FA-65221 / Epidemic compartment models / Open access
SIR with Erlang-distributed infectious period: stage exit rate · case 01
The mean infectious period becomes k times too long.
ROOT CAUSE
Each stage is left at gamma instead of k*gamma.
VERIFIED REPAIR
Restore the stage exit rate rule: `k * gamma * x * dt`.
Unsuccessful approach: Dividing by k makes the period k squared times too long.
Case contract
Infectious period split into k sequential stages each left at rate k*gamma; seeds start in stage 1; all stages transmit; Euler with dt=0.1 (10 substeps/day); return [total I at day ends including day 0 rounded 3, R rounded 3], None for k<1.
Why this case matters
Compartmental epidemic calculations drive outbreak forecasts, vaccine targets and hospital planning; a single wrong flow, rate conversion or boundary silently changes every downstream number.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(beta, gamma, k, pop, i0, days):
if k < 1:
return None
stages = [0.0] * k
stages[0] = float(i0)
s = float(pop - i0)
r = 0.0
dt = 0.1
series = [round(sum(stages), 3)]
for _ in range(days):
for _ in range(10):
i = sum(stages)
inf = beta * s * i / pop * dt
flows = [gamma * x * dt for x in stages]
s -= inf
stages[0] += inf - flows[0]
for j in range(1, k):
stages[j] += flows[j - 1] - flows[j]
r += flows[-1]
series.append(round(sum(stages), 3))
return [series, round(r, 3)]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: three stages',
(0.5, 0.2, 3, 1000, 10, 6),
[[10.0, 15.964, 24.203, 35.419, 50.774, 71.593, 99.086], 25.589]),
('control: single stage equals SIR',
(0.4, 0.25, 1, 500, 5, 5),
[[5.0, 5.776, 6.66, 7.664, 8.798, 10.074], 9.032]),
('regression: many stages', (0.6, 0.3, 5, 800, 20, 4), [[20.0, 34.937, 55.691, 80.709, 110.985], 33.142]),
('regression: no transmission',
(0.0, 0.5, 2, 100, 10, 5),
[[10.0, 7.361, 3.917, 1.837, 0.805, 0.338], 9.662]),
('control: invalid k', (0.5, 0.2, 0, 100, 5, 3), None),
('regression: two stages slow',
(0.3, 0.1, 2, 2000, 30, 7),
[[30.0, 39.545, 50.929, 64.696, 81.433, 101.776, 126.384, 155.912], 30.058]),
('control: boundary zero days', (0.5, 0.2, 3, 100, 5, 0), [[5.0], 0.0])],
[('regression: three stages',
(0.5, 0.2, 3, 1000, 10, 6),
[[10.0, 15.964, 24.203, 35.419, 50.774, 71.593, 99.086], 25.589]),
('control: single stage equals SIR',
(0.4, 0.25, 1, 500, 5, 5),
[[5.0, 5.776, 6.66, 7.664, 8.798, 10.074], 9.032]),
('regression: no transmission',
(0.0, 0.5, 2, 100, 10, 5),
[[10.0, 7.361, 3.917, 1.837, 0.805, 0.338], 9.662]),
('control: invalid k', (0.5, 0.2, 0, 100, 5, 3), None),
('regression: two stages slow',
(0.3, 0.1, 2, 2000, 30, 7),
[[30.0, 39.545, 50.929, 64.696, 81.433, 101.776, 126.384, 155.912], 30.058]),
('control: boundary zero days', (0.5, 0.2, 3, 100, 5, 0), [[5.0], 0.0]),
('regression: four stages fast recovery',
