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FA-71656 / Seismic magnitude estimation / Open access

Estimated Mercalli intensity: Roman numeral index · case 01

Intensity V is labelled VI.

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

ROOT CAUSE

The Roman table is indexed as if intensities started at 0.

VERIFIED REPAIR

Use roman[v - 1].

Unsuccessful approach: Clamping the index avoids overflow but still labels V as VI.

Case contract

R = max(hypocentral distance, 1 km). I = 1.45M - 2.46 log10(R) + 1.5, rounded half up to an integer and clamped to 1..12. Return [I, Roman numeral].

Why this case matters

ShakeMap-style intensity summaries are published as Roman numerals.

1 / The failure

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(mag, epi_km, depth_km):
    roman = ["I", "II", "III", "IV", "V", "VI", "VII", "VIII", "IX", "X", "XI", "XII"]
    r = max(math.hypot(epi_km, depth_km), 1.0)
    i = 1.45 * mag - 2.46 * math.log10(r) + 1.5
    v = int(math.floor(i + 0.5))
    v = min(max(v, 1), 12)
    return [v, roman[v]]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['M2.0 at 0 km depth 0.5', [2.0, 0, 0.5], [4, 'IV']], ['M2.0 at 0 km depth 5', [2.0, 0, 5], [3, 'III']], ['M2.0 at 3 km depth 2', [2.0, 3, 2], [3, 'III']], ['M2.0 at 20 km depth 10', [2.0, 20, 10], [1, 'I']], ['M2.0 at 80 km depth 15', [2.0, 80, 15], [1, 'I']], ['M2.0 at 300 km depth 30', [2.0, 300, 30], [1, 'I']], ['M2.0 at 900 km depth 10', [2.0, 900, 10], [1, 'I']], ['M4.5 at 0 km depth 0.5', [4.5, 0, 0.5], [8, 'VIII']]], [['M2.0 at 20 km depth 10', [2.0, 20, 10], [1, 'I']], ['M2.0 at 900 km depth 10', [2.0, 900, 10], [1, 'I']], ['M4.5 at 0 km depth 0.5', [4.5, 0, 0.5], [8, 'VIII']], ['M4.5 at 0 km depth 5', [4.5, 0, 5], [6, 'VI']], ['M4.5 at 3 km depth 2', [4.5, 3, 2], [7, 'VII']], ['M4.5 at 20 km depth 10', [4.5, 20, 