FA-65356 / Ecological population dynamics / Open access
Discrete logistic population with constant quota harvest: trajectory seed · case 01
Trajectories are one year shorter and lose the starting stock.
ROOT CAUSE
The initial stock is not recorded as year 0.
VERIFIED REPAIR
Restore the trajectory seed rule: `traj = [round(n, 4)]`.
Unsuccessful approach: Recording the post-harvest stock misreports year 0.
Case contract
Each year the quota is removed first; if the stock is then <= 0 the trajectory records 0.0 and stops; otherwise the survivors grow by r*N*(1-N/K); the trajectory starts with the unharvested N0; values rounded to 4; None for K<=0 or negative N0.
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(n0, r, k, harvest, years):
if k <= 0 or n0 < 0:
return None
n = float(n0)
traj = []
for _ in range(years):
n -= harvest
if n <= 0:
traj.append(0.0)
break
n = n + r * n * (1 - n / k)
traj.append(round(n, 4))
return traj
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: cod-like stock light quota',
(500, 0.4, 1000, 20, 8),
[500.0, 579.84, 658.4077, 730.745, 792.9796, 843.1725, 881.3963, 909.1534, 928.5772]),
('regression: quota exceeds growth collapse',
(300, 0.3, 1000, 120, 10),
[300.0, 224.28, 132.3017, 15.9468, 0.0]),
('regression: quota equals stock exactly', (50, 0.5, 400, 50, 5), [50.0, 0.0]),
('regression: no harvest recovery',
(100, 0.6, 800, 0, 7),
[100.0, 152.5, 226.5578, 323.9962, 439.6637, 558.4838, 659.646, 729.084]),
('regression: above carrying capacity',
(1200, 0.5, 1000, 10, 6),
[1200.0, 1076.95, 1031.2338, 1010.3915, 1000.1957, 995.0498, 992.4131]),
('control: invalid carrying capacity', (100, 0.5, 0, 10, 5), None),
('regression: zero years', (100, 0.5, 500, 10, 0), [100.0])],
[('regression: cod-like stock light quota',
(500, 0.4, 1000, 20, 8),
[500.0, 579.84, 658.4077, 730.745, 792.9796, 843.1725, 881.3963, 909.1534, 928.5772]),
('regression: no harvest recovery',
(100, 0.6, 800, 0, 7),
[100.0, 152.5, 226.5578, 323.9962, 439.6637, 558.4838, 659.646, 729.084]),
('regression: above carrying capacity',
(1200, 0.5, 1000, 10, 6),
[1200.0, 1076.95, 1031.2338, 1010.3915, 1000.1957, 995.0498, 992.4131]),
('control: invalid carrying capacity', (100, 0.5, 0, 10, 5), None),
('regression: zero years', (100, 0.5, 500, 10, 0), [100.0]),
('regression: slow grower',
(800, 0.1, 1000, 15, 9),
[800.0, 801.8775, 803.6476, 805.3159, 806.8876, 808.3677, 809.7613, 811.0728, 812.3069, 813.4678]),
('regression: two-year collapse', (60, 0.2, 500, 40, 6), [60.0, 23.84, 0.0])],
[('regression: cod-like stock light quota',
(500, 0.4, 1000, 20, 8),
[500.0, 579.84, 658.4077, 730.745, 792.9796, 843.1725, 881.3963, 909.1534, 928.5772]),
('regression: quota exceeds growth collapse',
(300, 0.3, 1000, 120, 10),
[300.0, 224.28, 132.3017, 15.9468, 0.0]),
('regression: quota equals stock exactly', (50, 0.5, 400, 50, 5), [50.0, 0.0]),
('control: invalid carrying capacity', (100, 0.5, 0, 10, 5), None),
('regression: zero years', (100, 0.5, 500, 10, 0), [100.0]),
('regression: slow grower',
(800, 0.1, 1000, 15, 9),
[800.0, 801.8775, 803.6476, 805.3159, 806.8876, 808.3677, 809.7613, 811.0728, 812.3069, 813.4678]),
('regression: two-year collapse', (60, 0.2, 500, 40, 6), [60.0, 23.84, 0.0])],
[('regression: cod-like stock light quota',
