FA-65411 / Ecological population dynamics / Open access
Lotka-Volterra predator-prey Euler integration: conversion efficiency · case 01
Predators gain one individual per prey eaten regardless of conversion efficiency.
ROOT CAUSE
The predator numerical response uses the attack coefficient beta instead of delta.
THE FAILURE
The predator numerical response uses the attack coefficient beta instead of delta.
Unsuccessful approach: Dropping the predator density makes predator growth independent of predator numbers.
Case contract
dx = alpha*x - beta*x*y, dy = delta*x*y - gamma*y evaluated from the same start-of-step state; Euler update with each population floored at 0; return [path of [x,y] rounded 4 including start, coexistence equilibrium [gamma/delta, alpha/beta] rounded 4 or None when beta or delta is not positive].
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(prey0, pred0, alpha, beta, delta, gamma, dt, steps):
x, y = float(prey0), float(pred0)
path = [[round(x, 4), round(y, 4)]]
for _ in range(steps):
dx = alpha * x - beta * x * y
dy = beta * x * y - gamma * y
x = max(x + dx * dt, 0.0)
y = max(y + dy * dt, 0.0)
path.append([round(x, 4), round(y, 4)])
eq = [round(gamma / delta, 4), round(alpha / beta, 4)] if beta > 0 and delta > 0 else None
return [path, eq]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: hare and lynx',
(40, 9, 0.1, 0.02, 0.01, 0.1, 0.5, 6),
[[[40.0, 9.0],
[38.4, 10.35],
[36.3456, 11.8197],
[33.8669, 13.3767],
[31.03, 14.973],
[27.9354, 16.5474],
[24.7096, 18.0313]],
[10.0, 5.0]]),
('regression: large step overshoot',
(10, 50, 0.5, 0.1, 0.02, 0.4, 1.0, 4),
[[[10.0, 50.0], [0.0, 40.0], [0.0, 24.0], [0.0, 14.4], [0.0, 8.64]], [20.0, 5.0]]),
('regression: predators absent',
(20, 0, 0.3, 0.05, 0.02, 0.2, 0.5, 4),
[[[20.0, 0.0], [23.0, 0.0], [26.45, 0.0], [30.4175, 0.0], [34.9801, 0.0]], [10.0, 6.0]]),
('control: prey absent',
(0, 10, 0.3, 0.05, 0.02, 0.2, 0.5, 4),
[[[0.0, 10.0], [0.0, 9.0], [0.0, 8.1], [0.0, 7.29], [0.0, 6.561]], [10.0, 6.0]]),
('control: no interaction',
(30, 5, 0.2, 0.0, 0.0, 0.1, 1.0, 3),
[[[30.0, 5.0], [36.0, 4.5], [43.2, 4.05], [51.84, 3.645]], None]),
('regression: at equilibrium',
(10, 5, 0.5, 0.1, 0.02, 0.2, 0.25, 4),
[[[10.0, 5.0], [10.0, 5.0], [10.0, 5.0], [10.0, 5.0], [10.0, 5.0]], [10.0, 5.0]]),
('regression: fine steps',
(15, 4, 0.8, 0.1, 0.05, 0.6, 0.1, 8),
[[[15.0, 4.0],
[15.6, 4.06],
[16.2146, 4.1331],
[16.8416, 4.2202],
[17.4782, 4.3223],
[18.121, 4.4407],
[18.766, 4.5766],
[19.4084, 4.7315],
[20.0428, 4.9067]],
[12.0, 8.0]])],
[('regression: hare and lynx',
