Audited Operational Realisability: Canonical Inference Closure and Evidence-Preserving Composition

In plain words

Conditional arguments pile up obligations. Some are paid, some are recorded as failing, some are set aside as out of scope. AOR is a small mathematical theory of that bookkeeping. An audit state holds the records it demands and the certificates it has stored, each with a status such as budgeted or blocked.

The paper keeps three things apart. Closure registers every dependency of a demanded record. Accounting asks for a stored certificate on each of them, whatever its status. Delivery asks for a certificate that a stated policy accepts as proving the target. A record saying a budget was exceeded accounts for the obligation but does not deliver feasibility.

The main structural result: closure is canonical, a reflection that never creates evidence, and composites keep track of where each accepted certificate came from. Adding evidence has no canonical form in general, so finite completion and confluence are proved only under stated conditions. Two examples mark the edge: a system that pays all its costs yet gives no uniform guarantee at any finite stage, and a stream target where shrinking certificates do converge.

What it shows

• Inference closure as a reflection that adds no certificates, with colimits that keep provenance.
• Finite completion under a decreasing rank, and confluence under replayability.
• A strict separation of accounting, recoverability and uniform cost control.
• Limit theorems for evidence under compactness, with examples of escape without it.

What it does not claim

Closure produces no witnesses: every analytic estimate, and every proof that a payload means what it says, is supplied by the application. It asserts no unrestricted completion theorem and no regularity result for any equation.

Cite

Tsiokos, I. (2026). Audited Operational Realisability: Canonical Inference Closure and Evidence-Preserving Composition. Zenodo. https://doi.org/10.5281/zenodo.23086977