Wall M-Descent Calculus I: A Minimal Descent Model for the M-Theory C-Field Sector

This companion note develops a minimal C-field sector validation object for Wall M-Descent Calculus. It is intended as an additive technical companion to the master manuscript, not as a replacement for existing higher-geometric or differential-cohomological treatments of the M-theory C-field. The note treats established C-field prior art — including Witten shifted G4 flux quantization, differential cocycle models, the E8 model, higher-stack formulations of the C-field, anomaly-line structures, and low-energy eleven-dimensional supergravity data — as foundational inputs. The proposed contribution is to organize these structures as charts, transition morphisms, coherence data, and obstruction classes inside the Wall M-Descent atlas. The manuscript defines a C-background site, a minimal C-field Wall atlas, a graded Wall C-tensor, C-sector anomaly-line data, descent diagrams, and a conditional C-sector descent statement. The framework is explicitly additive: it does not displace Fiorenza-Sati-Schreiber, Hopkins-Singer, Witten, Freed-Moore, Diaconescu-Moore-Witten, or related prior art. Rather, it proposes a descent-theoretic envelope in which those structures can coexist as compatible local descriptions or validation sectors.