(40, 9, 0.1, 0.02, 0.01, 0.1, 0.5, 6),
[[[40.0, 9.0],
[38.4, 10.35],
[36.3456, 11.8197],
[33.8669, 13.3767],
[31.03, 14.973],
[27.9354, 16.5474],
[24.7096, 18.0313]],
[10.0, 5.0]]),
('regression: large step overshoot',
(10, 50, 0.5, 0.1, 0.02, 0.4, 1.0, 4),
[[[10.0, 50.0], [0.0, 40.0], [0.0, 24.0], [0.0, 14.4], [0.0, 8.64]], [20.0, 5.0]]),
('control: prey absent',
(0, 10, 0.3, 0.05, 0.02, 0.2, 0.5, 4),
[[[0.0, 10.0], [0.0, 9.0], [0.0, 8.1], [0.0, 7.29], [0.0, 6.561]], [10.0, 6.0]]),
('control: no interaction',
(30, 5, 0.2, 0.0, 0.0, 0.1, 1.0, 3),
[[[30.0, 5.0], [36.0, 4.5], [43.2, 4.05], [51.84, 3.645]], None]),
('regression: at equilibrium',
(10, 5, 0.5, 0.1, 0.02, 0.2, 0.25, 4),
[[[10.0, 5.0], [10.0, 5.0], [10.0, 5.0], [10.0, 5.0], [10.0, 5.0]], [10.0, 5.0]]),
('regression: fine steps',
(15, 4, 0.8, 0.1, 0.05, 0.6, 0.1, 8),
[[[15.0, 4.0],
[15.6, 4.06],
[16.2146, 4.1331],
[16.8416, 4.2202],
[17.4782, 4.3223],
[18.121, 4.4407],
[18.766, 4.5766],
[19.4084, 4.7315],
[20.0428, 4.9067]],
[12.0, 8.0]]),
('regression: predator crash',
(5, 30, 0.4, 0.2, 0.01, 0.9, 1.0, 3),
[[[5.0, 30.0], [0.0, 4.5], [0.0, 0.45], [0.0, 0.045]], [90.0, 2.0]])],
[('regression: hare and lynx',
(40, 9, 0.1, 0.02, 0.01, 0.1, 0.5, 6),
[[[40.0, 9.0],
[38.4, 10.35],
[36.3456, 11.8197],
[33.8669, 13.3767],
[31.03, 14.973],
[27.9354, 16.5474],
[24.7096, 18.0313]],
[10.0, 5.0]]),
('regression: large step overshoot',
(10, 50, 0.5, 0.1, 0.02, 0.4, 1.0, 4),
[[[10.0, 50.0], [0.0, 40.0], [0.0, 24.0], [0.0, 14.4], [0.0, 8.64]], [20.0, 5.0]]),
('regression: predators absent',
(20, 0, 0.3, 0.05, 0.02, 0.2, 0.5, 4),
[[[20.0, 0.0], [23.0, 0.0], [26.45, 0.0], [30.4175, 0.0], [34.9801, 0.0]], [10.0, 6.0]]),
('control: prey absent',
(0, 10, 0.3, 0.05, 0.02, 0.2, 0.5, 4),
[[[0.0, 10.0], [0.0, 9.0], [0.0, 8.1], [0.0, 7.29], [0.0, 6.561]], [10.0, 6.0]]),
('control: no interaction',
(30, 5, 0.2, 0.0, 0.0, 0.1, 1.0, 3),
[[[30.0, 5.0], [36.0, 4.5], [43.2, 4.05], [51.84, 3.645]], None]),
('regression: fine steps',
(15, 4, 0.8, 0.1, 0.05, 0.6, 0.1, 8),
[[[15.0, 4.0],
[15.6, 4.06],
[16.2146, 4.1331],
[16.8416, 4.2202],
[17.4782, 4.3223],
[18.121, 4.4407],
[18.766, 4.5766],
[19.4084, 4.7315],
[20.0428, 4.9067]],
[12.0, 8.0]]),
('regression: predator crash',
(5, 30, 0.4, 0.2, 0.01, 0.9, 1.0, 3),
[[[5.0, 30.0], [0.0, 4.5], [0.0, 0.45], [0.0, 0.045]], [90.0, 2.0]])],
[('regression: large step overshoot',
(10, 50, 0.5, 0.1, 0.02, 0.4, 1.0, 4),
[[[10.0, 50.0], [0.0, 40.0], [0.0, 24.0], [0.0, 14.4], [0.0, 8.64]], [20.0, 5.0]]),
('regression: predators absent',
