FA-11951 / Discrete control systems / Open access

A relay forgets its state inside the hysteresis band · case 01

A relay forgets its state inside the hysteresis band.

Verified by executionVariant 1 · 6 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

A single upper threshold is evaluated without retaining relay state.

THE FAILURE

A single upper threshold is evaluated without retaining relay state.

Unsuccessful approach: Using the midpoint while already on shrinks the off hysteresis boundary.

Case contract

Schmitt relay with low<high: boundary equality switches; open interval retains previous boolean output.

Why this case matters

An offline discrete controller model isolates this state or arithmetic fault; it makes no physical plant or safety claim.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(on, value, low, high):
    return value >= high
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('hold on', solve(True, N, 0, 4*N), True)
check('hold off', solve(False, 3*N, 0, 4*N), False)
check('upper equality', solve(False, 4*N, 0, 4*N), True)
check('lower equality', solve(True, 0, 0, 4*N), False)
check('above', solve(False, 5*N, 0, 4*N), True)
check('below', solve(True, -N, 0, 4*N), False)
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
hold on	`False`	`True`	Failed
hold off	`False`	`False`	Passed
upper equality	`True`	`True`	Passed
lower equality	`False`	`False`	Passed
above	`True`	`True`	Passed
below	`False`	`False`	Passed

SHA-256 / b6acc94428dd6a9f4b8b2df411cd6a033b7a2c58b3338ce32a1df237eda1b285

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(on, value, low, high):
    return value >= ((low+high)//2 if on else high)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('hold on', solve(True, N, 0, 4*N), True)
check('hold off', solve(False, 3*N, 0, 4*N), False)
check('upper equality', solve(False, 4*N, 0, 4*N), True)
check('lower equality', solve(True, 0, 0, 4*N), False)
check('above', solve(False, 5*N, 0, 4*N), True)
check('below', solve(True, -N, 0, 4*N), False)
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
hold on	`False`	`True`	Failed
hold off	`False`	`False`	Passed
upper equality	`True`	`True`	Passed
lower equality	`False`	`False`	Passed
above	`True`	`True`	Passed
below	`False`	`False`	Passed

SHA-256 / 895fda49e27cbb285fa4bcb2638b208b18e90c03b4c7bf048031e6f12dbce68f

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 6 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

Integer-valued controlled examples only; no physical plant, stability guarantee, timing jitter, or hardware behavior is modeled. 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 2026-09-29T14:38:52.398186+00:00.

Case digest / e5e3ef77304239a7bcc4386f350dbc663289505ac9b188da43342a9914b2ee01