FAILURE MAP
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FA-64886 / Epidemic compartment models / Open access

SEIR daily symptom-onset incidence: seed compartment · case 01

Population totals exceed the census by exactly the seed count.

Verified by executionVariant 1 · 7 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Seeds are added on top of a fully susceptible population instead of being taken from it.

THE FAILURE

Seeds are added on top of a fully susceptible population instead of being taken from it.

Unsuccessful approach: Dropping the exposed seed entirely conserves population but nothing ever progresses.

Case contract

Daily forward-Euler SEIR with sigma=1/latent_days and gamma=1/infectious_days; only I transmits (beta*S*I/pop); seeds start in E and are part of pop; return [daily E->I onsets rounded to 4, total population rounded to 4], or None for non-positive durations or population.

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(beta, latent_days, infectious_days, pop, e0, days):
    if latent_days <= 0 or infectious_days <= 0 or pop <= 0:
        return None
    sigma = 1.0 / latent_days
    gamma = 1.0 / infectious_days
    s, e, i, r = float(pop), float(e0), 0.0, 0.0
    incidence = []
    for day in range(days):
        exposure = beta * s * i / pop
        onset = sigma * e
        removal = gamma * i
        s -= exposure
        e += exposure - onset
        i += onset - removal
        r += removal
        incidence.append(round(onset, 4))
    return [incidence, round(s + e + i + r, 4)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: influenza-like 2 day latency',
   (0.6, 2, 3, 1000, 10, 8),
   [[5.0, 2.5, 2.735, 3.0948, 3.5019, 3.9584, 4.4687, 5.0378], 1000.0]),
  ('regression: measles-like long latency',
   (1.5, 8, 7, 5000, 5, 12),
   [[0.625, 0.5469, 0.5956, 0.7239, 0.9186, 1.1836, 1.5328, 1.9882, 2.5798, 3.3471, 4.3413, 5.6281], 5000.0]),
  ('regression: one-day latency', (0.4, 1, 4, 200, 4, 6), [[4.0, 0.0, 1.568, 1.1666, 1.4758, 1.5459], 200.0]),
  ('regression: no transmission',
   (0.0, 3, 5, 100, 20, 6),
   [[6.6667, 4.4444, 2.963, 1.9753, 1.3169, 0.8779], 100.0]),
  ('regression: boundary zero days', (0.5, 3, 5, 100, 5, 0), [[], 100.0]),
  ('control: invalid zero latency', (0.5, 0, 5, 100, 5, 5), None),
  ('control: invalid zero population', (0.5, 2, 5, 0, 0, 5), None)],
 [('regression: no transmission',
   (0.0, 3, 5, 100, 20, 6),
   [[6.6667, 4.4444, 2.963, 1.9753, 1.3169, 0.8779], 100.0]),
  ('regression: boundary zero days', (0.5, 3, 5, 100, 5, 0), [[], 100.0]),
  ('control: invalid zero latency', (0.5, 0, 5, 100, 5, 5), None),
  ('control: invalid zero population', (0.5, 2, 5, 0, 0, 5), None),
  ('regression: fractional latency',
   (0.8, 1.5, 2.5, 300, 6, 7),
   [[4.0, 1.3333, 2.5351, 2.7755, 3.3698, 3.9741, 4.6871], 300.0]),
  ('regression: large seed', (0.9, 4, 3, 100, 60, 6), [[15.0, 11.25, 9.7875, 8.9949, 8.2544, 7.4237], 100.0]),
  ('regression: long infectious period',
   (0.3, 5, 14, 2000, 50, 10),
   [[10.0, 8.0, 6.985, 6.5977, 6.6203, 6.9212, 7.4223, 8.0781, 8.8635, 9.7655], 2000.0])],
 [('regression: influenza-like 2 day latency',
   (0.6, 2, 3, 1000, 10, 8),
   [[5.0, 2.5, 2.735, 3.0948, 3.5019, 3.9584, 4.4687, 5.0378], 1000.0]),