(500, 0.4, 1000, 20, 8),
[500.0, 579.84, 658.4077, 730.745, 792.9796, 843.1725, 881.3963, 909.1534, 928.5772]),
('regression: quota exceeds growth collapse',
(300, 0.3, 1000, 120, 10),
[300.0, 224.28, 132.3017, 15.9468, 0.0]),
('regression: quota equals stock exactly', (50, 0.5, 400, 50, 5), [50.0, 0.0]),
('regression: no harvest recovery',
(100, 0.6, 800, 0, 7),
[100.0, 152.5, 226.5578, 323.9962, 439.6637, 558.4838, 659.646, 729.084]),
('regression: above carrying capacity',
(1200, 0.5, 1000, 10, 6),
[1200.0, 1076.95, 1031.2338, 1010.3915, 1000.1957, 995.0498, 992.4131]),
('control: invalid carrying capacity', (100, 0.5, 0, 10, 5), None),
('regression: zero years', (100, 0.5, 500, 10, 0), [100.0])],
[('regression: cod-like stock light quota',
(500, 0.4, 1000, 20, 8),
[500.0, 579.84, 658.4077, 730.745, 792.9796, 843.1725, 881.3963, 909.1534, 928.5772]),
('regression: no harvest recovery',
(100, 0.6, 800, 0, 7),
[100.0, 152.5, 226.5578, 323.9962, 439.6637, 558.4838, 659.646, 729.084]),
('regression: above carrying capacity',
(1200, 0.5, 1000, 10, 6),
[1200.0, 1076.95, 1031.2338, 1010.3915, 1000.1957, 995.0498, 992.4131]),
('control: invalid carrying capacity', (100, 0.5, 0, 10, 5), None),
('regression: zero years', (100, 0.5, 500, 10, 0), [100.0]),
('regression: slow grower',
(800, 0.1, 1000, 15, 9),
[800.0, 801.8775, 803.6476, 805.3159, 806.8876, 808.3677, 809.7613, 811.0728, 812.3069, 813.4678]),
('regression: two-year collapse', (60, 0.2, 500, 40, 6), [60.0, 23.84, 0.0])]]
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: cod-like stock light quota | [579.84, 658.4077, 730.745, 792.9796, 843.1725, 881.3963, 909.1534, 928.5772] | [500.0, 579.84, 658.4077, 730.745, 792.9796, 843.1725, 881.3963, 909.1534, 928.5772] | Failed |
| regression: quota exceeds growth collapse | [224.28, 132.3017, 15.9468, 0.0] | [300.0, 224.28, 132.3017, 15.9468, 0.0] | Failed |
| regression: quota equals stock exactly | [0.0] | [50.0, 0.0] | Failed |
| regression: no harvest recovery | [152.5, 226.5578, 323.9962, 439.6637, 558.4838, 659.646, 729.084] | [100.0, 152.5, 226.5578, 323.9962, 439.6637, 558.4838, 659.646, 729.084] | Failed |
| regression: above carrying capacity | [1076.95, 1031.2338, 1010.3915, 1000.1957, 995.0498, 992.4131] | [1200.0, 1076.95, 1031.2338, 1010.3915, 1000.1957, 995.0498, 992.4131] | Failed |
| control: invalid carrying capacity | None | None | Passed |
| regression: zero years | [] | [100.0] | Failed |
SHA-256 / 829746783c26fa555cb2811e9e0182a450e18a91c1d1d52799598e05be1eeb6b
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(n0, r, k, harvest, years):
if k <= 0 or n0 < 0:
return None
n = float(n0)
traj = [round(n - harvest, 4)]
for _ in range(years):
n -= harvest
if n <= 0:
traj.append(0.0)
break
n = n + r * n * (1 - n / k)
traj.append(round(n, 4))
return traj
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: cod-like stock light quota',
(500, 0.4, 1000, 20, 8),
[500.0, 579.84, 658.4077, 730.745, 792.9796, 843.1725, 881.3963, 909.1534, 928.5772]),
('regression: quota exceeds growth collapse',
(300, 0.3, 1000, 120, 10),
[300.0, 224.28, 132.3017, 15.9468, 0.0]),
('regression: quota equals stock exactly', (50, 0.5, 400, 50, 5), [50.0, 0.0]),
('regression: no harvest recovery',
(100, 0.6, 800, 0, 7),