(0.9, 0.5, 4, 300, 6, 5),
[[6.0, 12.89, 21.627, 33.085, 46.281, 57.492], 51.385])],
[('regression: three stages',
(0.5, 0.2, 3, 1000, 10, 6),
[[10.0, 15.964, 24.203, 35.419, 50.774, 71.593, 99.086], 25.589]),
('control: single stage equals SIR',
(0.4, 0.25, 1, 500, 5, 5),
[[5.0, 5.776, 6.66, 7.664, 8.798, 10.074], 9.032]),
('regression: many stages', (0.6, 0.3, 5, 800, 20, 4), [[20.0, 34.937, 55.691, 80.709, 110.985], 33.142]),
('regression: no transmission',
(0.0, 0.5, 2, 100, 10, 5),
[[10.0, 7.361, 3.917, 1.837, 0.805, 0.338], 9.662]),
('control: invalid k', (0.5, 0.2, 0, 100, 5, 3), None),
('control: boundary zero days', (0.5, 0.2, 3, 100, 5, 0), [[5.0], 0.0]),
('regression: four stages fast recovery',
(0.9, 0.5, 4, 300, 6, 5),
[[6.0, 12.89, 21.627, 33.085, 46.281, 57.492], 51.385])],
[('control: single stage equals SIR',
(0.4, 0.25, 1, 500, 5, 5),
[[5.0, 5.776, 6.66, 7.664, 8.798, 10.074], 9.032]),
('regression: many stages', (0.6, 0.3, 5, 800, 20, 4), [[20.0, 34.937, 55.691, 80.709, 110.985], 33.142]),
('regression: no transmission',
(0.0, 0.5, 2, 100, 10, 5),
[[10.0, 7.361, 3.917, 1.837, 0.805, 0.338], 9.662]),
('control: invalid k', (0.5, 0.2, 0, 100, 5, 3), None),
('regression: two stages slow',
(0.3, 0.1, 2, 2000, 30, 7),
[[30.0, 39.545, 50.929, 64.696, 81.433, 101.776, 126.384, 155.912], 30.058]),
('control: boundary zero days', (0.5, 0.2, 3, 100, 5, 0), [[5.0], 0.0]),
('regression: four stages fast recovery',
(0.9, 0.5, 4, 300, 6, 5),
[[6.0, 12.89, 21.627, 33.085, 46.281, 57.492], 51.385])],
[('regression: three stages',
(0.5, 0.2, 3, 1000, 10, 6),
[[10.0, 15.964, 24.203, 35.419, 50.774, 71.593, 99.086], 25.589]),
('control: single stage equals SIR',
(0.4, 0.25, 1, 500, 5, 5),
[[5.0, 5.776, 6.66, 7.664, 8.798, 10.074], 9.032]),
('regression: many stages', (0.6, 0.3, 5, 800, 20, 4), [[20.0, 34.937, 55.691, 80.709, 110.985], 33.142]),
('control: invalid k', (0.5, 0.2, 0, 100, 5, 3), None),
('regression: two stages slow',
(0.3, 0.1, 2, 2000, 30, 7),
[[30.0, 39.545, 50.929, 64.696, 81.433, 101.776, 126.384, 155.912], 30.058]),
('control: boundary zero days', (0.5, 0.2, 3, 100, 5, 0), [[5.0], 0.0]),
('regression: four stages fast recovery',
(0.9, 0.5, 4, 300, 6, 5),
[[6.0, 12.89, 21.627, 33.085, 46.281, 57.492], 51.385])]]
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: three stages | [[10.0, 16.182, 26.01, 41.433, 65.244, 101.137, 153.329], 3.249] | [[10.0, 15.964, 24.203, 35.419, 50.774, 71.593, 99.086], 25.589] | Failed |
| control: single stage equals SIR | [[5.0, 5.776, 6.66, 7.664, 8.798, 10.074], 9.032] | [[5.0, 5.776, 6.66, 7.664, 8.798, 10.074], 9.032] | Passed |
| regression: many stages | [[20.0, 35.16, 60.953, 103.203, 168.258], 0.207] | [[20.0, 34.937, 55.691, 80.709, 110.985], 33.142] | Failed |
