01. The Proof Gap
A fluent answer sounds the same whether or not it is right.
Ask a language model about tax treatment, investor eligibility or a clinical protocol and the answer will usually sound right. Then one exception, one jurisdictional difference or one amendment will make it wrong, with no change in how confident it sounds. The market has started to price this, and the industry has taken three distinct positions on the same problem:
A model trained further on legal text
Better vocabulary, better citation style. Still probabilistic, still capable of being fluently wrong.
A model that retrieves the statute and cites it
Better grounded, and the sources are traceable. The reasoning between the source and the answer is still the model's.
A rule compiled into formal logic, with every answer checked against it
The output is not an answer but a proof: which rule applied, which branch was taken, whether any counterexample exists.
Each step trades flexibility for a guarantee, and the last is available only because tax law has a right answer. Most decisions inside a company are not like that. So what is the equivalent of the proof for everything else?
02. One Variable
How verifiable is the domain's ground truth?
That one variable comes in three grades. They are different conditions, not points on one line, and each calls for a different written form.
The right answer exists and can be checked at the time of the decision. The knowledge is written as rules, and every decision returns a trace an auditor can read.
The right answer arrives late, mixed with everything else. No rule can be proved; what can be written is a belief precise enough to be tested, and so to be wrong in a way someone can see.
The right answer is never fully revealed. Nothing can be verified; what can be written is how the decision was reached, as an account another person can inspect, challenge and repeat.
Using the wrong form fails in both directions: a prover pointed at a judgment with nothing to check against is machinery without feedback, and loose beliefs pointed at a regulation will not survive an audit. A model that gives confident answers with no written form underneath fits none of the three, which is why it can appear to work in all of them.
03. The Second Variable
How often is the decision made?
Verifiability tells you what the written form should look like. Frequency tells you where writing it down matters most: decisions frequent enough that a written form compounds, and slow enough to verify that nothing will learn them unaided.
The Knowledge Formalization Spectrum →
The full thesis: definitions, four claims, what would prove it wrong, and the work it builds on.