FA-65651 / Ecological population dynamics / Open access
Insect degree-day accumulation with horizontal cutoff: minimum substitution · case 01
Cold nights subtract development accumulated during the day.
ROOT CAUSE
Daily minimum temperatures below base are not raised to base.
VERIFIED REPAIR
Restore the minimum substitution rule: `lo_c = min(max(lo, base), upper)`.
Unsuccessful approach: Raising minima to 0 degrees instead of base still counts sub-base temperatures.
Case contract
Daily max is capped at upper; daily min is raised to base and capped at upper; DD = max(0, mean - base); emergence day is the first 1-based day with cumulative DD >= target; return [cumulative rounded 2, day or None]; None when upper <= base.
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(tmins, tmaxs, base, upper, target):
if upper <= base:
return None
total = 0.0
cum = []
day_hit = None
for d, (lo, hi) in enumerate(zip(tmins, tmaxs), start=1):
hi_c = min(hi, upper)
lo_c = lo
dd = max(0.0, (hi_c + lo_c) / 2 - base)
total += dd
cum.append(round(total, 2))
if day_hit is None and total >= target:
day_hit = d
return [cum, day_hit]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: spring warming codling moth',
([4, 6, 8, 10, 12, 14], [15, 18, 20, 24, 26, 30], 10, 31, 20),
[[2.5, 6.5, 11.5, 18.5, 27.5, 39.5], 5]),
('control: hot spell above cutoff', ([20, 22, 25], [34, 38, 40], 10, 30, 30), [[15.0, 31.0, 48.5], 2]),
('control: cold days below base', ([-2, 0, 3], [5, 8, 9], 10, 30, 1), [[0.0, 0.0, 0.0], None]),
('control: exact target', ([10, 10, 10], [20, 20, 20], 10, 30, 10), [[5.0, 10.0, 15.0], 2]),
('regression: never emerges', ([5, 6], [12, 13], 10, 30, 50), [[1.0, 2.5], None]),
('control: invalid thresholds', ([5], [15], 20, 20, 5), None),
('control: warm nights', ([18, 19, 21, 22], [28, 29, 33, 35], 12, 32, 40), [[11.0, 23.0, 37.5, 52.5], 4])],
[('control: exact target', ([10, 10, 10], [20, 20, 20], 10, 30, 10), [[5.0, 10.0, 15.0], 2]),
('regression: never emerges', ([5, 6], [12, 13], 10, 30, 50), [[1.0, 2.5], None]),
('control: invalid thresholds', ([5], [15], 20, 20, 5), None),
('control: warm nights', ([18, 19, 21, 22], [28, 29, 33, 35], 12, 32, 40), [[11.0, 23.0, 37.5, 52.5], 4]),
('control: no days', ([], [], 10, 30, 5), [[], None]),
('control: near-miss rounding', ([10, 10], [29.2, 10], 10, 30, 10), [[9.6, 9.6], None]),
('regression: frost then warm',
([-5, 2, 11, 14], [6, 16, 25, 29], 10, 30, 15),
[[0.0, 3.0, 11.0, 22.5], 4])],
[('regression: spring warming codling moth',
([4, 6, 8, 10, 12, 14], [15, 18, 20, 24, 26, 30], 10, 31, 20),
[[2.5, 6.5, 11.5, 18.5, 27.5, 39.5], 5]),
('control: hot spell above cutoff', ([20, 22, 25], [34, 38, 40], 10, 30, 30), [[15.0, 31.0, 48.5], 2]),
('control: cold days below base', ([-2, 0, 3], [5, 8, 9], 10, 30, 1), [[0.0, 0.0, 0.0], None]),
('control: warm nights', ([18, 19, 21, 22], [28, 29, 33, 35], 12, 32, 40), [[11.0, 23.0, 37.5, 52.5], 4]),
