FA-65026 / Epidemic compartment models / Open access
Two-group next-generation matrix R0: decoupled tie-break · case 01
Two identical decoupled groups report group 1 as leading.
ROOT CAUSE
The decoupled tie comparison is strict, sending ties to group 1.
VERIFIED REPAIR
Restore the decoupled tie-break rule: `if k[0][0] >= k[1][1] else`.
Unsuccessful approach: Choosing the larger population ignores which group actually has the larger reproduction number.
Case contract
K[i][j] = contact[i][j]*sizes[i]/sum(sizes)/gamma[j] (infections in group i caused by one infective in j); R0 is the dominant eigenvalue of the 2x2 K; lead group is the larger component of its eigenvector (ties and decoupled ties to group 0); return [flattened K rounded 6, R0 rounded 6, lead] or None for empty population or non-positive gamma.
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(contact, sizes, gamma):
total = sum(sizes)
if total <= 0 or min(gamma) <= 0:
return None
k = [[contact[i][j] * sizes[i] / total / gamma[j] for j in range(2)] for i in range(2)]
tr = k[0][0] + k[1][1]
det = k[0][0] * k[1][1] - k[0][1] * k[1][0]
disc = max(tr * tr - 4 * det, 0.0)
r0 = (tr + math.sqrt(disc)) / 2
if abs(k[0][1]) > 1e-12:
v = [k[0][1], r0 - k[0][0]]
elif abs(k[1][0]) > 1e-12:
v = [r0 - k[1][1], k[1][0]]
else:
v = [1.0, 0.0] if k[0][0] > k[1][1] else [0.0, 1.0]
lead = 0 if abs(v[0]) >= abs(v[1]) else 1
return [[round(x, 6) for row in k for x in row], round(r0, 6), lead]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('control: children and adults',
([[2.0, 0.5], [0.5, 1.0]], [300, 700], [0.25, 0.2]),
[[2.4, 0.75, 1.4, 3.5], 4.11297, 1]),
('control: asymmetric core group',
([[4.0, 0.2], [1.0, 0.3]], [100, 900], [0.3, 0.2]),
[[1.333333, 0.1, 3.0, 1.35], 1.889453, 1]),
('regression: decoupled equal groups tie',
([[1.0, 0.0], [0.0, 1.0]], [500, 500], [0.5, 0.5]),
[[1.0, 0.0, 0.0, 1.0], 1.0, 0]),
('regression: decoupled first dominant smaller group',
([[3.0, 0.0], [0.0, 0.5]], [300, 700], [0.5, 0.5]),
[[1.8, 0.0, 0.0, 0.7], 1.8, 0]),
('control: decoupled second dominant',
([[0.5, 0.0], [0.0, 3.0]], [400, 600], [0.5, 0.5]),
[[0.4, 0.0, 0.0, 3.6], 3.6, 1]),
('control: one-way coupling',
([[1.0, 0.0], [2.0, 1.5]], [200, 800], [0.2, 0.4]),
[[1.0, 0.0, 8.0, 3.0], 3.0, 1]),
('control: empty population', ([[1.0, 1.0], [1.0, 1.0]], [0, 0], [0.2, 0.2]), None)],
[('regression: decoupled equal groups tie',
([[1.0, 0.0], [0.0, 1.0]], [500, 500], [0.5, 0.5]),
[[1.0, 0.0, 0.0, 1.0], 1.0, 0]),
('regression: decoupled first dominant smaller group',
([[3.0, 0.0], [0.0, 0.5]], [300, 700], [0.5, 0.5]),