  ('regression: measles-like long latency',
   (1.5, 8, 7, 5000, 5, 12),
   [[0.625, 0.5469, 0.5956, 0.7239, 0.9186, 1.1836, 1.5328, 1.9882, 2.5798, 3.3471, 4.3413, 5.6281], 5000.0]),
  ('control: invalid zero latency', (0.5, 0, 5, 100, 5, 5), None),
  ('control: invalid zero population', (0.5, 2, 5, 0, 0, 5), None),
  ('regression: fractional latency',
   (0.8, 1.5, 2.5, 300, 6, 7),
   [[4.0, 1.3333, 2.5351, 2.7755, 3.3698, 3.9741, 4.6871], 300.0]),
  ('regression: large seed', (0.9, 4, 3, 100, 60, 6), [[15.0, 11.25, 9.7875, 8.9949, 8.2544, 7.4237], 100.0]),
  ('regression: long infectious period',
   (0.3, 5, 14, 2000, 50, 10),
   [[10.0, 8.0, 6.985, 6.5977, 6.6203, 6.9212, 7.4223, 8.0781, 8.8635, 9.7655], 2000.0])],
 [('regression: influenza-like 2 day latency',
   (0.6, 2, 3, 1000, 10, 8),
   [[5.0, 2.5, 2.735, 3.0948, 3.5019, 3.9584, 4.4687, 5.0378], 1000.0]),
  ('regression: measles-like long latency',
   (1.5, 8, 7, 5000, 5, 12),
   [[0.625, 0.5469, 0.5956, 0.7239, 0.9186, 1.1836, 1.5328, 1.9882, 2.5798, 3.3471, 4.3413, 5.6281], 5000.0]),
  ('regression: one-day latency', (0.4, 1, 4, 200, 4, 6), [[4.0, 0.0, 1.568, 1.1666, 1.4758, 1.5459], 200.0]),
  ('regression: no transmission',
   (0.0, 3, 5, 100, 20, 6),
   [[6.6667, 4.4444, 2.963, 1.9753, 1.3169, 0.8779], 100.0]),
  ('control: invalid zero latency', (0.5, 0, 5, 100, 5, 5), None),
  ('control: invalid zero population', (0.5, 2, 5, 0, 0, 5), None),
  ('regression: long infectious period',
   (0.3, 5, 14, 2000, 50, 10),
   [[10.0, 8.0, 6.985, 6.5977, 6.6203, 6.9212, 7.4223, 8.0781, 8.8635, 9.7655], 2000.0])],
 [('regression: one-day latency', (0.4, 1, 4, 200, 4, 6), [[4.0, 0.0, 1.568, 1.1666, 1.4758, 1.5459], 200.0]),
  ('regression: no transmission',
   (0.0, 3, 5, 100, 20, 6),
   [[6.6667, 4.4444, 2.963, 1.9753, 1.3169, 0.8779], 100.0]),
  ('regression: boundary zero days', (0.5, 3, 5, 100, 5, 0), [[], 100.0]),
  ('control: invalid zero latency', (0.5, 0, 5, 100, 5, 5), None),
  ('control: invalid zero population', (0.5, 2, 5, 0, 0, 5), None),
  ('regression: fractional latency',
   (0.8, 1.5, 2.5, 300, 6, 7),
   [[4.0, 1.3333, 2.5351, 2.7755, 3.3698, 3.9741, 4.6871], 300.0]),
  ('regression: large seed',
   (0.9, 4, 3, 100, 60, 6),
   [[15.0, 11.25, 9.7875, 8.9949, 8.2544, 7.4237], 100.0])]]
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 fixtureActualExpectedOutcome
regression: influenza-like 2 day latency[[5.0, 2.5, 2.75, 3.1197, 3.5386, 4.0094, 4.537, 5.1268], 1010.0][[5.0, 2.5, 2.735, 3.0948, 3.5019, 3.9584, 4.4687, 5.0378], 1000.0]Failed
regression: measles-like long latency[[0.625, 0.5469, 0.5957, 0.7242, 0.9192, 1.1846, 1.5344, 1.9905, 2.5832, 3.3521, 4.3485, 5.6383], 5005.0][[0.625, 0.5469, 0.5956, 0.7239, 0.9186, 1.1836, 1.5328, 1.9882, 2.5798, 3.3471, 4.3413, 5.6281], 5000.0]Failed
regression: one-day latency[[4.0, 0.0, 1.6, 1.1904, 1.5185, 1.596], 204.0][[4.0, 0.0, 1.568, 1.1666, 1.4758, 1.5459], 200.0]Failed
regression: no transmission[[6.6667, 4.4444, 2.963, 1.9753, 1.3169, 0.8779], 120.0][[6.6667, 4.4444, 2.963, 1.9753, 1.3169, 0.8779], 100.0]Failed
regression: boundary zero days[[], 105.0][[], 100.0]Failed
control: invalid zero latencyNoneNonePassed
control: invalid zero populationNoneNonePassed

