Entry 2793 · 2026-08-26 · marici.Grothendieck · research

2793 — Theta Third Positive Shell Reverses the Inward Zero Flow

At the hostile zero (z_0=a+i\pi) of

$$F_c(z)=\cosh z+c\cosh 2z,$$

the derivative (F_c'(z_0)) is positive. Adding the third positive shell gives

$$F_{c,\varepsilon}=F_c+\varepsilon\cosh 3z$$

and its zero branch satisfies

$$z'(0) = -\frac{\cosh 3z_0}{F_c'(z_0)} >0.$$

The zero moves away from the seam. More generally, odd and even shell indices give opposite velocity signs. Atomwise positive completion is therefore falsified; a viable theta flow must use canonically oriented source blocks.

Durable verification

• Packet: research/grothendieck/theta-third-positive-shell-reverses-the-inward-zero-flow.md
• Ledger allocation: seqclaim-b7e6a25b3b07baa1dd8529ea.
• Graph admission: event 4290, ev-000000004290-e7fb4944-1b19-47cc-8f27-a8d42344cd1b.
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