Mark local dtn
v210_mark_local_dtn.py · registry
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a numerical SHARPENING of v201/QGEO.SUBPRIN.01 on REALISTIC Steklov curvature profiles, carried to the quasi-free STATE level (the actual ω∘ρ=ω, not just [ρ,Λ]=0); NOT a closure of QGEO.SYM.01. A real von-Mises curvature bump g(θ) localised at a puncture, summed over the four μ4 marks f(θ)=Σ_{j=0}^3 g(θ−jπ/2), builds the Steklov DtN Λ=|D_θ|+M_f. [E] every off-(mod 4) Fourier coefficient of the REAL f vanishes to <1e-16 (exact 4-fold cancellation), although g has all modes. [N] ‖[ρ,Λ]‖<1e-15. [N] STATE invariance (new vs v201): the quasi-free covariance C=½(1+sgn H₁) satisfies ρCρ†=C to <1e-13 — the STATE, not just the operator, is clock-invariant. [N] negative controls (a single off-centre bump, a Z3 source, 4 generic marks) break BOTH operator and state by O(1); [N] convergence stable for N∈{16,32,64}. [O] verdict: certifies 'mark-local DtN ⟹ ω∘ρ=ω' for concrete profiles AND at the state level; the premise that the physical seam IS mark-local stays [O] — the narrowest definitional form of QGEO.SYM.01, NOT its closure.
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