FAILURE MAP
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FA-71631 / Seismic magnitude estimation / Open access

Omori-Utsu expected aftershock count: c offset in power law · case 01

Early-window forecasts are badly inflated.

Verified by executionVariant 1 · 8 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The c time offset is dropped from both integral bounds.

VERIFIED REPAIR

Add c to both bounds.

Unsuccessful approach: Adding c only to the lower bound is still inconsistent.

Case contract

Rate K/(t+c)^p aftershocks per day. Expected count on [t1, t2] days: for p == 1 (within 1e-12) K ln((t2+c)/(t1+c)); otherwise K((t1+c)^(1-p) - (t2+c)^(1-p))/(p-1). t1 < 0 or t2 <= t1 returns None. Round to 0.001.

Why this case matters

Aftershock forecasts integrate the Omori-Utsu rate over the forecast window.

1 / The failure

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(k, c, p, t1, t2):
    if t1 < 0 or t2 <= t1:
        return None
    if abs(p - 1.0) < 1e-12:
        n = k * (math.log(t2 + c) - math.log(t1 + c))
    else:
        n = k * (t1 ** (1 - p) - t2 ** (1 - p)) / (p - 1)
    return round(n, 3)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['K 50.0 c 0.01 p 0.8 window 0.0-1.0 d', [50.0, 0.01, 0.8, 0.0, 1.0], 150.971], ['K 50.0 c 0.01 p 0.8 window 0.5-10.0 d', [50.0, 0.01, 0.8, 0.5, 10.0], 177.801], ['K 50.0 c 0.01 p 0.8 window 1.0-30.0 d', [50.0, 0.01, 0.8, 1.0, 30.0], 243.123], ['K 50.0 c 0.01 p 0.8 window 5.0-5.0 d', [50.0, 0.01, 0.8, 5.0, 5.0], None], ['K 50.0 c 0.01 p 0.8 window 3.0-2.0 d', [50.0, 0.01, 0.8, 3.0, 2.0], None], ['K 50.0 c 0.01 p 0.8 window 0.0-0.0 d', [50.0, 0.01, 0.8, 0.0, 0.0], None], ['K 50.0 c 0.01 p 1.0 window 0.0-1.0 d', [50.0, 0.01, 1.0, 0.0, 1.0], 230.756], ['K 50.0 c 0.01 p 1.0 window 0.5-10.0 d', [50.0, 0.01, 1.0, 0.5, 10.0], 148.846]], [['K 50.0 c 0.01 p 1.0 window 0.5-10.0 d', [50.0, 0.01, 1.0, 0.5, 10.0], 148.846], ['K 50.0 c 0.01 p 1.0 window 1.0-30.0 d', [50.0, 0.01, 1.0, 1.0, 30.0], 169.579], ['K 50.0 c 0.01 p 1.0 window 5.0-5.0 d', [50.0, 0.01, 1.0, 5.0, 5.0], None], ['K 50.0 c 0.01 p 1.0 window 3.0-2.0 d', [50.0, 0.01, 1.0, 3.0, 2.0], None], ['K 50.0 c 0.01 p 1.0 window 0.0-0.0 d', [50.0, 0.01, 1.0, 0.0, 0.0], None], ['K 50.0 c 0.01 p 1.1 window 0.5-10.0 d', [50.0, 0.01, 1.1, 0.5, 10.0], 137.702], ['K 50.0 c 0.01 p 1.1 window 1.0-30.0 d', [50.0, 0.01, 1.1, 1.0, 30.0], 143.672], ['K 50.0 c 0.01 p 1.3 window 1.0-30.0 d', [50.0, 0.01, 1.3, 1.0, 30.0], 106.098]], [['K 50.0 c 0.01 