SHA-256 / 9b6162f29b80651d9fd5070242efc854afffb11e96b076c9dd978b9bb4a189e3

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(beta, latent_days, infectious_days, pop, e0, days):
    if latent_days <= 0 or infectious_days <= 0 or pop <= 0:
        return None
    sigma = 1.0 / latent_days
    gamma = 1.0 / infectious_days
    s, e, i, r = float(pop - e0), 0.0, 0.0, 0.0
    incidence = []
    for day in range(days):
        exposure = beta * s * i / pop
        onset = sigma * e
        removal = gamma * i
        s -= exposure
        e += exposure - onset
        i += onset - removal
        r += removal
        incidence.append(round(onset, 4))
    return [incidence, round(s + e + i + r, 4)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: influenza-like 2 day latency',
   (0.6, 2, 3, 1000, 10, 8),
   [[5.0, 2.5, 2.735, 3.0948, 3.5019, 3.9584, 4.4687, 5.0378], 1000.0]),
  ('regression: measles-like long latency',
   (1.5, 8, 7, 5000, 5, 12),
   [[0.625, 0.5469, 0.5956, 0.7239, 0.9186, 1.1836, 1.5328, 1.9882, 2.5798, 3.3471, 4.3413, 5.6281], 5000.0]),
  ('regression: one-day latency', (0.4, 1, 4, 200, 4, 6), [[4.0, 0.0, 1.568, 1.1666, 1.4758, 1.5459], 200.0]),
  ('regression: no transmission',
   (0.0, 3, 5, 100, 20, 6),
   [[6.6667, 4.4444, 2.963, 1.9753, 1.3169, 0.8779], 100.0]),
  ('regression: boundary zero days', (0.5, 3, 5, 100, 5, 0), [[], 100.0]),
  ('control: invalid zero latency', (0.5, 0, 5, 100, 5, 5), None),
  ('control: invalid zero population', (0.5, 2, 5, 0, 0, 5), None)],
 [('regression: no transmission',
   (0.0, 3, 5, 100, 20, 6),
   [[6.6667, 4.4444, 2.963, 1.9753, 1.3169, 0.8779], 100.0]),
  ('regression: boundary zero days', (0.5, 3, 5, 100, 5, 0), [[], 100.0]),
  ('control: invalid zero latency', (0.5, 0, 5, 100, 5, 5), None),
  ('control: invalid zero population', (0.5, 2, 5, 0, 0, 5), None),
  ('regression: fractional latency',
   (0.8, 1.5, 2.5, 300, 6, 7),
   [[4.0, 1.3333, 2.5351, 2.7755, 3.3698, 3.9741, 4.6871], 300.0]),
  ('regression: large seed', (0.9, 4, 3, 100, 60, 6), [[15.0, 11.25, 9.7875, 8.9949, 8.2544, 7.4237], 100.0]),
  ('regression: long infectious period',
   (0.3, 5, 14, 2000, 50, 10),
   [[10.0, 8.0, 6.985, 6.5977, 6.6203, 6.9212, 7.4223, 8.0781, 8.8635, 9.7655], 2000.0])],
 [('regression: influenza-like 2 day latency',
   (0.6, 2, 3, 1000, 10, 8),
   [[5.0, 2.5, 2.735, 3.0948, 3.5019, 3.9584, 4.4687, 5.0378], 1000.0]),
  ('regression: measles-like long latency',
   (1.5, 8, 7, 5000, 5, 12),
   [[0.625, 0.5469, 0.5956, 0.7239, 0.9186, 1.1836, 1.5328, 1.9882, 2.5798, 3.3471, 4.3413, 5.6281], 5000.0]),
  ('control: invalid zero latency', (0.5, 0, 5, 100, 5, 5), None),
  ('control: invalid zero population', (0.5, 2, 5, 0, 0, 5), None),
  ('regression: fractional latency',
   (0.8, 1.5, 2.5, 300, 6, 7),
   [[4.0, 1.3333, 2.5351, 2.7755, 3.3698, 3.9741, 4.6871], 300.0]),
  ('regression: large seed', (0.9, 4, 3, 100, 60, 6), [[15.0, 11.25, 9.7875, 8.9949, 8.2544, 7.4237], 100.0]),