[100.0, 152.5, 226.5578, 323.9962, 439.6637, 558.4838, 659.646, 729.084]),
('regression: above carrying capacity',
(1200, 0.5, 1000, 10, 6),
[1200.0, 1076.95, 1031.2338, 1010.3915, 1000.1957, 995.0498, 992.4131]),
('control: invalid carrying capacity', (100, 0.5, 0, 10, 5), None),
('regression: zero years', (100, 0.5, 500, 10, 0), [100.0])],
[('regression: cod-like stock light quota',
(500, 0.4, 1000, 20, 8),
[500.0, 579.84, 658.4077, 730.745, 792.9796, 843.1725, 881.3963, 909.1534, 928.5772]),
('regression: no harvest recovery',
(100, 0.6, 800, 0, 7),
[100.0, 152.5, 226.5578, 323.9962, 439.6637, 558.4838, 659.646, 729.084]),
('regression: above carrying capacity',
(1200, 0.5, 1000, 10, 6),
[1200.0, 1076.95, 1031.2338, 1010.3915, 1000.1957, 995.0498, 992.4131]),
('control: invalid carrying capacity', (100, 0.5, 0, 10, 5), None),
('regression: zero years', (100, 0.5, 500, 10, 0), [100.0]),
('regression: slow grower',
(800, 0.1, 1000, 15, 9),
[800.0, 801.8775, 803.6476, 805.3159, 806.8876, 808.3677, 809.7613, 811.0728, 812.3069, 813.4678]),
('regression: two-year collapse', (60, 0.2, 500, 40, 6), [60.0, 23.84, 0.0])],
[('regression: cod-like stock light quota',
(500, 0.4, 1000, 20, 8),
[500.0, 579.84, 658.4077, 730.745, 792.9796, 843.1725, 881.3963, 909.1534, 928.5772]),
('regression: quota exceeds growth collapse',
(300, 0.3, 1000, 120, 10),
[300.0, 224.28, 132.3017, 15.9468, 0.0]),
('regression: quota equals stock exactly', (50, 0.5, 400, 50, 5), [50.0, 0.0]),
('control: invalid carrying capacity', (100, 0.5, 0, 10, 5), None),
('regression: zero years', (100, 0.5, 500, 10, 0), [100.0]),
('regression: slow grower',
(800, 0.1, 1000, 15, 9),
[800.0, 801.8775, 803.6476, 805.3159, 806.8876, 808.3677, 809.7613, 811.0728, 812.3069, 813.4678]),
('regression: two-year collapse', (60, 0.2, 500, 40, 6), [60.0, 23.84, 0.0])],
[('regression: cod-like stock light quota',
(500, 0.4, 1000, 20, 8),
[500.0, 579.84, 658.4077, 730.745, 792.9796, 843.1725, 881.3963, 909.1534, 928.5772]),
('regression: quota exceeds growth collapse',
(300, 0.3, 1000, 120, 10),
[300.0, 224.28, 132.3017, 15.9468, 0.0]),
('regression: quota equals stock exactly', (50, 0.5, 400, 50, 5), [50.0, 0.0]),
('regression: no harvest recovery',
(100, 0.6, 800, 0, 7),
[100.0, 152.5, 226.5578, 323.9962, 439.6637, 558.4838, 659.646, 729.084]),
('regression: above carrying capacity',
(1200, 0.5, 1000, 10, 6),
[1200.0, 1076.95, 1031.2338, 1010.3915, 1000.1957, 995.0498, 992.4131]),
('control: invalid carrying capacity', (100, 0.5, 0, 10, 5), None),
('regression: zero years', (100, 0.5, 500, 10, 0), [100.0])],
[('regression: cod-like stock light quota',
(500, 0.4, 1000, 20, 8),
[500.0, 579.84, 658.4077, 730.745, 792.9796, 843.1725, 881.3963, 909.1534, 928.5772]),
('regression: no harvest recovery',
(100, 0.6, 800, 0, 7),
[100.0, 152.5, 226.5578, 323.9962, 439.6637, 558.4838, 659.646, 729.084]),
('regression: above carrying capacity',
(1200, 0.5, 1000, 10, 6),
[1200.0, 1076.95, 1031.2338, 1010.3915, 1000.1957, 995.0498, 992.4131]),
('control: invalid carrying capacity', (100, 0.5, 0, 10, 5), None),
('regression: zero years', (100, 0.5, 500, 10, 0), [100.0]),
('regression: slow grower',
(800, 0.1, 1000, 15, 9),
[800.0, 801.8775, 803.6476, 805.3159, 806.8876, 808.3677, 809.7613, 811.0728, 812.3069, 813.4678]),
