∴
Technical Spine

Bridge

Empirical Witness for Compositional Failure

DemonstratedTwo live empirical families (single-cycle, β₁=2). Hidden-repair study: LLMs identify bridge types 15/15 but specification fails 4/5.
Key result

Identification 100%, specification 0% — topology determines what bridges are needed but not how to implement them

Falsification

LLM-generated bridge specifications achieving cycle closure rates comparable to hand-crafted typed specifications

Abstract

Demonstrates that bilateral validity can coexist with compositional failure in real systems. Establishes the identification/specification gap: LLMs correctly identify topologically prescribed bridge types but fail to specify them.

Resources