[[1.8, 0.0, 0.0, 0.7], 1.8, 0]),
('control: decoupled second dominant',
([[0.5, 0.0], [0.0, 3.0]], [400, 600], [0.5, 0.5]),
[[0.4, 0.0, 0.0, 3.6], 3.6, 1]),
('control: one-way coupling',
([[1.0, 0.0], [2.0, 1.5]], [200, 800], [0.2, 0.4]),
[[1.0, 0.0, 8.0, 3.0], 3.0, 1]),
('control: empty population', ([[1.0, 1.0], [1.0, 1.0]], [0, 0], [0.2, 0.2]), None),
('control: invalid gamma', ([[1.0, 1.0], [1.0, 1.0]], [10, 10], [0.0, 0.2]), None),
('control: homogeneous mixing',
([[1.2, 1.2], [1.2, 1.2]], [250, 750], [0.4, 0.4]),
[[0.75, 0.75, 2.25, 2.25], 3.0, 1])],
[('regression: decoupled equal groups tie',
([[1.0, 0.0], [0.0, 1.0]], [500, 500], [0.5, 0.5]),
[[1.0, 0.0, 0.0, 1.0], 1.0, 0]),
('regression: decoupled first dominant smaller group',
([[3.0, 0.0], [0.0, 0.5]], [300, 700], [0.5, 0.5]),
[[1.8, 0.0, 0.0, 0.7], 1.8, 0]),
('control: empty population', ([[1.0, 1.0], [1.0, 1.0]], [0, 0], [0.2, 0.2]), None),
('control: invalid gamma', ([[1.0, 1.0], [1.0, 1.0]], [10, 10], [0.0, 0.2]), None),
('control: homogeneous mixing',
([[1.2, 1.2], [1.2, 1.2]], [250, 750], [0.4, 0.4]),
[[0.75, 0.75, 2.25, 2.25], 3.0, 1]),
('control: unequal recovery',
([[0.8, 0.6], [0.3, 0.9]], [600, 400], [0.1, 0.5]),
[[4.8, 0.72, 1.2, 0.72], 5.001785, 0]),
('control: only cross contacts',
([[0.0, 2.0], [1.0, 0.0]], [300, 300], [0.25, 0.5]),
[[0.0, 2.0, 2.0, 0.0], 2.0, 0])],
[('control: children and adults',
([[2.0, 0.5], [0.5, 1.0]], [300, 700], [0.25, 0.2]),
[[2.4, 0.75, 1.4, 3.5], 4.11297, 1]),
('control: asymmetric core group',
([[4.0, 0.2], [1.0, 0.3]], [100, 900], [0.3, 0.2]),
[[1.333333, 0.1, 3.0, 1.35], 1.889453, 1]),
('regression: decoupled equal groups tie',
([[1.0, 0.0], [0.0, 1.0]], [500, 500], [0.5, 0.5]),
[[1.0, 0.0, 0.0, 1.0], 1.0, 0]),
('regression: decoupled first dominant smaller group',
([[3.0, 0.0], [0.0, 0.5]], [300, 700], [0.5, 0.5]),
[[1.8, 0.0, 0.0, 0.7], 1.8, 0]),
('control: decoupled second dominant',
([[0.5, 0.0], [0.0, 3.0]], [400, 600], [0.5, 0.5]),
[[0.4, 0.0, 0.0, 3.6], 3.6, 1]),
('control: unequal recovery',
([[0.8, 0.6], [0.3, 0.9]], [600, 400], [0.1, 0.5]),
[[4.8, 0.72, 1.2, 0.72], 5.001785, 0]),
('control: only cross contacts',
([[0.0, 2.0], [1.0, 0.0]], [300, 300], [0.25, 0.5]),
[[0.0, 2.0, 2.0, 0.0], 2.0, 0])],
[('control: asymmetric core group',
([[4.0, 0.2], [1.0, 0.3]], [100, 900], [0.3, 0.2]),
[[1.333333, 0.1, 3.0, 1.35], 1.889453, 1]),
('regression: decoupled equal groups tie',
([[1.0, 0.0], [0.0, 1.0]], [500, 500], [0.5, 0.5]),
[[1.0, 0.0, 0.0, 1.0], 1.0, 0]),
('regression: decoupled first dominant smaller group',
([[3.0, 0.0], [0.0, 0.5]], [300, 700], [0.5, 0.5]),