('regression: two-year collapse', (60, 0.2, 500, 40, 6), [60.0, 23.84, 0.0])]]
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: cod-like stock light quota | [480.0, 579.84, 658.4077, 730.745, 792.9796, 843.1725, 881.3963, 909.1534, 928.5772] | [500.0, 579.84, 658.4077, 730.745, 792.9796, 843.1725, 881.3963, 909.1534, 928.5772] | Failed |
| regression: quota exceeds growth collapse | [180.0, 224.28, 132.3017, 15.9468, 0.0] | [300.0, 224.28, 132.3017, 15.9468, 0.0] | Failed |
| regression: quota equals stock exactly | [0.0, 0.0] | [50.0, 0.0] | Failed |
| regression: no harvest recovery | [100.0, 152.5, 226.5578, 323.9962, 439.6637, 558.4838, 659.646, 729.084] | [100.0, 152.5, 226.5578, 323.9962, 439.6637, 558.4838, 659.646, 729.084] | Passed |
| regression: above carrying capacity | [1190.0, 1076.95, 1031.2338, 1010.3915, 1000.1957, 995.0498, 992.4131] | [1200.0, 1076.95, 1031.2338, 1010.3915, 1000.1957, 995.0498, 992.4131] | Failed |
| control: invalid carrying capacity | None | None | Passed |
| regression: zero years | [90.0] | [100.0] | Failed |
SHA-256 / 3599d30b60550d2696f19e56ad1f238104ec2f313b2efd1155b6ad822f3666d3
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(n0, r, k, harvest, years):
if k <= 0 or n0 < 0:
return None
n = float(n0)
traj = [round(n, 4)]
for _ in range(years):
n -= harvest
if n <= 0:
traj.append(0.0)
break
n = n + r * n * (1 - n / k)
traj.append(round(n, 4))
return traj
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: cod-like stock light quota',
(500, 0.4, 1000, 20, 8),
[500.0, 579.84, 658.4077, 730.745, 792.9796, 843.1725, 881.3963, 909.1534, 928.5772]),
('regression: quota exceeds growth collapse',
(300, 0.3, 1000, 120, 10),
[300.0, 224.28, 132.3017, 15.9468, 0.0]),
('regression: quota equals stock exactly', (50, 0.5, 400, 50, 5), [50.0, 0.0]),
('regression: no harvest recovery',
(100, 0.6, 800, 0, 7),
[100.0, 152.5, 226.5578, 323.9962, 439.6637, 558.4838, 659.646, 729.084]),
('regression: above carrying capacity',
(1200, 0.5, 1000, 10, 6),
[1200.0, 1076.95, 1031.2338, 1010.3915, 1000.1957, 995.0498, 992.4131]),
('control: invalid carrying capacity', (100, 0.5, 0, 10, 5), None),
('regression: zero years', (100, 0.5, 500, 10, 0), [100.0])],
[('regression: cod-like stock light quota',
(500, 0.4, 1000, 20, 8),
[500.0, 579.84, 658.4077, 730.745, 792.9796, 843.1725, 881.3963, 909.1534, 928.5772]),
('regression: no harvest recovery',
(100, 0.6, 800, 0, 7),
[100.0, 152.5, 226.5578, 323.9962, 439.6637, 558.4838, 659.646, 729.084]),
('regression: above carrying capacity',
(1200, 0.5, 1000, 10, 6),
[1200.0, 1076.95, 1031.2338, 1010.3915, 1000.1957, 995.0498, 992.4131]),
('control: invalid carrying capacity', (100, 0.5, 0, 10, 5), None),
('regression: zero years', (100, 0.5, 500, 10, 0), [100.0]),
('regression: slow grower',
(800, 0.1, 1000, 15, 9),
[800.0, 801.8775, 803.6476, 805.3159, 806.8876, 808.3677, 809.7613, 811.0728, 812.3069, 813.4678]),
('regression: two-year collapse', (60, 0.2, 500, 40, 6), [60.0, 23.84, 0.0])],
[('regression: cod-like stock light quota',
(500, 0.4, 1000, 20, 8),
[500.0, 579.84, 658.4077, 730.745, 792.9796, 843.1725, 881.3963, 909.1534, 928.5772]),
('regression: quota exceeds growth collapse',
(300, 0.3, 1000, 120, 10),
