We apply the QFT dictionary of the Algorithmic Motives (AM) framework to three central problems in arithmetic dynamics and number theory: the Collatz conjecture, the abc conjecture, and the Riemann hypothesis. For the Collatz system, we formalize the (2, 3) -adic structure as a transfer operator on L² (Z₂), derive the coupling constant = 3 / 2, and compute an anomaly index = 3 / 6. We show that the forward–reverse asymmetry corresponds to a broken S-duality between the 2-adic and 3-adic sectors, and interpret the Livšic gap as a confinement strength. For the abc conjecture, we identify a vertical anomaly arising from the interaction between additive (weight 0) and multiplicative (weight 1) structures. The quality q = c / rad (abc) defines an anomaly parameter, and the conjecture is reformulated as a boundedness condition on this anomaly. For the spectral problem associated with the Riemann hypothesis, we interpret the functional equation and Artin factorization as manifestations of a spectral symmetry and Higgs-type decomposition within the QFT dictionary. We define a formal trace formula for the Collatz transfer operator via the Atiyah–Bott fixed-point framework and relate its spectral properties to periodic orbits, with explicit caveats regarding convergence. All results are explicitly classified as Theorem, Conditional statement, Structural correspondence, or Conjecture. No claim is made to resolve any of the three problems; rather, the paper develops a unified structural framework identifying common algebraic mechanisms underlying them.
Matthew Eltgroth (Sat,) studied this question.