p 1.1 window 5.0-5.0 d', [50.0, 0.01, 1.1, 5.0, 5.0], None], ['K 50.0 c 0.01 p 1.1 window 3.0-2.0 d', [50.0, 0.01, 1.1, 3.0, 2.0], None], ['K 50.0 c 0.01 p 1.1 window 0.0-0.0 d', [50.0, 0.01, 1.1, 0.0, 0.0], None], ['K 50.0 c 0.01 p 1.3 window 0.5-10.0 d', [50.0, 0.01, 1.3, 0.5, 10.0], 120.469], ['K 50.0 c 0.01 p 1.3 window 1.0-30.0 d', [50.0, 0.01, 1.3, 1.0, 30.0], 106.098], ['K 50.0 c 0.01 p 1.3 window 5.0-5.0 d', [50.0, 0.01, 1.3, 5.0, 5.0], None], ['K 50.0 c 0.01 p 1.3 window 3.0-2.0 d', [50.0, 0.01, 1.3, 3.0, 2.0], None], ['K 50.0 c 0.05 p 1.1 window 1.0-30.0 d', [50.0, 0.05, 1.1, 1.0, 30.0], 141.783]], [['K 50.0 c 0.01 p 1.3 window 0.0-0.0 d', [50.0, 0.01, 1.3, 0.0, 0.0], None], ['K 50.0 c 0.05 p 0.8 window 0.0-1.0 d', [50.0, 0.05, 0.8, 0.0, 1.0], 115.131], ['K 50.0 c 0.05 p 0.8 window 0.5-10.0 d', [50.0, 0.05, 0.8, 0.5, 10.0], 174.793], ['K 50.0 c 0.05 p 0.8 window 1.0-30.0 d', [50.0, 0.05, 0.8, 1.0, 30.0], 241.301], ['K 50.0 c 0.05 p 0.8 window 5.0-5.0 d', [50.0, 0.05, 0.8, 5.0, 5.0], None], ['K 50.0 c 0.05 p 0.8 window 3.0-2.0 d', [50.0, 0.05, 0.8, 3.0, 2.0], None], ['K 50.0 c 0.05 p 0.8 window 0.0-0.0 d', [50.0, 0.05, 0.8, 0.0, 0.0], None], ['K 200.0 c 0.01 p 0.8 window 1.0-30.0 d', [200.0, 0.01, 0.8, 1.0, 30.0], 972.49]], [['K 50.0 c 0.05 p 1.0 window 0.0-1.0 d', [50.0, 0.05, 1.0, 0.0, 1.0], 152.226], ['K 50.0 c 0.05 p 1.0 window 0.5-10.0 d', [50.0, 0.05, 1.0, 0.5, 10.0], 145.27], ['K 50.0 c 0.05 p 1.0 window 1.0-30.0 d', [50.0, 0.05, 1.0, 1.0, 30.0], 167.704], ['K 50.0 c 0.05 p 1.0 window 5.0-5.0 d', [50.0, 0.05, 1.0, 5.0, 5.0], None], ['K 50.0 c 0.05 p 1.0 window 3.0-2.0 d', [50.0, 0.05, 1.0, 3.0, 2.0], None], ['K 50.0 c 0.05 p 1.0 window 0.0-0.0 d', [50.0, 0.05, 1.0, 0.0, 0.0], None], ['K 50.0 c 0.05 p 1.3 window 0.5-10.0 d', [50.0, 0.05, 1.3, 0.5, 10.0], 116.0], ['K 200.0 c 0.05 p 0.8 window 0.0-1.0 d', [200.0, 0.05, 0.8, 0.0, 1.0], 460.526]]]
for label, args, expected in fixtures[N - 1]:
    check(label, solve(*args), 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 fixtureActualExpectedOutcome
K 50.0 c 0.01 p 0.8 window 0.0-1.0 d250.0150.971Failed
K 50.0 c 0.01 p 0.8 window 0.5-10.0 d178.586177.801Failed
K 50.0 c 0.01 p 0.8 window 1.0-30.0 d243.588243.123Failed
K 50.0 c 0.01 p 0.8 window 5.0-5.0 dNoneNonePassed
K 50.0 c 0.01 p 0.8 window 3.0-2.0 dNoneNonePassed
K 50.0 c 0.01 p 0.8 window 0.0-0.0 dNoneNonePassed
K 50.0 c 0.01 p 1.0 window 0.0-1.0 d230.756230.756Passed
K 50.0 c 0.01 p 1.0 window 0.5-10.0 d148.846148.846Passed

