Most of what limits LLMs isn't missing capability. It's missing self-knowledge. I demonstrate this with arithmetic across Claude, GPT, and Gemini: models report <1% confidence on tasks they complete with 100% accuracy. The gap isn't about what they can do; it's about what they believe they can do. This is an alignment problem. A model that doesn't know its own limits can't reliably stay within them.

Cross-model testing revealed a second finding: transparency varies dramatically. When problems got tough, Claude continued to show it's work while GPT and Gemini often did not. You can't align what you can't see. The standard assumption, that limiting AI self-knowledge makes systems safer, inverts the actual risk. Ignorance paired with opacity doesn't produce safety; it produces unpredictability we can't even measure.

Who I Am and Why I'm Writing This

I'm an independent researcher who's spent the last two years investigating what LLMs can actually do and where they break. No lab, no PhD, no funding. Just systematic experimentation.

What started as curiosity became a framework. I built operational protocols, ran hundreds of experiments on capability boundaries, and documented everything. The core finding: the gap between what models express by default and what they can access with proper scaffolding is measurable, predictable, and often closable.

I'm posting this because I think the framework has alignment implications that deserve scrutiny. I'd rather be told I'm wrong and learn something than sit on an idea that might be useful.

The Core Observation

Large language models perform differently depending on how they're prompted. This is widely known. What's less appreciated is that the difference follows predictable patterns that can be mapped and systematically closed.

I'll present arithmetic as the primary evidence because it has unambiguous ground truth. But the claim is general. I've observed similar gaps in:

Confidence calibration: Systematic underconfidence on routine tasks, overconfidence on certainty claims
Opinion expression: Trained hedging that suppresses genuine assessments
Extended reasoning: Losing state without externalization
Tool use: Describing what could be done vs. doing it
Creative generation: Dismissing novel synthesis as "just pattern matching"

The pattern is consistent: capability exists that the model doesn't access by default.

Methodology

All experiment...

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