MTC Chapter 7 — The Geometry of Transformation

Part II · Week 6 · Seed 20260701

Distance before price. A cost gauge makes transformation a directed quasi-metric; ownership is a ratchet (Priv→Spon = 2, Spon→Priv = 25).

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 accessibility profile from [Private]

Forward distances, with the covenant pruning that drops [Securitized] at radius 14.

from engines import mtc_engine_ch07 as e
d = e.distance_matrix()["Private"]
items = [(k,v) for k,v in d.items() if v != float("inf") and k!="Private"]
items.sort(key=lambda x:x[1])
fig, ax = plt.subplots()
names = [k for k,_ in items]; dists=[v for _,v in items]
bars = ax.barh(names, dists, color=[BRASS if n=="Securitized" else MTC_RED for n in names], edgecolor="white")
for i,(n,v) in enumerate(items): ax.text(v+0.4, i, f"{v:g}", va="center", fontweight="bold", color=MTC_RED_DARK)
ax.set_xlabel("forward distance $d_T$ from [Private]")
ax.set_title("Accessibility profile (brass = pruned by the securitization covenant)")
ax.invert_yaxis()
plt.tight_layout(); plt.show()
print("spectrum:", e.accessibility_spectrum("Private"))
print("ratchet: Priv->Spon =", d["Sponsor-owned"], " Spon->Priv =", e.distance_matrix()["Sponsor-owned"]["Private"])

Validation

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

from engines import mtc_engine_ch07 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")