Reflective Fold Obstruction: Internal Closure Does Not Exhaust Architectural Transition
We prove a general theorem of fold obstruction: if a predicate I is preserved along the primitive steps of an internal relation r, then I is preserved along the full reflexive-transitive closure r*, and any target failing I is not internally reachable from a source satisfying I. In the hull form, when every seed in a set S0 satisfies I and I is forward-closed, the entire reachable hull remains inside I. Applied to architectural transitions, this shows that internal fold operations cannot escape the architectural constraints imposed by forward-closed predicates. All theorems are machine-checked in Lean 4.
Authors
- Nova Spivack
Publication Details
- Journal
- Zenodo (CERN European Organization for Nuclear Research)
- Published
- 2026-06-26
- DOI
- https://doi.org/10.5281/zenodo.20951712
- Primary Topic
- Logic, programming, and type systems
- Type
- preprint