  ('regression: long infectious period',
   (0.3, 5, 14, 2000, 50, 10),
   [[10.0, 8.0, 6.985, 6.5977, 6.6203, 6.9212, 7.4223, 8.0781, 8.8635, 9.7655], 2000.0])],
 [('regression: influenza-like 2 day latency',
   (0.6, 2, 3, 1000, 10, 8),
   [[5.0, 2.5, 2.735, 3.0948, 3.5019, 3.9584, 4.4687, 5.0378], 1000.0]),
  ('regression: measles-like long latency',
   (1.5, 8, 7, 5000, 5, 12),
   [[0.625, 0.5469, 0.5956, 0.7239, 0.9186, 1.1836, 1.5328, 1.9882, 2.5798, 3.3471, 4.3413, 5.6281], 5000.0]),
  ('regression: one-day latency', (0.4, 1, 4, 200, 4, 6), [[4.0, 0.0, 1.568, 1.1666, 1.4758, 1.5459], 200.0]),
  ('regression: no transmission',
   (0.0, 3, 5, 100, 20, 6),
   [[6.6667, 4.4444, 2.963, 1.9753, 1.3169, 0.8779], 100.0]),
  ('control: invalid zero latency', (0.5, 0, 5, 100, 5, 5), None),
  ('control: invalid zero population', (0.5, 2, 5, 0, 0, 5), None),
  ('regression: long infectious period',
   (0.3, 5, 14, 2000, 50, 10),
   [[10.0, 8.0, 6.985, 6.5977, 6.6203, 6.9212, 7.4223, 8.0781, 8.8635, 9.7655], 2000.0])],
 [('regression: one-day latency', (0.4, 1, 4, 200, 4, 6), [[4.0, 0.0, 1.568, 1.1666, 1.4758, 1.5459], 200.0]),
  ('regression: no transmission',
   (0.0, 3, 5, 100, 20, 6),
   [[6.6667, 4.4444, 2.963, 1.9753, 1.3169, 0.8779], 100.0]),
  ('regression: boundary zero days', (0.5, 3, 5, 100, 5, 0), [[], 100.0]),
  ('control: invalid zero latency', (0.5, 0, 5, 100, 5, 5), None),
  ('control: invalid zero population', (0.5, 2, 5, 0, 0, 5), None),
  ('regression: fractional latency',
   (0.8, 1.5, 2.5, 300, 6, 7),
   [[4.0, 1.3333, 2.5351, 2.7755, 3.3698, 3.9741, 4.6871], 300.0]),
  ('regression: large seed',
   (0.9, 4, 3, 100, 60, 6),
   [[15.0, 11.25, 9.7875, 8.9949, 8.2544, 7.4237], 100.0])]]
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 fixtureActualExpectedOutcome
regression: influenza-like 2 day latency[[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], 990.0][[5.0, 2.5, 2.735, 3.0948, 3.5019, 3.9584, 4.4687, 5.0378], 1000.0]Failed
regression: measles-like long latency[[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], 4995.0][[0.625, 0.5469, 0.5956, 0.7239, 0.9186, 1.1836, 1.5328, 1.9882, 2.5798, 3.3471, 4.3413, 5.6281], 5000.0]Failed
regression: one-day latency[[0.0, 0.0, 0.0, 0.0, 0.0, 0.0], 196.0][[4.0, 0.0, 1.568, 1.1666, 1.4758, 1.5459], 200.0]Failed
regression: no transmission[[0.0, 0.0, 0.0, 0.0, 0.0, 0.0], 80.0][[6.6667, 4.4444, 2.963, 1.9753, 1.3169, 0.8779], 100.0]Failed
regression: boundary zero days[[], 95.0][[], 100.0]Failed
control: invalid zero latencyNoneNonePassed
control: invalid zero populationNoneNonePassed

SHA-256 / 8146d2b661d798d0fcaa12cbbaad2b596f551cad2986ceef49ca5d79c43c4eb8

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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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 2026-09-29T14:47:28.838933+00:00.

Case digest / 2fdecd56635e8b7b8e4dbc5d5610af2866169912de645408f5dae37ffc0319b0