MTC Chapter 9 — Architecture Value and Separation

Part III · Week 8 · Seed 20260901

Architecture value is compound-option value on an unrolled architecture — exactly. But the unrolling is exponentially expensive: $n$ latent pathways force $2^n$ meta-states.

import sys, os
sys.path.insert(0, r"/home/claude/mtc/mtc-course/downloads/engine_lib")
sys.path.insert(0, r"/home/claude/mtc/nbbuild")
from mtcplot import apply_style, MTC_RED, BRASS, SLATE, MTC_RED_LITE, MTC_RED_DARK
import matplotlib.pyplot as plt
import numpy as np
apply_style()

The exponential meta-state count (Lemma 9.3)

from engines import mtc_engine_ch09 as e
ns = list(range(1,9))
ms = [e.meta_states(n) for n in ns]
fig, ax = plt.subplots()
ax.bar([str(n) for n in ns], ms, color=MTC_RED, edgecolor="white")
for i,m in enumerate(ms): ax.text(i, m+max(ms)*0.01, str(m), ha="center", fontweight="bold", color=MTC_RED_DARK)
ax.set_xlabel("latent pathways $n$"); ax.set_ylabel("meta-states $2^n$")
ax.set_title("The unrolled architecture cannot be smaller than $2^n$")
plt.tight_layout(); plt.show()
print("premium:", e.premium_unrolled(), " kappa*:", e.kappa_star())

Validation

Every number above is reproduced by the seeded engine; the checks below must all pass.

from engines import mtc_engine_ch09 as _e
v = _e.validation_checks(); v.pop("_values", None)
for k, val in v.items():
    print(f"  {k}: {val}")
assert v["ALL_PASS"], "validation failed"
print("\nALL_PASS — matches notebook + workbook + API")