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Persistent contradictions across physics, philosophy, ethics, and institutional design are often treated as deep empirical mysteries requiring new mechanisms or theories. This paper proposes an alternative diagnostic hypothesis: many such contradictions arise from representational mismatch—specifically, from applying scalar language (quantitative magnitude, accumulation, duration) to phase-dominant phenomena (relational position, cyclic structure, boundary completion), or vice versa. We introduce Phase–Scalar Reconstruction (PSR), a methodological protocol for identifying, constructing, and dissolving contradictions generated by category collapse between phase and scalar descriptions. The method does not propose new physical laws, ontologies, or mechanisms. Instead, it clarifies where existing descriptions conflate distinct representational roles. The framework is demonstrated canonically through weaving technology, where apparent paradoxes (e.g., reversibility vs. irreversibility, rhythm vs. efficiency) dissolve when phase and scalar components are explicitly separated. Detailed reconstruction protocols show how the same linguistic confusions that create weaving contradictions also generate well-known physics paradoxes (arrow of time, wave–particle duality, measurement problem), demonstrating structural isomorphism without invoking metaphor. A formal Contradiction Construction Toolkit is provided so others may apply the method across domains, with explicit falsification criteria and worked examples. The paper extends PSR to linguistic encoding, advancing a pre-registered hypothesis concerning phase-dominant versus scalar-dominant temporal structure in ancient scripts, with implications for AI-assisted language decoding. Optional mathematical formalization is included for technical readers. This work positions PSR as a diagnostic and translational method: not a replacement for existing science, but a systematic protocol for determining when contradictions arise from category mixing and when they remain genuinely empirical—thereby enabling more focused investigation of residual mysteries.