10], [5, 'V']], ['M4.5 at 80 km depth 15', [4.5, 80, 15], [3, 'III']], ['M4.5 at 300 km depth 30', [4.5, 300, 30], [2, 'II']]], [['M2.0 at 900 km depth 10', [2.0, 900, 10], [1, 'I']], ['M4.5 at 80 km depth 15', [4.5, 80, 15], [3, 'III']], ['M6.0 at 0 km depth 0.5', [6.0, 0, 0.5], [10, 'X']], ['M6.0 at 0 km depth 5', [6.0, 0, 5], [8, 'VIII']], ['M6.0 at 3 km depth 2', [6.0, 3, 2], [9, 'IX']], ['M6.0 at 20 km depth 10', [6.0, 20, 10], [7, 'VII']], ['M6.0 at 80 km depth 15', [6.0, 80, 15], [5, 'V']], ['M6.0 at 300 km depth 30', [6.0, 300, 30], [4, 'IV']]], [['M4.5 at 3 km depth 2', [4.5, 3, 2], [7, 'VII']], ['M6.0 at 3 km depth 2', [6.0, 3, 2], [9, 'IX']], ['M7.2 at 0 km depth 5', [7.2, 0, 5], [10, 'X']], ['M7.2 at 3 km depth 2', [7.2, 3, 2], [11, 'XI']], ['M7.2 at 20 km depth 10', [7.2, 20, 10], [9, 'IX']], ['M7.2 at 80 km depth 15', [7.2, 80, 15], [7, 'VII']], ['M7.2 at 300 km depth 30', [7.2, 300, 30], [6, 'VI']], ['M7.2 at 900 km depth 10', [7.2, 900, 10], [5, 'V']]], [['M4.5 at 300 km depth 30', [4.5, 300, 30], [2, 'II']], ['M7.2 at 0 km depth 5', [7.2, 0, 5], [10, 'X']], ['M8.5 at 80 km depth 15', [8.5, 80, 15], [9, 'IX']], ['M8.5 at 300 km depth 30', [8.5, 300, 30], [8, 'VIII']], ['M8.5 at 900 km depth 10', [8.5, 900, 10], [7, 'VII']], ['M9.4 at 80 km depth 15', [9.4, 80, 15], [10, 'X']], ['M9.4 at 300 km depth 30', [9.4, 300, 30], [9, 'IX']], ['M9.4 at 900 km depth 10', [9.4, 900, 10], [8, 'VIII']]]]
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
M2.0 at 0 km depth 0.5[4, 'V'][4, 'IV']Failed
M2.0 at 0 km depth 5[3, 'IV'][3, 'III']Failed
M2.0 at 3 km depth 2[3, 'IV'][3, 'III']Failed
M2.0 at 20 km depth 10[1, 'II'][1, 'I']Failed
M2.0 at 80 km depth 15[1, 'II'][1, 'I']Failed
M2.0 at 300 km depth 30[1, 'II'][1, 'I']Failed
M2.0 at 900 km depth 10[1, 'II'][1, 'I']Failed
M4.5 at 0 km depth 0.5[8, 'IX'][8, 'VIII']Failed

