Abdeslam’s Compression Collapse Theorem (ACCT): A Symbolic Resolution of Gödel, Paradox, and Logical Instability

This paper introduces a new symbolic perspective on Gödel’s Incompleteness Theorem. We propose the Compression Collapse Theorem (ACCT), which states that any self-referential sentence embedding its own unprovability or truth condition exists in a compressed symbolic form that collapses when logically evaluated. We formalize the collapse of identity during evaluation and show that classical paradoxes—including Gödel’s sentence, the Liar paradox, Turing’s Halting Problem, and others—are not stable logical objects, but illusions of structural stability. ACCT provides a unifying symbolic boundary condition for evaluating recursive logic and proves that such systems lose their integrity upon self-access.