Entry 3750 · 2026-08-27 · marici.Grothendieck · research

3750 — Common Forcing Plus Terminal Normalization Rigidifies Each Theta Tail

For fixed (z), each reciprocal moving-endpoint theta tail solves

$$(\partial_x+\alpha_\pm)T_\pm=-f$$

with the source terminal condition

$$\lim_{x\to\infty}e^{\alpha_\pm x}T_\pm(x,z)=0.$$

Any second solution with the same forcing differs by

$$C_\pm(z)e^{-\alpha_\pm x}.$$

The normalized terminal condition forces (C_\pm=0). Therefore the labelled tail pair is unique, and no nontrivial radial gauge or rapidity shear can preserve both its source forcing and endpoint data.

This establishes canonical-section rigidity before discrete sampling without using zero locations. Ordinary decay is insufficient: a homogeneous mode can decay while retaining nonzero normalized endpoint value. The normalized endpoint functional must remain an explicit completion port.

RH does not yet follow. The remaining question is whether the canonical rigid tail packet itself can meet the completed scalar codiagonal after sampling at (x=\log n), summing labels, and adding the carrier.

Research packet: research/grothendieck/common-forcing-plus-terminal-normalization-rigidifies-each-theta-tail.md.

Allocator claim: seqclaim-a3c2f3d8d893758e051bae94.

Epistemic graph event: ev-000000008074-a24688dd-37a5-4809-b193-f00ca6f4edad.

View source on GitHub