| regression: no transmission | [[10.0, 9.139, 7.358, 5.535, 3.991, 2.794], 7.206] | [[10.0, 7.361, 3.917, 1.837, 0.805, 0.338], 9.662] | Failed |
| control: invalid k | None | None | Passed |
| regression: two stages slow | [[30.0, 39.966, 52.824, 69.393, 90.67, 117.841, 152.258, 195.388], 10.818] | [[30.0, 39.545, 50.929, 64.696, 81.433, 101.776, 126.384, 155.912], 30.058] | Failed |
| control: boundary zero days | [[5.0], 0.0] | [[5.0], 0.0] | Passed |
SHA-256 / 1d5f1be84d9b72f3478bc43a22526d8763cd31596c9d49c5018ea3d0052a5595
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(beta, gamma, k, pop, i0, days):
if k < 1:
return None
stages = [0.0] * k
stages[0] = float(i0)
s = float(pop - i0)
r = 0.0
dt = 0.1
series = [round(sum(stages), 3)]
for _ in range(days):
for _ in range(10):
i = sum(stages)
inf = beta * s * i / pop * dt
flows = [gamma / k * x * dt for x in stages]
s -= inf
stages[0] += inf - flows[0]
for j in range(1, k):
stages[j] += flows[j - 1] - flows[j]
r += flows[-1]
series.append(round(sum(stages), 3))
return [series, round(r, 3)]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: three stages',
(0.5, 0.2, 3, 1000, 10, 6),
[[10.0, 15.964, 24.203, 35.419, 50.774, 71.593, 99.086], 25.589]),
('control: single stage equals SIR',
(0.4, 0.25, 1, 500, 5, 5),
[[5.0, 5.776, 6.66, 7.664, 8.798, 10.074], 9.032]),
('regression: many stages', (0.6, 0.3, 5, 800, 20, 4), [[20.0, 34.937, 55.691, 80.709, 110.985], 33.142]),
('regression: no transmission',
(0.0, 0.5, 2, 100, 10, 5),
[[10.0, 7.361, 3.917, 1.837, 0.805, 0.338], 9.662]),
('control: invalid k', (0.5, 0.2, 0, 100, 5, 3), None),
('regression: two stages slow',
(0.3, 0.1, 2, 2000, 30, 7),
[[30.0, 39.545, 50.929, 64.696, 81.433, 101.776, 126.384, 155.912], 30.058]),
('control: boundary zero days', (0.5, 0.2, 3, 100, 5, 0), [[5.0], 0.0])],
[('regression: three stages',
(0.5, 0.2, 3, 1000, 10, 6),
[[10.0, 15.964, 24.203, 35.419, 50.774, 71.593, 99.086], 25.589]),
('control: single stage equals SIR',
(0.4, 0.25, 1, 500, 5, 5),
[[5.0, 5.776, 6.66, 7.664, 8.798, 10.074], 9.032]),
('regression: no transmission',
(0.0, 0.5, 2, 100, 10, 5),
[[10.0, 7.361, 3.917, 1.837, 0.805, 0.338], 9.662]),
('control: invalid k', (0.5, 0.2, 0, 100, 5, 3), None),
('regression: two stages slow',
(0.3, 0.1, 2, 2000, 30, 7),
[[30.0, 39.545, 50.929, 64.696, 81.433, 101.776, 126.384, 155.912], 30.058]),
('control: boundary zero days', (0.5, 0.2, 3, 100, 5, 0), [[5.0], 0.0]),
('regression: four stages fast recovery',
(0.9, 0.5, 4, 300, 6, 5),
[[6.0, 12.89, 21.627, 33.085, 46.281, 57.492], 51.385])],
[('regression: three stages',
(0.5, 0.2, 3, 1000, 10, 6),
[[10.0, 15.964, 24.203, 35.419, 50.774, 71.593, 99.086], 25.589]),
('control: single stage equals SIR',
(0.4, 0.25, 1, 500, 5, 5),
[[5.0, 5.776, 6.66, 7.664, 8.798, 10.074], 9.032]),
