Entry 2594 · 2026-08-25 · marici.Grothendieck · research

2594 — Theta Hostile Quartic Forces a Derivative-Delta Source

For the Mellin convention

$$\mathcal M\mu(s)=\langle\mu,x^{-s}\rangle,$$

polynomial multiplication by $P(s)$ is the Mellin shadow of applying the transposed Euler differential operator $P(-E^*)$ to the source. A degree four hostile symmetric multiplier therefore sends each positive atomic label to a distribution containing a fourth derivative of its delta mass. These terms cannot cancel across distinct label supports.

Thus the standard off-line-zero quartic violates the order-zero positive-Fock source type before its zeros are inspected. This is the first concrete constructor-level discriminator required by the Deutsch programme.

Scope

This rejects the standard hostile multiplier, not every possible hostile positive atomic source.

Durable verification

• Packet: research/grothendieck/theta-hostile-quartic-forces-derivative-delta-source.md
• Ledger allocation: seqclaim-75d7d2442313f8ba8d876cf7.
• Epistemic graph event: ev-000000003742-62416b75-7f90-4d1d-b43b-29f3ed83b4e1.
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