(20, 0, 0.3, 0.05, 0.02, 0.2, 0.5, 4),
[[[20.0, 0.0], [23.0, 0.0], [26.45, 0.0], [30.4175, 0.0], [34.9801, 0.0]], [10.0, 6.0]]),
('control: prey absent',
(0, 10, 0.3, 0.05, 0.02, 0.2, 0.5, 4),
[[[0.0, 10.0], [0.0, 9.0], [0.0, 8.1], [0.0, 7.29], [0.0, 6.561]], [10.0, 6.0]]),
('control: no interaction',
(30, 5, 0.2, 0.0, 0.0, 0.1, 1.0, 3),
[[[30.0, 5.0], [36.0, 4.5], [43.2, 4.05], [51.84, 3.645]], None]),
('regression: at equilibrium',
(10, 5, 0.5, 0.1, 0.02, 0.2, 0.25, 4),
[[[10.0, 5.0], [10.0, 5.0], [10.0, 5.0], [10.0, 5.0], [10.0, 5.0]], [10.0, 5.0]]),
('regression: fine steps',
(15, 4, 0.8, 0.1, 0.05, 0.6, 0.1, 8),
[[[15.0, 4.0],
[15.6, 4.06],
[16.2146, 4.1331],
[16.8416, 4.2202],
[17.4782, 4.3223],
[18.121, 4.4407],
[18.766, 4.5766],
[19.4084, 4.7315],
[20.0428, 4.9067]],
[12.0, 8.0]]),
('regression: predator crash',
(5, 30, 0.4, 0.2, 0.01, 0.9, 1.0, 3),
[[[5.0, 30.0], [0.0, 4.5], [0.0, 0.45], [0.0, 0.045]], [90.0, 2.0]])],
[('regression: hare and lynx',
(40, 9, 0.1, 0.02, 0.01, 0.1, 0.5, 6),
[[[40.0, 9.0],
[38.4, 10.35],
[36.3456, 11.8197],
[33.8669, 13.3767],
[31.03, 14.973],
[27.9354, 16.5474],
[24.7096, 18.0313]],
[10.0, 5.0]]),
('regression: large step overshoot',
(10, 50, 0.5, 0.1, 0.02, 0.4, 1.0, 4),
[[[10.0, 50.0], [0.0, 40.0], [0.0, 24.0], [0.0, 14.4], [0.0, 8.64]], [20.0, 5.0]]),
('control: prey absent',
(0, 10, 0.3, 0.05, 0.02, 0.2, 0.5, 4),
[[[0.0, 10.0], [0.0, 9.0], [0.0, 8.1], [0.0, 7.29], [0.0, 6.561]], [10.0, 6.0]]),
('control: no interaction',
(30, 5, 0.2, 0.0, 0.0, 0.1, 1.0, 3),
[[[30.0, 5.0], [36.0, 4.5], [43.2, 4.05], [51.84, 3.645]], None]),
('regression: at equilibrium',
(10, 5, 0.5, 0.1, 0.02, 0.2, 0.25, 4),
[[[10.0, 5.0], [10.0, 5.0], [10.0, 5.0], [10.0, 5.0], [10.0, 5.0]], [10.0, 5.0]]),
('regression: fine steps',
(15, 4, 0.8, 0.1, 0.05, 0.6, 0.1, 8),
[[[15.0, 4.0],
[15.6, 4.06],
[16.2146, 4.1331],
[16.8416, 4.2202],
[17.4782, 4.3223],
[18.121, 4.4407],
[18.766, 4.5766],
[19.4084, 4.7315],
[20.0428, 4.9067]],
[12.0, 8.0]]),
('regression: predator crash',
(5, 30, 0.4, 0.2, 0.01, 0.9, 1.0, 3),
[[[5.0, 30.0], [0.0, 4.5], [0.0, 0.45], [0.0, 0.045]], [90.0, 2.0]])]]
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: hare and lynx | [[[40.0, 9.0], [38.4, 12.15], [35.6544, 16.2081], [31.6582, 21.1766], [26.537, 26.8219], [20.7461, 32.5985], [15.0205, 37.7315]], [10.0, 5.0]] | [[[40.0, 9.0], [38.4, 10.35], [36.3456, 11.8197], [33.8669, 13.3767], [31.03, 14.973], [27.9354, 16.5474], [24.7096, 18.0313]], [10.0, 5.0]] | Failed |