('regression: many stages', (0.6, 0.3, 5, 800, 20, 4), [[20.0, 34.937, 55.691, 80.709, 110.985], 33.142]),
('regression: no transmission',
(0.0, 0.5, 2, 100, 10, 5),
[[10.0, 7.361, 3.917, 1.837, 0.805, 0.338], 9.662]),
('control: invalid k', (0.5, 0.2, 0, 100, 5, 3), None),
('control: boundary zero days', (0.5, 0.2, 3, 100, 5, 0), [[5.0], 0.0]),
('regression: four stages fast recovery',
(0.9, 0.5, 4, 300, 6, 5),
[[6.0, 12.89, 21.627, 33.085, 46.281, 57.492], 51.385])],
[('control: single stage equals SIR',
(0.4, 0.25, 1, 500, 5, 5),
[[5.0, 5.776, 6.66, 7.664, 8.798, 10.074], 9.032]),
('regression: many stages', (0.6, 0.3, 5, 800, 20, 4), [[20.0, 34.937, 55.691, 80.709, 110.985], 33.142]),
('regression: no transmission',
(0.0, 0.5, 2, 100, 10, 5),
[[10.0, 7.361, 3.917, 1.837, 0.805, 0.338], 9.662]),
('control: invalid k', (0.5, 0.2, 0, 100, 5, 3), None),
('regression: two stages slow',
(0.3, 0.1, 2, 2000, 30, 7),
[[30.0, 39.545, 50.929, 64.696, 81.433, 101.776, 126.384, 155.912], 30.058]),
('control: boundary zero days', (0.5, 0.2, 3, 100, 5, 0), [[5.0], 0.0]),
('regression: four stages fast recovery',
(0.9, 0.5, 4, 300, 6, 5),
[[6.0, 12.89, 21.627, 33.085, 46.281, 57.492], 51.385])],
[('regression: three stages',
(0.5, 0.2, 3, 1000, 10, 6),
[[10.0, 15.964, 24.203, 35.419, 50.774, 71.593, 99.086], 25.589]),
('control: single stage equals SIR',
(0.4, 0.25, 1, 500, 5, 5),
[[5.0, 5.776, 6.66, 7.664, 8.798, 10.074], 9.032]),
('regression: many stages', (0.6, 0.3, 5, 800, 20, 4), [[20.0, 34.937, 55.691, 80.709, 110.985], 33.142]),
('control: invalid k', (0.5, 0.2, 0, 100, 5, 3), None),
('regression: two stages slow',
(0.3, 0.1, 2, 2000, 30, 7),
[[30.0, 39.545, 50.929, 64.696, 81.433, 101.776, 126.384, 155.912], 30.058]),
('control: boundary zero days', (0.5, 0.2, 3, 100, 5, 0), [[5.0], 0.0]),
('regression: four stages fast recovery',
(0.9, 0.5, 4, 300, 6, 5),
[[6.0, 12.89, 21.627, 33.085, 46.281, 57.492], 51.385])]]
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: three stages | [[10.0, 16.191, 26.117, 41.871, 66.499, 104.09, 159.423], 0.188] | [[10.0, 15.964, 24.203, 35.419, 50.774, 71.593, 99.086], 25.589] | Failed |
| control: single stage equals SIR | [[5.0, 5.776, 6.66, 7.664, 8.798, 10.074], 9.032] | [[5.0, 5.776, 6.66, 7.664, 8.798, 10.074], 9.032] | Passed |
| regression: many stages | [[20.0, 35.16, 60.96, 103.266, 168.547], 0.0] | [[20.0, 34.937, 55.691, 80.709, 110.985], 33.142] | Failed |
| regression: no transmission | [[10.0, 9.754, 9.118, 8.278, 7.358, 6.435], 3.565] | [[10.0, 7.361, 3.917, 1.837, 0.805, 0.338], 9.662] | Failed |
| control: invalid k | None | None | Passed |
| regression: two stages slow | [[30.0, 40.078, 53.362, 70.809, 93.611, 123.215, 161.315, 209.791], 3.25] | [[30.0, 39.545, 50.929, 64.696, 81.433, 101.776, 126.384, 155.912], 30.058] | Failed |
