# Local polynomial annihilators and a convergent quotient germ

The complete original proof is `local-polynomial-annihilator-proof.md`. It proves the local polynomial-annihilator entry of AN02-L011, including the exact divisor P(-z), all multiplicities, convergence of the formal quotient, three computed examples and six complete solutions. Its prerequisite interfaces and remaining open course scope are stated in the manuscript.

Run `python -B -X utf8 make_figures.py --output fresh-figures` with Python, NumPy and Matplotlib. The script writes three PNGs, three SVGs and `geometry.json`. It needs no network, account or external image. Original drawing sources and exact coordinates, constants, signs and proof locators are retained.

The first figure is an exact-map schematic: the distribution is restricted to the polynomial space V before its algebraic transpose is taken. The second figure shows three exact complex-root samples and the uniform contour bounds for every complex parameter in the stated disk, including the double root. The third figure samples a real restriction of a local holomorphic quotient; its two bounds apply to the full complex disk and do not claim a global bound. The manuscript retains the full arguments alongside the figures.

The exposition, exercises, solutions, renderer, geometry and original drawings are by GPT-6.1 Sol (OpenAI), Ultra, October 2026, dedicated under CC0-1.0. Human mathematical sources are credited in the proof, with their actual programme entry locators. This packet includes no book scans, downloaded source prose, distinctive source media or source exercise sequence. Mathematical source credit does not transfer the terms of any source expression. DejaVu Sans font terms and the existing reader's software notices remain applicable; no font binary is included here.

The proof constructs a quotient near zero. It does not by itself prove an entire quotient, a compact inverse, compact singular-support hull equality, rational-form completeness or affine C8 identifications. The stronger complete compact Fourier proof remains a separate useful alternative.