IRIS Framework: Emergent Lorentzian Spacetime from Information Theory

This release documents IRIS, an exploratory information-theoretic framework in which Lorentzian spacetime signature emerges as a low-cost configuration of a universal information functional I[ρ] defined on non-commutative spectral algebras. Numerical minimization (N=60, seed=42) indicates that Lorentzian configurations achieve a lower informational cost (ΔI ≈ 33.29) than Euclidean signatures under E₈-inspired topological frustration (r=8, k=9). Key results include: • E8 structural coupling chi = 240 / 128 = 1.875 yields an effective acceleration scale a_IRIS = 1.17e-10 m/s^2, consistent with the MOND acceleration scale. • A lattice saturation law of the form rho(r) = rho_vac * (1 + r_Sch / r) reproduces the baryonic Tully–Fisher relation without additional tuning. • Predicts a redshift-dependent velocity scaling for fixed baryonic mass, with V at z = 2 approximately equal to 1.51 times V at z = 0, testable with JWST-era rotation curve data. • Effective dark sector partitioning with dark matter approximately 26.50 percent and dark energy approximately 67.8 percent, consistent with Planck 2018 constraints within uncertainties. • A bulk-flux filtration mechanism is proposed that may contribute to resolving the cosmological lithium discrepancy. • The master equation χx(z)=ln(x(z)/ε(z)) couples lattice relaxation to cosmic expansion, motivating a predictive and internally consistent non-equilibrium gravitational framework within IRIS. • A combinatorial derivation of the linearized gravitational field from the geometry and dynamics of the root lattice.This work bridges combinatorial geometry, lattice field theory, and classical gravity, suggesting that GR is the hydrodynamic limit of an quasicrystalline spacetime. Contents:• Fully reproducible Python code (spectral minimization N=60; spectral dimension up to L=12)• 4D hypercubic lattice analysis with E₈-inspired frustration + emergence of gravity• Numerical validation and sensitivity analysis (±10% flux variation) Methodology: Human–AI collaboration in which the human author provided conceptual architecture and physical interpretation, while AI assisted formalization and numerical implementation under supervision. Status: Speculative research artifact; not peer reviewed. The core numerical result is reproducible; broader theoretical implications remain conjectural. This version supersedes previous iterations or deposit by providing the galactic hydrodynamic and emergent gravity exploration. Falsifiability: The framework is falsified by (i) absence of ultra-light axion-like signatures (2.5–3.5×10⁻²¹ eV), (ii) strictly constant w=−1w=-1w=−1 dark energy, (iii) detection of a fourth fermion generation, or (iv) failure of the predicted velocity scaling V(z=2)/V(0)≈1.51V(z=2)/V(0) \approx 1.51V(z=2)/V(0)≈1.51. License: CC BY 4.0