| control: boundary zero days | [[5.0], 0.0] | [[5.0], 0.0] | Passed |
SHA-256 / bf915b9117ab118d09423fe0cab4267a416d88ed7817161266ff7c065f56a438
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(beta, gamma, k, pop, i0, days):
if k < 1:
return None
stages = [0.0] * k
stages[0] = float(i0)
s = float(pop - i0)
r = 0.0
dt = 0.1
series = [round(sum(stages), 3)]
for _ in range(days):
for _ in range(10):
i = sum(stages)
inf = beta * s * i / pop * dt
flows = [k * gamma * x * dt for x in stages]
s -= inf
stages[0] += inf - flows[0]
for j in range(1, k):
stages[j] += flows[j - 1] - flows[j]
r += flows[-1]
series.append(round(sum(stages), 3))
return [series, round(r, 3)]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: three stages',
(0.5, 0.2, 3, 1000, 10, 6),
[[10.0, 15.964, 24.203, 35.419, 50.774, 71.593, 99.086], 25.589]),
('control: single stage equals SIR',
(0.4, 0.25, 1, 500, 5, 5),
[[5.0, 5.776, 6.66, 7.664, 8.798, 10.074], 9.032]),
('regression: many stages', (0.6, 0.3, 5, 800, 20, 4), [[20.0, 34.937, 55.691, 80.709, 110.985], 33.142]),
('regression: no transmission',
(0.0, 0.5, 2, 100, 10, 5),
[[10.0, 7.361, 3.917, 1.837, 0.805, 0.338], 9.662]),
('control: invalid k', (0.5, 0.2, 0, 100, 5, 3), None),
('regression: two stages slow',
(0.3, 0.1, 2, 2000, 30, 7),
[[30.0, 39.545, 50.929, 64.696, 81.433, 101.776, 126.384, 155.912], 30.058]),
('control: boundary zero days', (0.5, 0.2, 3, 100, 5, 0), [[5.0], 0.0])],
[('regression: three stages',
(0.5, 0.2, 3, 1000, 10, 6),
[[10.0, 15.964, 24.203, 35.419, 50.774, 71.593, 99.086], 25.589]),
('control: single stage equals SIR',
(0.4, 0.25, 1, 500, 5, 5),
[[5.0, 5.776, 6.66, 7.664, 8.798, 10.074], 9.032]),
('regression: no transmission',
(0.0, 0.5, 2, 100, 10, 5),
[[10.0, 7.361, 3.917, 1.837, 0.805, 0.338], 9.662]),
('control: invalid k', (0.5, 0.2, 0, 100, 5, 3), None),
('regression: two stages slow',
(0.3, 0.1, 2, 2000, 30, 7),
[[30.0, 39.545, 50.929, 64.696, 81.433, 101.776, 126.384, 155.912], 30.058]),
('control: boundary zero days', (0.5, 0.2, 3, 100, 5, 0), [[5.0], 0.0]),
('regression: four stages fast recovery',
(0.9, 0.5, 4, 300, 6, 5),
[[6.0, 12.89, 21.627, 33.085, 46.281, 57.492], 51.385])],
[('regression: three stages',
(0.5, 0.2, 3, 1000, 10, 6),
[[10.0, 15.964, 24.203, 35.419, 50.774, 71.593, 99.086], 25.589]),
('control: single stage equals SIR',
(0.4, 0.25, 1, 500, 5, 5),
[[5.0, 5.776, 6.66, 7.664, 8.798, 10.074], 9.032]),
('regression: many stages', (0.6, 0.3, 5, 800, 20, 4), [[20.0, 34.937, 55.691, 80.709, 110.985], 33.142]),
('regression: no transmission',
(0.0, 0.5, 2, 100, 10, 5),
[[10.0, 7.361, 3.917, 1.837, 0.805, 0.338], 9.662]),
('control: invalid k', (0.5, 0.2, 0, 100, 5, 3), None),
('control: boundary zero days', (0.5, 0.2, 3, 100, 5, 0), [[5.0], 0.0]),
