littledivy

#!/bin/bash
set -e

rm -rf gen_temp gen
mkdir -p gen_temp

gh run download 21040538462 -p "src_binding_*.rs" -D gen_temp

mkdir -p gen
for dir in gen_temp/*/; do

littledivy

$ deno sandbox new --expose-http 18789 --memory 3gb --ssh

Created sandbox with id 'sbx_ord_f02azv7t0x7tjxz4y51n'
Exposed port 18789 to https://1ef0cf0c631d49b9b5ad1300ec939252.sandbox.deno.net
ssh 1531786bd2d9b9c96f56095a0f7e2dcd@ssh.deno.net

            __    ╭─────────────────────────────────────╮
           /ᵔ_)  <  Welcome to Deno Sandbox             │
 .-----/ / │ Sandbox sbx_ord_f02azv7t0x7tjxz4y51n│

littledivy

clawpatrol — local dev setup

Prerequisites: Go 1.22+, Node 18+, npm

Step 1 — create dev config

cat > dev.hcl <<'HCL'
listen      = "0.0.0.0:8443"
info_listen = "0.0.0.0:8080"

littledivy

/-
  Jacobian "counterexample" verifier.

  The map  F : ℂ³ → ℂ³  (here checked over ℚ ⊂ ℂ; all data is rational)

    F₀ = (1+xy)³ z + y² (1+xy) (4+3xy)
    F₁ = y + 3x (1+xy)² z + 3x y² (4+3xy)
    F₂ = 2x − 3x² y − x³ z

  Claimed facts, machine-verified below:

littledivy

The "-2 Jacobian" non-injective map — what a search turns up

Search query: Jacobian conjecture fake counterexample constant Jacobian -2 non-injective

The hit: Vitushkin's classic example

A map with Jacobian determinant exactly −2 that is not injective is a well-known "trick" example, usually attributed to Vitushkin:

littledivy

#!/usr/bin/env python3
"""
Verify the claimed properties of the polynomial map F: C^3 -> C^3

    F0 = (1+xy)^3 z + y^2 (1+xy)(4+3xy)
    F1 = y + 3x(1+xy)^2 z + 3x y^2 (4+3xy)
    F2 = 2x - 3x^2 y - x^3 z

Claims checked:
  1. det(Jacobian F) is the constant -2  (nonzero constant everywhere)

littledivy

import sympy as sp

x, y, z = sp.symbols('x y z')
u = 1 + x*y
w = 4 + 3*x*y
F = [u**3*z + y**2*u*w, y + 3*x*u**2*z + 3*x*y**2*w, 2*x - 3*x**2*y - x**3*z]

J = sp.Matrix([[sp.diff(f, v) for v in (x, y, z)] for f in F])
print(sp.expand(J.det()))

littledivy

# claude-shell.zsh — make Claude the fallback language of zsh.
#
# Install:
#   source /path/to/claude-shell.zsh
#
# Then normal commands execute normally, while unknown commands are sent to the
# most recent Claude Code session for the current project:
#   git status                  # normal command
#   explain why this test fails # Claude
#   ? "why is this slow?"       # Claude explicitly (safe for punctuation)