We develop a complete quantum information formalization of the spectralstructure of a rigid projection tensor (pseudovolume), establishing twostructural results that go strictly beyond Khrennikov's quantum integerframework (2010). The spectral Hilbert space H_b = C^|M(b)| assigns to each basis shape b (avector of positive rational components) a Hilbert space whose dimension equalsthe number of spectral classes — equivalence classes of 32 projection planesunder a grid-equality relation. The first main result is scale-invariance:|M(b)| depends only on the ratio class [b], not on the scalar magnitudeS = sum(b_i). In Khrennikov's framework the partition count p(n) is strictlyincreasing; here the quantum structure is magnitude-free. The second result is cross-scale indistinguishability: basis shapes fromdistinct ratio classes at distinct magnitudes routinely share identical Hilbertspaces and projection-valued measures, with hundreds of thousands of non-trivialcollision pairs across small magnitudes and onset of asymptotic universality athigher sums. In Khrennikov's framework no two distinct integers are everquantum-mechanically indistinguishable; here indistinguishability is the norm. The natural scalar observables are degenerate for 99.8% of basis shapes. Thecorrect observable structure is the spectral PVM {Pi_i = |m_i>