('control: no days', ([], [], 10, 30, 5), [[], None]),
('control: near-miss rounding', ([10, 10], [29.2, 10], 10, 30, 10), [[9.6, 9.6], None]),
('regression: frost then warm',
([-5, 2, 11, 14], [6, 16, 25, 29], 10, 30, 15),
[[0.0, 3.0, 11.0, 22.5], 4])],
[('regression: spring warming codling moth',
([4, 6, 8, 10, 12, 14], [15, 18, 20, 24, 26, 30], 10, 31, 20),
[[2.5, 6.5, 11.5, 18.5, 27.5, 39.5], 5]),
('control: hot spell above cutoff', ([20, 22, 25], [34, 38, 40], 10, 30, 30), [[15.0, 31.0, 48.5], 2]),
('control: cold days below base', ([-2, 0, 3], [5, 8, 9], 10, 30, 1), [[0.0, 0.0, 0.0], None]),
('control: exact target', ([10, 10, 10], [20, 20, 20], 10, 30, 10), [[5.0, 10.0, 15.0], 2]),
('regression: never emerges', ([5, 6], [12, 13], 10, 30, 50), [[1.0, 2.5], None]),
('control: invalid thresholds', ([5], [15], 20, 20, 5), None),
('regression: frost then warm',
([-5, 2, 11, 14], [6, 16, 25, 29], 10, 30, 15),
[[0.0, 3.0, 11.0, 22.5], 4])],
[('control: cold days below base', ([-2, 0, 3], [5, 8, 9], 10, 30, 1), [[0.0, 0.0, 0.0], None]),
('control: exact target', ([10, 10, 10], [20, 20, 20], 10, 30, 10), [[5.0, 10.0, 15.0], 2]),
('regression: never emerges', ([5, 6], [12, 13], 10, 30, 50), [[1.0, 2.5], None]),
('control: invalid thresholds', ([5], [15], 20, 20, 5), None),
('control: warm nights', ([18, 19, 21, 22], [28, 29, 33, 35], 12, 32, 40), [[11.0, 23.0, 37.5, 52.5], 4]),
('control: no days', ([], [], 10, 30, 5), [[], None]),
('regression: frost then warm',
([-5, 2, 11, 14], [6, 16, 25, 29], 10, 30, 15),
[[0.0, 3.0, 11.0, 22.5], 4])]]
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: spring warming codling moth | [[0.0, 2.0, 6.0, 13.0, 22.0, 34.0], 5] | [[2.5, 6.5, 11.5, 18.5, 27.5, 39.5], 5] | Failed |
| control: hot spell above cutoff | [[15.0, 31.0, 48.5], 2] | [[15.0, 31.0, 48.5], 2] | Passed |
| control: cold days below base | [[0.0, 0.0, 0.0], None] | [[0.0, 0.0, 0.0], None] | Passed |
| control: exact target | [[5.0, 10.0, 15.0], 2] | [[5.0, 10.0, 15.0], 2] | Passed |
| regression: never emerges | [[0.0, 0.0], None] | [[1.0, 2.5], None] | Failed |
| control: invalid thresholds | None | None | Passed |
| control: warm nights | [[11.0, 23.0, 37.5, 52.5], 4] | [[11.0, 23.0, 37.5, 52.5], 4] | Passed |
SHA-256 / e0b08d61b8f42e4273eb3e0ff9ae3e9ffabd9ad334457b110efd9b85a764cb7a
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(tmins, tmaxs, base, upper, target):
if upper <= base:
return None
total = 0.0
cum = []
day_hit = None
for d, (lo, hi) in enumerate(zip(tmins, tmaxs), start=1):
hi_c = min(hi, upper)
lo_c = max(lo, 0)
dd = max(0.0, (hi_c + lo_c) / 2 - base)
total += dd
cum.append(round(total, 2))
if day_hit is None and total >= target:
day_hit = d
return [cum, day_hit]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: spring warming codling moth',
([4, 6, 8, 10, 12, 14], [15, 18, 20, 24, 26, 30], 10, 31, 20),
