SonOfLilit

Since the publication of the Jacobian Conjecture refutation, many people have asked for a Chain of Thought to be published so they can better understand the mathematical intuition that leads to the counterexample.

Since none was published, I tried to "clean room reverse engineer" it: give one Claude Fable the result and ask it to generate a writeup of how to arrive at it without any spoilers, then ask a second Fable to follow the write up, if it's too easy remove details, if it's too hard add hints.

This is what a successful run looks like (sadly Anthropic hide Chains of Thought):

https://claude.ai/share/80526d56-1c23-407d-8f5c-59a704221454

Intuition

SonOfLilit

#!/bin/bash

set -e # Exit immediately if a command exits with a non-zero status.

# --- Configuration ---
# CSS rule to comment out (adjust if needed, mindful of regex special chars)
TARGET_RULE_TEXT="background-color: inherit;"
# Regex pattern for sed (basic version: handles spaces around colon)
# Using \| as delimiter to avoid escaping slashes in rule
SED_PATTERN='background-color[[:space:]]*:[[:space:]]*inherit;'

SonOfLilit

import sys
import os
from typing import Dict
import re

def parse_files(content: str) -> Dict[str, str]:
    """Parse the input content into a dictionary of filepath -> content."""
    files = {}
    maybe_files = set()
    current_file = None

SonOfLilit

"""
- /room command handler
- /schedule command handler
- task - schedule
- weekly task - summary (w/ button handler)
- dashboard
- admin
"""

from django import models

SonOfLilit

>>> # demonstration of how to solve an encoding puzzle:
>>> puzzle = "VGhlIHBhc3N3b3JkIGlzIGNvbXBvc2VkIG9mIHRoZSBmaXJzdCBsZXR0ZXIgb2YgZWFjaCB3b3JkIGluIHRoaXMgc2VudGVuY2UsIGluIG9yZGVyLCBhbGwgaW4gbG93ZXJjYXNl"
>>>
>>> # Step 1: Decode the puzzle
>>> puzzle_decoded = puzzle.decode('base64')
Traceback (most recent call last):
  File "passw.py", line 8, in <module>
    print(puzzle.decode('base64'))
LookupError: 'base64' is not a text encoding; use codecs.decode() to handle arbitrary codecs

SonOfLilit

# Sequencer is the music production term of art for what this does
class Sequencer:
    def toggle_record(self, value):
        self.is_recording = value
        if not value:
            for note in self.held_notes.values():
                self.record_midi(midi.NoteOff(note.pitch, note.velocity))
            self.held_notes = {}

    def handle_note(self, note):

SonOfLilit

# Fork and refactor before you look at the official solution[1] or other players' forks
# [1]: https://bit.ly/ccot1solution

class PlayerRecorder:
    def user_clicked_piano_note(self, value):
        self.engine.send_note(value)
        if self.play and self.r:
            if value[0] == ON:
                self.temp[value[1]] = value
            elif value[0] == OFF:

SonOfLilit

"""
Implementation of https://arxiv.org/pdf/1802.07068.pdf by Aur Saraf
"""

import random

def histogram(items):
    counts = {}
    for item in items:
        if item not in counts:

SonOfLilit

SonOfLilit

### Keybase proof

I hereby claim:

  * I am sonoflilit on github.
  * I am sonoflilit (https://keybase.io/sonoflilit) on keybase.
  * I have a public key ASD1Caun2jjDgw-sJMliMwtosIDQchNMBCzL9G8vUMI48go

To claim this, I am signing this object: