FA-65746 / Ecological population dynamics / Open access
Discrete delayed logistic (Hutchinson) with lag: overshoot reference · case 01
Overshoot is measured from the initial density instead of carrying capacity.
ROOT CAUSE
The reference level is N0.
THE FAILURE
The reference level is N0.
Unsuccessful approach: Excluding the initial value ignores a start above capacity.
Case contract
hist[0]=N0; N[t+1] = max(0, N[t] + r*N[t]*(1 - N[t-lag]/K)) where values before time 0 equal N0; return [history rounded 4, overshoot max(0, max(history)-K) rounded 4].
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, lag, steps):
hist = [float(n0)]
for t in range(steps):
past = hist[t - lag] if t - lag >= 0 else hist[0]
now = hist[t]
hist.append(max(0.0, now + r * now * (1 - past / k)))
over = max(0.0, max(hist) - hist[0])
return [[round(x, 4) for x in hist], round(over, 4)]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: daphnia with 2 step lag',
(10, 0.8, 100, 2, 8),
[[10.0, 17.2, 29.584, 50.8845, 84.5904, 132.2425, 184.2037, 206.9118, 153.541], 106.9118]),
('regression: no lag',
(10, 0.5, 100, 0, 6),
[[10.0, 14.5, 20.6988, 28.9059, 39.1811, 51.0959, 63.5899], 0.0]),
('regression: long lag oscillation',
(50, 0.6, 100, 3, 10),
[[50.0, 65.0, 84.5, 109.85, 142.805, 172.794, 188.8639, 177.702, 132.0628, 74.3825, 34.723], 88.8639]),
('regression: start above capacity',
(150, 0.3, 100, 1, 5),
[[150.0, 127.5, 108.375, 99.4341, 96.9358, 97.1004], 50.0]),
('regression: one-step lag',
(20, 1.2, 200, 1, 7),
[[20.0, 41.6, 86.528, 168.7642, 283.6643, 336.8272, 167.7447, 30.0325], 136.8272]),
('control: zero steps', (30, 0.5, 100, 2, 0), [[30.0], 0.0]),
('regression: crash to zero', (180, 2.5, 100, 1, 4), [[180.0, 0.0, 0.0, 0.0, 0.0], 80.0])],
[('regression: daphnia with 2 step lag',
(10, 0.8, 100, 2, 8),
[[10.0, 17.2, 29.584, 50.8845, 84.5904, 132.2425, 184.2037, 206.9118, 153.541], 106.9118]),
('regression: no lag',
(10, 0.5, 100, 0, 6),
[[10.0, 14.5, 20.6988, 28.9059, 39.1811, 51.0959, 63.5899], 0.0]),
('regression: long lag oscillation',
(50, 0.6, 100, 3, 10),
[[50.0, 65.0, 84.5, 109.85, 142.805, 172.794, 188.8639, 177.702, 132.0628, 74.3825, 34.723], 88.8639]),
('regression: start above capacity',
(150, 0.3, 100, 1, 5),
[[150.0, 127.5, 108.375, 99.4341, 96.9358, 97.1004], 50.0]),
('regression: one-step lag',
(20, 1.2, 200, 1, 7),
[[20.0, 41.6, 86.528, 168.7642, 283.6643, 336.8272, 167.7447, 30.0325], 136.8272]),
('control: zero steps', (30, 0.5, 100, 2, 0), [[30.0], 0.0]),
('regression: crash to zero', (180, 2.5, 100, 1, 4), [[180.0, 0.0, 0.0, 0.0, 0.0], 80.0])],
[('regression: daphnia with 2 step lag',
(10, 0.8, 100, 2, 8),
[[10.0, 17.2, 29.584, 50.8845, 84.5904, 132.2425, 184.2037, 206.9118, 153.541], 106.9118]),
('regression: no lag',
(10, 0.5, 100, 0, 6),
[[10.0, 14.5, 20.6988, 28.9059, 39.1811, 51.0959, 63.5899], 0.0]),
('regression: long lag oscillation',
(50, 0.6, 100, 3, 10),
[[50.0, 65.0, 84.5, 109.85, 142.805, 172.794, 188.8639, 177.702, 132.0628, 74.3825, 34.723], 88.8639]),
('regression: start above capacity',
(150, 0.3, 100, 1, 5),
[[150.0, 127.5, 108.375, 99.4341, 96.9358, 97.1004], 50.0]),
('regression: one-step lag',
(20, 1.2, 200, 1, 7),
[[20.0, 41.6, 86.528, 168.7642, 283.6643, 336.8272, 167.7447, 30.0325], 136.8272]),
('control: zero steps', (30, 0.5, 100, 2, 0), [[30.0], 0.0]),
('regression: crash to zero', (180, 2.5, 100, 1, 4), [[180.0, 0.0, 0.0, 0.0, 0.0], 80.0])],
[('regression: daphnia with 2 step lag',
(10, 0.8, 100, 2, 8),
[[10.0, 17.2, 29.584, 50.8845, 84.5904, 132.2425, 184.2037, 206.9118, 153.541], 106.9118]),
('regression: no lag',
(10, 0.5, 100, 0, 6),
[[10.0, 14.5, 20.6988, 28.9059, 39.1811, 51.0959, 63.5899], 0.0]),
('regression: long lag oscillation',
(50, 0.6, 100, 3, 10),
[[50.0, 65.0, 84.5, 109.85, 142.805, 172.794, 188.8639, 177.702, 132.0628, 74.3825, 34.723], 88.8639]),
('regression: start above capacity',
(150, 0.3, 100, 1, 5),
[[150.0, 127.5, 108.375, 99.4341, 96.9358, 97.1004], 50.0]),
('regression: one-step lag',
(20, 1.2, 200, 1, 7),
[[20.0, 41.6, 86.528, 168.7642, 283.6643, 336.8272, 167.7447, 30.0325], 136.8272]),
('control: zero steps', (30, 0.5, 100, 2, 0), [[30.0], 0.0]),
('regression: crash to zero', (180, 2.5, 100, 1, 4), [[180.0, 0.0, 0.0, 0.0, 0.0], 80.0])],
[('regression: daphnia with 2 step lag',
(10, 0.8, 100, 2, 8),
[[10.0, 17.2, 29.584, 50.8845, 84.5904, 132.2425, 184.2037, 206.9118, 153.541], 106.9118]),
('regression: no lag',
(10, 0.5, 100, 0, 6),
[[10.0, 14.5, 20.6988, 28.9059, 39.1811, 51.0959, 63.5899], 0.0]),
('regression: long lag oscillation',
(50, 0.6, 100, 3, 10),
[[50.0, 65.0, 84.5, 109.85, 142.805, 172.794, 188.8639, 177.702, 132.0628, 74.3825, 34.723], 88.8639]),
('regression: start above capacity',
(150, 0.3, 100, 1, 5),
[[150.0, 127.5, 108.375, 99.4341, 96.9358, 97.1004], 50.0]),
('regression: one-step lag',
(20, 1.2, 200, 1, 7),
[[20.0, 41.6, 86.528, 168.7642, 283.6643, 336.8272, 167.7447, 30.0325], 136.8272]),
('control: zero steps', (30, 0.5, 100, 2, 0), [[30.0], 0.0]),
('regression: crash to zero', (180, 2.5, 100, 1, 4), [[180.0, 0.0, 0.0, 0.0, 0.0], 80.0])]]
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: daphnia with 2 step lag | [[10.0, 17.2, 29.584, 50.8845, 84.5904, 132.2425, 184.2037, 206.9118, 153.541], 196.9118] | [[10.0, 17.2, 29.584, 50.8845, 84.5904, 132.2425, 184.2037, 206.9118, 153.541], 106.9118] | Failed |
| regression: no lag | [[10.0, 14.5, 20.6988, 28.9059, 39.1811, 51.0959, 63.5899], 53.5899] | [[10.0, 14.5, 20.6988, 28.9059, 39.1811, 51.0959, 63.5899], 0.0] | Failed |
| regression: long lag oscillation | [[50.0, 65.0, 84.5, 109.85, 142.805, 172.794, 188.8639, 177.702, 132.0628, 74.3825, 34.723], 138.8639] | [[50.0, 65.0, 84.5, 109.85, 142.805, 172.794, 188.8639, 177.702, 132.0628, 74.3825, 34.723], 88.8639] | Failed |
| regression: start above capacity | [[150.0, 127.5, 108.375, 99.4341, 96.9358, 97.1004], 0.0] | [[150.0, 127.5, 108.375, 99.4341, 96.9358, 97.1004], 50.0] | Failed |
| regression: one-step lag | [[20.0, 41.6, 86.528, 168.7642, 283.6643, 336.8272, 167.7447, 30.0325], 316.8272] | [[20.0, 41.6, 86.528, 168.7642, 283.6643, 336.8272, 167.7447, 30.0325], 136.8272] | Failed |
| control: zero steps | [[30.0], 0.0] | [[30.0], 0.0] | Passed |
| regression: crash to zero | [[180.0, 0.0, 0.0, 0.0, 0.0], 0.0] | [[180.0, 0.0, 0.0, 0.0, 0.0], 80.0] | Failed |
SHA-256 / 9ef37a044815214947bb998d056aae88a65a19641264b7dec312d6c1d6c58c17
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, lag, steps):
hist = [float(n0)]
for t in range(steps):
past = hist[t - lag] if t - lag >= 0 else hist[0]
now = hist[t]
hist.append(max(0.0, now + r * now * (1 - past / k)))
over = max(0.0, max(hist[1:] or [0.0]) - k)
return [[round(x, 4) for x in hist], round(over, 4)]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: daphnia with 2 step lag',
(10, 0.8, 100, 2, 8),
[[10.0, 17.2, 29.584, 50.8845, 84.5904, 132.2425, 184.2037, 206.9118, 153.541], 106.9118]),
('regression: no lag',
(10, 0.5, 100, 0, 6),
[[10.0, 14.5, 20.6988, 28.9059, 39.1811, 51.0959, 63.5899], 0.0]),
('regression: long lag oscillation',
(50, 0.6, 100, 3, 10),
[[50.0, 65.0, 84.5, 109.85, 142.805, 172.794, 188.8639, 177.702, 132.0628, 74.3825, 34.723], 88.8639]),
('regression: start above capacity',
(150, 0.3, 100, 1, 5),
[[150.0, 127.5, 108.375, 99.4341, 96.9358, 97.1004], 50.0]),
('regression: one-step lag',
(20, 1.2, 200, 1, 7),
[[20.0, 41.6, 86.528, 168.7642, 283.6643, 336.8272, 167.7447, 30.0325], 136.8272]),
('control: zero steps', (30, 0.5, 100, 2, 0), [[30.0], 0.0]),
('regression: crash to zero', (180, 2.5, 100, 1, 4), [[180.0, 0.0, 0.0, 0.0, 0.0], 80.0])],
[('regression: daphnia with 2 step lag',
(10, 0.8, 100, 2, 8),
[[10.0, 17.2, 29.584, 50.8845, 84.5904, 132.2425, 184.2037, 206.9118, 153.541], 106.9118]),
('regression: no lag',
(10, 0.5, 100, 0, 6),
[[10.0, 14.5, 20.6988, 28.9059, 39.1811, 51.0959, 63.5899], 0.0]),
('regression: long lag oscillation',
(50, 0.6, 100, 3, 10),
[[50.0, 65.0, 84.5, 109.85, 142.805, 172.794, 188.8639, 177.702, 132.0628, 74.3825, 34.723], 88.8639]),
('regression: start above capacity',
(150, 0.3, 100, 1, 5),
[[150.0, 127.5, 108.375, 99.4341, 96.9358, 97.1004], 50.0]),
('regression: one-step lag',
(20, 1.2, 200, 1, 7),
[[20.0, 41.6, 86.528, 168.7642, 283.6643, 336.8272, 167.7447, 30.0325], 136.8272]),
('control: zero steps', (30, 0.5, 100, 2, 0), [[30.0], 0.0]),
('regression: crash to zero', (180, 2.5, 100, 1, 4), [[180.0, 0.0, 0.0, 0.0, 0.0], 80.0])],
[('regression: daphnia with 2 step lag',
(10, 0.8, 100, 2, 8),
[[10.0, 17.2, 29.584, 50.8845, 84.5904, 132.2425, 184.2037, 206.9118, 153.541], 106.9118]),
('regression: no lag',
(10, 0.5, 100, 0, 6),
[[10.0, 14.5, 20.6988, 28.9059, 39.1811, 51.0959, 63.5899], 0.0]),
('regression: long lag oscillation',
(50, 0.6, 100, 3, 10),
[[50.0, 65.0, 84.5, 109.85, 142.805, 172.794, 188.8639, 177.702, 132.0628, 74.3825, 34.723], 88.8639]),
('regression: start above capacity',
(150, 0.3, 100, 1, 5),
[[150.0, 127.5, 108.375, 99.4341, 96.9358, 97.1004], 50.0]),
('regression: one-step lag',
(20, 1.2, 200, 1, 7),
[[20.0, 41.6, 86.528, 168.7642, 283.6643, 336.8272, 167.7447, 30.0325], 136.8272]),
('control: zero steps', (30, 0.5, 100, 2, 0), [[30.0], 0.0]),
('regression: crash to zero', (180, 2.5, 100, 1, 4), [[180.0, 0.0, 0.0, 0.0, 0.0], 80.0])],
[('regression: daphnia with 2 step lag',
(10, 0.8, 100, 2, 8),
[[10.0, 17.2, 29.584, 50.8845, 84.5904, 132.2425, 184.2037, 206.9118, 153.541], 106.9118]),
