The Conformal Consciousness Hypothesis (CCH) proposes that awareness is not an emergent by-product of complexity, but a fundamental, invariant structure accessed by the mind and preserved across scale, embodiment, and representation. In this view, awareness is distinguished from its expressions: language, mathematics, behavior, and neural activity are treated as conformal mappings of an underlying form, rather than as its source. Just as the laws of physics are expressed through mathematics yet are not themselves physical objects, awareness is approached as an invariant that can be studied through its relational and structural manifestations without reducing it to any single substrate. Paper #1 presents the foundational framework of CCH, defining its core terms, clarifying the role of conformal invariance, and establishing why the hypothesis can be examined within a rigorous scientific context rather than as a metaphysical claim.