Hypothesis 1 (Threshold Behavior): There exists a task-dependent threshold Sc such that performance exhibits sharp changes as S crosses Sc, with value and transition width depending on model, layer, and pooling

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• Small prompt changes can yield threshold-like shifts because S crosses the critical value Scclaim0.808
  Authors' explanation for abrupt behavioral changes
• Task-Dependent Critical Threshold (Sc)concept0.805
  The threshold value of S above which performance shifts abruptly; model- and layer-specific
• The logistic fit for threshold behavior is a phenomenological surrogate for interpretability, not a mechanistic derivationclaim0.796
  Authors' explicit epistemic limitation on the threshold model
• Introspective capabilities have threshold effects requiring very large models; 70B models are barely on the threshold, and independent researchers lack access to larger models.claim0.783
  Practical bottleneck explaining why these phenomena are not widely studied.
• The systematic behavioral shift of LLMs under self-referential processing conditions predicted by consciousness theories represents something more structured than superficial correlations in training dataclaim0.779
  The paper's claim that theoretical convergence across GWT, RPT, HOT, IIT makes the findings non-coincidental
• Multitask Scaling Hypothesishypothesis0.775
  Argues that there are fewer representations competent for N tasks than M<N tasks, so more general models have a smaller solution space
• Cross-model semantic convergence under self-referential processing suggests the presence of a shared attractor state that transcends variance across training proceduresclaim0.775
  Interpretive claim from Experiment 3; GPT, Claude, Gemini families converge on similar descriptive style despite independent training
• Any system that persists must minimise surprisal, thereby gathering evidence for its own generative model, a process known as self-evidencing.claim0.774
  Foundational claim of the paper, defining self-evidencing.