TME: Thermodynamic Measure of Intelligence manuscript calculations

This repository contains a small, auditable code collection for reproducing the numerical calibration values used in the manuscript Thermodynamic Measure of Intelligence.

The central scope distinction is:

• TME computes manuscript-scale quantities: rare-valid lift I, log scale L = log10(I + 1), compressed scale Lambda = log10(L + 1), controller examples, Maxwell-demon examples, velocity-selection demon values, and manuscript-ready CSV/JSON/LaTeX outputs.
• TME does not recompute the GPT/human entropy-rate estimates from raw text. Those empirical entropy-rate values are imported from the workflow in https://github.com/zeroknowledgediscovery/nero and recorded as input constants.
• https://github.com/zeroknowledgediscovery/nero is the source repository for the GPT/human text entropy-rate analysis. Cite https://github.com/zeroknowledgediscovery/nero for the preprocessing, corpus handling, GPT/human text analysis, and entropy-rate estimates used as symbolic inputs here.

The code generates the values used for Fig. 1, Table I, Table II, Appendix C, and derived JSON/CSV/LaTeX outputs for direct manuscript use.

What is computed here, and what is imported?

Quantity	Computed in TME?	Source / formula
Passive baseline	Yes	I = 0, L = 0, Lambda = 0
Fixed-feedback controller	Yes	I = alpha - 1, with alpha range from inputs/controller_inputs.json
Repeated dynamic controller	Yes	I + 1 approx 2^m, with stage range from inputs/controller_inputs.json
Maxwell demon, single entropy reduction	Yes	L = (Delta S / k_B) / ln(10), with constants from inputs/demon_inputs.json
Velocity-selection demon	Yes	Maxwell-Boltzmann tail calculation in src/tme/demons.py, with parameters from inputs/demon_inputs.json
Human symbolic scale	Yes, from symbolic assumptions	I_H + 1 = q_H N_V / N_G; N_V, N_G, and q_H are manuscript assumptions in inputs/symbolic_entropy_inputs.json
GPT-5 symbolic scale	Yes, from imported entropy rates	log2(q_GPT/q_H) = n_star (H_GPT - H_H) + rho; H_GPT and H_H are imported from https://github.com/zeroknowledgediscovery/nero and recorded in inputs/symbolic_entropy_inputs.json
GPT/human entropy-rate estimation from raw or generated text	No	Performed in https://github.com/zeroknowledgediscovery/nero, not in TME

Symbolic GPT/human calculation

TME uses the following symbolic-scale calculation.

For the expert-human symbolic row,

I_H + 1 = q_H N_V / N_G.

The current default inputs are recorded in inputs/symbolic_entropy_inputs.json:

N_V = 5e21
N_G = 1e7
q_H = 1

Thus

I_H + 1 = 5e14,
L_H = log10(5e14),
Lambda_H = log10(L_H + 1).

For the GPT-5 symbolic row, TME imports the entropy-rate estimates from https://github.com/zeroknowledgediscovery/nero:

H_human = 0.77 bits/character
H_gpt = 0.74 bits/character

TME then applies the finite-resolution symbolic correction

log2(q_GPT / q_H) = n_star * (H_gpt - H_human) + rho_n_star.

With the default central values

n_star = 100
rho_n_star = 0

this gives

log2(q_GPT / q_H) = 100 * (0.74 - 0.77) = -3,
q_GPT / q_H = 2^-3 = 0.125,
I_GPT + 1 = (I_H + 1) * 0.125 = 6.25e13.

TME then computes

L_GPT = log10(I_GPT + 1),
Lambda_GPT = log10(L_GPT + 1).

The entropy-rate values themselves are not produced by TME. They should be traced to https://github.com/zeroknowledgediscovery/nero and to the provenance file inputs/nero_entropy_provenance.json.

Quick start

From the repository root:

python scripts/make_all.py

This writes outputs into outputs/:

figure1_numbers.csv
figure1_numbers.json
table1_velocity_demon.csv
table1_velocity_demon.tex
table2_scale.csv
table2_scale.tex
manuscript_constants.json
appendix_c_reproduction.json

Run tests with:

python -m unittest discover -s tests

Inputs

The manuscript assumptions are stored as explicit JSON files in inputs/:

• figure1_examples.json: example categories and ordering used in Fig. 1.
• controller_inputs.json: fixed-feedback and repeated-control assumptions.
• demon_inputs.json: Maxwell-demon and velocity-selection parameters.
• symbolic_entropy_inputs.json: symbolic-scale parameters, including entropy-rate values derived from https://github.com/zeroknowledgediscovery/nero.
• nero_entropy_provenance.json: provenance metadata for entropy-rate values imported from https://github.com/zeroknowledgediscovery/nero.

The symbolic defaults are:

• N_V = 5e21: finite-resolution estimate of interpretable English sentence-scale strings.
• N_G = 1e7: illustrative high-quality sentence-scale target-set cardinality.
• n_star = 100: character-scale sentence length after the 27-symbol coarse-graining.
• H_human = 0.77 bits/character: Gutenberg prose entropy-rate estimate from https://github.com/zeroknowledgediscovery/nero.
• H_gpt = 0.74 bits/character: GPT-5 long-form prose entropy-rate estimate from https://github.com/zeroknowledgediscovery/nero.
• rho = 0: central finite-length AEP slack value.

Sensitivity to rho, N_V, and N_G can be explored by editing the input JSON files or by importing tme.symbolic directly.

Scope

This code reproduces numerical scale calculations. It does not prove the manuscript theorems and does not regenerate the entropy-rate estimates from raw text; those estimates are produced by https://github.com/zeroknowledgediscovery/nero. The intent is to make every number plotted or tabulated in the TME manuscript traceable to a named formula, an explicit parameter file, and, where needed, a named external provenance source.

Suggested manuscript data/code availability sentence

The code used to reproduce the numerical scale calculations in Fig. 1, Table I, Table II, and Appendix C is available in the public TME calculation repository. The GPT-human entropy-rate estimates used as symbolic inputs are imported from https://github.com/zeroknowledgediscovery/nero, which performs the text preprocessing and entropy-rate estimation described in Appendix B. TME records these imported values, applies the finite-resolution symbolic-scale formulas, and provides derived CSV, JSON, and LaTeX outputs for the plotted and tabulated manuscript values.