FA-70896 / Weather index computation / Open access

Magnus dew point with ice branch: inverse Magnus solve · case 01

Dew points collapse toward zero regardless of humidity.

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

ROOT CAUSE

The algebraic inversion swaps the roles of a and b.

VERIFIED REPAIR

Return b*g/(a-g).

Unsuccessful approach: Changing the denominator sign to (a+g) keeps the wrong inversion for nonzero g.

Case contract

Input temperature in degC and RH in percent. RH <= 0 or RH > 100 returns None. Use Magnus constants a=17.62, b=243.12 when T >= 0 and a=22.46, b=272.62 below freezing; g = ln(RH/100) + aT/(b+T); dew/frost point = b*g/(a-g) rounded to 0.01.

Why this case matters

Dew and frost point drive fog, icing and frost forecasts.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(t_c, rh):
    if rh <= 0 or rh > 100:
        return None
    a, b = (17.62, 243.12) if t_c >= 0 else (22.46, 272.62)
    g = math.log(rh / 100.0) + a * t_c / (b + t_c)
    return round(a * g / (b - g), 2)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['-20 C at 0% RH', [-20, 0], None], ['-20 C at 0.5% RH', [-20, 0.5], -65.32], ['-20 C at 5% RH', [-20, 5], -47.79], ['-20 C at 30% RH', [-20, 30], -31.95], ['-20 C at 50% RH', [-20, 50], -27.02], ['-20 C at 80% RH', [-20, 80], -22.3], ['-20 C at 100% RH', [-20, 100], -20.0], ['-20 C at 104% RH', [-20, 104], None]], [['-20 C at 50% RH', [-20, 50], -27.02], ['-20 C at 104% RH', [-20, 104], None], ['-5 C at 0% RH', [-5, 0], None], ['-5 C at 0.5% RH', [-5, 0.5], -55.32], ['-5 C at 5% RH', [-5, 5], -35.98], ['-5 C at 30% RH', [-5, 30], -18.38], ['-5 C at 50% RH', [-5, 50], -12.87], ['-5 C at 80% RH', [-5, 80], -7.58]], [['-5 C at 0.5% RH', [-5, 0.5], -55.32], ['-5 C at 100% RH', [-5, 100], -5.0], ['-5 C at 104% RH', [-5, 104], None], ['-0.5 C at 0% RH', [-0.5, 0], None], ['-0.5 C at 0.5% RH', [-0.5, 0.5], -52.36], ['-0.5 C at 5% RH', [-0.5, 5], -32.47], ['-0.5 C at 30% RH', [-0.5, 30], -14.32], ['-0.5 C at 50% RH', [-0.5, 50], -8.63]], [['-5 C at 50% RH', [-5, 50], -12.87], ['-0.5 C at 80% RH', [-0.5, 80], -3.17], ['-0.5 C at 100% RH', [-0.5, 100], -0.5], ['-0.5 C at 104% RH', [-0.5, 104], None], ['0 C at 0% RH', [0, 0], None], ['0 C at 0.5% RH', [0, 0.5], -56.21], ['0 C at 5% RH', [0, 5], -35.33], ['0 C at 30% RH', [0, 30], -15.55]], [['-0.5 C at 0.5% RH', [-0.5, 0.5], -52.36], ['0 C at 50% RH', [0, 50], -9.2], ['0 C at 80% RH', [0, 80], -3.04], ['0 C at 100% RH', [0, 100], 0.0], ['0 C at 104% RH', [0, 104], None], ['0.5 C at 0% RH', [0.5, 0], None], ['0.5 C at 0.5% RH', [0.5, 0.5], -55.91], ['0.5 C at 5% RH', [0.5, 5], -34.96]]]
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 fixture	Actual	Expected	Outcome
-20 C at 0% RH	`None`	`None`	Passed
-20 C at 0.5% RH	`-0.57`	`-65.32`	Failed
-20 C at 5% RH	`-0.39`	`-47.79`	Failed
-20 C at 30% RH	`-0.24`	`-31.95`	Failed
-20 C at 50% RH	`-0.2`	`-27.02`	Failed
-20 C at 80% RH	`-0.16`	`-22.3`	Failed
-20 C at 100% RH	`-0.15`	`-20.0`	Failed
-20 C at 104% RH	`None`	`None`	Passed

