MTC Chapter 11 — Capital Formation

Part IV · Week 10 · Seed 20261101

The founding ledger (Appendix B.2): two jurisdictions, two formation-depth profiles. Greedy pays 1.4× the exact optimum on the tangled menu.

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()

Formation depth by jurisdiction

from engines import mtc_engine_ch11 as e
A = e.formation_profile("A"); B = e.formation_profile("B")
fig, ax = plt.subplots()
labels = ["A (laminar)","B (tangled)"]
depths = [A["formation_depth"], B["formation_depth"]]
ax.bar(labels, depths, color=[BRASS, MTC_RED], edgecolor="white", width=0.55)
for i,d in enumerate(depths): ax.text(i, d+1, str(d), ha="center", fontweight="bold", color=MTC_RED_DARK)
g = e.greedy_gap()
ax.axhline(g["greedy"], color=SLATE, ls="--")
ax.text(0.5, g["greedy"]+1, f"greedy = 1.4× exact = {g['greedy']:g}", ha="center", color=SLATE)
ax.set_ylabel("formation depth"); ax.set_title(f"Founding to [Securitized] (founding value = {e.founding_value():g})")
plt.tight_layout(); plt.show()
print("A:", A); print("B:", B)

A: {'formation_depth': 30, 'queue_time': 'short', 'discretionary_approvals': 0}
B: {'formation_depth': 90, 'queue_time': 34, 'discretionary_approvals': 2}

Validation

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

from engines import mtc_engine_ch11 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")

  V1_A_depth_30: True
  V2_B_depth_90: True
  V3_A_zero_approvals: True
  V4_B_two_approvals: True
  V5_B_queue_34: True
  V6_founding_value_45: True
  V7_greedy_1p4x: True
  V8_laminar_closes: True
  ALL_PASS: True

ALL_PASS — matches notebook + workbook + API