FA-65496 / Ecological population dynamics / Open access

Cohort life table statistics: life expectancy trapezoid · case 01

Life expectancy ignores that deaths occur during the interval.

Verified by executionVariant 1 · 7 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Person-years use start-of-interval survivorship.

VERIFIED REPAIR

Restore the life expectancy trapezoid rule: `(l[x] + l[x + 1]) / 2`.

Unsuccessful approach: End-of-interval survivorship understates person-years.

Case contract

l0=1 and l[x+1]=l[x]*px[x]; R0=sum l[x]*mx[x]; generation time T=sum x*l[x]*mx[x]/R0; r=ln(R0)/T (None if T=0); e0 = sum over x of (l[x]+l[x+1])/2; return [R0, T, r, e0] rounded 6 with [0.0, None, None, e0] when R0=0; None for empty or mismatched schedules.

Why this case matters

Population projections set harvest quotas, conservation status and pest-control timing; a wrong update order, boundary or rate conversion silently changes management advice.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(px, mx):
    n = len(px)
    if n == 0 or len(mx) != n:
        return None
    l = [1.0]
    for x in range(1, n + 1):
        l.append(l[-1] * px[x - 1])
    e0 = round(sum(l[x] for x in range(n)), 6)
    r0 = sum(l[x] * mx[x] for x in range(n))
    if r0 <= 0:
        return [0.0, None, None, e0]
    gen = sum(x * l[x] * mx[x] for x in range(n)) / r0
    rate = math.log(r0) / gen if gen > 0 else None
    return [round(r0, 6), round(gen, 6), None if rate is None else round(rate, 6), e0]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: songbird', ([0.3, 0.6, 0.6, 0.5], [0.0, 1.5, 2.0, 2.0]), [1.026, 1.77193, 0.014486, 1.115]),
  ('regression: perennial plant',
   ([0.1, 0.8, 0.9, 0.9, 0.0], [0.0, 0.0, 5.0, 8.0, 8.0]),
   [1.4944, 3.079229, 0.130463, 0.8168]),
  ('regression: replacement cohort', ([0.5, 0.5], [0.0, 4.0]), [2.0, 1.0, 0.693147, 1.125]),
  ('regression: age zero breeding only', ([0.5, 0.2], [1.5, 0.0]), [1.5, 0.0, None, 1.05]),
  ('regression: sterile cohort', ([0.9, 0.9], [0.0, 0.0]), [0.0, None, None, 1.805]),
  ('control: mismatched schedules', ([0.5], [0.0, 1.0]), None),
  ('regression: annual insect', ([0.05, 0.0], [0.0, 30.0]), [1.5, 1.0, 0.405465, 0.55])],
 [('regression: songbird', ([0.3, 0.6, 0.6, 0.5], [0.0, 1.5, 2.0, 2.0]), [1.026, 1.77193, 0.014486, 1.115]),
  ('regression: perennial plant',
   ([0.1, 0.8, 0.9, 0.9, 0.0], [0.0, 0.0, 5.0, 8.0, 8.0]),
   [1.4944, 3.079229, 0.130463, 0.8168]),
  ('regression: age zero breeding only', ([0.5, 0.2], [1.5, 0.0]), [1.5, 0.0, None, 1.05]),
  ('regression: sterile cohort', ([0.9, 0.9], [0.0, 0.0]), [0.0, None, None, 1.805]),
  ('control: mismatched schedules', ([0.5], [0.0, 1.0]), None),
  ('regression: annual insect', ([0.05, 0.0], [0.0, 30.0]), [1.5, 1.0, 0.405465, 0.55]),
  ('regression: long-lived',
   ([0.95, 0.95, 0.95, 0.95, 0.95, 0.9], [0.0, 0.0, 0.2, 0.4, 0.4, 0.4]),
