FA-58546 / Loan amortization schedules / Open access
Adjustable rate reset with caps: lifetime ceiling base · case 01
Note rates are pinned to the lifetime cap spread itself.
ROOT CAUSE
The lifetime cap is treated as an absolute ceiling instead of a spread over the initial rate.
VERIFIED REPAIR
Compute the ceiling as the initial rate plus the lifetime cap.
Unsuccessful approach: Measuring the lifetime cap from the previous rate lets the ceiling ratchet up every reset.
Case contract
x = {'initial_bp', 'index_path': index at each reset, 'margin_bp', 'round_to', 'initial_cap_bp', 'periodic_cap_bp', 'lifetime_cap_bp' (above initial), 'floor_bp'}. At each reset the fully indexed rate index + margin is rounded half-up to a multiple of round_to, limited to within the cap of the previous note rate (initial cap at the first reset, periodic afterwards, both directions), then limited to [floor_bp, initial + lifetime cap]. Return the list of note rates.
Why this case matters
Amortization engines drive borrower statements, payoff quotes and investor remittances; a misplaced rounding step, boundary or ordering rule compounds across hundreds of periods.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(x):
rate = x['initial_bp']
out = []
life_max = x['lifetime_cap_bp']
for i, idx in enumerate(x['index_path']):
fi = idx + x['margin_bp']
q, r = divmod(fi, x['round_to'])
fi = (q + (1 if 2 * r >= x['round_to'] else 0)) * x['round_to']
cap = x['initial_cap_bp'] if i == 0 else x['periodic_cap_bp']
new = max(rate - cap, min(fi, rate + cap))
new = max(x['floor_bp'], min(new, life_max))
out.append(new)
rate = new
return out
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: lifetime ceiling base', {'initial_bp': 500, 'index_path': [212, 100, 50, 250, 700], 'margin_bp': 275, 'round_to': 125, 'initial_cap_bp': 200, 'periodic_cap_bp': 100, 'lifetime_cap_bp': 500, 'floor_bp': 400}, [500, 400, 400, 500, 600]], ['regression: lifetime ceiling base, partial-repair probe', {'initial_bp': 300, 'index_path': [400, 650, 537, 650], 'margin_bp': 250, 'round_to': 50, 'initial_cap_bp': 500, 'periodic_cap_bp': 100, 'lifetime_cap_bp': 500, 'floor_bp': 300}, [650, 750, 800, 800]], ['control 1', {'initial_bp': 300, 'index_path': [212, 212], 'margin_bp': 275, 'round_to': 25, 'initial_cap_bp': 200, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 500, 'floor_bp': 225}, [475, 475]], ['control 2', {'initial_bp': 300, 'index_path': [100, 50, 250], 'margin_bp': 275, 'round_to': 50, 'initial_cap_bp': 500, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 600, 'floor_bp': 300}, [400, 350, 550]], ['control 3', {'initial_bp': 300, 'index_path': [650, 212, 100], 'margin_bp': 275, 'round_to': 50, 'initial_cap_bp': 200, 'periodic_cap_bp': 100, 'lifetime_cap_bp': 600, 'floor_bp': 400}, [500, 500, 400]], ['control 4', {'initial_bp': 450, 'index_path': [50, 100], 'margin_bp': 225, 'round_to': 25, 'initial_cap_bp': 200, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 600, 'floor_bp': 300}, [300, 325]], ['control 5', {'initial_bp': 500, 'index_path': [212, 212, 250], 'margin_bp': 250, 'round_to': 125, 'initial_cap_bp': 200, 'periodic_cap_bp': 100, 'lifetime_cap_bp': 600, 'floor_bp': 225}, [500, 500, 500]]], [['regression: lifetime ceiling base', {'initial_bp': 450, 'index_path': [650, 50, 212], 'margin_bp': 275, 'round_to': 125, 'initial_cap_bp': 200, 'periodic_cap_bp': 100, 'lifetime_cap_bp': 600, 'floor_bp': 225}, [650, 550, 500]], ['regression: lifetime ceiling base, partial-repair probe', {'initial_bp': 300, 'index_path': [100, 700, 537, 700, 650], 'margin_bp': 250, 'round_to': 125, 