Applied ITT — Executable Physics V: Toward Variational Programming

Applied ITT — Executable Physics V: Toward Variational Programming Armstrong Knight (Sensei Intent Tensor) · intent-tensor-theory.com Modern computing is architecturally linear at every level. We introduce variational programming as a paradigm in which programs are energy functionals and execution is physical relaxation to minimum energy. The ITT semantic field is the first working instance: its Allen-Cahn/Laplacian computation is irreducibly non-linear, exhibiting inverse scaling (update cost decreasing as domain knowledge accumulates) versus transformer attention (quadratic scaling regardless of prior knowledge). Natural substrates are analog circuits, neuromorphic processors, and quantum annealers. Key claims: C1: ITT field irreducibly non-linear. C2 (Inverse Scaling): Cost_field → O(n²) as domain knowledge saturates vs transformer O(n²_seq·d·L·H). C3: Natural substrate is analog/neuromorphic/quantum. Memory: GPT-4 ~3.5 TB vs ITT field ~19.2 MB at 100K tokens. Variational language sketch provided. Part of the Applied ITT — Executable Physics series. Foundation for WP-06, WP-07, WP-08. Repository: https://gitlab.com/intent-tensor-theory.com-group/git-0-0-applied-intent-tensor-theoryWebsite: https://intent-tensor-theory.com