SHA-256 / 0629c0fb34b627f30c0d41cdf3476a56c4aa9f28d7648276e43c1d37e1f1b021

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(t_c, rh):
    if rh <= 0 or rh > 100:
        return None
    a, b = (17.62, 243.12) if t_c >= 0 else (22.46, 272.62)
    g = math.log(rh / 100.0) + a * t_c / (b + t_c)
    return round(b * g / (a + g), 2)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['-20 C at 0% RH', [-20, 0], None], ['-20 C at 0.5% RH', [-20, 0.5], -65.32], ['-20 C at 5% RH', [-20, 5], -47.79], ['-20 C at 30% RH', [-20, 30], -31.95], ['-20 C at 50% RH', [-20, 50], -27.02], ['-20 C at 80% RH', [-20, 80], -22.3], ['-20 C at 100% RH', [-20, 100], -20.0], ['-20 C at 104% RH', [-20, 104], None]], [['-20 C at 50% RH', [-20, 50], -27.02], ['-20 C at 104% RH', [-20, 104], None], ['-5 C at 0% RH', [-5, 0], None], ['-5 C at 0.5% RH', [-5, 0.5], -55.32], ['-5 C at 5% RH', [-5, 5], -35.98], ['-5 C at 30% RH', [-5, 30], -18.38], ['-5 C at 50% RH', [-5, 50], -12.87], ['-5 C at 80% RH', [-5, 80], -7.58]], [['-5 C at 0.5% RH', [-5, 0.5], -55.32], ['-5 C at 100% RH', [-5, 100], -5.0], ['-5 C at 104% RH', [-5, 104], None], ['-0.5 C at 0% RH', [-0.5, 0], None], ['-0.5 C at 0.5% RH', [-0.5, 0.5], -52.36], ['-0.5 C at 5% RH', [-0.5, 5], -32.47], ['-0.5 C at 30% RH', [-0.5, 30], -14.32], ['-0.5 C at 50% RH', [-0.5, 50], -8.63]], [['-5 C at 50% RH', [-5, 50], -12.87], ['-0.5 C at 80% RH', [-0.5, 80], -3.17], ['-0.5 C at 100% RH', [-0.5, 100], -0.5], ['-0.5 C at 104% RH', [-0.5, 104], None], ['0 C at 0% RH', [0, 0], None], ['0 C at 0.5% RH', [0, 0.5], -56.21], ['0 C at 5% RH', [0, 5], -35.33], ['0 C at 30% RH', [0, 30], -15.55]], [['-0.5 C at 0.5% RH', [-0.5, 0.5], -52.36], ['0 C at 50% RH', [0, 50], -9.2], ['0 C at 80% RH', [0, 80], -3.04], ['0 C at 100% RH', [0, 100], 0.0], ['0 C at 104% RH', [0, 104], None], ['0.5 C at 0% RH', [0.5, 0], None], ['0.5 C at 0.5% RH', [0.5, 0.5], -55.91], ['0.5 C at 5% RH', [0.5, 5], -34.96]]]
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 fixture	Actual	Expected	Outcome
-20 C at 0% RH	`None`	`None`	Passed
-20 C at 0.5% RH	`-125.41`	`-65.32`	Failed
-20 C at 5% RH	`-73.59`	`-47.79`	Failed
-20 C at 30% RH	`-41.74`	`-31.95`	Failed
-20 C at 50% RH	`-33.71`	`-27.02`	Failed
-20 C at 80% RH	`-26.67`	`-22.3`	Failed
-20 C at 100% RH	`-23.44`	`-20.0`	Failed
-20 C at 104% RH	`None`	`None`	Passed