| regression: large step overshoot | [[[10.0, 50.0], [0.0, 80.0], [0.0, 48.0], [0.0, 28.8], [0.0, 17.28]], [20.0, 5.0]] | [[[10.0, 50.0], [0.0, 40.0], [0.0, 24.0], [0.0, 14.4], [0.0, 8.64]], [20.0, 5.0]] | Failed |
| regression: predators absent | [[[20.0, 0.0], [23.0, 0.0], [26.45, 0.0], [30.4175, 0.0], [34.9801, 0.0]], [10.0, 6.0]] | [[[20.0, 0.0], [23.0, 0.0], [26.45, 0.0], [30.4175, 0.0], [34.9801, 0.0]], [10.0, 6.0]] | Passed |
| control: prey absent | [[[0.0, 10.0], [0.0, 9.0], [0.0, 8.1], [0.0, 7.29], [0.0, 6.561]], [10.0, 6.0]] | [[[0.0, 10.0], [0.0, 9.0], [0.0, 8.1], [0.0, 7.29], [0.0, 6.561]], [10.0, 6.0]] | Passed |
| control: no interaction | [[[30.0, 5.0], [36.0, 4.5], [43.2, 4.05], [51.84, 3.645]], None] | [[[30.0, 5.0], [36.0, 4.5], [43.2, 4.05], [51.84, 3.645]], None] | Passed |
| regression: at equilibrium | [[[10.0, 5.0], [10.0, 6.0], [9.75, 7.2], [9.2137, 8.595], [8.3857, 10.1451]], [10.0, 5.0]] | [[[10.0, 5.0], [10.0, 5.0], [10.0, 5.0], [10.0, 5.0], [10.0, 5.0]], [10.0, 5.0]] | Failed |
| regression: fine steps | [[[15.0, 4.0], [15.6, 4.36], [16.1678, 4.7786], [16.6887, 5.2644], [17.1452, 5.8271], [17.5177, 6.4766], [17.7846, 7.2225], [17.9229, 8.0737], [17.9097, 9.0363]], [12.0, 8.0]] | [[[15.0, 4.0], [15.6, 4.06], [16.2146, 4.1331], [16.8416, 4.2202], [17.4782, 4.3223], [18.121, 4.4407], [18.766, 4.5766], [19.4084, 4.7315], [20.0428, 4.9067]], [12.0, 8.0]] | Failed |
SHA-256 / 3248e6bd09f96df7990c3196084dd4b35c4f826732ee72f668562eed021eb4c2
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(prey0, pred0, alpha, beta, delta, gamma, dt, steps):
x, y = float(prey0), float(pred0)
path = [[round(x, 4), round(y, 4)]]
for _ in range(steps):
dx = alpha * x - beta * x * y
dy = delta * x - gamma * y
x = max(x + dx * dt, 0.0)
y = max(y + dy * dt, 0.0)
path.append([round(x, 4), round(y, 4)])
eq = [round(gamma / delta, 4), round(alpha / beta, 4)] if beta > 0 and delta > 0 else None
return [path, eq]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: hare and lynx',
(40, 9, 0.1, 0.02, 0.01, 0.1, 0.5, 6),
[[[40.0, 9.0],
[38.4, 10.35],
[36.3456, 11.8197],
[33.8669, 13.3767],
[31.03, 14.973],
[27.9354, 16.5474],
[24.7096, 18.0313]],
[10.0, 5.0]]),
('regression: large step overshoot',
(10, 50, 0.5, 0.1, 0.02, 0.4, 1.0, 4),
[[[10.0, 50.0], [0.0, 40.0], [0.0, 24.0], [0.0, 14.4], [0.0, 8.64]], [20.0, 5.0]]),
('regression: predators absent',
(20, 0, 0.3, 0.05, 0.02, 0.2, 0.5, 4),
[[[20.0, 0.0], [23.0, 0.0], [26.45, 0.0], [30.4175, 0.0], [34.9801, 0.0]], [10.0, 6.0]]),
('control: prey absent',
(0, 10, 0.3, 0.05, 0.02, 0.2, 0.5, 4),