[[1.8, 0.0, 0.0, 0.7], 1.8, 0]),
('control: decoupled second dominant',
([[0.5, 0.0], [0.0, 3.0]], [400, 600], [0.5, 0.5]),
[[0.4, 0.0, 0.0, 3.6], 3.6, 1]),
('control: one-way coupling',
([[1.0, 0.0], [2.0, 1.5]], [200, 800], [0.2, 0.4]),
[[1.0, 0.0, 8.0, 3.0], 3.0, 1]),
('control: empty population', ([[1.0, 1.0], [1.0, 1.0]], [0, 0], [0.2, 0.2]), None),
('control: invalid gamma', ([[1.0, 1.0], [1.0, 1.0]], [10, 10], [0.0, 0.2]), None)]]
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 |
|---|---|---|---|
| control: children and adults | [[2.4, 0.75, 1.4, 3.5], 4.11297, 1] | [[2.4, 0.75, 1.4, 3.5], 4.11297, 1] | Passed |
| control: asymmetric core group | [[1.333333, 0.1, 3.0, 1.35], 1.889453, 1] | [[1.333333, 0.1, 3.0, 1.35], 1.889453, 1] | Passed |
| regression: decoupled equal groups tie | [[1.0, 0.0, 0.0, 1.0], 1.0, 1] | [[1.0, 0.0, 0.0, 1.0], 1.0, 0] | Failed |
| regression: decoupled first dominant smaller group | [[1.8, 0.0, 0.0, 0.7], 1.8, 0] | [[1.8, 0.0, 0.0, 0.7], 1.8, 0] | Passed |
| control: decoupled second dominant | [[0.4, 0.0, 0.0, 3.6], 3.6, 1] | [[0.4, 0.0, 0.0, 3.6], 3.6, 1] | Passed |
| control: one-way coupling | [[1.0, 0.0, 8.0, 3.0], 3.0, 1] | [[1.0, 0.0, 8.0, 3.0], 3.0, 1] | Passed |
| control: empty population | None | None | Passed |
SHA-256 / c541f8740370794cbdf8e6d15ce013edb506368c195366a65556894d03def001
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(contact, sizes, gamma):
total = sum(sizes)
if total <= 0 or min(gamma) <= 0:
return None
k = [[contact[i][j] * sizes[i] / total / gamma[j] for j in range(2)] for i in range(2)]
tr = k[0][0] + k[1][1]
det = k[0][0] * k[1][1] - k[0][1] * k[1][0]
disc = max(tr * tr - 4 * det, 0.0)
r0 = (tr + math.sqrt(disc)) / 2
if abs(k[0][1]) > 1e-12:
v = [k[0][1], r0 - k[0][0]]
elif abs(k[1][0]) > 1e-12:
v = [r0 - k[1][1], k[1][0]]
else:
v = [1.0, 0.0] if sizes[0] >= sizes[1] else [0.0, 1.0]
lead = 0 if abs(v[0]) >= abs(v[1]) else 1
return [[round(x, 6) for row in k for x in row], round(r0, 6), lead]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('control: children and adults',
([[2.0, 0.5], [0.5, 1.0]], [300, 700], [0.25, 0.2]),
[[2.4, 0.75, 1.4, 3.5], 4.11297, 1]),
('control: asymmetric core group',
([[4.0, 0.2], [1.0, 0.3]], [100, 900], [0.3, 0.2]),
[[1.333333, 0.1, 3.0, 1.35], 1.889453, 1]),
('regression: decoupled equal groups tie',
([[1.0, 0.0], [0.0, 1.0]], [500, 500], [0.5, 0.5]),
[[1.0, 0.0, 0.0, 1.0], 1.0, 0]),
('regression: decoupled first dominant smaller group',
([[3.0, 0.0], [0.0, 0.5]], [300, 700], [0.5, 0.5]),
[[1.8, 0.0, 0.0, 0.7], 1.8, 0]),
('control: decoupled second dominant',
