Epivalent

If you are encountering the "error: externally-managed-environment" when trying to install or upgrade packages using pip, it means that your Python environment is being managed externally and you do not have permission to modify it. In this case, you will need to either gain the necessary permissions or use a virtual environment.

Here are two possible solutions:

Gain necessary permissions:
- Run the pip command with administrative privileges by using sudo:
```
sudo pip3 install package_name
```

To make the Python environment not externally managed on Debian 12, you can follow these steps:

Update your system's package list:
```
sudo apt update
```
Install pip3 (if not already installed):

sudo apt install python3-pip

	[00:00.000 --> 00:05.440] And if you beat up somebody enough, it does stop up his or her love springs.
	[00:05.440 --> 00:08.240] They become a being who is incapable of love.
	[00:08.240 --> 00:14.000] I wrote a sonnet once,
	[00:14.000 --> 00:32.200] The man, when all is said, what fallen man calls sin is but another name for love locked in.
	[00:34.960 --> 00:41.480] Here speaks the nature of the damage done that man knew not how it and he are one.
	[00:41.480 --> 00:51.080] Thus outlawed from the secret of the earth, entrusted in his being at his birth,
	[00:51.080 --> 01:01.880] His sin a code, its key a turn of fate, man struck, struck man, ere woman let him mate.
	[01:01.880 --> 01:11.460] But codes made up by man, by man are broken, and names will man to man deny the call.
	[01:11.460 --> 01:14.640] And something, something lost it there.
	[01:16.520 --> 01:17.500] Something token.

	#!/usr/bin/env python3
	from __future__ import annotations

	import argparse
	import json
	from functools import lru_cache
	from typing import Dict, List, Tuple

	import mpmath as mp
	import sympy as sp

	#!/usr/bin/env python3
	"""TopCVP_beta CLI

	This script packages the current working construction (paper-faithful):

	Primitives (all are string lambda terms built via plc_suite.terms):
	- fetch_{i,n} (paper), with NOT-substitution implemented by swapping CSTT/CSTF
	only at the (t==n+1 and j==i) app-slot inside the fetch constructor.
	- and'_n (paper)
	- OR derived purely by De Morgan using NOT-substitution + and'

	#!/usr/bin/env python3
	# -- coding: utf-8 --
	# THRML unified sampler (clean rewrite)
	# - Perfect matching on planar cubic bridgeless graphs via 2-face-coloring + NAE vertex constraints.
	# - Face K-coloring (default K=4) on the dual graph via Potts (penalize equal colors on adjacent faces).
	# Supports two input modes:
	# (1) Lambda term -> primal rotation system -> dual faces, Tutte embedding for plotting
	# (2) Adjacency matrix (0/1 square text file) of the dual graph for direct face K-coloring
	# Includes:
	# * Block Gibbs with optional block partition via greedy vertex-coloring (--block-coloring)

	#!/usr/bin/env python
	# -- coding: utf-8 --

	from sage.all import Graph, matrix, ZZ
	import unittest

	# ============================================================
	# Data Representation and Helper Functions
	# ============================================================