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

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
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preprint

Reflective Fold Obstruction: Internal Closure Does Not Exhaust Architectural Transition

Nova Spivack
Zenodo (CERN European Organization for Nuclear Research)
Logic, programming, and type systems
preprint

Reflective Fold Obstruction: Internal Closure Does Not Exhaust Architectural Transition

Nova Spivack
preprint en

Abstract

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.

Zenodo (CERN European Organization for Nuclear Research)
Sustainable cities and communities
Logic, programming, and type systems
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