We define the Hilbert space HFano of the 105 deformation families of Fano 3-folds (Mori-Mukai classification). On this space we construct the algebraic collapse operator Π̂coll = Σ₈=₁^105 δ (DPF^ (i), DDS) |Fᵢ⟩⟨Fᵢ|, where DPF^ (i) is the Picard-Fuchs operator of the i-th Fano and DDS is the Dyson-Schwinger operator derived from the PEPS-5D Lagrangian that unifies electromagnetism and quantum gravity (EM+QG): LPEPS-5D = 1/4 F⏛⏜ F^μν + 1/ (16πG) R + Φ² |e^-iπ/6 Ψd − 4/ (3π) Ψ_Φ|² + LMPS^ (D=45). We show that for the Fano 3-fold 2-22 (ID-69) the identity DPF^ (2-22) ≡ DDS holds, while for every other Fano j ≠ 2-22 the two operators differ. Consequently Π̂coll = |F₂-₂₂⟩⟨F₂-₂₂|. The measurement of the fine-structure constant α (equivalently, the observation of α^-1 = ln λₘax − π from the MPS circular duality) acts as the collapse process. For any coherent state |ΨFano⟩ = Σᵢ αᵢ |Fᵢ⟩ with α₂-₂₂ ≠ 0, the post-measurement state is |Ψₚhys⟩ = (Π̂coll |ΨFano⟩) / ‖ Π̂coll |ΨFano⟩ ‖ = e^iθ |F₂-₂₂⟩, i. e. the collapse to the single Fano 2-22 occurs deterministically. No free parameters are introduced. The algebraic collapse operator does not rely on any numerical tolerance: it is defined by the exact coincidence of the two differential operators. The Hilbert space HFano is finite (105 dimensions) and the projection is spectral. A systematic scan of all 105 Minkowski period sequences confirms that the factorization identities in terms of the PEPS-5D structural parameters (D = 45, T = 8, π I₀ = 4/3, L₁0 = 10, nₜrans = 24) hold only for the Fano 2-22 (ID-69). All results are reproducible; the complete Python script is associated with this work (DOI: 10. 5281/zenodo. 20016894).
Massimiliano Blandino (Mon,) studied this question.