SHA-256 / cf4df2917bc22391ed43347a4c07a6801b2dd6f9de9800c5889a42cee0b6afc2

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(k, c, p, t1, t2):
    if t1 < 0 or t2 <= t1:
        return None
    if abs(p - 1.0) < 1e-12:
        n = k * (math.log(t2 + c) - math.log(t1 + c))
    else:
        n = k * ((t1 + c) ** (1 - p) - t2 ** (1 - p)) / (p - 1)
    return round(n, 3)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['K 50.0 c 0.01 p 0.8 window 0.0-1.0 d', [50.0, 0.01, 0.8, 0.0, 1.0], 150.971], ['K 50.0 c 0.01 p 0.8 window 0.5-10.0 d', [50.0, 0.01, 0.8, 0.5, 10.0], 177.801], ['K 50.0 c 0.01 p 0.8 window 1.0-30.0 d', [50.0, 0.01, 0.8, 1.0, 30.0], 243.123], ['K 50.0 c 0.01 p 0.8 window 5.0-5.0 d', [50.0, 0.01, 0.8, 5.0, 5.0], None], ['K 50.0 c 0.01 p 0.8 window 3.0-2.0 d', [50.0, 0.01, 0.8, 3.0, 2.0], None], ['K 50.0 c 0.01 p 0.8 window 0.0-0.0 d', [50.0, 0.01, 0.8, 0.0, 0.0], None], ['K 50.0 c 0.01 p 1.0 window 0.0-1.0 d', [50.0, 0.01, 1.0, 0.0, 1.0], 230.756], ['K 50.0 c 0.01 p 1.0 window 0.5-10.0 d', [50.0, 0.01, 1.0, 0.5, 10.0], 148.846]], [['K 50.0 c 0.01 p 1.0 window 0.5-10.0 d', [50.0, 0.01, 1.0, 0.5, 10.0], 148.846], ['K 50.0 c 0.01 p 1.0 window 1.0-30.0 d', [50.0, 0.01, 1.0, 1.0, 30.0], 169.579], ['K 50.0 c 0.01 p 1.0 window 5.0-5.0 d', [50.0, 0.01, 1.0, 5.0, 5.0], None], ['K 50.0 c 0.01 p 1.0 window 3.0-2.0 d', [50.0, 0.01, 1.0, 3.0, 2.0], None], ['K 50.0 c 0.01 p 1.0 window 0.0-0.0 d', [50.0, 0.01, 1.0, 0.0, 0.0], None], ['K 50.0 c 0.01 p 1.1 window 0.5-10.0 d', [50.0, 0.01, 1.1, 0.5, 10.0], 137.702], ['K 50.0 c 0.01 p 1.1 window 1.0-30.0 d', [50.0, 0.01, 1.1, 1.0, 30.0], 143.672], ['K 50.0 c 0.01 p 1.3 window 1.0-30.0 d', [50.0, 0.01, 1.3, 1.0, 30.0], 106.098]], [['K 50.0 c 0.01 p 1.1 window 5.0-5.0 d', [50.0, 0.01, 1.1, 5.0, 5.0], None], ['K 50.0 c 0.01 p 1.1 window 3.0-2.0 d', [50.0, 0.01, 1.1, 3.0, 2.0], None], ['K 50.0 c 0.01 p 1.1 window 0.0-0.0 d', [50.0, 0.01, 1.1, 0.0, 0.0], None], ['K 50.0 c 0.01 p 1.3 window 0.5-10.0 d', [50.0, 0.01, 1.3, 0.5, 10.0], 120.469], ['K 50.0 c 0.01 p 1.3 window 1.0-30.0 d', [50.0, 0.01, 1.3, 1.0, 30.0], 106.098], ['K 