   [1.158765, 3.659605, 0.040265, 5.146364])],
 [('regression: songbird', ([0.3, 0.6, 0.6, 0.5], [0.0, 1.5, 2.0, 2.0]), [1.026, 1.77193, 0.014486, 1.115]),
  ('regression: perennial plant',
   ([0.1, 0.8, 0.9, 0.9, 0.0], [0.0, 0.0, 5.0, 8.0, 8.0]),
   [1.4944, 3.079229, 0.130463, 0.8168]),
  ('regression: replacement cohort', ([0.5, 0.5], [0.0, 4.0]), [2.0, 1.0, 0.693147, 1.125]),
  ('regression: age zero breeding only', ([0.5, 0.2], [1.5, 0.0]), [1.5, 0.0, None, 1.05]),
  ('control: mismatched schedules', ([0.5], [0.0, 1.0]), None),
  ('regression: annual insect', ([0.05, 0.0], [0.0, 30.0]), [1.5, 1.0, 0.405465, 0.55]),
  ('regression: long-lived',
   ([0.95, 0.95, 0.95, 0.95, 0.95, 0.9], [0.0, 0.0, 0.2, 0.4, 0.4, 0.4]),
   [1.158765, 3.659605, 0.040265, 5.146364])],
 [('regression: perennial plant',
   ([0.1, 0.8, 0.9, 0.9, 0.0], [0.0, 0.0, 5.0, 8.0, 8.0]),
   [1.4944, 3.079229, 0.130463, 0.8168]),
  ('regression: replacement cohort', ([0.5, 0.5], [0.0, 4.0]), [2.0, 1.0, 0.693147, 1.125]),
  ('regression: age zero breeding only', ([0.5, 0.2], [1.5, 0.0]), [1.5, 0.0, None, 1.05]),
  ('regression: sterile cohort', ([0.9, 0.9], [0.0, 0.0]), [0.0, None, None, 1.805]),
  ('control: mismatched schedules', ([0.5], [0.0, 1.0]), None),
  ('regression: annual insect', ([0.05, 0.0], [0.0, 30.0]), [1.5, 1.0, 0.405465, 0.55]),
  ('regression: long-lived',
   ([0.95, 0.95, 0.95, 0.95, 0.95, 0.9], [0.0, 0.0, 0.2, 0.4, 0.4, 0.4]),
   [1.158765, 3.659605, 0.040265, 5.146364])],
 [('regression: songbird', ([0.3, 0.6, 0.6, 0.5], [0.0, 1.5, 2.0, 2.0]), [1.026, 1.77193, 0.014486, 1.115]),
  ('regression: perennial plant',
   ([0.1, 0.8, 0.9, 0.9, 0.0], [0.0, 0.0, 5.0, 8.0, 8.0]),
   [1.4944, 3.079229, 0.130463, 0.8168]),
  ('regression: replacement cohort', ([0.5, 0.5], [0.0, 4.0]), [2.0, 1.0, 0.693147, 1.125]),
  ('regression: sterile cohort', ([0.9, 0.9], [0.0, 0.0]), [0.0, None, None, 1.805]),
  ('control: mismatched schedules', ([0.5], [0.0, 1.0]), None),
  ('regression: annual insect', ([0.05, 0.0], [0.0, 30.0]), [1.5, 1.0, 0.405465, 0.55]),
  ('regression: long-lived',
   ([0.95, 0.95, 0.95, 0.95, 0.95, 0.9], [0.0, 0.0, 0.2, 0.4, 0.4, 0.4]),
   [1.158765, 3.659605, 0.040265, 5.146364])]]
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
regression: songbird	`[1.026, 1.77193, 0.014486, 1.588]`	`[1.026, 1.77193, 0.014486, 1.115]`	Failed
regression: perennial plant	`[1.4944, 3.079229, 0.130463, 1.3168]`	`[1.4944, 3.079229, 0.130463, 0.8168]`	Failed
regression: replacement cohort	`[2.0, 1.0, 0.693147, 1.5]`	`[2.0, 1.0, 0.693147, 1.125]`	Failed
regression: age zero breeding only	`[1.5, 0.0, None, 1.5]`	`[1.5, 0.0, None, 1.05]`	Failed
regression: sterile cohort	`[0.0, None, None, 1.9]`	`[0.0, None, None, 1.805]`	Failed
control: mismatched schedules	`None`	`None`	Passed
regression: annual insect	`[1.5, 1.0, 0.405465, 1.05]`	`[1.5, 1.0, 0.405465, 0.55]`	Failed

