failures, the negative gap sign stabilized 7,000 and 14,000 optimization steps before the sustained-accuracy landmark. In the seven measured N=257 failures, it stabilized 47,500 to 105,500 steps before that landmark. Successful trajectories do not support a symmetric late-stabilization claim: their positive sign was already stable through grok from the first logged checkpoint. Three successful N=127 runs later changed sign 34,000 to 43,500 steps after grok, showing that stability through grok is not terminal permanence. Three additional N=257 runs never reached an analysis landmark and are excluded from timing estimates. These observations support a bounded statement: among the measured failing trajectories, the scaffold-versus-competitor gap becomes stably negative before sustained validation accuracy identifies grokking. They do not establish a causal commitment point, or a latest flippable time.
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