([[0.5, 0.0], [0.0, 3.0]], [400, 600], [0.5, 0.5]),
[[0.4, 0.0, 0.0, 3.6], 3.6, 1]),
('control: one-way coupling',
([[1.0, 0.0], [2.0, 1.5]], [200, 800], [0.2, 0.4]),
[[1.0, 0.0, 8.0, 3.0], 3.0, 1]),
('control: empty population', ([[1.0, 1.0], [1.0, 1.0]], [0, 0], [0.2, 0.2]), None)],
[('regression: decoupled equal groups tie',
([[1.0, 0.0], [0.0, 1.0]], [500, 500], [0.5, 0.5]),
[[1.0, 0.0, 0.0, 1.0], 1.0, 0]),
('regression: decoupled first dominant smaller group',
([[3.0, 0.0], [0.0, 0.5]], [300, 700], [0.5, 0.5]),
[[1.8, 0.0, 0.0, 0.7], 1.8, 0]),
('control: decoupled second dominant',
([[0.5, 0.0], [0.0, 3.0]], [400, 600], [0.5, 0.5]),
[[0.4, 0.0, 0.0, 3.6], 3.6, 1]),
('control: one-way coupling',
([[1.0, 0.0], [2.0, 1.5]], [200, 800], [0.2, 0.4]),
[[1.0, 0.0, 8.0, 3.0], 3.0, 1]),
('control: empty population', ([[1.0, 1.0], [1.0, 1.0]], [0, 0], [0.2, 0.2]), None),
('control: invalid gamma', ([[1.0, 1.0], [1.0, 1.0]], [10, 10], [0.0, 0.2]), None),
('control: homogeneous mixing',
([[1.2, 1.2], [1.2, 1.2]], [250, 750], [0.4, 0.4]),
[[0.75, 0.75, 2.25, 2.25], 3.0, 1])],
[('regression: decoupled equal groups tie',
([[1.0, 0.0], [0.0, 1.0]], [500, 500], [0.5, 0.5]),
[[1.0, 0.0, 0.0, 1.0], 1.0, 0]),
('regression: decoupled first dominant smaller group',
([[3.0, 0.0], [0.0, 0.5]], [300, 700], [0.5, 0.5]),
[[1.8, 0.0, 0.0, 0.7], 1.8, 0]),
('control: empty population', ([[1.0, 1.0], [1.0, 1.0]], [0, 0], [0.2, 0.2]), None),
('control: invalid gamma', ([[1.0, 1.0], [1.0, 1.0]], [10, 10], [0.0, 0.2]), None),
('control: homogeneous mixing',
([[1.2, 1.2], [1.2, 1.2]], [250, 750], [0.4, 0.4]),
[[0.75, 0.75, 2.25, 2.25], 3.0, 1]),
('control: unequal recovery',
([[0.8, 0.6], [0.3, 0.9]], [600, 400], [0.1, 0.5]),
[[4.8, 0.72, 1.2, 0.72], 5.001785, 0]),
('control: only cross contacts',
([[0.0, 2.0], [1.0, 0.0]], [300, 300], [0.25, 0.5]),
[[0.0, 2.0, 2.0, 0.0], 2.0, 0])],
[('control: children and adults',
([[2.0, 0.5], [0.5, 1.0]], [300, 700], [0.25, 0.2]),
[[2.4, 0.75, 1.4, 3.5], 4.11297, 1]),
('control: asymmetric core group',
([[4.0, 0.2], [1.0, 0.3]], [100, 900], [0.3, 0.2]),
[[1.333333, 0.1, 3.0, 1.35], 1.889453, 1]),
('regression: decoupled equal groups tie',
([[1.0, 0.0], [0.0, 1.0]], [500, 500], [0.5, 0.5]),
[[1.0, 0.0, 0.0, 1.0], 1.0, 0]),
('regression: decoupled first dominant smaller group',
([[3.0, 0.0], [0.0, 0.5]], [300, 700], [0.5, 0.5]),
[[1.8, 0.0, 0.0, 0.7], 1.8, 0]),
('control: decoupled second dominant',
([[0.5, 0.0], [0.0, 3.0]], [400, 600], [0.5, 0.5]),
[[0.4, 0.0, 0.0, 3.6], 3.6, 1]),
('control: unequal recovery',
([[0.8, 0.6], [0.3, 0.9]], [600, 400], [0.1, 0.5]),