SHA-256 / b875e0c34397d4b9e007108d0bc18f9de327692b3d40336a7c45163768d1dfba

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(px, mx):
    n = len(px)
    if n == 0 or len(mx) != n:
        return None
    l = [1.0]
    for x in range(1, n + 1):
        l.append(l[-1] * px[x - 1])
    e0 = round(sum(l[x + 1] for x in range(n)), 6)
    r0 = sum(l[x] * mx[x] for x in range(n))
    if r0 <= 0:
        return [0.0, None, None, e0]
    gen = sum(x * l[x] * mx[x] for x in range(n)) / r0
    rate = math.log(r0) / gen if gen > 0 else None
    return [round(r0, 6), round(gen, 6), None if rate is None else round(rate, 6), e0]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: songbird', ([0.3, 0.6, 0.6, 0.5], [0.0, 1.5, 2.0, 2.0]), [1.026, 1.77193, 0.014486, 1.115]),
  ('regression: perennial plant',
   ([0.1, 0.8, 0.9, 0.9, 0.0], [0.0, 0.0, 5.0, 8.0, 8.0]),
   [1.4944, 3.079229, 0.130463, 0.8168]),
  ('regression: replacement cohort', ([0.5, 0.5], [0.0, 4.0]), [2.0, 1.0, 0.693147, 1.125]),
  ('regression: age zero breeding only', ([0.5, 0.2], [1.5, 0.0]), [1.5, 0.0, None, 1.05]),
  ('regression: sterile cohort', ([0.9, 0.9], [0.0, 0.0]), [0.0, None, None, 1.805]),
  ('control: mismatched schedules', ([0.5], [0.0, 1.0]), None),
  ('regression: annual insect', ([0.05, 0.0], [0.0, 30.0]), [1.5, 1.0, 0.405465, 0.55])],
 [('regression: songbird', ([0.3, 0.6, 0.6, 0.5], [0.0, 1.5, 2.0, 2.0]), [1.026, 1.77193, 0.014486, 1.115]),
  ('regression: perennial plant',
   ([0.1, 0.8, 0.9, 0.9, 0.0], [0.0, 0.0, 5.0, 8.0, 8.0]),
   [1.4944, 3.079229, 0.130463, 0.8168]),
  ('regression: age zero breeding only', ([0.5, 0.2], [1.5, 0.0]), [1.5, 0.0, None, 1.05]),
  ('regression: sterile cohort', ([0.9, 0.9], [0.0, 0.0]), [0.0, None, None, 1.805]),
  ('control: mismatched schedules', ([0.5], [0.0, 1.0]), None),
  ('regression: annual insect', ([0.05, 0.0], [0.0, 30.0]), [1.5, 1.0, 0.405465, 0.55]),
  ('regression: long-lived',
   ([0.95, 0.95, 0.95, 0.95, 0.95, 0.9], [0.0, 0.0, 0.2, 0.4, 0.4, 0.4]),
   [1.158765, 3.659605, 0.040265, 5.146364])],
 [('regression: songbird', ([0.3, 0.6, 0.6, 0.5], [0.0, 1.5, 2.0, 2.0]), [1.026, 1.77193, 0.014486, 1.115]),
  ('regression: perennial plant',
   ([0.1, 0.8, 0.9, 0.9, 0.0], [0.0, 0.0, 5.0, 8.0, 8.0]),
   [1.4944, 3.079229, 0.130463, 0.8168]),
  ('regression: replacement cohort', ([0.5, 0.5], [0.0, 4.0]), [2.0, 1.0, 0.693147, 1.125]),
  ('regression: age zero breeding only', ([0.5, 0.2], [1.5, 0.0]), [1.5, 0.0, None, 1.05]),