('regression: no lag',
(10, 0.5, 100, 0, 6),
[[10.0, 14.5, 20.6988, 28.9059, 39.1811, 51.0959, 63.5899], 0.0]),
('regression: long lag oscillation',
(50, 0.6, 100, 3, 10),
[[50.0, 65.0, 84.5, 109.85, 142.805, 172.794, 188.8639, 177.702, 132.0628, 74.3825, 34.723], 88.8639]),
('regression: start above capacity',
(150, 0.3, 100, 1, 5),
[[150.0, 127.5, 108.375, 99.4341, 96.9358, 97.1004], 50.0]),
('regression: one-step lag',
(20, 1.2, 200, 1, 7),
[[20.0, 41.6, 86.528, 168.7642, 283.6643, 336.8272, 167.7447, 30.0325], 136.8272]),
('control: zero steps', (30, 0.5, 100, 2, 0), [[30.0], 0.0]),
('regression: crash to zero', (180, 2.5, 100, 1, 4), [[180.0, 0.0, 0.0, 0.0, 0.0], 80.0])],
[('regression: daphnia with 2 step lag',
(10, 0.8, 100, 2, 8),
[[10.0, 17.2, 29.584, 50.8845, 84.5904, 132.2425, 184.2037, 206.9118, 153.541], 106.9118]),
('regression: no lag',
(10, 0.5, 100, 0, 6),
[[10.0, 14.5, 20.6988, 28.9059, 39.1811, 51.0959, 63.5899], 0.0]),
('regression: long lag oscillation',
(50, 0.6, 100, 3, 10),
[[50.0, 65.0, 84.5, 109.85, 142.805, 172.794, 188.8639, 177.702, 132.0628, 74.3825, 34.723], 88.8639]),
('regression: start above capacity',
(150, 0.3, 100, 1, 5),
[[150.0, 127.5, 108.375, 99.4341, 96.9358, 97.1004], 50.0]),
('regression: one-step lag',
(20, 1.2, 200, 1, 7),
[[20.0, 41.6, 86.528, 168.7642, 283.6643, 336.8272, 167.7447, 30.0325], 136.8272]),
('control: zero steps', (30, 0.5, 100, 2, 0), [[30.0], 0.0]),
('regression: crash to zero', (180, 2.5, 100, 1, 4), [[180.0, 0.0, 0.0, 0.0, 0.0], 80.0])]]
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: daphnia with 2 step lag | [[10.0, 17.2, 29.584, 50.8845, 84.5904, 132.2425, 184.2037, 206.9118, 153.541], 106.9118] | [[10.0, 17.2, 29.584, 50.8845, 84.5904, 132.2425, 184.2037, 206.9118, 153.541], 106.9118] | Passed |
| regression: no lag | [[10.0, 14.5, 20.6988, 28.9059, 39.1811, 51.0959, 63.5899], 0.0] | [[10.0, 14.5, 20.6988, 28.9059, 39.1811, 51.0959, 63.5899], 0.0] | Passed |
| regression: long lag oscillation | [[50.0, 65.0, 84.5, 109.85, 142.805, 172.794, 188.8639, 177.702, 132.0628, 74.3825, 34.723], 88.8639] | [[50.0, 65.0, 84.5, 109.85, 142.805, 172.794, 188.8639, 177.702, 132.0628, 74.3825, 34.723], 88.8639] | Passed |
| regression: start above capacity | [[150.0, 127.5, 108.375, 99.4341, 96.9358, 97.1004], 27.5] | [[150.0, 127.5, 108.375, 99.4341, 96.9358, 97.1004], 50.0] | Failed |
| regression: one-step lag | [[20.0, 41.6, 86.528, 168.7642, 283.6643, 336.8272, 167.7447, 30.0325], 136.8272] | [[20.0, 41.6, 86.528, 168.7642, 283.6643, 336.8272, 167.7447, 30.0325], 136.8272] | Passed |
| control: zero steps | [[30.0], 0.0] | [[30.0], 0.0] | Passed |
| regression: crash to zero | [[180.0, 0.0, 0.0, 0.0, 0.0], 0.0] | [[180.0, 0.0, 0.0, 0.0, 0.0], 80.0] | Failed |
SHA-256 / 5f3c80f049f2b40009ba9e6d8dd7f19d43b4134426902cee608f7814717a252a
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.
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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 2026-09-29T14:47:36.745626+00:00.
Case digest / 8a16e0e1324d005bddd5ca535e5d9fe2afe82e3ab103274a46518b1f51a9ab51