Primes as a Field on a Discrete Torus: Primorial Field Dynamics, Gap Composition Profiles, and an Information-Theoretic Reformulation -- PrimSpace v3.0

We introduce Primorial Field Dynamics (PFD), a geometric and information-theoretic framework for studying the local distribution of prime numbers. Primes are embedded into a hierarchy of discrete tori 𝕋ᵏ = ∏ ℤ/pᵢℤ indexed by the k-th primorial Mₖ. The central object is the prime preference field ρ (s), a non-uniform measure on the allowed torus states encoding where primes cluster beyond the classical sieve prediction. The framework introduces four structural objects: Liquid Media (divisibility threads as pressure fields), the Swaddle Effect (every prime p>3 is surrounded by multiples of 2 and 3), the Gap Composition Profile (GCP, a binary matrix encoding divisibility structure inside each prime gap), and an information-theoretic reformulation of the master equation P (prime at s) = μ (s) ·S (s) ·ρ (s). Six theorems are proved, including: the Row Entropy theorem (primes are informationally silent — H (βᵣow (p) ) =0 for all p>pₖ), a discrete entropy spectrum theorem, and a corrected W-convergence theorem. The information decomposition H (ℙ) = I (βᵣow; ℙ) + H (ℙ|βᵣow) shows the sieve accounts for 57. 4% of primality entropy; ρ (s) carries the remaining 42. 6%. Numerical test of Conjecture Q4 (GCP singular values ↔ Riemann zeta zeros): at N=10⁸, covering 5, 761, 453 prime gaps, the GCP Fourier spectrum shows statistically significant amplitude excess at Riemann zeta zero positions (mean Z=2. 52, max Z=10. 67, p<10⁻²⁹). The signal grows with N and is strongest for small zeros (γ<35). This is empirical evidence consistent with Q4; mathematical proof remains open. All claims are explicitly marked: Theorem (proved), Conjecture (empirically supported), Observation (weak signal), or Open question. One corrected conjecture (the original W-convergence target was wrong; the correct limit is proved) is documented as a methodological note.