  ('control: mismatched schedules', ([0.5], [0.0, 1.0]), None),
  ('regression: annual insect', ([0.05, 0.0], [0.0, 30.0]), [1.5, 1.0, 0.405465, 0.55]),
  ('regression: long-lived',
   ([0.95, 0.95, 0.95, 0.95, 0.95, 0.9], [0.0, 0.0, 0.2, 0.4, 0.4, 0.4]),
   [1.158765, 3.659605, 0.040265, 5.146364])],
 [('regression: perennial plant',
   ([0.1, 0.8, 0.9, 0.9, 0.0], [0.0, 0.0, 5.0, 8.0, 8.0]),
   [1.4944, 3.079229, 0.130463, 0.8168]),
  ('regression: replacement cohort', ([0.5, 0.5], [0.0, 4.0]), [2.0, 1.0, 0.693147, 1.125]),
  ('regression: age zero breeding only', ([0.5, 0.2], [1.5, 0.0]), [1.5, 0.0, None, 1.05]),
  ('regression: sterile cohort', ([0.9, 0.9], [0.0, 0.0]), [0.0, None, None, 1.805]),
  ('control: mismatched schedules', ([0.5], [0.0, 1.0]), None),
  ('regression: annual insect', ([0.05, 0.0], [0.0, 30.0]), [1.5, 1.0, 0.405465, 0.55]),
  ('regression: long-lived',
   ([0.95, 0.95, 0.95, 0.95, 0.95, 0.9], [0.0, 0.0, 0.2, 0.4, 0.4, 0.4]),
   [1.158765, 3.659605, 0.040265, 5.146364])],
 [('regression: songbird', ([0.3, 0.6, 0.6, 0.5], [0.0, 1.5, 2.0, 2.0]), [1.026, 1.77193, 0.014486, 1.115]),
  ('regression: perennial plant',
   ([0.1, 0.8, 0.9, 0.9, 0.0], [0.0, 0.0, 5.0, 8.0, 8.0]),
   [1.4944, 3.079229, 0.130463, 0.8168]),
  ('regression: replacement cohort', ([0.5, 0.5], [0.0, 4.0]), [2.0, 1.0, 0.693147, 1.125]),
  ('regression: sterile cohort', ([0.9, 0.9], [0.0, 0.0]), [0.0, None, None, 1.805]),
  ('control: mismatched schedules', ([0.5], [0.0, 1.0]), None),
  ('regression: annual insect', ([0.05, 0.0], [0.0, 30.0]), [1.5, 1.0, 0.405465, 0.55]),
  ('regression: long-lived',
   ([0.95, 0.95, 0.95, 0.95, 0.95, 0.9], [0.0, 0.0, 0.2, 0.4, 0.4, 0.4]),
   [1.158765, 3.659605, 0.040265, 5.146364])]]
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
regression: songbird	`[1.026, 1.77193, 0.014486, 0.642]`	`[1.026, 1.77193, 0.014486, 1.115]`	Failed
regression: perennial plant	`[1.4944, 3.079229, 0.130463, 0.3168]`	`[1.4944, 3.079229, 0.130463, 0.8168]`	Failed
regression: replacement cohort	`[2.0, 1.0, 0.693147, 0.75]`	`[2.0, 1.0, 0.693147, 1.125]`	Failed
regression: age zero breeding only	`[1.5, 0.0, None, 0.6]`	`[1.5, 0.0, None, 1.05]`	Failed
regression: sterile cohort	`[0.0, None, None, 1.71]`	`[0.0, None, None, 1.805]`	Failed
control: mismatched schedules	`None`	`None`	Passed
regression: annual insect	`[1.5, 1.0, 0.405465, 0.05]`	`[1.5, 1.0, 0.405465, 0.55]`	Failed

