logic • Mechanization target
Infinite Stabilisation Formula — Ordinal Stabilization Target
A recursively specified DFT process should either terminate or stabilize when its transitions are governed by a well-founded ordinal ranking.
Assumptions
- Each process state has an assigned ordinal rank.
- Every non-terminal transition strictly decreases or stabilizes the relevant rank.
- The transition relation is well-founded.
- Fixed points are defined modulo accepted policy equivalence.
Proof Obligations
- Define state space and transition relation.
- Define ordinal rank function.
- Prove monotonic descent or stabilization.
- Prove absence of infinite descending chains.
- Classify fixed-point equivalence.
Typed Definitions for ISF
State Space (State)
A finite or abstract set of admissible configurations for a recursive digital process.
Boundary: A state-space draft is not a proof of recursive stabilization.
Transition Relation (step)
A relation step : State → State → Prop expressing one admissible recursive transformation.
Boundary: The relation requires proof obligations before convergence claims.
Ordinal / Natural Rank (rank)
A ranking function assigning each state a value in a well-founded order, first modeled as Nat for a restricted finite abstraction.
Boundary: A finite rank abstraction is a first model, not the full ISF theorem.
Claim Boundary
Formalization target. Public description must not be treated as completed proof until mechanized and externally reviewed.