[[2.5, 6.5, 11.5, 18.5, 27.5, 39.5], 5]),
('control: hot spell above cutoff', ([20, 22, 25], [34, 38, 40], 10, 30, 30), [[15.0, 31.0, 48.5], 2]),
('control: cold days below base', ([-2, 0, 3], [5, 8, 9], 10, 30, 1), [[0.0, 0.0, 0.0], None]),
('control: exact target', ([10, 10, 10], [20, 20, 20], 10, 30, 10), [[5.0, 10.0, 15.0], 2]),
('regression: never emerges', ([5, 6], [12, 13], 10, 30, 50), [[1.0, 2.5], None]),
('control: invalid thresholds', ([5], [15], 20, 20, 5), None),
('control: warm nights', ([18, 19, 21, 22], [28, 29, 33, 35], 12, 32, 40), [[11.0, 23.0, 37.5, 52.5], 4])],
[('control: exact target', ([10, 10, 10], [20, 20, 20], 10, 30, 10), [[5.0, 10.0, 15.0], 2]),
('regression: never emerges', ([5, 6], [12, 13], 10, 30, 50), [[1.0, 2.5], None]),
('control: invalid thresholds', ([5], [15], 20, 20, 5), None),
('control: warm nights', ([18, 19, 21, 22], [28, 29, 33, 35], 12, 32, 40), [[11.0, 23.0, 37.5, 52.5], 4]),
('control: no days', ([], [], 10, 30, 5), [[], None]),
('control: near-miss rounding', ([10, 10], [29.2, 10], 10, 30, 10), [[9.6, 9.6], None]),
('regression: frost then warm',
([-5, 2, 11, 14], [6, 16, 25, 29], 10, 30, 15),
[[0.0, 3.0, 11.0, 22.5], 4])],
[('regression: spring warming codling moth',
([4, 6, 8, 10, 12, 14], [15, 18, 20, 24, 26, 30], 10, 31, 20),
[[2.5, 6.5, 11.5, 18.5, 27.5, 39.5], 5]),
('control: hot spell above cutoff', ([20, 22, 25], [34, 38, 40], 10, 30, 30), [[15.0, 31.0, 48.5], 2]),
('control: cold days below base', ([-2, 0, 3], [5, 8, 9], 10, 30, 1), [[0.0, 0.0, 0.0], None]),
('control: warm nights', ([18, 19, 21, 22], [28, 29, 33, 35], 12, 32, 40), [[11.0, 23.0, 37.5, 52.5], 4]),
('control: no days', ([], [], 10, 30, 5), [[], None]),
('control: near-miss rounding', ([10, 10], [29.2, 10], 10, 30, 10), [[9.6, 9.6], None]),
('regression: frost then warm',
([-5, 2, 11, 14], [6, 16, 25, 29], 10, 30, 15),
[[0.0, 3.0, 11.0, 22.5], 4])],
[('regression: spring warming codling moth',
([4, 6, 8, 10, 12, 14], [15, 18, 20, 24, 26, 30], 10, 31, 20),
[[2.5, 6.5, 11.5, 18.5, 27.5, 39.5], 5]),
('control: hot spell above cutoff', ([20, 22, 25], [34, 38, 40], 10, 30, 30), [[15.0, 31.0, 48.5], 2]),
('control: cold days below base', ([-2, 0, 3], [5, 8, 9], 10, 30, 1), [[0.0, 0.0, 0.0], None]),
('control: exact target', ([10, 10, 10], [20, 20, 20], 10, 30, 10), [[5.0, 10.0, 15.0], 2]),
('regression: never emerges', ([5, 6], [12, 13], 10, 30, 50), [[1.0, 2.5], None]),
('control: invalid thresholds', ([5], [15], 20, 20, 5), None),
('regression: frost then warm',
([-5, 2, 11, 14], [6, 16, 25, 29], 10, 30, 15),
[[0.0, 3.0, 11.0, 22.5], 4])],
[('control: cold days below base', ([-2, 0, 3], [5, 8, 9], 10, 30, 1), [[0.0, 0.0, 0.0], None]),
('control: exact target', ([10, 10, 10], [20, 20, 20], 10, 30, 10), [[5.0, 10.0, 15.0], 2]),
('regression: never emerges', ([5, 6], [12, 13], 10, 30, 50), [[1.0, 2.5], None]),