'initial_cap_bp': 200, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 600, 'floor_bp': 225}, [375, 575, 750, 900, 875]], ['control 1', {'initial_bp': 450, 'index_path': [250, 100, 700], 'margin_bp': 225, 'round_to': 25, 'initial_cap_bp': 200, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 600, 'floor_bp': 225}, [475, 325, 525]], ['control 2', {'initial_bp': 500, 'index_path': [212], 'margin_bp': 225, 'round_to': 125, 'initial_cap_bp': 500, 'periodic_cap_bp': 100, 'lifetime_cap_bp': 500, 'floor_bp': 225}, [375]], ['control 3', {'initial_bp': 450, 'index_path': [50], 'margin_bp': 250, 'round_to': 50, 'initial_cap_bp': 200, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 600, 'floor_bp': 400}, [400]], ['control 4', {'initial_bp': 500, 'index_path': [212], 'margin_bp': 275, 'round_to': 125, 'initial_cap_bp': 500, 'periodic_cap_bp': 100, 'lifetime_cap_bp': 600, 'floor_bp': 225}, [500]], ['control 5', {'initial_bp': 450, 'index_path': [100, 50, 400, 700, 100], 'margin_bp': 225, 'round_to': 25, 'initial_cap_bp': 200, 'periodic_cap_bp': 100, 'lifetime_cap_bp': 600, 'floor_bp': 225}, [325, 275, 375, 475, 375]]], [['regression: lifetime ceiling base', {'initial_bp': 450, 'index_path': [212, 650, 50, 650], 'margin_bp': 250, 'round_to': 125, 'initial_cap_bp': 200, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 500, 'floor_bp': 300}, [500, 700, 500, 700]], ['regression: lifetime ceiling base, partial-repair probe', {'initial_bp': 300, 'index_path': [537, 700, 50], 'margin_bp': 275, 'round_to': 25, 'initial_cap_bp': 500, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 500, 'floor_bp': 225}, [800, 800, 600]], ['control 1', {'initial_bp': 450, 'index_path': [250, 250, 212], 'margin_bp': 225, 'round_to': 50, 'initial_cap_bp': 500, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 600, 'floor_bp': 225}, [500, 500, 450]], ['control 2', {'initial_bp': 450, 'index_path': [100], 'margin_bp': 225, 'round_to': 25, 'initial_cap_bp': 500, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 500, 'floor_bp': 400}, [400]], ['control 3', {'initial_bp': 300, 'index_path': [650], 'margin_bp': 250, 'round_to': 50, 'initial_cap_bp': 200, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 600, 'floor_bp': 400}, [500]], ['control 4', {'initial_bp': 450, 'index_path': [250, 212, 100, 50, 700], 'margin_bp': 225, 'round_to': 25, 'initial_cap_bp': 200, 'periodic_cap_bp': 100, 'lifetime_cap_bp': 500, 'floor_bp': 400}, [475, 425, 400, 400, 500]], ['control 5', {'initial_bp': 300, 'index_path': [212, 50, 100, 50, 400], 'margin_bp': 225, 'round_to': 25, 'initial_cap_bp': 500, 'periodic_cap_bp': 100, 'lifetime_cap_bp': 500, 'floor_bp': 400}, [425, 400, 400, 400, 500]]], [['regression: lifetime ceiling base', {'initial_bp': 300, 'index_path': [400, 400, 537], 'margin_bp': 275, 'round_to': 25, 'initial_cap_bp': 200, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 500, 'floor_bp': 400}, [500, 675, 800]], ['regression: lifetime ceiling base, partial-repair probe', {'initial_bp': 300, 'index_path': [650, 700], 'margin_bp': 250, 'round_to': 50, 'initial_cap_bp': 500, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 600, 'floor_bp': 300}, [800, 900]], ['control 1', {'initial_bp': 300, 'index_path': [650, 250, 50, 537, 50], 'margin_bp': 275, 'round_to': 125, 'initial_cap_bp': 200, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 600, 'floor_bp': 225}, [500, 500, 375, 575, 375]], ['control 2', {'initial_bp': 300, 'index_path': [250, 250, 250], 'margin_bp': 250, 'round_to': 50, 'initial_cap_bp': 500, 'periodic_cap_bp': 100, 'lifetime_cap_bp': 600, 'floor_bp': 