[[[0.0, 10.0], [0.0, 9.0], [0.0, 8.1], [0.0, 7.29], [0.0, 6.561]], [10.0, 6.0]]),
('control: no interaction',
(30, 5, 0.2, 0.0, 0.0, 0.1, 1.0, 3),
[[[30.0, 5.0], [36.0, 4.5], [43.2, 4.05], [51.84, 3.645]], None]),
('regression: at equilibrium',
(10, 5, 0.5, 0.1, 0.02, 0.2, 0.25, 4),
[[[10.0, 5.0], [10.0, 5.0], [10.0, 5.0], [10.0, 5.0], [10.0, 5.0]], [10.0, 5.0]]),
('regression: fine steps',
(15, 4, 0.8, 0.1, 0.05, 0.6, 0.1, 8),
[[[15.0, 4.0],
[15.6, 4.06],
[16.2146, 4.1331],
[16.8416, 4.2202],
[17.4782, 4.3223],
[18.121, 4.4407],
[18.766, 4.5766],
[19.4084, 4.7315],
[20.0428, 4.9067]],
[12.0, 8.0]])],
[('regression: hare and lynx',
(40, 9, 0.1, 0.02, 0.01, 0.1, 0.5, 6),
[[[40.0, 9.0],
[38.4, 10.35],
[36.3456, 11.8197],
[33.8669, 13.3767],
[31.03, 14.973],
[27.9354, 16.5474],
[24.7096, 18.0313]],
[10.0, 5.0]]),
('regression: large step overshoot',
(10, 50, 0.5, 0.1, 0.02, 0.4, 1.0, 4),
[[[10.0, 50.0], [0.0, 40.0], [0.0, 24.0], [0.0, 14.4], [0.0, 8.64]], [20.0, 5.0]]),
('control: prey absent',
(0, 10, 0.3, 0.05, 0.02, 0.2, 0.5, 4),
[[[0.0, 10.0], [0.0, 9.0], [0.0, 8.1], [0.0, 7.29], [0.0, 6.561]], [10.0, 6.0]]),
('control: no interaction',
(30, 5, 0.2, 0.0, 0.0, 0.1, 1.0, 3),
[[[30.0, 5.0], [36.0, 4.5], [43.2, 4.05], [51.84, 3.645]], None]),
('regression: at equilibrium',
(10, 5, 0.5, 0.1, 0.02, 0.2, 0.25, 4),
[[[10.0, 5.0], [10.0, 5.0], [10.0, 5.0], [10.0, 5.0], [10.0, 5.0]], [10.0, 5.0]]),
('regression: fine steps',
(15, 4, 0.8, 0.1, 0.05, 0.6, 0.1, 8),
[[[15.0, 4.0],
[15.6, 4.06],
[16.2146, 4.1331],
[16.8416, 4.2202],
[17.4782, 4.3223],
[18.121, 4.4407],
[18.766, 4.5766],
[19.4084, 4.7315],
[20.0428, 4.9067]],
[12.0, 8.0]]),
('regression: predator crash',
(5, 30, 0.4, 0.2, 0.01, 0.9, 1.0, 3),
[[[5.0, 30.0], [0.0, 4.5], [0.0, 0.45], [0.0, 0.045]], [90.0, 2.0]])],
[('regression: hare and lynx',
(40, 9, 0.1, 0.02, 0.01, 0.1, 0.5, 6),
[[[40.0, 9.0],
[38.4, 10.35],
[36.3456, 11.8197],
[33.8669, 13.3767],
[31.03, 14.973],
[27.9354, 16.5474],
[24.7096, 18.0313]],
[10.0, 5.0]]),
('regression: large step overshoot',
(10, 50, 0.5, 0.1, 0.02, 0.4, 1.0, 4),
[[[10.0, 50.0], [0.0, 40.0], [0.0, 24.0], [0.0, 14.4], [0.0, 8.64]], [20.0, 5.0]]),
('regression: predators absent',
(20, 0, 0.3, 0.05, 0.02, 0.2, 0.5, 4),
[[[20.0, 0.0], [23.0, 0.0], [26.45, 0.0], [30.4175, 0.0], [34.9801, 0.0]], [10.0, 6.0]]),
('control: prey absent',
(0, 10, 0.3, 0.05, 0.02, 0.2, 0.5, 4),
[[[0.0, 10.0], [0.0, 9.0], [0.0, 8.1], [0.0, 7.29], [0.0, 6.561]], [10.0, 6.0]]),
('control: no interaction',
(30, 5, 0.2, 0.0, 0.0, 0.1, 1.0, 3),
