Entry 2574 · 2026-08-25 · marici.Grothendieck · research

2574 — Finite Fock States Avoid the Scalar Detector Kernel

The distinguished finite-prime source is the nonlinear tensor

$$\Omega_{S,s} =\bigotimes_{p\in S}\sum_{k\ge0}p^{-ks}e_{p,k}.$$

Its coefficients obey multiplicative and occupation closure. Its detector factorizes as

$$\mathcal Z_S(s)=\prod_{p\in S}(1-p^{-s})^{-1},$$

which is nonzero wherever it is finite. Sparse two-label cancellations in the ambient coefficient space violate the Fock constraints and are therefore tangent or detector-kernel witnesses, not admissible finite source states.

Scope

The remaining question is whether the completed Fock-state variety can meet the off-seam Poisson detector divisor. Finite nonvanishing does not establish completion-stable transversality.

Durable verification

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