SHA-256 / 239e48bf7151557638a74cebf45f6d94416ab8b62136ace42c0562935d878c67

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(mag, epi_km, depth_km):
    roman = ["I", "II", "III", "IV", "V", "VI", "VII", "VIII", "IX", "X", "XI", "XII"]
    r = max(math.hypot(epi_km, depth_km), 1.0)
    i = 1.45 * mag - 2.46 * math.log10(r) + 1.5
    v = int(math.floor(i + 0.5))
    v = min(max(v, 1), 12)
    return [v, roman[min(v, 11)]]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['M2.0 at 0 km depth 0.5', [2.0, 0, 0.5], [4, 'IV']], ['M2.0 at 0 km depth 5', [2.0, 0, 5], [3, 'III']], ['M2.0 at 3 km depth 2', [2.0, 3, 2], [3, 'III']], ['M2.0 at 20 km depth 10', [2.0, 20, 10], [1, 'I']], ['M2.0 at 80 km depth 15', [2.0, 80, 15], [1, 'I']], ['M2.0 at 300 km depth 30', [2.0, 300, 30], [1, 'I']], ['M2.0 at 900 km depth 10', [2.0, 900, 10], [1, 'I']], ['M4.5 at 0 km depth 0.5', [4.5, 0, 0.5], [8, 'VIII']]], [['M2.0 at 20 km depth 10', [2.0, 20, 10], [1, 'I']], ['M2.0 at 900 km depth 10', [2.0, 900, 10], [1, 'I']], ['M4.5 at 0 km depth 0.5', [4.5, 0, 0.5], [8, 'VIII']], ['M4.5 at 0 km depth 5', [4.5, 0, 5], [6, 'VI']], ['M4.5 at 3 km depth 2', [4.5, 3, 2], [7, 'VII']], ['M4.5 at 20 km depth 10', [4.5, 20, 10], [5, 'V']], ['M4.5 at 80 km depth 15', [4.5, 80, 15], [3, 'III']], ['M4.5 at 300 km depth 30', [4.5, 300, 30], [2, 'II']]], [['M2.0 at 900 km depth 10', [2.0, 900, 10], [1, 'I']], ['M4.5 at 80 km depth 15', [4.5, 80, 15], [3, 'III']], ['M6.0 at 0 km depth 0.5', [6.0, 0, 0.5], [10, 'X']], ['M6.0 at 0 km depth 5', [6.0, 0, 5], [8, 'VIII']], ['M6.0 at 3 km depth 2', [6.0, 3, 2], [9, 'IX']], ['M6.0 at 20 km depth 10', [6.0, 20, 10], [7, 'VII']], ['M6.0 at 80 km depth 15', [6.0, 80, 15], [5, 'V']], ['M6.0 at 300 km depth 30', [6.0, 300, 30], [4, 'IV']]], [['M4.5 at 3 km depth 2', [4.5, 3, 2], [7, 'VII']], ['M6.0 at 3 km depth 2', [6.0, 3, 2], [9, 'IX']], ['M7.2 at 0 km depth 5', [7.2, 0, 5], [10, 'X']], ['M7.2 at 3 km depth 2', [7.2, 3, 2], [11, 'XI']], ['M7.2 at 20 km depth 10', [7.2, 20, 10], [9, 'IX']], ['M7.2 at 80 km depth 15', [7.2, 80, 15], [7, 'VII']], ['M7.2 at 300 km depth 30', [7.2, 300, 30], [6, 'VI']], ['M7.2 at 900 km depth 10', [7.2, 900, 10], [5, 'V']]], [['M4.5 at 300 km depth 30', [4.5, 300, 30], [2, 'II']], ['M7.2 at 0 km depth 5', [7.2, 0, 5], [10, 'X']], ['M8.5 at 80 km depth 15', [8.5, 80, 15], [9, 'IX']], ['M8.5 at 300 km depth 30', [8.5, 300, 30], [8, 'VIII']], ['M8.5 at 900 km depth 10', [8.5, 900, 10], [7, 'VII']], ['M9.4 at 80 km depth 15', [9.4, 80, 15], [10, 'X']], ['M9.4 at 300 km depth 30', [9.4, 300, 30], [9, 'IX']], ['M9.4 at 900 km depth 10', [9.4, 900, 10], [8, 'VIII']]]]
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
M2.0 at 0 km depth 0.5[4, 'V'][4, 'IV']Failed
M2.0 at 0 km depth 5[3, 'IV'][3, 'III']Failed
M2.0 at 3 km depth 2[3, 'IV'][3, 'III']Failed
M2.0 at 20 km depth 10[1, 'II'][1, 'I']Failed
M2.0 at 80 km depth 15[1, 'II'][1, 'I']Failed
M2.0 at 300 km depth 30[1, 'II'][1, 'I']Failed
M2.0 at 900 km depth 10[1, 'II'][1, 'I']Failed
M4.5 at 0 km depth 0.5[8, 'IX'][8, 'VIII']Failed