SHA-256 / c9b9d2b0581bca567c7fc3bd6fe968e806d2472aebb2f1f17c004b95ba7b1f48

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(px, mx):
    n = len(px)
    if n == 0 or len(mx) != n:
        return None
    l = [1.0]
    for x in range(1, n + 1):
        l.append(l[-1] * px[x - 1])
    e0 = round(sum((l[x] + l[x + 1]) / 2 for x in range(n)), 6)
    r0 = sum(l[x] * mx[x] for x in range(n))
    if r0 <= 0:
        return [0.0, None, None, e0]
    gen = sum(x * l[x] * mx[x] for x in range(n)) / r0
    rate = math.log(r0) / gen if gen > 0 else None
    return [round(r0, 6), round(gen, 6), None if rate is None else round(rate, 6), e0]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: songbird', ([0.3, 0.6, 0.6, 0.5], [0.0, 1.5, 2.0, 2.0]), [1.026, 1.77193, 0.014486, 1.115]),
  ('regression: perennial plant',
   ([0.1, 0.8, 0.9, 0.9, 0.0], [0.0, 0.0, 5.0, 8.0, 8.0]),
   [1.4944, 3.079229, 0.130463, 0.8168]),
  ('regression: replacement cohort', ([0.5, 0.5], [0.0, 4.0]), [2.0, 1.0, 0.693147, 1.125]),
  ('regression: age zero breeding only', ([0.5, 0.2], [1.5, 0.0]), [1.5, 0.0, None, 1.05]),
  ('regression: sterile cohort', ([0.9, 0.9], [0.0, 0.0]), [0.0, None, None, 1.805]),
  ('control: mismatched schedules', ([0.5], [0.0, 1.0]), None),
  ('regression: annual insect', ([0.05, 0.0], [0.0, 30.0]), [1.5, 1.0, 0.405465, 0.55])],
 [('regression: songbird', ([0.3, 0.6, 0.6, 0.5], [0.0, 1.5, 2.0, 2.0]), [1.026, 1.77193, 0.014486, 1.115]),
  ('regression: perennial plant',
   ([0.1, 0.8, 0.9, 0.9, 0.0], [0.0, 0.0, 5.0, 8.0, 8.0]),
   [1.4944, 3.079229, 0.130463, 0.8168]),
  ('regression: age zero breeding only', ([0.5, 0.2], [1.5, 0.0]), [1.5, 0.0, None, 1.05]),
  ('regression: sterile cohort', ([0.9, 0.9], [0.0, 0.0]), [0.0, None, None, 1.805]),
  ('control: mismatched schedules', ([0.5], [0.0, 1.0]), None),
  ('regression: annual insect', ([0.05, 0.0], [0.0, 30.0]), [1.5, 1.0, 0.405465, 0.55]),
  ('regression: long-lived',
   ([0.95, 0.95, 0.95, 0.95, 0.95, 0.9], [0.0, 0.0, 0.2, 0.4, 0.4, 0.4]),
   [1.158765, 3.659605, 0.040265, 5.146364])],
 [('regression: songbird', ([0.3, 0.6, 0.6, 0.5], [0.0, 1.5, 2.0, 2.0]), [1.026, 1.77193, 0.014486, 1.115]),
  ('regression: perennial plant',
   ([0.1, 0.8, 0.9, 0.9, 0.0], [0.0, 0.0, 5.0, 8.0, 8.0]),
   [1.4944, 3.079229, 0.130463, 0.8168]),
  ('regression: replacement cohort', ([0.5, 0.5], [0.0, 4.0]), [2.0, 1.0, 0.693147, 1.125]),
  ('regression: age zero breeding only', ([0.5, 0.2], [1.5, 0.0]), [1.5, 0.0, None, 1.05]),
  ('control: mismatched schedules', ([0.5], [0.0, 1.0]), None),
  ('regression: annual insect', ([0.05, 0.0], [0.0, 30.0]), [1.5, 1.0, 0.405465, 0.55]),