50.0 c 0.01 p 1.3 window 5.0-5.0 d', [50.0, 0.01, 1.3, 5.0, 5.0], None], ['K 50.0 c 0.01 p 1.3 window 3.0-2.0 d', [50.0, 0.01, 1.3, 3.0, 2.0], None], ['K 50.0 c 0.05 p 1.1 window 1.0-30.0 d', [50.0, 0.05, 1.1, 1.0, 30.0], 141.783]], [['K 50.0 c 0.01 p 1.3 window 0.0-0.0 d', [50.0, 0.01, 1.3, 0.0, 0.0], None], ['K 50.0 c 0.05 p 0.8 window 0.0-1.0 d', [50.0, 0.05, 0.8, 0.0, 1.0], 115.131], ['K 50.0 c 0.05 p 0.8 window 0.5-10.0 d', [50.0, 0.05, 0.8, 0.5, 10.0], 174.793], ['K 50.0 c 0.05 p 0.8 window 1.0-30.0 d', [50.0, 0.05, 0.8, 1.0, 30.0], 241.301], ['K 50.0 c 0.05 p 0.8 window 5.0-5.0 d', [50.0, 0.05, 0.8, 5.0, 5.0], None], ['K 50.0 c 0.05 p 0.8 window 3.0-2.0 d', [50.0, 0.05, 0.8, 3.0, 2.0], None], ['K 50.0 c 0.05 p 0.8 window 0.0-0.0 d', [50.0, 0.05, 0.8, 0.0, 0.0], None], ['K 200.0 c 0.01 p 0.8 window 1.0-30.0 d', [200.0, 0.01, 0.8, 1.0, 30.0], 972.49]], [['K 50.0 c 0.05 p 1.0 window 0.0-1.0 d', [50.0, 0.05, 1.0, 0.0, 1.0], 152.226], ['K 50.0 c 0.05 p 1.0 window 0.5-10.0 d', [50.0, 0.05, 1.0, 0.5, 10.0], 145.27], ['K 50.0 c 0.05 p 1.0 window 1.0-30.0 d', [50.0, 0.05, 1.0, 1.0, 30.0], 167.704], ['K 50.0 c 0.05 p 1.0 window 5.0-5.0 d', [50.0, 0.05, 1.0, 5.0, 5.0], None], ['K 50.0 c 0.05 p 1.0 window 3.0-2.0 d', [50.0, 0.05, 1.0, 3.0, 2.0], None], ['K 50.0 c 0.05 p 1.0 window 0.0-0.0 d', [50.0, 0.05, 1.0, 0.0, 0.0], None], ['K 50.0 c 0.05 p 1.3 window 0.5-10.0 d', [50.0, 0.05, 1.3, 0.5, 10.0], 116.0], ['K 200.0 c 0.05 p 0.8 window 0.0-1.0 d', [200.0, 0.05, 0.8, 0.0, 1.0], 460.526]]]
for label, args, expected in fixtures[N - 1]:
    check(label, solve(*args), 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 fixtureActualExpectedOutcome
K 50.0 c 0.01 p 0.8 window 0.0-1.0 d150.473150.971Failed
K 50.0 c 0.01 p 0.8 window 0.5-10.0 d177.722177.801Failed
K 50.0 c 0.01 p 0.8 window 1.0-30.0 d243.09243.123Failed
K 50.0 c 0.01 p 0.8 window 5.0-5.0 dNoneNonePassed
K 50.0 c 0.01 p 0.8 window 3.0-2.0 dNoneNonePassed
K 50.0 c 0.01 p 0.8 window 0.0-0.0 dNoneNonePassed
K 50.0 c 0.01 p 1.0 window 0.0-1.0 d230.756230.756Passed
K 50.0 c 0.01 p 1.0 window 0.5-10.0 d148.846148.846Passed