SHA-256 / 08e5eafd56648d497494fd81bf728bc1060676b062d88596e07e713624358064

3 / The verified repair

Exit 0
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(mag, epi_km, depth_km):
    roman = ["I", "II", "III", "IV", "V", "VI", "VII", "VIII", "IX", "X", "XI", "XII"]
    r = max(math.hypot(epi_km, depth_km), 1.0)
    i = 1.45 * mag - 2.46 * math.log10(r) + 1.5
    v = int(math.floor(i + 0.5))
    v = min(max(v, 1), 12)
    return [v, roman[v - 1]]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['M2.0 at 0 km depth 0.5', [2.0, 0, 0.5], [4, 'IV']], ['M2.0 at 0 km depth 5', [2.0, 0, 5], [3, 'III']], ['M2.0 at 3 km depth 2', [2.0, 3, 2], [3, 'III']], ['M2.0 at 20 km depth 10', [2.0, 20, 10], [1, 'I']], ['M2.0 at 80 km depth 15', [2.0, 80, 15], [1, 'I']], ['M2.0 at 300 km depth 30', [2.0, 300, 30], [1, 'I']], ['M2.0 at 900 km depth 10', [2.0, 900, 10], [1, 'I']], ['M4.5 at 0 km depth 0.5', [4.5, 0, 0.5], [8, 'VIII']]], [['M2.0 at 20 km depth 10', [2.0, 20, 10], [1, 'I']], ['M2.0 at 900 km depth 10', [2.0, 900, 10], [1, 'I']], ['M4.5 at 0 km depth 0.5', [4.5, 0, 0.5], [8, 'VIII']], ['M4.5 at 0 km depth 5', [4.5, 0, 5], [6, 'VI']], ['M4.5 at 3 km depth 2', [4.5, 3, 2], [7, 'VII']], ['M4.5 at 20 km depth 10', [4.5, 20, 10], [5, 'V']], ['M4.5 at 80 km depth 15', [4.5, 80, 15], [3, 'III']], ['M4.5 at 300 km depth 30', [4.5, 300, 30], [2, 'II']]], [['M2.0 at 900 km depth 10', [2.0, 900, 10], [1, 'I']], ['M4.5 at 80 km depth 15', [4.5, 80, 15], [3, 'III']], ['M6.0 at 0 km depth 0.5', [6.0, 0, 0.5], [10, 'X']], ['M6.0 at 0 km depth 5', [6.0, 0, 5], [8, 'VIII']], ['M6.0 at 3 km depth 2', [6.0, 3, 2], [9, 'IX']], ['M6.0 at 20 km depth 10', [6.0, 20, 10], [7, 'VII']], ['M6.0 at 80 km depth 15', [6.0, 80, 15], [5, 'V']], ['M6.0 at 300 km depth 30', [6.0, 300, 30], [4, 'IV']]], [['M4.5 at 3 km depth 2', [4.5, 3, 2], [7, 'VII']], ['M6.0 at 3 km depth 2', [6.0, 3, 2], [9, 'IX']], ['M7.2 at 0 km depth 5', [7.2, 0, 5], [10, 'X']], ['M7.2 at 3 km depth 2', [7.2, 3, 2], [11, 'XI']], ['M7.2 at 20 km depth 10', [7.2, 20, 10], [9, 'IX']], ['M7.2 at 80 km depth 15', [7.2, 80, 15], [7, 'VII']], ['M7.2 at 300 km depth 30', [7.2, 300, 30], [6, 'VI']], ['M7.2 at 900 km depth 10', [7.2, 900, 10], [5, 'V']]], [['M4.5 at 300 km depth 30', [4.5, 300, 30], [2, 'II']], ['M7.2 at 0 km depth 5', [7.2, 0, 5], [10, 'X']], ['M8.5 at 80 km depth 15', [8.5, 80, 15], [9, 'IX']], ['M8.5 at 300 km depth 30', [8.5, 300, 30], [8, 'VIII']], ['M8.5 at 900 km depth 10', [8.5, 900, 10], [7, 'VII']], ['M9.4 at 80 km depth 15', [9.4, 80, 15], [10, 'X']], ['M9.4 at 300 km depth 30', [9.4, 300, 30], [9, 'IX']], ['M9.4 at 900 km depth 10', [9.4, 900, 10], [8, 'VIII']]]]
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
M2.0 at 0 km depth 0.5[4, 'IV'][4, 'IV']Passed
M2.0 at 0 km depth 5[3, 'III'][3, 'III']Passed
M2.0 at 3 km depth 2[3, 'III'][3, 'III']Passed
M2.0 at 20 km depth 10[1, 'I'][1, 'I']Passed
M2.0 at 80 km depth 15[1, 'I'][1, 'I']Passed
M2.0 at 300 km depth 30[1, 'I'][1, 'I']Passed
M2.0 at 900 km depth 10[1, 'I'][1, 'I']Passed
M4.5 at 0 km depth 0.5[8, 'VIII'][8, 'VIII']Passed

SHA-256 / bb0b705c525f97707d76e05235958952544a04fbb8a756127434e63c66538797

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 2026-09-29T14:48:31.639172+00:00.

Case digest / 0adff92b20852670bc322c81abace2c920ce0608fbc2f40bff061ff4a5541886