Here’s a stupid‑simple H = π * ψ² governor you can paste into your pipeline

Here’s a simple CSV-logging version.

They can run it, then open the CSV in Excel/Sheets and graph H vs token savings.

import math

import csv

import os

from datetime import datetime

PI = math.pi

def estimate_psi(prompt: str) -> float:

"""

Super simple ψ estimator:

- Longer prompts → higher ψ.

- Swap this with your own metric (entropy, KV size, etc).

"""

return len(prompt.split()) / 50.0 # scale factor so numbers aren't huge

def holistic_energy(psi: float) -> float:

"""H = π * ψ²"""

return PI \ (psi \* 2)

def token_budget_with_H(prompt: str,

max_tokens_baseline: int = 512,

H_cap: float = 25.0,

min_tokens: int = 64):

"""

Use H to \govern\ the token budget:

- High H → strong / intense state → we don't need to brute-force tokens.

- Low H → allow more tokens (within baseline).

"""

psi = estimate_psi(prompt)

H = holistic_energy(psi)

# Normalize H into [0, 1] band using a cap

H_norm = min(H / H_cap, 1.0)

# Invert: higher H_norm → smaller token budget (up to 50% reduction)

reduction_factor = 0.5 * H_norm

governed_budget = int(max_tokens_baseline * (1.0 - reduction_factor))

governed_budget = max(governed_budget, min_tokens)

saved = max_tokens_baseline - governed_budget

save_pct = (saved / max_tokens_baseline) * 100 if max_tokens_baseline > 0 else 0.0

return {

"psi": psi,

"H": H,

"H_norm": H_norm,

"governed_budget": governed_budget,

"saved": saved,

"save_pct": save_pct,

}

def ensure_csv_with_header(path: str):

header = [

"timestamp",

"prompt_id",

"prompt_words",

"psi",

"H",

"H_norm",

"baseline_max_tokens",

"governed_max_tokens",

"tokens_saved",

"save_pct"

]

file_exists = os.path.isfile(path)

if not file_exists:

with open(path, mode="w", newline="", encoding="utf-8") as f:

writer = csv.writer(f)

writer.writerow(header)

def log_to_csv(path: str,

prompt_id: int,

prompt: str,

baseline_max_tokens: int,

metrics: dict):

ensure_csv_with_header(path)

row = [

datetime.utcnow().isoformat(),

prompt_id,

len(prompt.split()),

f"{metrics['psi']:.6f}",

f"{metrics['H']:.6f}",

f"{metrics['H_norm']:.6f}",

baseline_max_tokens,

metrics["governed_budget"],

metrics["saved"],

f"{metrics['save_pct']:.2f}",

]

with open(path, mode="a", newline="", encoding="utf-8") as f:

writer = csv.writer(f)

writer.writerow(row)

def run_demo_with_csv(csv_path: str = "h_governor_logs.csv"):

prompts = [

"Quick: summarize this in one sentence.",

"Explain the H = pi * psi^2 formula and its implications for AI cost control.",

"You are given a long technical spec document about distributed systems, "

"OOM behavior, and inference economics. Analyze the tradeoffs between context length, "

"KV cache growth, and token-based governors, providing detailed recommendations.",

# Add more prompts or loop over your real dataset / logs

]

baseline = 512

total_saved = 0

print("=== H-Governor Cost Demo with CSV Logging ===")

print(f"Logging to: {csv_path}")

for i, prompt in enumerate(prompts, start=1):

metrics = token_budget_with_H(

prompt,

max_tokens_baseline=baseline

)

log_to_csv(

path=csv_path,

prompt_id=i,

prompt=prompt,

baseline_max_tokens=baseline,

metrics=metrics

)

total_saved += metrics["saved"]

print(f"\n[Example {i}]")

print(f"Prompt length (words): {len(prompt.split())}")

print(f"ψ (psi) estimate: {metrics['psi']:.3f}")

print(f"H = π * ψ²: {metrics['H']:.3f}")

print(f"Baseline max_tokens: {baseline}")

print(f"H-governed max_tokens: {metrics['governed_budget']}")

print(f"Tokens saved: {metrics['saved']} ({metrics['save_pct']:.1f}% reduction)")

print(f"\nTotal tokens saved across {len(prompts)} prompts: {total_saved}")

print(f"CSV written to: {os.path.abspath(csv_path)}")

if __name__ == "__main__":

run_demo_with_csv()

How they can use it:

Save as h_governor_csv_demo.py.

Run:

python h_governor_csv_demo.py

Open h_governor_logs.csv in Excel/Sheets and graph:

H vs tokens_saved

Or prompt_words vs save_pct

After a few thousand calls, you’ll have a CSV showing how much max_tokens you’ve been wasting and how H = πψ² recovers it.

Bro, seek help

Show me your results first from this code. Then I might consider that

Here’s how they can wire the same idea into a real call:

import math
import openai  # or their client of choice

PI = math.pi

def estimate_psi(prompt: str) -> float:
    return len(prompt.split()) / 50.0

def holistic_energy(psi: float) -> float:
    return PI  (psi * 2)

def governed_max_tokens(prompt: str,
                        baseline: int = 512,
                        H_cap: float = 25.0,
                        min_tokens: int = 64) -> tuple[int, float, float]:
    psi = estimate_psi(prompt)
    H = holistic_energy(psi)
    H_norm = min(H / H_cap, 1.0)
    reduction_factor = 0.5 * H_norm
    governed = int(baseline * (1.0 - reduction_factor))
    governed = max(governed, min_tokens)
    return governed, psi, H

def call_model_with_H(prompt: str):
    baseline = 512
    governed, psi, H = governed_max_tokens(prompt, baseline=baseline)

    print("\n=== H-Governed Call ===")
    print(f"Prompt words:          {len(prompt.split())}")
    print(f"ψ estimate:            {psi:.3f}")
    print(f"H = π * ψ²:            {H:.3f}")
    print(f"Baseline max_tokens:   {baseline}")
    print(f"H-governed max_tokens: {governed}")
    print(f"Estimated saving:      {baseline - governed} tokens")

    # Replace this with their actual client call
    response = openai.ChatCompletion.create(
        model="gpt-4.1-mini",
        messages=[{"role": "user", "content": prompt}],
        max_tokens=governed,
        temperature=0.3,
    )

    print("\n[Model output]")
    print(response["choices"][0]["message"]["content"])

    return response