300}, [500, 500, 500]], ['control 3', {'initial_bp': 500, 'index_path': [100, 212, 100], 'margin_bp': 250, 'round_to': 25, 'initial_cap_bp': 200, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 500, 'floor_bp': 225}, [350, 450, 350]], ['control 4', {'initial_bp': 300, 'index_path': [400, 100, 400, 250, 50], 'margin_bp': 275, 'round_to': 25, 'initial_cap_bp': 200, 'periodic_cap_bp': 100, 'lifetime_cap_bp': 600, 'floor_bp': 400}, [500, 400, 500, 525, 425]], ['control 5', {'initial_bp': 450, 'index_path': [250, 50, 700], 'margin_bp': 250, 'round_to': 25, 'initial_cap_bp': 200, 'periodic_cap_bp': 100, 'lifetime_cap_bp': 500, 'floor_bp': 400}, [500, 400, 500]]], [['regression: lifetime ceiling base', {'initial_bp': 450, 'index_path': [650], 'margin_bp': 275, 'round_to': 125, 'initial_cap_bp': 500, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 500, 'floor_bp': 300}, [875]], ['regression: lifetime ceiling base, partial-repair probe', {'initial_bp': 300, 'index_path': [537, 50, 650, 537, 650], 'margin_bp': 250, 'round_to': 125, 'initial_cap_bp': 500, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 500, 'floor_bp': 225}, [750, 550, 750, 750, 800]], ['control 1', {'initial_bp': 300, 'index_path': [250], 'margin_bp': 225, 'round_to': 125, 'initial_cap_bp': 200, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 600, 'floor_bp': 300}, [500]], ['control 2', {'initial_bp': 450, 'index_path': [250, 537, 250, 700], 'margin_bp': 275, 'round_to': 125, 'initial_cap_bp': 200, 'periodic_cap_bp': 100, 'lifetime_cap_bp': 600, 'floor_bp': 225}, [500, 600, 500, 600]], ['control 3', {'initial_bp': 300, 'index_path': [50, 537, 250, 100], 'margin_bp': 225, 'round_to': 25, 'initial_cap_bp': 500, 'periodic_cap_bp': 100, 'lifetime_cap_bp': 600, 'floor_bp': 300}, [300, 400, 475, 375]], ['control 4', {'initial_bp': 300, 'index_path': [50, 50], 'margin_bp': 250, 'round_to': 125, 'initial_cap_bp': 200, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 500, 'floor_bp': 400}, [400, 400]], ['control 5', {'initial_bp': 450, 'index_path': [100, 250, 100, 650], 'margin_bp': 275, 'round_to': 25, 'initial_cap_bp': 500, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 600, 'floor_bp': 225}, [375, 525, 375, 575]]]]
for label, args, expected in fixtures[N-1]:
try:
actual = solve(args)
except Exception as exc:
actual = 'raised ' + type(exc).__name__
check(label, actual, expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| regression: lifetime ceiling base | [500, 400, 400, 500, 500] | [500, 400, 400, 500, 600] | Failed |
| regression: lifetime ceiling base, partial-repair probe | [500, 500, 500, 500] | [650, 750, 800, 800] | Failed |
| control 1 | [475, 475] | [475, 475] | Passed |
| control 2 | [400, 350, 550] | [400, 350, 550] | Passed |
| control 3 | [500, 500, 400] | [500, 500, 400] | Passed |
| control 4 | [300, 325] | [300, 325] | Passed |
| control 5 | [500, 500, 500] | [500, 500, 500] | Passed |
SHA-256 / 1c139744ec7b008c499cb757cb709e6ae11538090d281d13266a209c17abc0e2
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(x):
rate = x['initial_bp']
out = []
life_max = x['initial_bp'] + x['lifetime_cap_bp']
for i, idx in enumerate(x['index_path']):
fi = idx + x['margin_bp']
q, r = divmod(fi, x['round_to'])
fi = (q + (1 if 2 * r >= x['round_to'] else 0)) * x['round_to']
cap = x['initial_cap_bp'] if i == 0 else x['periodic_cap_bp']
new = max(rate - cap, min(fi, rate + cap))
new = max(x['floor_bp'], min(new, rate + x['lifetime_cap_bp']))
out.append(new)
rate = new
return out
