From Entanglement–Algebraic Spacetime to Finite Electroweak Noncommutative Geometry I: The Leptonic Finite Spectral Representation

This paper is archived as a speculative research work.We construct the finite leptonic electroweak noncommutative-geometric representation associated with established structural results in Entanglement–Algebraic Spacetime (EAS), while maintaining a strict separation between primitive Scalar-Field (SF) ontology and interface mathematics. The neutral antecedent is the previously established seven-point neutrino candidate, whose phase-resolved association ledger contains one active exterior association in every phase. Independently established charged-lepton structures supply three family sectors. These SF organizations are not transformed into one another; they are assigned, at the standard electroweak interface, to the neutral and charged roles of the active leptonic doublet. The resulting target representation is ( _L,e_L) ( 2,-1/2), e_R ( 1,-1). The charged-lepton left–right intertwiner therefore transforms as Hom(e_R, W_L) ( 2,+1/2). For the specified finite electroweak noncommutative geometry A_F^EW= C H, with family-complete particle carrier L= C^2 C^3_ fam, R= C^3_ fam, the finite Dirac block is represented as B=n M_ℓ, n=(0,1)^T, 0≠q M_ℓ∈ M_3( C). The exact finite differential is ^1_D_F(A_F^EW)_LR = ≤ft M_ℓ: ∈ C^2 , so the family-complete finite geometry generates exactly one family-common scalar doublet transforming as Φ ( 2,+1/2). The result is a finite-representation theorem. It does not identify electroweak gauge structure, the finite algebra, the finite Dirac operator, or the scalar doublet as primitive SF ontology; does not derive three distinct SF neutrino flavors or weak-interaction dynamics from the seven-point neutrino structure; and does not yet invoke the spectral action, spontaneous symmetry breaking, gauge-boson masses, or the broken-phase QED reduction. Those dynamical consequences belong to a separate construction.