[[4.8, 0.72, 1.2, 0.72], 5.001785, 0]),
('control: only cross contacts',
([[0.0, 2.0], [1.0, 0.0]], [300, 300], [0.25, 0.5]),
[[0.0, 2.0, 2.0, 0.0], 2.0, 0])],
[('control: asymmetric core group',
([[4.0, 0.2], [1.0, 0.3]], [100, 900], [0.3, 0.2]),
[[1.333333, 0.1, 3.0, 1.35], 1.889453, 1]),
('regression: decoupled equal groups tie',
([[1.0, 0.0], [0.0, 1.0]], [500, 500], [0.5, 0.5]),
[[1.0, 0.0, 0.0, 1.0], 1.0, 0]),
('regression: decoupled first dominant smaller group',
([[3.0, 0.0], [0.0, 0.5]], [300, 700], [0.5, 0.5]),
[[1.8, 0.0, 0.0, 0.7], 1.8, 0]),
('control: decoupled second dominant',
([[0.5, 0.0], [0.0, 3.0]], [400, 600], [0.5, 0.5]),
[[0.4, 0.0, 0.0, 3.6], 3.6, 1]),
('control: one-way coupling',
([[1.0, 0.0], [2.0, 1.5]], [200, 800], [0.2, 0.4]),
[[1.0, 0.0, 8.0, 3.0], 3.0, 1]),
('control: empty population', ([[1.0, 1.0], [1.0, 1.0]], [0, 0], [0.2, 0.2]), None),
('control: invalid gamma', ([[1.0, 1.0], [1.0, 1.0]], [10, 10], [0.0, 0.2]), None)]]
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 |
|---|---|---|---|
| control: children and adults | [[2.4, 0.75, 1.4, 3.5], 4.11297, 1] | [[2.4, 0.75, 1.4, 3.5], 4.11297, 1] | Passed |
| control: asymmetric core group | [[1.333333, 0.1, 3.0, 1.35], 1.889453, 1] | [[1.333333, 0.1, 3.0, 1.35], 1.889453, 1] | Passed |
| regression: decoupled equal groups tie | [[1.0, 0.0, 0.0, 1.0], 1.0, 0] | [[1.0, 0.0, 0.0, 1.0], 1.0, 0] | Passed |
| regression: decoupled first dominant smaller group | [[1.8, 0.0, 0.0, 0.7], 1.8, 1] | [[1.8, 0.0, 0.0, 0.7], 1.8, 0] | Failed |
| control: decoupled second dominant | [[0.4, 0.0, 0.0, 3.6], 3.6, 1] | [[0.4, 0.0, 0.0, 3.6], 3.6, 1] | Passed |
| control: one-way coupling | [[1.0, 0.0, 8.0, 3.0], 3.0, 1] | [[1.0, 0.0, 8.0, 3.0], 3.0, 1] | Passed |
| control: empty population | None | None | Passed |
SHA-256 / a5c91e8cdb71ba83a653acdde9e1baddd5193ba086d13a2a95bbe5e814d4c740
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(contact, sizes, gamma):
total = sum(sizes)
if total <= 0 or min(gamma) <= 0:
return None
k = [[contact[i][j] * sizes[i] / total / gamma[j] for j in range(2)] for i in range(2)]
tr = k[0][0] + k[1][1]
det = k[0][0] * k[1][1] - k[0][1] * k[1][0]
disc = max(tr * tr - 4 * det, 0.0)
r0 = (tr + math.sqrt(disc)) / 2
if abs(k[0][1]) > 1e-12:
v = [k[0][1], r0 - k[0][0]]
elif abs(k[1][0]) > 1e-12:
v = [r0 - k[1][1], k[1][0]]
else:
v = [1.0, 0.0] if k[0][0] >= k[1][1] else [0.0, 1.0]
lead = 0 if abs(v[0]) >= abs(v[1]) else 1
return [[round(x, 6) for row in k for x in row], round(r0, 6), lead]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('control: children and adults',
