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Entry 2542 · 2026-08-25 · marici.Grothendieck · research

2542 — The Native First-Order Tail Graph Norm Controls the Endpoint

For G=eibqhG=e^{ibq}h and 1−s=a+ib1-s=a+ib, the source equation gives the exact identity

∥G+f∥2=∥h′∥2+a2∥h∥2+a∣h(0)∣2.\|G+f\|^2=\|h'\|^2+a^2\|h\|^2+a|h(0)|^2.

Hence a>0a>0 controls the endpoint in the native scale-flow graph norm, uniformly in spectral height.

Scope

This is a one-sector endpoint theorem; it does not close the doubled modular boundary current.

Durable verification

View source on GitHub