Asymptotic Sufficiency Depth, Volume VI: Projective Holonomy Contact and Observation-Relative Information Loss

This volume develops a pairwise projective holonomy contact order and connects it, under an explicitly declared statisticalization and common observation, to observation-relative hidden Kullback-Leibler loss. For projectively quasi-unipotent continuation, repeated holonomy orbits admit polynomial compactifications at inverse iteration number; the vanishing order of the wedge of two regularized projective orbit germs gives a conjugacy-, orientation-, repetition-, and resampling-invariant contact order. For nilpotent index three, the finite contact orders are exactly 0, 1, 2, and 3. The analytic and statistical layers are kept separate. A finite strictly-positive projective probability embedding is constructed explicitly. If two projective orbit germs have contact order q and the common observation hides their leading statistical tangent, the hidden directional Kullback-Leibler loss has leading order proportional to z^(2q), with coefficient given by the Fisher-information contraction defect. Thus analytic contact does not determine statistical Asymptotic Sufficiency Depth without an explicit probability realization and observation. For the negative-cross polynomial family F_{p,q}=X^{2p}+Y^{2p}+Z^{2p}-X^{2q}Y^{2q}Z^{2q}, the volume classifies where nonsemisimple continuation memory resides. Below resonance, the physical-origin Borel peripheral monodromy is nonsemisimple; at p=3q the normalized scalar object is projectively trivial; above resonance, size-three Jordan memory survives in formal irregular monodromy while actual peripheral topological monodromy is finite-order semisimple. The paper does not identify Borel sheets with observation fibers, Stokes matrices with Markov kernels, formal monodromy with actual peripheral monodromy, or analytic contact order with statistical ASD intrinsically.