The Missing Definition of Right: An Axiomatic Protocol for AI Judgment, with Conformance and Production Evidence
Download PDF (preprint v1.1, 9 pages) LaTeX source DOI: 10.5281/zenodo.22882691 (this version) · 10.5281/zenodo.22882690 (all versions) · License CC BY 4.0 Abstract Large language models are optimised to produce the most probable continuation. Nothing in that objective says which continuation is right, and no amount of added precision supplies the missing definition. We argue that hallucination is therefore not primarily a precision problem but a specification problem, and that it becomes measurable — and correctable — only once “right” is written down in a form a machine can be held to. I-Lang is such a form. Its judgment layer rests on four axioms (no rule carries weight 0 or 1; an irreversibility gate; consistency detection; conservation of externality), an eleven-dimension judgment vector with a uniform polarity convention, and a fixed, total reference function from vector to one of eight decision modes. Perception is learned; the decision is specified. We test what follows from this definition in two settings. In a deterministic 320-case conformance benchmark run on 45 model deployments, protocol form is largely attainable (median grammar pass rate 0.80) while protocol action is not (median execution pass rate 0.09; seven of 34 comparable runs score exactly zero), eleven runs emit perfectly valid judgment schemas yet nine of them fail most execution cases, and 93.3% of all rule violations fall on a single rule: acting with authority one does not hold. No run reaches the conformance gate. In three days of production, an inexpensive judge model placed under the protocol agrees with the operator’s written rules on 68.4%, 75.1% and 80.9% of an unbiased sample, and on 87.2% of messages where it reports confidence of at least 0.85; after one rule constant was changed, deviations from that rule fell from 13 to 7 under a single, fixed criterion. The axioms, the benchmark, both result sets and the code are public and archived with DOIs. We ask readers not to trust our numbers but to re-run them. ...