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: lifetime ceiling base', {'initial_bp': 500, 'index_path': [212, 100, 50, 250, 700], 'margin_bp': 275, 'round_to': 125, 'initial_cap_bp': 200, 'periodic_cap_bp': 100, 'lifetime_cap_bp': 500, 'floor_bp': 400}, [500, 400, 400, 500, 600]], ['regression: lifetime ceiling base, partial-repair probe', {'initial_bp': 300, 'index_path': [400, 650, 537, 650], 'margin_bp': 250, 'round_to': 50, 'initial_cap_bp': 500, 'periodic_cap_bp': 100, 'lifetime_cap_bp': 500, 'floor_bp': 300}, [650, 750, 800, 800]], ['control 1', {'initial_bp': 300, 'index_path': [212, 212], 'margin_bp': 275, 'round_to': 25, 'initial_cap_bp': 200, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 500, 'floor_bp': 225}, [475, 475]], ['control 2', {'initial_bp': 300, 'index_path': [100, 50, 250], 'margin_bp': 275, 'round_to': 50, 'initial_cap_bp': 500, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 600, 'floor_bp': 300}, [400, 350, 550]], ['control 3', {'initial_bp': 300, 'index_path': [650, 212, 100], 'margin_bp': 275, 'round_to': 50, 'initial_cap_bp': 200, 'periodic_cap_bp': 100, 'lifetime_cap_bp': 600, 'floor_bp': 400}, [500, 500, 400]], ['control 4', {'initial_bp': 450, 'index_path': [50, 100], 'margin_bp': 225, 'round_to': 25, 'initial_cap_bp': 200, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 600, 'floor_bp': 300}, [300, 325]], ['control 5', {'initial_bp': 500, 'index_path': [212, 212, 250], 'margin_bp': 250, 'round_to': 125, 'initial_cap_bp': 200, 'periodic_cap_bp': 100, 'lifetime_cap_bp': 600, 'floor_bp': 225}, [500, 500, 500]]], [['regression: lifetime ceiling base', {'initial_bp': 450, 'index_path': [650, 50, 212], 'margin_bp': 275, 'round_to': 125, 'initial_cap_bp': 200, 'periodic_cap_bp': 100, 'lifetime_cap_bp': 600, 'floor_bp': 225}, [650, 550, 500]], ['regression: lifetime ceiling base, partial-repair probe', {'initial_bp': 300, 'index_path': [100, 700, 537, 700, 650], 'margin_bp': 250, 'round_to': 125, 'initial_cap_bp': 200, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 600, 'floor_bp': 225}, [375, 575, 750, 900, 875]], ['control 1', {'initial_bp': 450, 'index_path': [250, 100, 700], 'margin_bp': 225, 'round_to': 25, 'initial_cap_bp': 200, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 600, 'floor_bp': 225}, [475, 325, 525]], ['control 2', {'initial_bp': 500, 'index_path': [212], 'margin_bp': 225, 'round_to': 125, 'initial_cap_bp': 500, 'periodic_cap_bp': 100, 'lifetime_cap_bp': 500, 'floor_bp': 225}, [375]], ['control 3', {'initial_bp': 450, 'index_path': [50], 'margin_bp': 250, 'round_to': 50, 'initial_cap_bp': 200, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 600, 'floor_bp': 400}, [400]], ['control 4', {'initial_bp': 500, 'index_path': [212], 'margin_bp': 275, 'round_to': 125, 'initial_cap_bp': 500, 'periodic_cap_bp': 100, 'lifetime_cap_bp': 600, 'floor_bp': 225}, [500]], ['control 5', {'initial_bp': 450, 'index_path': [100, 50, 400, 700, 100], 'margin_bp': 225, 'round_to': 25, 'initial_cap_bp': 200, 'periodic_cap_bp': 100, 'lifetime_cap_bp': 600, 'floor_bp': 225}, [325, 275, 375, 475, 375]]], [['regression: lifetime ceiling base', {'initial_bp': 450, 'index_path': [212, 650, 50, 650], 'margin_bp': 250, 'round_to': 125, 'initial_cap_bp': 200, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 500, 'floor_bp': 300}, [500, 700, 500, 700]], ['regression: lifetime ceiling base, partial-repair probe', {'initial_bp': 300, 'index_path': [537, 700, 50], 'margin_bp': 275, 'round_to': 25, 'initial_cap_bp': 500, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 500, 'floor_bp': 225}, [800, 800, 600]], ['control 1', {'initial_bp': 450, 'index_path': [250, 250, 212], 'margin_bp': 