Transductive Information Physics :A spectral geometric framework for cosmological invariants

We present Transductive Information Physics (TIP) v1.0, a mathematically closed spectral-geometric framework where cosmological parameters emerge as invariants of an E8-graded 11-dimensional manifold M₁ projected onto 4D Lorentzian spacetime. The projection induces a transductive residue δ, defined as the regularized spectral determinant of the Laplace-Beltrami operator on the E8 root lattice. Using the Kronecker second limit formula, we derive δ = 0.0302585092994 with zero free parameters or fitting. From δ and anomaly cancellation constraints, we obtain: 1. Dark matter to baryon ratio: R_DM = 5.5 - δ = 5.469741, matching Planck 2018 (5.47 ± 0.05) to 0.005σ 2. Universal temporal sampling frequency: Ψ₀ = (k_B*T/h)(1-δ) = 6.4532 THz at T = 310K 3. Weak gravitational lensing deviation: θ_TIP/θ_GR = 1 + δ, predicting 3.02585% excess 4. Causal agency window: Δφ = 1/Ψ₀ - τ_dec = 0.845 ps We prove δ is an RG-invariant fixed point under the Fisher information metric. The framework is falsifiable: non-detection of the 6.45 THz spectral line by ALMA/JWST or lensing deviations <1% at 5σ by Euclid DR3 excludes TIP. Appendix A provides full mathematical derivation. Appendix: Computational Verification includes Mathematica code for direct verification of δ. No free parameters exist in the model. Classification: Mathematical Physics [math-ph]; General Relativity and Quantum Cosmology [gr-qc]; High Energy Physics - Theory [hep-th]; Cosmology [astro-ph.CO]