[[[30.0, 5.0], [36.0, 4.5], [43.2, 4.05], [51.84, 3.645]], None]),
('regression: fine steps',
(15, 4, 0.8, 0.1, 0.05, 0.6, 0.1, 8),
[[[15.0, 4.0],
[15.6, 4.06],
[16.2146, 4.1331],
[16.8416, 4.2202],
[17.4782, 4.3223],
[18.121, 4.4407],
[18.766, 4.5766],
[19.4084, 4.7315],
[20.0428, 4.9067]],
[12.0, 8.0]]),
('regression: predator crash',
(5, 30, 0.4, 0.2, 0.01, 0.9, 1.0, 3),
[[[5.0, 30.0], [0.0, 4.5], [0.0, 0.45], [0.0, 0.045]], [90.0, 2.0]])],
[('regression: large step overshoot',
(10, 50, 0.5, 0.1, 0.02, 0.4, 1.0, 4),
[[[10.0, 50.0], [0.0, 40.0], [0.0, 24.0], [0.0, 14.4], [0.0, 8.64]], [20.0, 5.0]]),
('regression: predators absent',
(20, 0, 0.3, 0.05, 0.02, 0.2, 0.5, 4),
[[[20.0, 0.0], [23.0, 0.0], [26.45, 0.0], [30.4175, 0.0], [34.9801, 0.0]], [10.0, 6.0]]),
('control: prey absent',
(0, 10, 0.3, 0.05, 0.02, 0.2, 0.5, 4),
[[[0.0, 10.0], [0.0, 9.0], [0.0, 8.1], [0.0, 7.29], [0.0, 6.561]], [10.0, 6.0]]),
('control: no interaction',
(30, 5, 0.2, 0.0, 0.0, 0.1, 1.0, 3),
[[[30.0, 5.0], [36.0, 4.5], [43.2, 4.05], [51.84, 3.645]], None]),
('regression: at equilibrium',
(10, 5, 0.5, 0.1, 0.02, 0.2, 0.25, 4),
[[[10.0, 5.0], [10.0, 5.0], [10.0, 5.0], [10.0, 5.0], [10.0, 5.0]], [10.0, 5.0]]),
('regression: fine steps',
(15, 4, 0.8, 0.1, 0.05, 0.6, 0.1, 8),
[[[15.0, 4.0],
[15.6, 4.06],
[16.2146, 4.1331],
[16.8416, 4.2202],
[17.4782, 4.3223],
[18.121, 4.4407],
[18.766, 4.5766],
[19.4084, 4.7315],
[20.0428, 4.9067]],
[12.0, 8.0]]),
('regression: predator crash',
(5, 30, 0.4, 0.2, 0.01, 0.9, 1.0, 3),
[[[5.0, 30.0], [0.0, 4.5], [0.0, 0.45], [0.0, 0.045]], [90.0, 2.0]])],
[('regression: hare and lynx',
(40, 9, 0.1, 0.02, 0.01, 0.1, 0.5, 6),
[[[40.0, 9.0],
[38.4, 10.35],
[36.3456, 11.8197],
[33.8669, 13.3767],
[31.03, 14.973],
[27.9354, 16.5474],
[24.7096, 18.0313]],
[10.0, 5.0]]),
('regression: large step overshoot',
(10, 50, 0.5, 0.1, 0.02, 0.4, 1.0, 4),
[[[10.0, 50.0], [0.0, 40.0], [0.0, 24.0], [0.0, 14.4], [0.0, 8.64]], [20.0, 5.0]]),
('control: prey absent',
(0, 10, 0.3, 0.05, 0.02, 0.2, 0.5, 4),
[[[0.0, 10.0], [0.0, 9.0], [0.0, 8.1], [0.0, 7.29], [0.0, 6.561]], [10.0, 6.0]]),
('control: no interaction',
(30, 5, 0.2, 0.0, 0.0, 0.1, 1.0, 3),
[[[30.0, 5.0], [36.0, 4.5], [43.2, 4.05], [51.84, 3.645]], None]),
('regression: at equilibrium',
(10, 5, 0.5, 0.1, 0.02, 0.2, 0.25, 4),
[[[10.0, 5.0], [10.0, 5.0], [10.0, 5.0], [10.0, 5.0], [10.0, 5.0]], [10.0, 5.0]]),
('regression: fine steps',
(15, 4, 0.8, 0.1, 0.05, 0.6, 0.1, 8),
[[[15.0, 4.0],
[15.6, 4.06],
[16.2146, 4.1331],
[16.8416, 4.2202],
[17.4782, 4.3223],
[18.121, 4.4407],
[18.766, 4.5766],