225, 'round_to': 50, 'initial_cap_bp': 500, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 600, 'floor_bp': 225}, [500, 500, 450]], ['control 2', {'initial_bp': 450, 'index_path': [100], 'margin_bp': 225, 'round_to': 25, 'initial_cap_bp': 500, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 500, 'floor_bp': 400}, [400]], ['control 3', {'initial_bp': 300, 'index_path': [650], 'margin_bp': 250, 'round_to': 50, 'initial_cap_bp': 200, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 600, 'floor_bp': 400}, [500]], ['control 4', {'initial_bp': 450, 'index_path': [250, 212, 100, 50, 700], 'margin_bp': 225, 'round_to': 25, 'initial_cap_bp': 200, 'periodic_cap_bp': 100, 'lifetime_cap_bp': 500, 'floor_bp': 400}, [475, 425, 400, 400, 500]], ['control 5', {'initial_bp': 300, 'index_path': [212, 50, 100, 50, 400], 'margin_bp': 225, 'round_to': 25, 'initial_cap_bp': 500, 'periodic_cap_bp': 100, 'lifetime_cap_bp': 500, 'floor_bp': 400}, [425, 400, 400, 400, 500]]], [['regression: lifetime ceiling base', {'initial_bp': 300, 'index_path': [400, 400, 537], 'margin_bp': 275, 'round_to': 25, 'initial_cap_bp': 200, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 500, 'floor_bp': 400}, [500, 675, 800]], ['regression: lifetime ceiling base, partial-repair probe', {'initial_bp': 300, 'index_path': [650, 700], 'margin_bp': 250, 'round_to': 50, 'initial_cap_bp': 500, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 600, 'floor_bp': 300}, [800, 900]], ['control 1', {'initial_bp': 300, 'index_path': [650, 250, 50, 537, 50], 'margin_bp': 275, 'round_to': 125, 'initial_cap_bp': 200, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 600, 'floor_bp': 225}, [500, 500, 375, 575, 375]], ['control 2', {'initial_bp': 300, 'index_path': [250, 250, 250], 'margin_bp': 250, 'round_to': 50, 'initial_cap_bp': 500, 'periodic_cap_bp': 100, 'lifetime_cap_bp': 600, 'floor_bp': 300}, [500, 500, 500]], ['control 3', {'initial_bp': 500, 'index_path': [100, 212, 100], 'margin_bp': 250, 'round_to': 25, 'initial_cap_bp': 200, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 500, 'floor_bp': 225}, [350, 450, 350]], ['control 4', {'initial_bp': 300, 'index_path': [400, 100, 400, 250, 50], 'margin_bp': 275, 'round_to': 25, 'initial_cap_bp': 200, 'periodic_cap_bp': 100, 'lifetime_cap_bp': 600, 'floor_bp': 400}, [500, 400, 500, 525, 425]], ['control 5', {'initial_bp': 450, 'index_path': [250, 50, 700], 'margin_bp': 250, 'round_to': 25, 'initial_cap_bp': 200, 'periodic_cap_bp': 100, 'lifetime_cap_bp': 500, 'floor_bp': 400}, [500, 400, 500]]], [['regression: lifetime ceiling base', {'initial_bp': 450, 'index_path': [650], 'margin_bp': 275, 'round_to': 125, 'initial_cap_bp': 500, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 500, 'floor_bp': 300}, [875]], ['regression: lifetime ceiling base, partial-repair probe', {'initial_bp': 300, 'index_path': [537, 50, 650, 537, 650], 'margin_bp': 250, 'round_to': 125, 'initial_cap_bp': 500, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 500, 'floor_bp': 225}, [750, 550, 750, 750, 800]], ['control 1', {'initial_bp': 300, 'index_path': [250], 'margin_bp': 225, 'round_to': 125, 'initial_cap_bp': 200, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 600, 'floor_bp': 300}, [500]], ['control 2', {'initial_bp': 450, 'index_path': [250, 537, 250, 700], 'margin_bp': 275, 'round_to': 125, 'initial_cap_bp': 200, 'periodic_cap_bp': 100, 'lifetime_cap_bp': 600, 'floor_bp': 225}, [500, 600, 500, 600]], ['control 3', {'initial_bp': 300, 'index_path': [50, 537, 250, 100], 'margin_bp': 225, 'round_to': 25, 'initial_cap_bp': 500, 'periodic_cap_bp': 100, 'lifetime_cap_bp': 600, 'floor_bp': 300}, [300, 400, 475, 375]], ['control 4', {'initial_bp': 300, 'index_path': [50, 50], 'margin_bp': 250, 'round_to': 125, 'initial_cap_bp': 200, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 500, 'floor_bp': 400}, [400, 400]], ['control 5', {'initial_bp': 450, 'index_path': [100, 250, 100, 650], 'margin_bp': 275, 'round_to': 25, 'initial_cap_bp': 500, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 600, 'floor_bp': 225}, [375, 525, 375, 575]]]]
