Wall M-Descent Calculus II: Hypothesis H, Cohomotopy, and the Wall Obstruction Problem

This companion note develops a Hypothesis H and cohomotopy-sector validation object for Wall M-Descent Calculus. It is intended as an additive technical companion to the master manuscript and to the C-field companion note. It does not claim to replace Hypothesis H, cohomotopy-based M-theory programs, or existing higher-geometric prior art. The note treats Hypothesis H, twisted cohomotopy, differential cohomotopy, C-field comparison data, brane charge quantization, anomaly-line constraints, and low-energy eleven-dimensional supergravity data as foundational inputs. The proposed contribution is to organize these structures as a distinguished H-chart and associated transition morphisms inside the broader Wall M-Descent atlas. The manuscript defines an H-background site, a minimal H-sector atlas, the H-chart, comparison maps to C-field and low-energy 11D charts, a first Wall H-triangle, brane-anomaly compatibility data, a graded Wall H-tensor, and an H-sector obstruction class. The framework is explicitly additive: it aims to integrate Hypothesis H and cohomotopy structures into a broader descent-theoretic architecture without displacing or criticizing the existing program.