('control: invalid thresholds', ([5], [15], 20, 20, 5), None),
('control: warm nights', ([18, 19, 21, 22], [28, 29, 33, 35], 12, 32, 40), [[11.0, 23.0, 37.5, 52.5], 4]),
('control: no days', ([], [], 10, 30, 5), [[], None]),
('regression: frost then warm',
([-5, 2, 11, 14], [6, 16, 25, 29], 10, 30, 15),
[[0.0, 3.0, 11.0, 22.5], 4])]]
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: spring warming codling moth | [[0.0, 2.0, 6.0, 13.0, 22.0, 34.0], 5] | [[2.5, 6.5, 11.5, 18.5, 27.5, 39.5], 5] | Failed |
| control: hot spell above cutoff | [[15.0, 31.0, 48.5], 2] | [[15.0, 31.0, 48.5], 2] | Passed |
| control: cold days below base | [[0.0, 0.0, 0.0], None] | [[0.0, 0.0, 0.0], None] | Passed |
| control: exact target | [[5.0, 10.0, 15.0], 2] | [[5.0, 10.0, 15.0], 2] | Passed |
| regression: never emerges | [[0.0, 0.0], None] | [[1.0, 2.5], None] | Failed |
| control: invalid thresholds | None | None | Passed |
| control: warm nights | [[11.0, 23.0, 37.5, 52.5], 4] | [[11.0, 23.0, 37.5, 52.5], 4] | Passed |
SHA-256 / 4b21ace5bd5f761caeedfc259020e885cb1c9b717c9368f1fe4fb352708f8b95
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(tmins, tmaxs, base, upper, target):
if upper <= base:
return None
total = 0.0
cum = []
day_hit = None
for d, (lo, hi) in enumerate(zip(tmins, tmaxs), start=1):
hi_c = min(hi, upper)
lo_c = min(max(lo, base), upper)
dd = max(0.0, (hi_c + lo_c) / 2 - base)
total += dd
cum.append(round(total, 2))
if day_hit is None and total >= target:
day_hit = d
return [cum, day_hit]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: spring warming codling moth',
([4, 6, 8, 10, 12, 14], [15, 18, 20, 24, 26, 30], 10, 31, 20),
[[2.5, 6.5, 11.5, 18.5, 27.5, 39.5], 5]),
('control: hot spell above cutoff', ([20, 22, 25], [34, 38, 40], 10, 30, 30), [[15.0, 31.0, 48.5], 2]),
('control: cold days below base', ([-2, 0, 3], [5, 8, 9], 10, 30, 1), [[0.0, 0.0, 0.0], None]),
('control: exact target', ([10, 10, 10], [20, 20, 20], 10, 30, 10), [[5.0, 10.0, 15.0], 2]),
('regression: never emerges', ([5, 6], [12, 13], 10, 30, 50), [[1.0, 2.5], None]),
('control: invalid thresholds', ([5], [15], 20, 20, 5), None),
('control: warm nights', ([18, 19, 21, 22], [28, 29, 33, 35], 12, 32, 40), [[11.0, 23.0, 37.5, 52.5], 4])],
[('control: exact target', ([10, 10, 10], [20, 20, 20], 10, 30, 10), [[5.0, 10.0, 15.0], 2]),
('regression: never emerges', ([5, 6], [12, 13], 10, 30, 50), [[1.0, 2.5], None]),
('control: invalid thresholds', ([5], [15], 20, 20, 5), None),
('control: warm nights', ([18, 19, 21, 22], [28, 29, 33, 35], 12, 32, 40), [[11.0, 23.0, 37.5, 52.5], 4]),
('control: no days', ([], [], 10, 30, 5), [[], None]),
('control: near-miss rounding', ([10, 10], [29.2, 10], 10, 30, 10), [[9.6, 9.6], None]),
('regression: frost then warm',
([-5, 2, 11, 14], [6, 16, 25, 29], 10, 30, 15),
[[0.0, 3.0, 11.0, 22.5], 4])],
[('regression: spring warming codling moth',