SHA-256 / b2bad2b296fd1f16463eaf945fc668916d05f33c284271a42501a004c7937db8

3 / The verified repair

Exit 0
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(k, c, p, t1, t2):
    if t1 < 0 or t2 <= t1:
        return None
    if abs(p - 1.0) < 1e-12:
        n = k * (math.log(t2 + c) - math.log(t1 + c))
    else:
        n = k * ((t1 + c) ** (1 - p) - (t2 + c) ** (1 - p)) / (p - 1)
    return round(n, 3)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['K 50.0 c 0.01 p 0.8 window 0.0-1.0 d', [50.0, 0.01, 0.8, 0.0, 1.0], 150.971], ['K 50.0 c 0.01 p 0.8 window 0.5-10.0 d', [50.0, 0.01, 0.8, 0.5, 10.0], 177.801], ['K 50.0 c 0.01 p 0.8 window 1.0-30.0 d', [50.0, 0.01, 0.8, 1.0, 30.0], 243.123], ['K 50.0 c 0.01 p 0.8 window 5.0-5.0 d', [50.0, 0.01, 0.8, 5.0, 5.0], None], ['K 50.0 c 0.01 p 0.8 window 3.0-2.0 d', [50.0, 0.01, 0.8, 3.0, 2.0], None], ['K 50.0 c 0.01 p 0.8 window 0.0-0.0 d', [50.0, 0.01, 0.8, 0.0, 0.0], None], ['K 50.0 c 0.01 p 1.0 window 0.0-1.0 d', [50.0, 0.01, 1.0, 0.0, 1.0], 230.756], ['K 50.0 c 0.01 p 1.0 window 0.5-10.0 d', [50.0, 0.01, 1.0, 0.5, 10.0], 148.846]], [['K 50.0 c 0.01 p 1.0 window 0.5-10.0 d', [50.0, 0.01, 1.0, 0.5, 10.0], 148.846], ['K 50.0 c 0.01 p 1.0 window 1.0-30.0 d', [50.0, 0.01, 1.0, 1.0, 30.0], 169.579], ['K 50.0 c 0.01 p 1.0 window 5.0-5.0 d', [50.0, 0.01, 1.0, 5.0, 5.0], None], ['K 50.0 c 0.01 p 1.0 window 3.0-2.0 d', [50.0, 0.01, 1.0, 3.0, 2.0], None], ['K 50.0 c 0.01 p 1.0 window 0.0-0.0 d', [50.0, 0.01, 1.0, 0.0, 0.0], None], ['K 50.0 c 0.01 p 1.1 window 0.5-10.0 d', [50.0, 0.01, 1.1, 0.5, 10.0], 137.702], ['K 50.0 c 0.01 p 1.1 window 1.0-30.0 d', [50.0, 0.01, 1.1, 1.0, 30.0], 143.672], ['K 50.0 c 0.01 p 1.3 window 1.0-30.0 d', [50.0, 0.01, 1.3, 1.0, 30.0], 106.098]], [['K 50.0 c 0.01 p 1.1 window 5.0-5.0 d', [50.0, 0.01, 1.1, 5.0, 5.0], None], ['K 50.0 c 0.01 p 1.1 window 3.0-2.0 d', [50.0, 0.01, 1.1, 3.0, 2.0], None], ['K 50.0 c 0.01 p 1.1 window 0.0-0.0 d', [50.0, 0.01, 1.1, 0.0, 0.0], None], ['K 50.0 c 0.01 p 1.3 window 0.5-10.0 d', [50.0, 0.01, 1.3, 0.5, 10.0], 120.469], ['K 50.0 c 0.01 p 1.3 window 1.0-30.0 d', [50.0, 0.01, 1.3, 1.0, 30.0], 106.098], ['K 50.0 c 0.01 p 1.3 window 5.0-5.0 d', [50.0, 0.01, 1.3, 5.0, 5.0], None], ['K 50.0 c 0.01 p 1.3 window 3.0-2.0 d', [50.0, 0.01, 1.3, 3.0, 2.0], None], ['K 50.0 c 0.05 p 1.1 window 1.0-30.0 d', [50.0, 0.05, 