The Computable Authority Equation

V = Eval_A(a, F, t)

A   the authority     an institution's sealed, versioned rules
a   the action        the exact change being proposed
F   the facts         the evidence the rules read, each one proven
t   the time          the moment of action
V   the verdict       AUTHORIZED | DENIED | ESCALATED | INCOMPLETE

Read it as one sentence: authority is the institution's sealed rules, applied to proven facts about the exact action, at the moment of action, by the system that would change.

1. From first principles

• Institutions act through rules. A policy, a regulation or a mandate states the conditions under which an action may happen.
• An AI agent holds no authority of its own. It can propose an action and it can carry one out, but its identity is not the source of the right to do so.
• So authority is decided by applying the rules to the action and to the facts that bear on it, at the time the action would happen: A + a + F + t → V.
• Evaluating that function is not enough. Each input has to be trustworthy to a party that did not produce it, and the result has to be enforced where the action takes effect.

The first three steps describe how institutions have always worked. The fourth is the problem machines introduce, and it is the problem this discipline exists to solve.

2. The agent is not in the equation

Access control has been organised around the subject: who is asking, and what that identity has been granted. The Computable Authority equation has no subject term. This is a position, not a simplification.

• The authority determines what may be done.
• The facts determine whether the conditions hold.
• The action determines exactly what is being authorized.
• The time determines whether the authority and the evidence are still valid.

Whoever presents the action, an agent, a script or a person, cannot change any of those four. An agent cannot argue its way to a different verdict, and an agent disguised as something else gains nothing, because nothing about the verdict depended on what it is. NOMOS-SPEC-008 writes this into the protocol: an Act carries no presenter signature, and a relying party must not let presenter identity affect the verdict.

What an agent may do still depends on whom it acts for. That dependency lives inside A and F, where it can be proven: the institution's rules state which delegations they recognise, and certificates (NOMOS-SPEC-007) establish who issued those rules and who may state which facts.

3. Context is not a separate input

Most authorization models carry a context or environment term, the least defined variable in any of them. Here context is facts. A fact is either proven or it is not an input. The amount is part of the action. The applicant's debt-to-income ratio is testimony from a witness certified to state it. The account balance is read by the system of record itself. Nothing enters the evaluation through an unnamed side door.

4. The equation is familiar. The inputs are not.

Computing an authorization decision from several inputs is established practice. Attribute-based access control (NIST SP 800-162) evaluates subject, resource, action and environment against a policy. Trust-management systems such as PolicyMaker and KeyNote evaluate a request against presented credentials and a local policy. Computable Authority builds on both. Its contribution is the type of each input: what A, F and a must be for the verdict to hold for someone who did not write the rules, did not supply the facts and does not trust the agent.

5. The four conditions

V counts only when all four hold. Each is specified, implemented and tested.

• A is genuine. Its issuer chains to a root the relying party pinned itself, and nothing on that chain is revoked at t. (NOMOS-SPEC-007; NOMOS-SPEC-006 for revocation.)
• F is proven. Every fact came through its declared channel, and every witnessed fact is signed by a key certified for that claim. A fact the evidence does not establish is unknown, never false. (NOMOS-SPEC-008 §6, §7.)
• a is bound. Approvals are signed over a digest of the action, the rules, the facts, the audience and a single-use nonce. Change any of them and the approvals are void. (NOMOS-SPEC-008 §4.)
• V is computed where the change lands. The system of record evaluates the Act itself and commits exactly the action it verified, or nothing. (NOMOS-SPEC-008 §6, §8.)

Under these conditions an agent cannot obtain an authorization by withholding facts. If the verdict is AUTHORIZED, no fact the agent left out could have made a higher-ranked deny rule fire. R-16 states and proves this.

6. Two questions

Access control asks: does this subject have permission to perform this action?

Computable Authority asks: given this authority, these proven facts, this exact action and this moment, is the action authorized? And can the system about to change verify that answer itself and enforce it?

The second question is where the word computable earns its place. The answer is not a lookup in someone else's server. The authority, the evidence, the binding and the evaluation travel with the action, and any party can recompute the verdict from them.

The question is not who has permission. The question is whether authority exists for this action, under these facts, at this time, and whether the system can prove it.

7. Where it is built

The four conditions are specified in NOMOS-SPEC-001 through NOMOS-SPEC-008, published under CC BY 4.0 at github.com/nomos-spec/spec. Two implementations pass all 29 Act-binding test vectors and agree on 729 derived mutants, and verification takes about a millisecond per action. R-16, Passports for Agents, gives the full threat model, proofs and evaluation. NOMOS is one implementation of the discipline; the equation belongs to the discipline.