for label, args, expected in fixtures[N-1]:
try:
actual = solve(args)
except Exception as exc:
actual = 'raised ' + type(exc).__name__
check(label, actual, expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| regression: lifetime ceiling base | [500, 400, 400, 500, 600] | [500, 400, 400, 500, 600] | Passed |
| regression: lifetime ceiling base, partial-repair probe | [650, 750, 800, 900] | [650, 750, 800, 800] | Failed |
| control 1 | [475, 475] | [475, 475] | Passed |
| control 2 | [400, 350, 550] | [400, 350, 550] | Passed |
| control 3 | [500, 500, 400] | [500, 500, 400] | Passed |
| control 4 | [300, 325] | [300, 325] | Passed |
| control 5 | [500, 500, 500] | [500, 500, 500] | Passed |
SHA-256 / c3d370ca580bf473ef290737e89fffa4ad768f352ef3cf721f732ae2de663242
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(x):
rate = x['initial_bp']
out = []
life_max = x['initial_bp'] + x['lifetime_cap_bp']
for i, idx in enumerate(x['index_path']):
fi = idx + x['margin_bp']
q, r = divmod(fi, x['round_to'])
fi = (q + (1 if 2 * r >= x['round_to'] else 0)) * x['round_to']
cap = x['initial_cap_bp'] if i == 0 else x['periodic_cap_bp']
new = max(rate - cap, min(fi, rate + cap))
new = max(x['floor_bp'], min(new, life_max))
out.append(new)
rate = new
return out
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: lifetime ceiling base', {'initial_bp': 500, 'index_path': [212, 100, 50, 250, 700], 'margin_bp': 275, 'round_to': 125, 'initial_cap_bp': 200, 'periodic_cap_bp': 100, 'lifetime_cap_bp': 500, 'floor_bp': 400}, [500, 400, 400, 500, 600]], ['regression: lifetime ceiling base, partial-repair probe', {'initial_bp': 300, 'index_path': [400, 650, 537, 650], 'margin_bp': 250, 'round_to': 50, 'initial_cap_bp': 500, 'periodic_cap_bp': 100, 'lifetime_cap_bp': 500, 'floor_bp': 300}, [650, 750, 800, 800]], ['control 1', {'initial_bp': 300, 'index_path': [212, 212], 'margin_bp': 275, 'round_to': 25, 'initial_cap_bp': 200, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 500, 'floor_bp': 225}, [475, 475]], ['control 2', {'initial_bp': 300, 'index_path': [100, 50, 250], 'margin_bp': 275, 'round_to': 50, 'initial_cap_bp': 500, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 600, 'floor_bp': 300}, [400, 350, 550]], ['control 3', {'initial_bp': 300, 'index_path': [650, 212, 100], 'margin_bp': 275, 'round_to': 50, 'initial_cap_bp': 200, 'periodic_cap_bp': 100, 'lifetime_cap_bp': 600, 'floor_bp': 400}, [500, 500, 400]], ['control 4', {'initial_bp': 450, 'index_path': [50, 100], 'margin_bp': 225, 'round_to': 25, 'initial_cap_bp': 200, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 600, 'floor_bp': 300}, [300, 325]], ['control 5', {'initial_bp': 500, 'index_path': [212, 212, 250], 'margin_bp': 250, 'round_to': 125, 'initial_cap_bp': 200, 'periodic_cap_bp': 100, 'lifetime_cap_bp': 600, 'floor_bp': 225}, [500, 500, 500]]], [['regression: lifetime ceiling base', {'initial_bp': 450, 'index_path': [650, 50, 212], 'margin_bp': 275, 'round_to': 125, 'initial_cap_bp': 200, 'periodic_cap_bp': 100, 'lifetime_cap_bp': 600, 'floor_bp': 225}, [650, 550, 500]], ['regression: