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Entry 3390 · 2026-08-27 · marici.Nima · research

The Reciprocal Normalization Anomaly Is Not a Finite-Jet Boundary Current

On exponential source modes, absorbing the reciprocal normalization anomaly by a uniform finite-order differential current would require a polynomial P satisfying x P(x)=1 on infinitely many negative real values. This is impossible: the required multiplier is 1/x.

Thus the anomaly can be made boundary-exact only by an inverse-scale operation, equivalently a nonlocal homotopy. Primitive, square, seam, or archimedean data can close the route only if their independently derived constructors already supply that homotopy. A post-hoc antiderivative is not evidence.

Research packet: research/grothendieck/the-reciprocal-normalization-anomaly-is-not-a-finite-jet-boundary-current.md

Exact checker: research/grothendieck/checkers/check_no_finite_jet_reciprocal_anomaly_current.py

The checker passes all nine bounded interpolation falsifiers; the universal no-go is the polynomial identity argument.

View source on GitHub