([4, 6, 8, 10, 12, 14], [15, 18, 20, 24, 26, 30], 10, 31, 20),
[[2.5, 6.5, 11.5, 18.5, 27.5, 39.5], 5]),
('control: hot spell above cutoff', ([20, 22, 25], [34, 38, 40], 10, 30, 30), [[15.0, 31.0, 48.5], 2]),
('control: cold days below base', ([-2, 0, 3], [5, 8, 9], 10, 30, 1), [[0.0, 0.0, 0.0], None]),
('control: warm nights', ([18, 19, 21, 22], [28, 29, 33, 35], 12, 32, 40), [[11.0, 23.0, 37.5, 52.5], 4]),
('control: no days', ([], [], 10, 30, 5), [[], None]),
('control: near-miss rounding', ([10, 10], [29.2, 10], 10, 30, 10), [[9.6, 9.6], None]),
('regression: frost then warm',
([-5, 2, 11, 14], [6, 16, 25, 29], 10, 30, 15),
[[0.0, 3.0, 11.0, 22.5], 4])],
[('regression: spring warming codling moth',
([4, 6, 8, 10, 12, 14], [15, 18, 20, 24, 26, 30], 10, 31, 20),
[[2.5, 6.5, 11.5, 18.5, 27.5, 39.5], 5]),
('control: hot spell above cutoff', ([20, 22, 25], [34, 38, 40], 10, 30, 30), [[15.0, 31.0, 48.5], 2]),
('control: cold days below base', ([-2, 0, 3], [5, 8, 9], 10, 30, 1), [[0.0, 0.0, 0.0], None]),
('control: exact target', ([10, 10, 10], [20, 20, 20], 10, 30, 10), [[5.0, 10.0, 15.0], 2]),
('regression: never emerges', ([5, 6], [12, 13], 10, 30, 50), [[1.0, 2.5], None]),
('control: invalid thresholds', ([5], [15], 20, 20, 5), None),
('regression: frost then warm',
([-5, 2, 11, 14], [6, 16, 25, 29], 10, 30, 15),
[[0.0, 3.0, 11.0, 22.5], 4])],
[('control: cold days below base', ([-2, 0, 3], [5, 8, 9], 10, 30, 1), [[0.0, 0.0, 0.0], None]),
('control: exact target', ([10, 10, 10], [20, 20, 20], 10, 30, 10), [[5.0, 10.0, 15.0], 2]),
('regression: never emerges', ([5, 6], [12, 13], 10, 30, 50), [[1.0, 2.5], None]),
('control: invalid thresholds', ([5], [15], 20, 20, 5), None),
('control: warm nights', ([18, 19, 21, 22], [28, 29, 33, 35], 12, 32, 40), [[11.0, 23.0, 37.5, 52.5], 4]),
('control: no days', ([], [], 10, 30, 5), [[], None]),
('regression: frost then warm',
([-5, 2, 11, 14], [6, 16, 25, 29], 10, 30, 15),
[[0.0, 3.0, 11.0, 22.5], 4])]]
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: spring warming codling moth | [[2.5, 6.5, 11.5, 18.5, 27.5, 39.5], 5] | [[2.5, 6.5, 11.5, 18.5, 27.5, 39.5], 5] | Passed |
| control: hot spell above cutoff | [[15.0, 31.0, 48.5], 2] | [[15.0, 31.0, 48.5], 2] | Passed |
| control: cold days below base | [[0.0, 0.0, 0.0], None] | [[0.0, 0.0, 0.0], None] | Passed |
| control: exact target | [[5.0, 10.0, 15.0], 2] | [[5.0, 10.0, 15.0], 2] | Passed |
| regression: never emerges | [[1.0, 2.5], None] | [[1.0, 2.5], None] | Passed |
| control: invalid thresholds | None | None | Passed |
| control: warm nights | [[11.0, 23.0, 37.5, 52.5], 4] | [[11.0, 23.0, 37.5, 52.5], 4] | Passed |
SHA-256 / ded1e2608dd4fa5d6fff744eccf39951356d9c147551d0fdf84662f6df31bb2b
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 2026-09-29T14:47:35.976836+00:00.
Case digest / d8e3dc6cdbc759c0451a084c8989e21361f7d892db0616d3e7a067858bbb189a