lifetime ceiling base, partial-repair probe', {'initial_bp': 300, 'index_path': [100, 700, 537, 700, 650], 'margin_bp': 250, 'round_to': 125, 'initial_cap_bp': 200, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 600, 'floor_bp': 225}, [375, 575, 750, 900, 875]], ['control 1', {'initial_bp': 450, 'index_path': [250, 100, 700], 'margin_bp': 225, 'round_to': 25, 'initial_cap_bp': 200, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 600, 'floor_bp': 225}, [475, 325, 525]], ['control 2', {'initial_bp': 500, 'index_path': [212], 'margin_bp': 225, 'round_to': 125, 'initial_cap_bp': 500, 'periodic_cap_bp': 100, 'lifetime_cap_bp': 500, 'floor_bp': 225}, [375]], ['control 3', {'initial_bp': 450, 'index_path': [50], 'margin_bp': 250, 'round_to': 50, 'initial_cap_bp': 200, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 600, 'floor_bp': 400}, [400]], ['control 4', {'initial_bp': 500, 'index_path': [212], 'margin_bp': 275, 'round_to': 125, 'initial_cap_bp': 500, 'periodic_cap_bp': 100, 'lifetime_cap_bp': 600, 'floor_bp': 225}, [500]], ['control 5', {'initial_bp': 450, 'index_path': [100, 50, 400, 700, 100], 'margin_bp': 225, 'round_to': 25, 'initial_cap_bp': 200, 'periodic_cap_bp': 100, 'lifetime_cap_bp': 600, 'floor_bp': 225}, [325, 275, 375, 475, 375]]], [['regression: lifetime ceiling base', {'initial_bp': 450, 'index_path': [212, 650, 50, 650], 'margin_bp': 250, 'round_to': 125, 'initial_cap_bp': 200, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 500, 'floor_bp': 300}, [500, 700, 500, 700]], ['regression: lifetime ceiling base, partial-repair probe', {'initial_bp': 300, 'index_path': [537, 700, 50], 'margin_bp': 275, 'round_to': 25, 'initial_cap_bp': 500, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 500, 'floor_bp': 225}, [800, 800, 600]], ['control 1', {'initial_bp': 450, 'index_path': [250, 250, 212], 'margin_bp': 225, 'round_to': 50, 'initial_cap_bp': 500, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 600, 'floor_bp': 225}, [500, 500, 450]], ['control 2', {'initial_bp': 450, 'index_path': [100], 'margin_bp': 225, 'round_to': 25, 'initial_cap_bp': 500, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 500, 'floor_bp': 400}, [400]], ['control 3', {'initial_bp': 300, 'index_path': [650], 'margin_bp': 250, 'round_to': 50, 'initial_cap_bp': 200, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 600, 'floor_bp': 400}, [500]], ['control 4', {'initial_bp': 450, 'index_path': [250, 212, 100, 50, 700], 'margin_bp': 225, 'round_to': 25, 'initial_cap_bp': 200, 'periodic_cap_bp': 100, 'lifetime_cap_bp': 500, 'floor_bp': 400}, [475, 425, 400, 400, 500]], ['control 5', {'initial_bp': 300, 'index_path': [212, 50, 100, 50, 400], 'margin_bp': 225, 'round_to': 25, 'initial_cap_bp': 500, 'periodic_cap_bp': 100, 'lifetime_cap_bp': 500, 'floor_bp': 400}, [425, 400, 400, 400, 500]]], [['regression: lifetime ceiling base', {'initial_bp': 300, 'index_path': [400, 400, 537], 'margin_bp': 275, 'round_to': 25, 'initial_cap_bp': 200, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 500, 'floor_bp': 400}, [500, 675, 800]], ['regression: lifetime ceiling base, partial-repair probe', {'initial_bp': 300, 'index_path': [650, 700], 'margin_bp': 250, 'round_to': 50, 'initial_cap_bp': 500, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 600, 'floor_bp': 300}, [800, 900]], ['control 1', {'initial_bp': 300, 'index_path': [650, 250, 50, 537, 50], 'margin_bp': 275, 'round_to': 125, 'initial_cap_bp': 200, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 600, 'floor_bp': 225}, [500, 500, 375, 575, 375]], ['control 2', {'initial_bp': 300, 