[300.0, 224.28, 132.3017, 15.9468, 0.0]),
('regression: quota equals stock exactly', (50, 0.5, 400, 50, 5), [50.0, 0.0]),
('control: invalid carrying capacity', (100, 0.5, 0, 10, 5), None),
('regression: zero years', (100, 0.5, 500, 10, 0), [100.0]),
('regression: slow grower',
(800, 0.1, 1000, 15, 9),
[800.0, 801.8775, 803.6476, 805.3159, 806.8876, 808.3677, 809.7613, 811.0728, 812.3069, 813.4678]),
('regression: two-year collapse', (60, 0.2, 500, 40, 6), [60.0, 23.84, 0.0])],
[('regression: cod-like stock light quota',
(500, 0.4, 1000, 20, 8),
[500.0, 579.84, 658.4077, 730.745, 792.9796, 843.1725, 881.3963, 909.1534, 928.5772]),
('regression: quota exceeds growth collapse',
(300, 0.3, 1000, 120, 10),
[300.0, 224.28, 132.3017, 15.9468, 0.0]),
('regression: quota equals stock exactly', (50, 0.5, 400, 50, 5), [50.0, 0.0]),
('regression: no harvest recovery',
(100, 0.6, 800, 0, 7),
[100.0, 152.5, 226.5578, 323.9962, 439.6637, 558.4838, 659.646, 729.084]),
('regression: above carrying capacity',
(1200, 0.5, 1000, 10, 6),
[1200.0, 1076.95, 1031.2338, 1010.3915, 1000.1957, 995.0498, 992.4131]),
('control: invalid carrying capacity', (100, 0.5, 0, 10, 5), None),
('regression: zero years', (100, 0.5, 500, 10, 0), [100.0])],
[('regression: cod-like stock light quota',
(500, 0.4, 1000, 20, 8),
[500.0, 579.84, 658.4077, 730.745, 792.9796, 843.1725, 881.3963, 909.1534, 928.5772]),
('regression: no harvest recovery',
(100, 0.6, 800, 0, 7),
[100.0, 152.5, 226.5578, 323.9962, 439.6637, 558.4838, 659.646, 729.084]),
('regression: above carrying capacity',
(1200, 0.5, 1000, 10, 6),
[1200.0, 1076.95, 1031.2338, 1010.3915, 1000.1957, 995.0498, 992.4131]),
('control: invalid carrying capacity', (100, 0.5, 0, 10, 5), None),
('regression: zero years', (100, 0.5, 500, 10, 0), [100.0]),
('regression: slow grower',
(800, 0.1, 1000, 15, 9),
[800.0, 801.8775, 803.6476, 805.3159, 806.8876, 808.3677, 809.7613, 811.0728, 812.3069, 813.4678]),
('regression: two-year collapse', (60, 0.2, 500, 40, 6), [60.0, 23.84, 0.0])]]
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: cod-like stock light quota | [500.0, 579.84, 658.4077, 730.745, 792.9796, 843.1725, 881.3963, 909.1534, 928.5772] | [500.0, 579.84, 658.4077, 730.745, 792.9796, 843.1725, 881.3963, 909.1534, 928.5772] | Passed |
| regression: quota exceeds growth collapse | [300.0, 224.28, 132.3017, 15.9468, 0.0] | [300.0, 224.28, 132.3017, 15.9468, 0.0] | Passed |
| regression: quota equals stock exactly | [50.0, 0.0] | [50.0, 0.0] | Passed |
| regression: no harvest recovery | [100.0, 152.5, 226.5578, 323.9962, 439.6637, 558.4838, 659.646, 729.084] | [100.0, 152.5, 226.5578, 323.9962, 439.6637, 558.4838, 659.646, 729.084] | Passed |
| regression: above carrying capacity | [1200.0, 1076.95, 1031.2338, 1010.3915, 1000.1957, 995.0498, 992.4131] | [1200.0, 1076.95, 1031.2338, 1010.3915, 1000.1957, 995.0498, 992.4131] | Passed |
| control: invalid carrying capacity | None | None | Passed |
| regression: zero years | [100.0] | [100.0] | Passed |
SHA-256 / 2cbc595f5e3c84be630d19f101ef2879b2cb5d56d398944daaa8b04d051759bb
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 2026-09-29T14:47:33.323890+00:00.
Case digest / 1415ad96cfb3bc6b8474e0d4ff405f9f7c8de2bae3cb2a987476d01251230461