1.1, 1.0, 30.0], 141.783]], [['K 50.0 c 0.01 p 1.3 window 0.0-0.0 d', [50.0, 0.01, 1.3, 0.0, 0.0], None], ['K 50.0 c 0.05 p 0.8 window 0.0-1.0 d', [50.0, 0.05, 0.8, 0.0, 1.0], 115.131], ['K 50.0 c 0.05 p 0.8 window 0.5-10.0 d', [50.0, 0.05, 0.8, 0.5, 10.0], 174.793], ['K 50.0 c 0.05 p 0.8 window 1.0-30.0 d', [50.0, 0.05, 0.8, 1.0, 30.0], 241.301], ['K 50.0 c 0.05 p 0.8 window 5.0-5.0 d', [50.0, 0.05, 0.8, 5.0, 5.0], None], ['K 50.0 c 0.05 p 0.8 window 3.0-2.0 d', [50.0, 0.05, 0.8, 3.0, 2.0], None], ['K 50.0 c 0.05 p 0.8 window 0.0-0.0 d', [50.0, 0.05, 0.8, 0.0, 0.0], None], ['K 200.0 c 0.01 p 0.8 window 1.0-30.0 d', [200.0, 0.01, 0.8, 1.0, 30.0], 972.49]], [['K 50.0 c 0.05 p 1.0 window 0.0-1.0 d', [50.0, 0.05, 1.0, 0.0, 1.0], 152.226], ['K 50.0 c 0.05 p 1.0 window 0.5-10.0 d', [50.0, 0.05, 1.0, 0.5, 10.0], 145.27], ['K 50.0 c 0.05 p 1.0 window 1.0-30.0 d', [50.0, 0.05, 1.0, 1.0, 30.0], 167.704], ['K 50.0 c 0.05 p 1.0 window 5.0-5.0 d', [50.0, 0.05, 1.0, 5.0, 5.0], None], ['K 50.0 c 0.05 p 1.0 window 3.0-2.0 d', [50.0, 0.05, 1.0, 3.0, 2.0], None], ['K 50.0 c 0.05 p 1.0 window 0.0-0.0 d', [50.0, 0.05, 1.0, 0.0, 0.0], None], ['K 50.0 c 0.05 p 1.3 window 0.5-10.0 d', [50.0, 0.05, 1.3, 0.5, 10.0], 116.0], ['K 200.0 c 0.05 p 0.8 window 0.0-1.0 d', [200.0, 0.05, 0.8, 0.0, 1.0], 460.526]]]
for label, args, expected in fixtures[N - 1]:
    check(label, solve(*args), 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 fixtureActualExpectedOutcome
K 50.0 c 0.01 p 0.8 window 0.0-1.0 d150.971150.971Passed
K 50.0 c 0.01 p 0.8 window 0.5-10.0 d177.801177.801Passed
K 50.0 c 0.01 p 0.8 window 1.0-30.0 d243.123243.123Passed
K 50.0 c 0.01 p 0.8 window 5.0-5.0 dNoneNonePassed
K 50.0 c 0.01 p 0.8 window 3.0-2.0 dNoneNonePassed
K 50.0 c 0.01 p 0.8 window 0.0-0.0 dNoneNonePassed
K 50.0 c 0.01 p 1.0 window 0.0-1.0 d230.756230.756Passed
K 50.0 c 0.01 p 1.0 window 0.5-10.0 d148.846148.846Passed

SHA-256 / 73c7fa0025f81e06a637ca5ecaacee0807615110fe87aceee8d3dc0a1fa487ec

Verification & scope

Stipulated deterministic teaching model of a seismological magnitude procedure; constants and tables are fixed by the contract and no claim of agency or standards conformance is made. 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 2026-09-29T14:48:31.349284+00:00.

Case digest / 728b1176d87a955888df9f2265b304c5e880c4dd99941f8531ed8e0322e007bd