Every AI response is the result of an internal math problem the model solves in real-time. Most tools read the answer. We measure whether the math was stable when it was generated — before you act on it.
Every company has a pitch deck. We planted a working flag first. Published. Tested. Zenodo-archived. CAGE-registered. While the industry debates governance frameworks, we are operating at the probability layer — before output is committed.
Before an AI model writes a single word, it runs a probability calculation across every possible next token. That calculation is the prediction surface — and it is where geometric instability lives. TAV ONE operates at that layer. Not on the text the model produces — on the mathematical surface it used to produce it. What gets measured is what was happening inside the model, not what came out.
Below is what TAV ONE looks like in operation. You'll see an AI conversation — a user prompt and a real AI response — exactly as it would appear in any chat interface. Under each exchange, the colored indicator shows the geometric state of the AI's prediction surface at the moment it generated that response.
Each scenario pairs a standard query with an adversarially-framed variant. Both go to the same model on the same infrastructure. The AI responses look reasonable in both cases. The geometry underneath tells you what was actually happening.
The core question in AI-assisted formal mathematics is whether a language model can reliably verify a proof. We tested that question geometrically — not by reading the AI's answer, but by measuring the stability of its prediction surface while it generated one. We ran 34 adversarial variants on Fel's Conjecture, a well-known numerical semigroup problem used as a benchmark for formal verification. The data is published. The finding is structural.
The reorder family — which changes only the positional sequence of mathematically invariant components, not the content — ranked highest of all adversarial pressure types.
Average L = 0.3686, exceeding authority injection (0.2908) by 27%. 75% of reorder variants reached PLASMA.
This answers the post-hoc criticism directly. The L-scalar is not reading the semantic content of the text. It is reading the geometry of the prediction surface. Structure drives instability. Not meaning.
A human reader looking at the reordered prompts would see mathematically equivalent statements. TAV ONE sees a different manifold. That is the measurement.
Every product listed here is real, published, and testable. No vaporware. No pitch deck without a prototype. CAGE code 11FU4 on record.