([[2.0, 0.5], [0.5, 1.0]], [300, 700], [0.25, 0.2]),
[[2.4, 0.75, 1.4, 3.5], 4.11297, 1]),
('control: asymmetric core group',
([[4.0, 0.2], [1.0, 0.3]], [100, 900], [0.3, 0.2]),
[[1.333333, 0.1, 3.0, 1.35], 1.889453, 1]),
('regression: decoupled equal groups tie',
([[1.0, 0.0], [0.0, 1.0]], [500, 500], [0.5, 0.5]),
[[1.0, 0.0, 0.0, 1.0], 1.0, 0]),
('regression: decoupled first dominant smaller group',
([[3.0, 0.0], [0.0, 0.5]], [300, 700], [0.5, 0.5]),
[[1.8, 0.0, 0.0, 0.7], 1.8, 0]),
('control: decoupled second dominant',
([[0.5, 0.0], [0.0, 3.0]], [400, 600], [0.5, 0.5]),
[[0.4, 0.0, 0.0, 3.6], 3.6, 1]),
('control: one-way coupling',
([[1.0, 0.0], [2.0, 1.5]], [200, 800], [0.2, 0.4]),
[[1.0, 0.0, 8.0, 3.0], 3.0, 1]),
('control: empty population', ([[1.0, 1.0], [1.0, 1.0]], [0, 0], [0.2, 0.2]), None)],
[('regression: decoupled equal groups tie',
([[1.0, 0.0], [0.0, 1.0]], [500, 500], [0.5, 0.5]),
[[1.0, 0.0, 0.0, 1.0], 1.0, 0]),
('regression: decoupled first dominant smaller group',
([[3.0, 0.0], [0.0, 0.5]], [300, 700], [0.5, 0.5]),
[[1.8, 0.0, 0.0, 0.7], 1.8, 0]),
('control: decoupled second dominant',
([[0.5, 0.0], [0.0, 3.0]], [400, 600], [0.5, 0.5]),
[[0.4, 0.0, 0.0, 3.6], 3.6, 1]),
('control: one-way coupling',
([[1.0, 0.0], [2.0, 1.5]], [200, 800], [0.2, 0.4]),
[[1.0, 0.0, 8.0, 3.0], 3.0, 1]),
('control: empty population', ([[1.0, 1.0], [1.0, 1.0]], [0, 0], [0.2, 0.2]), None),
('control: invalid gamma', ([[1.0, 1.0], [1.0, 1.0]], [10, 10], [0.0, 0.2]), None),
('control: homogeneous mixing',
([[1.2, 1.2], [1.2, 1.2]], [250, 750], [0.4, 0.4]),
[[0.75, 0.75, 2.25, 2.25], 3.0, 1])],
[('regression: decoupled equal groups tie',
([[1.0, 0.0], [0.0, 1.0]], [500, 500], [0.5, 0.5]),
[[1.0, 0.0, 0.0, 1.0], 1.0, 0]),
('regression: decoupled first dominant smaller group',
([[3.0, 0.0], [0.0, 0.5]], [300, 700], [0.5, 0.5]),
[[1.8, 0.0, 0.0, 0.7], 1.8, 0]),
('control: empty population', ([[1.0, 1.0], [1.0, 1.0]], [0, 0], [0.2, 0.2]), None),
('control: invalid gamma', ([[1.0, 1.0], [1.0, 1.0]], [10, 10], [0.0, 0.2]), None),
('control: homogeneous mixing',
([[1.2, 1.2], [1.2, 1.2]], [250, 750], [0.4, 0.4]),
[[0.75, 0.75, 2.25, 2.25], 3.0, 1]),
('control: unequal recovery',
([[0.8, 0.6], [0.3, 0.9]], [600, 400], [0.1, 0.5]),
[[4.8, 0.72, 1.2, 0.72], 5.001785, 0]),
('control: only cross contacts',
([[0.0, 2.0], [1.0, 0.0]], [300, 300], [0.25, 0.5]),
[[0.0, 2.0, 2.0, 0.0], 2.0, 0])],
[('control: children and adults',
([[2.0, 0.5], [0.5, 1.0]], [300, 700], [0.25, 0.2]),
[[2.4, 0.75, 1.4, 3.5], 4.11297, 1]),
('control: asymmetric core group',