[19.4084, 4.7315],
[20.0428, 4.9067]],
[12.0, 8.0]]),
('regression: predator crash',
(5, 30, 0.4, 0.2, 0.01, 0.9, 1.0, 3),
[[[5.0, 30.0], [0.0, 4.5], [0.0, 0.45], [0.0, 0.045]], [90.0, 2.0]])]]
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: hare and lynx | [[[40.0, 9.0], [38.4, 8.75], [36.96, 8.5045], [35.6647, 8.2641], [34.5006, 8.0292], [33.4555, 7.8002], [32.5187, 7.5775]], [10.0, 5.0]] | [[[40.0, 9.0], [38.4, 10.35], [36.3456, 11.8197], [33.8669, 13.3767], [31.03, 14.973], [27.9354, 16.5474], [24.7096, 18.0313]], [10.0, 5.0]] | Failed |
| regression: large step overshoot | [[[10.0, 50.0], [0.0, 30.2], [0.0, 18.12], [0.0, 10.872], [0.0, 6.5232]], [20.0, 5.0]] | [[[10.0, 50.0], [0.0, 40.0], [0.0, 24.0], [0.0, 14.4], [0.0, 8.64]], [20.0, 5.0]] | Failed |
| regression: predators absent | [[[20.0, 0.0], [23.0, 0.2], [26.335, 0.41], [30.0153, 0.6324], [34.0431, 0.8693]], [10.0, 6.0]] | [[[20.0, 0.0], [23.0, 0.0], [26.45, 0.0], [30.4175, 0.0], [34.9801, 0.0]], [10.0, 6.0]] | Failed |
| control: prey absent | [[[0.0, 10.0], [0.0, 9.0], [0.0, 8.1], [0.0, 7.29], [0.0, 6.561]], [10.0, 6.0]] | [[[0.0, 10.0], [0.0, 9.0], [0.0, 8.1], [0.0, 7.29], [0.0, 6.561]], [10.0, 6.0]] | Passed |
| control: no interaction | [[[30.0, 5.0], [36.0, 4.5], [43.2, 4.05], [51.84, 3.645]], None] | [[[30.0, 5.0], [36.0, 4.5], [43.2, 4.05], [51.84, 3.645]], None] | Passed |
| regression: at equilibrium | [[[10.0, 5.0], [10.0, 4.8], [10.05, 4.61], [10.148, 4.4297], [10.2927, 4.259]], [10.0, 5.0]] | [[[10.0, 5.0], [10.0, 5.0], [10.0, 5.0], [10.0, 5.0], [10.0, 5.0]], [10.0, 5.0]] | Failed |
| regression: fine steps | [[[15.0, 4.0], [15.6, 3.835], [16.2497, 3.6829], [16.9513, 3.5432], [17.7067, 3.4153], [18.5185, 3.299], [19.3891, 3.1936], [20.321, 3.0989], [21.317, 3.0146]], [12.0, 8.0]] | [[[15.0, 4.0], [15.6, 4.06], [16.2146, 4.1331], [16.8416, 4.2202], [17.4782, 4.3223], [18.121, 4.4407], [18.766, 4.5766], [19.4084, 4.7315], [20.0428, 4.9067]], [12.0, 8.0]] | Failed |
SHA-256 / 5209e6326ff7d9d30d56830438737d152454c9f7d064ec6146d9b000ea35b386
HELD IN THE MEMBER ARCHIVE
The verified repair and its recorded checks are member-only.
This mechanism has 7 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.
Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.
Member access is invitation-based. Sign in with your invited account to inspect the repair.
Sign in to the archive ↗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 2026-09-29T14:47:33.869782+00:00.
Case digest / a828f2beba953a0e4f7d325e106b93ce4b0e799e43b1e1536e38b486575780bf