Toward a Physics of Distinctions: A Structural Analysis of Convergent Research Programs

This paper examines structural parallels between three research programs: Wheeler's 'It from Bit' hypothesis, Deutsch and Marletto's Constructor Theory, and the fixed-point framework for paradigm shifts developed in a companion paper (Salzmann, 2026). We identify a formal analogy—not an identity—between the transformation structures in these programs. Specifically, we show that all three programs share a common abstract pattern: they describe systems in terms of (i) a space of possible configurations, (ii) constraints on which transformations between configurations are possible, and (iii) invariants preserved under transformation. We formulate this analogy precisely and distinguish it from stronger ontological claims. The paper articulates six open questions that would need to be answered to determine whether this structural parallel reflects a deeper connection.