Apparent Temperature Evolution, Energy‑Scale Projection Closure, and Blackbody Spectrum Covariance in Scale‑Relative Cosmology

The observed apparent‑temperature relation T(z)=T₀(1+z) from high‑redshift molecular‑cloud measurements is interpreted within the standard Λ‑CDM framework as relic evidence of an objectively hot early universe. This reading relies on three unexamined ontological presuppositions: absolute temperature, time‑invariant molecular energy levels, and space conceived as an expanding substantial container. Based on algebraic relational ontology and the Scale Equivalence Principle (SEP), this paper develops a purely relativistic alternative account. We argue that the unidirectional dynamics of Tomita‑Takesaki modular flow necessarily generates a monotonically increasing amplification factor for an observer’s energy‑scale gauge relative to any past cosmic epoch; this factor arises endogenously within the theory rather than being introduced as an ad‑hoc parameter. Constrained by the finite speed of light, cosmological observations implement an inherent bidirectional duality closure: an IR‑to‑UV ontological evolution of the observer’s scale anchor, followed by a UV‑to‑IR observational projection onto ancient physical configurations. Under the 3+3 skew‑dual geometry of the quantum flag manifold, the spectral eigenvalue of the composite total projection operator yields a quadratic energy‑scale amplification factor f(z)∝(1+z)², while the directly measured redshift factor 1+z corresponds to the square‑root of this quadratic effect. Within a scale‑covariant measurement protocol, the intrinsic relative excitation ratio at the source decreases monotonically with redshift, meaning ancient epochs are infrared‑biased. After applying the quadratic amplification from projection closure, the resulting apparent temperature exactly reproduces the empirically observed linear scaling T(z)=T₀(1+z). The black‑body spectral shape remains perfectly preserved because all energy‑carrying observables obey identical projection rules. This framework requires no postulate of an objectively hot primordial universe and dispenses with absolute temperature or absolute energy scales. It reproduces existing empirical data with fewer ontological commitments and constitutes a rigorous alternative to the standard thermal‑history interpretation of cosmology.