This preprint states the primitive axiomatics for finite cohomological obstruction theory. It develops an observer-relative obstruction calculus beginning from localized scalar comparison, evaluation preorders, and finite simplicial carriers. Pairwise inconsistency is modeled as a cochain defect, with exact repair represented by the image of the degree-zero coboundary and irreducible obstruction represented by the quotient space Q¹ = C¹ / im(d₀). The paper separates derived structure from injected observer assumptions. In particular, the obstruction magnitude Φ₁ is treated as a quotient norm induced by a declared observer gauge rather than as a primitive universal metric. The framework further separates quotient mass Φ₁ from closure-failure mass Γ₂ through the closure map κ¹ : Q¹ → C², yielding a two-axis obstruction signature and the closure-ratio guardrail R_cl. The paper also introduces observer passivity, contextual congruence, witness-rank invariance, conditional reflective congruence completion, well-founded finite descent, and licensed lift contracts. These structures formalize when a system may repair, lift, refuse, or terminate with a typed unknown. Universal physical, semantic, or consciousness claims are explicitly excluded; the theory applies only under declared finite carriers, observer gauges, context actions, and admissibility hypotheses.