  ('regression: long-lived',
   ([0.95, 0.95, 0.95, 0.95, 0.95, 0.9], [0.0, 0.0, 0.2, 0.4, 0.4, 0.4]),
   [1.158765, 3.659605, 0.040265, 5.146364])],
 [('regression: perennial plant',
   ([0.1, 0.8, 0.9, 0.9, 0.0], [0.0, 0.0, 5.0, 8.0, 8.0]),
   [1.4944, 3.079229, 0.130463, 0.8168]),
  ('regression: replacement cohort', ([0.5, 0.5], [0.0, 4.0]), [2.0, 1.0, 0.693147, 1.125]),
  ('regression: age zero breeding only', ([0.5, 0.2], [1.5, 0.0]), [1.5, 0.0, None, 1.05]),
  ('regression: sterile cohort', ([0.9, 0.9], [0.0, 0.0]), [0.0, None, None, 1.805]),
  ('control: mismatched schedules', ([0.5], [0.0, 1.0]), None),
  ('regression: annual insect', ([0.05, 0.0], [0.0, 30.0]), [1.5, 1.0, 0.405465, 0.55]),
  ('regression: long-lived',
   ([0.95, 0.95, 0.95, 0.95, 0.95, 0.9], [0.0, 0.0, 0.2, 0.4, 0.4, 0.4]),
   [1.158765, 3.659605, 0.040265, 5.146364])],
 [('regression: songbird', ([0.3, 0.6, 0.6, 0.5], [0.0, 1.5, 2.0, 2.0]), [1.026, 1.77193, 0.014486, 1.115]),
  ('regression: perennial plant',
   ([0.1, 0.8, 0.9, 0.9, 0.0], [0.0, 0.0, 5.0, 8.0, 8.0]),
   [1.4944, 3.079229, 0.130463, 0.8168]),
  ('regression: replacement cohort', ([0.5, 0.5], [0.0, 4.0]), [2.0, 1.0, 0.693147, 1.125]),
  ('regression: sterile cohort', ([0.9, 0.9], [0.0, 0.0]), [0.0, None, None, 1.805]),
  ('control: mismatched schedules', ([0.5], [0.0, 1.0]), None),
  ('regression: annual insect', ([0.05, 0.0], [0.0, 30.0]), [1.5, 1.0, 0.405465, 0.55]),
  ('regression: long-lived',
   ([0.95, 0.95, 0.95, 0.95, 0.95, 0.9], [0.0, 0.0, 0.2, 0.4, 0.4, 0.4]),
   [1.158765, 3.659605, 0.040265, 5.146364])]]
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
regression: songbird	`[1.026, 1.77193, 0.014486, 1.115]`	`[1.026, 1.77193, 0.014486, 1.115]`	Passed
regression: perennial plant	`[1.4944, 3.079229, 0.130463, 0.8168]`	`[1.4944, 3.079229, 0.130463, 0.8168]`	Passed
regression: replacement cohort	`[2.0, 1.0, 0.693147, 1.125]`	`[2.0, 1.0, 0.693147, 1.125]`	Passed
regression: age zero breeding only	`[1.5, 0.0, None, 1.05]`	`[1.5, 0.0, None, 1.05]`	Passed
regression: sterile cohort	`[0.0, None, None, 1.805]`	`[0.0, None, None, 1.805]`	Passed
control: mismatched schedules	`None`	`None`	Passed
regression: annual insect	`[1.5, 1.0, 0.405465, 0.55]`	`[1.5, 1.0, 0.405465, 0.55]`	Passed

SHA-256 / ca3511178ca0f4d6474e809257ca347cf7aa35cd49976da13fbea900bd0b9aed

Verification & scope

Deterministic bounded teaching model with a stipulated contract; not a validated scientific or public-health modelling library. 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 2026-09-29T14:47:34.652925+00:00.

Case digest / 18d8da193dd8e0f72c25305e289ff242d48f600ce404e8bb020d820c05906faa