IFM2 Unified Informational Geometry: Earth-Conditioned Anchoring and Likelihood-Weighted Inflationary Core

AbstractThis unified manuscript integrates two IFM2-based investigations under a single operatorlevelframework of anchored informational geometry. Study I uses Earth as a definitional baselineanchor, inducing an Earth-conditioned informational geometry over astrophysical objectsand yielding baseline-conditioned ordering and center/core notions in feature space. Study IIuses observational constraints to construct weights over inflationary parameter space and extractsa stable likelihood-weighted core summarized by diagnostics in (ns, r) and reheatingrelatedproxies. We formalize a shared mechanism: anchoring induces coherent cores andcan support measurable directionality toward them. In the inflationary ensemble, defining aninformational potential ΦI = −log w, we demonstrate a compass-like descent property: for8000 out-of-core samples, a small step toward the core centroid decreases ΦI with probability0.998625 (step fraction t = 0.15). We include robustness tests (prior sweeps and bootstrapfor inflation; baseline swaps for the Earth-conditioned analysis) to control scope and preventover-interpretation. Throughout, “center” is used only in the induced informational space anddoes not denote spatial centrality.