Geometry from Information: Complete Series (Papers 1–17) — Uniqueness of Relative Entropy as the Gravitational Potential, Canonical Realisation of the Informational Index Principle, and the Dimensional Algebra of Spacetime

This volume collects the complete Geometry from Information (GFI) series (Papers 1–17). The central result is that gravitational dynamics emerges uniquely from four information-theoretic axioms via relative entropy as gravitational potential on the space of metrics. The volume establishes: (I) axiomatic uniqueness of relative entropy (Petz), (II) the Central Identity — second variation of relative entropy equals linearised Lovelock gravity, (III) the Informational Index Principle — tau(P_ker) = chi(S^{2m-2}) = 2, proved by two independent methods, (IV) derivation of Newton's constant from operator-algebraic self-consistency, (V) the dimensional phase transition d=3→d=4 as algebraic transition Type II_1 → Type II_∞, (VI) discrete cosmological constant spectrum Lambda_m = 6/(piml_P^2), (VII) Bekenstein–Hawking entropy from one topological bit chi(S^2) = 2.