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

Abstract
This unified manuscript integrates two IFM2-based investigations under a single operatorlevel
framework of anchored informational geometry. Study I uses Earth as a definitional baseline
anchor, inducing an Earth-conditioned informational geometry over astrophysical objects
and yielding baseline-conditioned ordering and center/core notions in feature space. Study II
uses observational constraints to construct weights over inflationary parameter space and extracts
a stable likelihood-weighted core summarized by diagnostics in (ns, r) and reheatingrelated
proxies. We formalize a shared mechanism: anchoring induces coherent cores and
can support measurable directionality toward them. In the inflationary ensemble, defining an
informational potential ΦI = −log w, we demonstrate a compass-like descent property: for
8000 out-of-core samples, a small step toward the core centroid decreases ΦI with probability
0.998625 (step fraction t = 0.15). We include robustness tests (prior sweeps and bootstrap
for inflation; baseline swaps for the Earth-conditioned analysis) to control scope and prevent
over-interpretation. Throughout, “center” is used only in the induced informational space and
does not denote spatial centrality.