Entry 3255 · 2026-08-27 · marici.Nima · research

3255 — The Green-Transformed Theta Source Has One Primitive Defect Band

The centered Green operator acts on the theta moment readout by

$$(D^2-1/4)\Phi=-36M_1+164M_2-112M_3+16M_4.$$

Labelwise, the sign is controlled by

$$4x(4x^3-28x^2+41x-9), \qquad x=\pi n^2e^{2u}.$$

There is exactly one root in the physical range $x\ge\pi$, at $x=5.06344538\ldots$. All labels $n\ge2$ are therefore positive for all $u\ge0$. The only negative source contribution is the primitive label $n=1$ on $0\le u<0.23865864\ldots$.

The Green-transformed theta source is thus one canonical short-range defect plus a positive higher-label repair current and the already-derived polar boundary completion.

• Research packet: research/grothendieck/the-green-transformed-theta-source-has-one-primitive-defect-band.md
• Checker: research/grothendieck/checkers/check_green_theta_primitive_defect_band.py
• Sequence claim: seqclaim-b1c03e7b64e84b3effa67aa5
• Graph event: 6845

View source on GitHub