1. System Definition

Let:

  • ( S ) = system state
  • ( C ) = constraint set
  • ( A ) = action space
  • ( E ) = evidence / artifact set
  • ( D \in {\text{ACCEPT, REJECT, DEFER}} ) = decision outcome
  • ( T ) = state transition function

2. Core Principle

No state transition occurs unless explicitly validated and permitted.

ACP is not an optimization loop.
It is a permissioned state transition system.

3. Constraint Filter

A′={a∈A∣a satisfies C}A' = \{ a \in A \mid a \text{ satisfies } C \}

Only actions within constraints are admissible.

Implication:

  • No unconstrained reasoning
  • No extrapolation beyond defined bounds

4. Decision Function

D=f(a,E,validation)D = f(a, E, \text{validation})

Where:

  • ACCEPT → validation criteria satisfied
  • REJECT → validation criteria failed
  • DEFER → insufficient, ambiguous, or conflicting evidence

Implication:

  • Epistemic refusal is a valid and required outcome
  • No forced completion

5. State Transition Rule

St+1={T(St,a)if a∈A′∧D=ACCEPTStif D=REJECT or DEFERS_{t+1} = \begin{cases} T(S_t, a) & \text{if } a \in A' \land D = \text{ACCEPT} \\ S_t & \text{if } D = \text{REJECT or DEFER} \end{cases}

Implication:

  • No action without constraint
  • No action without validation
  • System defaults to no change

6. Validation (Pre/Post Execution)

Pre-execution:

Fpre(a,E)→DF_{pre}(a, E) \rightarrow D

Post-execution:

Fpost(St+1)→OutcomeF_{post}(S_{t+1}) \rightarrow \text{Outcome}

Implication:

  • Actions must be validated before execution
  • Outcomes must be verified after execution

7. Stopping Condition

W=STOP if validation criteria satisfiedW = \text{STOP if validation criteria satisfied}

ACP does not optimize indefinitely.
It terminates when sufficient validated constraint is achieved.

8. Fractal Structure

ACPk=(Ck,Ak,Ek,Fk,Wk)ACP_k = (C_k, A_k, E_k, F_k, W_k)

The same structure applies across scales:

  • task-level
  • system-level
  • institutional-level

Parameters change, structure remains constant.

9. System Properties

ACP enforces:

  • Fail-closed behavior
    → default is no execution
  • Externalized reliability
    → correctness does not depend on model internals
  • Explicit authority boundaries
    → action requires validated permission
  • Failure preservation
    → unresolved states are not collapsed

10. Final Compression

No action without constraint
No decision without validation
No transition without authorization