('regression: four stages fast recovery',
(0.9, 0.5, 4, 300, 6, 5),
[[6.0, 12.89, 21.627, 33.085, 46.281, 57.492], 51.385])],
[('control: single stage equals SIR',
(0.4, 0.25, 1, 500, 5, 5),
[[5.0, 5.776, 6.66, 7.664, 8.798, 10.074], 9.032]),
('regression: many stages', (0.6, 0.3, 5, 800, 20, 4), [[20.0, 34.937, 55.691, 80.709, 110.985], 33.142]),
('regression: no transmission',
(0.0, 0.5, 2, 100, 10, 5),
[[10.0, 7.361, 3.917, 1.837, 0.805, 0.338], 9.662]),
('control: invalid k', (0.5, 0.2, 0, 100, 5, 3), None),
('regression: two stages slow',
(0.3, 0.1, 2, 2000, 30, 7),
[[30.0, 39.545, 50.929, 64.696, 81.433, 101.776, 126.384, 155.912], 30.058]),
('control: boundary zero days', (0.5, 0.2, 3, 100, 5, 0), [[5.0], 0.0]),
('regression: four stages fast recovery',
(0.9, 0.5, 4, 300, 6, 5),
[[6.0, 12.89, 21.627, 33.085, 46.281, 57.492], 51.385])],
[('regression: three stages',
(0.5, 0.2, 3, 1000, 10, 6),
[[10.0, 15.964, 24.203, 35.419, 50.774, 71.593, 99.086], 25.589]),
('control: single stage equals SIR',
(0.4, 0.25, 1, 500, 5, 5),
[[5.0, 5.776, 6.66, 7.664, 8.798, 10.074], 9.032]),
('regression: many stages', (0.6, 0.3, 5, 800, 20, 4), [[20.0, 34.937, 55.691, 80.709, 110.985], 33.142]),
('control: invalid k', (0.5, 0.2, 0, 100, 5, 3), None),
('regression: two stages slow',
(0.3, 0.1, 2, 2000, 30, 7),
[[30.0, 39.545, 50.929, 64.696, 81.433, 101.776, 126.384, 155.912], 30.058]),
('control: boundary zero days', (0.5, 0.2, 3, 100, 5, 0), [[5.0], 0.0]),
('regression: four stages fast recovery',
(0.9, 0.5, 4, 300, 6, 5),
[[6.0, 12.89, 21.627, 33.085, 46.281, 57.492], 51.385])]]
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: three stages | [[10.0, 15.964, 24.203, 35.419, 50.774, 71.593, 99.086], 25.589] | [[10.0, 15.964, 24.203, 35.419, 50.774, 71.593, 99.086], 25.589] | Passed |
| control: single stage equals SIR | [[5.0, 5.776, 6.66, 7.664, 8.798, 10.074], 9.032] | [[5.0, 5.776, 6.66, 7.664, 8.798, 10.074], 9.032] | Passed |
| regression: many stages | [[20.0, 34.937, 55.691, 80.709, 110.985], 33.142] | [[20.0, 34.937, 55.691, 80.709, 110.985], 33.142] | Passed |
| regression: no transmission | [[10.0, 7.361, 3.917, 1.837, 0.805, 0.338], 9.662] | [[10.0, 7.361, 3.917, 1.837, 0.805, 0.338], 9.662] | Passed |
| control: invalid k | None | None | Passed |
| regression: two stages slow | [[30.0, 39.545, 50.929, 64.696, 81.433, 101.776, 126.384, 155.912], 30.058] | [[30.0, 39.545, 50.929, 64.696, 81.433, 101.776, 126.384, 155.912], 30.058] | Passed |
| control: boundary zero days | [[5.0], 0.0] | [[5.0], 0.0] | Passed |
SHA-256 / 147f167b1673c9402d4dd9a045605c63c60b05540ca136797ab231ba52f3d3c5
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 2026-09-29T14:47:31.997837+00:00.
Case digest / 8c596500da62df5c61424bef2c8f9e574f7a762b0ac55261fc858bf8c0000771