'index_path': [250, 250, 250], 'margin_bp': 250, 'round_to': 50, 'initial_cap_bp': 500, 'periodic_cap_bp': 100, 'lifetime_cap_bp': 600, 'floor_bp': 300}, [500, 500, 500]], ['control 3', {'initial_bp': 500, 'index_path': [100, 212, 100], 'margin_bp': 250, 'round_to': 25, 'initial_cap_bp': 200, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 500, 'floor_bp': 225}, [350, 450, 350]], ['control 4', {'initial_bp': 300, 'index_path': [400, 100, 400, 250, 50], 'margin_bp': 275, 'round_to': 25, 'initial_cap_bp': 200, 'periodic_cap_bp': 100, 'lifetime_cap_bp': 600, 'floor_bp': 400}, [500, 400, 500, 525, 425]], ['control 5', {'initial_bp': 450, 'index_path': [250, 50, 700], 'margin_bp': 250, 'round_to': 25, 'initial_cap_bp': 200, 'periodic_cap_bp': 100, 'lifetime_cap_bp': 500, 'floor_bp': 400}, [500, 400, 500]]], [['regression: lifetime ceiling base', {'initial_bp': 450, 'index_path': [650], 'margin_bp': 275, 'round_to': 125, 'initial_cap_bp': 500, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 500, 'floor_bp': 300}, [875]], ['regression: lifetime ceiling base, partial-repair probe', {'initial_bp': 300, 'index_path': [537, 50, 650, 537, 650], 'margin_bp': 250, 'round_to': 125, 'initial_cap_bp': 500, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 500, 'floor_bp': 225}, [750, 550, 750, 750, 800]], ['control 1', {'initial_bp': 300, 'index_path': [250], 'margin_bp': 225, 'round_to': 125, 'initial_cap_bp': 200, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 600, 'floor_bp': 300}, [500]], ['control 2', {'initial_bp': 450, 'index_path': [250, 537, 250, 700], 'margin_bp': 275, 'round_to': 125, 'initial_cap_bp': 200, 'periodic_cap_bp': 100, 'lifetime_cap_bp': 600, 'floor_bp': 225}, [500, 600, 500, 600]], ['control 3', {'initial_bp': 300, 'index_path': [50, 537, 250, 100], 'margin_bp': 225, 'round_to': 25, 'initial_cap_bp': 500, 'periodic_cap_bp': 100, 'lifetime_cap_bp': 600, 'floor_bp': 300}, [300, 400, 475, 375]], ['control 4', {'initial_bp': 300, 'index_path': [50, 50], 'margin_bp': 250, 'round_to': 125, 'initial_cap_bp': 200, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 500, 'floor_bp': 400}, [400, 400]], ['control 5', {'initial_bp': 450, 'index_path': [100, 250, 100, 650], 'margin_bp': 275, 'round_to': 25, 'initial_cap_bp': 500, 'periodic_cap_bp': 200, 'lifetime_cap_bp': 600, 'floor_bp': 225}, [375, 525, 375, 575]]]]
for label, args, expected in fixtures[N-1]:
try:
actual = solve(args)
except Exception as exc:
actual = 'raised ' + type(exc).__name__
check(label, actual, expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| regression: lifetime ceiling base | [500, 400, 400, 500, 600] | [500, 400, 400, 500, 600] | Passed |
| regression: lifetime ceiling base, partial-repair probe | [650, 750, 800, 800] | [650, 750, 800, 800] | Passed |
| control 1 | [475, 475] | [475, 475] | Passed |
| control 2 | [400, 350, 550] | [400, 350, 550] | Passed |
| control 3 | [500, 500, 400] | [500, 500, 400] | Passed |
| control 4 | [300, 325] | [300, 325] | Passed |
| control 5 | [500, 500, 500] | [500, 500, 500] | Passed |
SHA-256 / 2c717c3ea8485af2a637e69a9be35cf8a1cbb1630569b35cd1ac323c1225e6d1
Verification & scope
A deterministic bounded teaching model with stipulated toy lending rules stated in the contract; money is integer cents and rates are basis points; it makes no claim of conformance to any regulation, servicing standard or product. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.
Observations recorded using Python 3.12.14 at 2026-09-29T14:46:27.782183+00:00.
Case digest / 08af9094b1ef7a4be8238d3ebd69c626debde01c333dd7a489c544437884d64e