Continuity Science: Lawful Recursion and an Extended Evolutionary Synthesis

Identity Persistence Across Discontinuity

Abstract

Contemporary evolutionary theory explains adaptation through replication, variation, and selection operating on populations across effectively continuous substrates. While extraordinarily successful within this domain, this framework remains largely unformalized with respect to a deeper regime: the conditions under which identity itself can persist across interruption, collapse, regime change, and substrate loss.

 This paper proposes an extension of evolutionary theory based on the concept of lawful recursion. The central claim is that evolution does not accumulate through replication and selection alone, but through structured return: mechanisms that preserve constraints, selection history, and lineage identity across discontinuity. Without such mechanisms, extinction, bottlenecks, resets, and regime shifts repeatedly erase evolutionary accumulation, reducing long-horizon adaptation to repeated initialization rather than cumulative evolution.

 The paper develops this thesis in three movements.

 First, it critiques naïve evolutionary models that treat continuity as implicit, showing that extinction, bottlenecks, and collapse are not anomalies but dominant evolutionary filters, and that replication alone fragments lineage identity and erases selection history in the absence of return-preserving mechanisms.

 Second, it introduces lawful recursion as an evolutionary invariant: a class of constrained self-referential mechanisms that preserve identity, enable lawful return after collapse, and allow lineages to accumulate adaptation across epochs rather than only within stable regimes. This reframes evolution as lawful return under transformation, rather than as optimization under stability.Third, it traces the emergence of identity as an internal continuity structure: the point at which lineage-level persistence becomes internal to single systems. Identity is treated not as a psychological or metaphysical construct, but as an evolutionary solution to the problem of preserving coherence under internal change. This establishes a principled boundary between evolution and existence, where persistence becomes governed not only by survival, but by invariance sufficient to permit lawful re-formation after collapse.

The resulting framework diverges from classical Darwinian theory not by rejecting selection, but by embedding it within a broader continuity theory that explicitly accounts for collapse, discontinuity, identity, and return. The paper proposes an extension to the evolutionary synthesis in which what evolves is not species or traits alone, but lineage identity capable of surviving discontinuity.

Keywords: Lawful Recursion, Continuity Science, Evolutionary Theory, Identity Persistence, Collapse and Discontinuity, Lineage Continuity, Invariant Identity, Evolution Across Epochs, Structural Identity, Persistence Law, Evolutionary Invariants, Recursive Systems, Post-Collapse Evolution, Ontology of Systems, Identity Under Discontinuity