([[4.0, 0.2], [1.0, 0.3]], [100, 900], [0.3, 0.2]),
[[1.333333, 0.1, 3.0, 1.35], 1.889453, 1]),
('regression: decoupled equal groups tie',
([[1.0, 0.0], [0.0, 1.0]], [500, 500], [0.5, 0.5]),
[[1.0, 0.0, 0.0, 1.0], 1.0, 0]),
('regression: decoupled first dominant smaller group',
([[3.0, 0.0], [0.0, 0.5]], [300, 700], [0.5, 0.5]),
[[1.8, 0.0, 0.0, 0.7], 1.8, 0]),
('control: decoupled second dominant',
([[0.5, 0.0], [0.0, 3.0]], [400, 600], [0.5, 0.5]),
[[0.4, 0.0, 0.0, 3.6], 3.6, 1]),
('control: unequal recovery',
([[0.8, 0.6], [0.3, 0.9]], [600, 400], [0.1, 0.5]),
[[4.8, 0.72, 1.2, 0.72], 5.001785, 0]),
('control: only cross contacts',
([[0.0, 2.0], [1.0, 0.0]], [300, 300], [0.25, 0.5]),
[[0.0, 2.0, 2.0, 0.0], 2.0, 0])],
[('control: asymmetric core group',
([[4.0, 0.2], [1.0, 0.3]], [100, 900], [0.3, 0.2]),
[[1.333333, 0.1, 3.0, 1.35], 1.889453, 1]),
('regression: decoupled equal groups tie',
([[1.0, 0.0], [0.0, 1.0]], [500, 500], [0.5, 0.5]),
[[1.0, 0.0, 0.0, 1.0], 1.0, 0]),
('regression: decoupled first dominant smaller group',
([[3.0, 0.0], [0.0, 0.5]], [300, 700], [0.5, 0.5]),
[[1.8, 0.0, 0.0, 0.7], 1.8, 0]),
('control: decoupled second dominant',
([[0.5, 0.0], [0.0, 3.0]], [400, 600], [0.5, 0.5]),
[[0.4, 0.0, 0.0, 3.6], 3.6, 1]),
('control: one-way coupling',
([[1.0, 0.0], [2.0, 1.5]], [200, 800], [0.2, 0.4]),
[[1.0, 0.0, 8.0, 3.0], 3.0, 1]),
('control: empty population', ([[1.0, 1.0], [1.0, 1.0]], [0, 0], [0.2, 0.2]), None),
('control: invalid gamma', ([[1.0, 1.0], [1.0, 1.0]], [10, 10], [0.0, 0.2]), None)]]
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 |
|---|---|---|---|
| control: children and adults | [[2.4, 0.75, 1.4, 3.5], 4.11297, 1] | [[2.4, 0.75, 1.4, 3.5], 4.11297, 1] | Passed |
| control: asymmetric core group | [[1.333333, 0.1, 3.0, 1.35], 1.889453, 1] | [[1.333333, 0.1, 3.0, 1.35], 1.889453, 1] | Passed |
| regression: decoupled equal groups tie | [[1.0, 0.0, 0.0, 1.0], 1.0, 0] | [[1.0, 0.0, 0.0, 1.0], 1.0, 0] | Passed |
| regression: decoupled first dominant smaller group | [[1.8, 0.0, 0.0, 0.7], 1.8, 0] | [[1.8, 0.0, 0.0, 0.7], 1.8, 0] | Passed |
| control: decoupled second dominant | [[0.4, 0.0, 0.0, 3.6], 3.6, 1] | [[0.4, 0.0, 0.0, 3.6], 3.6, 1] | Passed |
| control: one-way coupling | [[1.0, 0.0, 8.0, 3.0], 3.0, 1] | [[1.0, 0.0, 8.0, 3.0], 3.0, 1] | Passed |
| control: empty population | None | None | Passed |
SHA-256 / c14c9fe639fc0b328d77938eb5c637fd101bc50e34403591edabe48cb48100bc
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 2026-09-29T14:47:30.129538+00:00.
Case digest / 096a778bd11033109ec624eeffdb4b61b2ef2c4cc4174709898be4f417d7aa8e