SHA-256 / be75e729e7e70b6a80e8e26b1a20be62f3767c90131c6c92544b741ecbf17af8

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(t_c, rh):
    if rh <= 0 or rh > 100:
        return None
    a, b = (17.62, 243.12) if t_c >= 0 else (22.46, 272.62)
    g = math.log(rh / 100.0) + a * t_c / (b + t_c)
    return round(b * g / (a - g), 2)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['-20 C at 0% RH', [-20, 0], None], ['-20 C at 0.5% RH', [-20, 0.5], -65.32], ['-20 C at 5% RH', [-20, 5], -47.79], ['-20 C at 30% RH', [-20, 30], -31.95], ['-20 C at 50% RH', [-20, 50], -27.02], ['-20 C at 80% RH', [-20, 80], -22.3], ['-20 C at 100% RH', [-20, 100], -20.0], ['-20 C at 104% RH', [-20, 104], None]], [['-20 C at 50% RH', [-20, 50], -27.02], ['-20 C at 104% RH', [-20, 104], None], ['-5 C at 0% RH', [-5, 0], None], ['-5 C at 0.5% RH', [-5, 0.5], -55.32], ['-5 C at 5% RH', [-5, 5], -35.98], ['-5 C at 30% RH', [-5, 30], -18.38], ['-5 C at 50% RH', [-5, 50], -12.87], ['-5 C at 80% RH', [-5, 80], -7.58]], [['-5 C at 0.5% RH', [-5, 0.5], -55.32], ['-5 C at 100% RH', [-5, 100], -5.0], ['-5 C at 104% RH', [-5, 104], None], ['-0.5 C at 0% RH', [-0.5, 0], None], ['-0.5 C at 0.5% RH', [-0.5, 0.5], -52.36], ['-0.5 C at 5% RH', [-0.5, 5], -32.47], ['-0.5 C at 30% RH', [-0.5, 30], -14.32], ['-0.5 C at 50% RH', [-0.5, 50], -8.63]], [['-5 C at 50% RH', [-5, 50], -12.87], ['-0.5 C at 80% RH', [-0.5, 80], -3.17], ['-0.5 C at 100% RH', [-0.5, 100], -0.5], ['-0.5 C at 104% RH', [-0.5, 104], None], ['0 C at 0% RH', [0, 0], None], ['0 C at 0.5% RH', [0, 0.5], -56.21], ['0 C at 5% RH', [0, 5], -35.33], ['0 C at 30% RH', [0, 30], -15.55]], [['-0.5 C at 0.5% RH', [-0.5, 0.5], -52.36], ['0 C at 50% RH', [0, 50], -9.2], ['0 C at 80% RH', [0, 80], -3.04], ['0 C at 100% RH', [0, 100], 0.0], ['0 C at 104% RH', [0, 104], None], ['0.5 C at 0% RH', [0.5, 0], None], ['0.5 C at 0.5% RH', [0.5, 0.5], -55.91], ['0.5 C at 5% RH', [0.5, 5], -34.96]]]
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 fixture	Actual	Expected	Outcome
-20 C at 0% RH	`None`	`None`	Passed
-20 C at 0.5% RH	`-65.32`	`-65.32`	Passed
-20 C at 5% RH	`-47.79`	`-47.79`	Passed
-20 C at 30% RH	`-31.95`	`-31.95`	Passed
-20 C at 50% RH	`-27.02`	`-27.02`	Passed
-20 C at 80% RH	`-22.3`	`-22.3`	Passed
-20 C at 100% RH	`-20.0`	`-20.0`	Passed
-20 C at 104% RH	`None`	`None`	Passed

SHA-256 / 833c38b411ae992dd6146ff27c2176ba9d67aaf3ef8a4ffb960668f1e5b7c6fc

Verification & scope

Stipulated deterministic teaching model of an operational weather index; coefficients and thresholds are fixed by the contract and no claim of 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 2026-09-29T14:48:24.866494+00:00.

Case digest / 3740541eb2ce941e278a3ac20157093f0f38829563f6a65aa7f5de3eef8a93ee