FA-11986 / Discrete control systems / Open access

A sampled command delay reads newly written input too early · case 01

A sampled command delay reads newly written input too early.

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

ROOT CAUSE

The input is returned immediately instead of passing through the delay queue.

VERIFIED REPAIR

Read the oldest queue element before shifting in the current input.

Unsuccessful approach: Shifting first shortens the delay by one sample.

Case contract

A nonempty queue stores pending oldest-first delayed commands; return [output,new_queue] after one tick. Its length is the exact integer sample delay.

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(queue, command):
    return [command, queue[1:]+[command]]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('single delay', solve([0], N), [0,[N]])
check('two delay', solve([N,2*N], 3*N), [N,[2*N,3*N]])
check('negative history', solve([-N,0], N), [-N,[0,N]])
check('zero command', solve([N], 0), [N,[0]])
check('constant stream', solve([N,N], N), [N,[N,N]])
check('long queue', solve([N,0,-N], 2*N), [N,[0,-N,2*N]])
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
single delay	`[1, [1]]`	`[0, [1]]`	Failed
two delay	`[3, [2, 3]]`	`[1, [2, 3]]`	Failed
negative history	`[1, [0, 1]]`	`[-1, [0, 1]]`	Failed
zero command	`[0, [0]]`	`[1, [0]]`	Failed
constant stream	`[1, [1, 1]]`	`[1, [1, 1]]`	Passed
long queue	`[2, [0, -1, 2]]`	`[1, [0, -1, 2]]`	Failed

SHA-256 / 0c125ef260958750dbf713b89dbb3c1f809b1fd5e94ed04522d013aa57c12704

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(queue, command):
    updated=queue[1:]+[command]
    return [updated[0],updated]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('single delay', solve([0], N), [0,[N]])
check('two delay', solve([N,2*N], 3*N), [N,[2*N,3*N]])
check('negative history', solve([-N,0], N), [-N,[0,N]])
check('zero command', solve([N], 0), [N,[0]])
check('constant stream', solve([N,N], N), [N,[N,N]])
check('long queue', solve([N,0,-N], 2*N), [N,[0,-N,2*N]])
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
single delay	`[1, [1]]`	`[0, [1]]`	Failed
two delay	`[2, [2, 3]]`	`[1, [2, 3]]`	Failed
negative history	`[0, [0, 1]]`	`[-1, [0, 1]]`	Failed
zero command	`[0, [0]]`	`[1, [0]]`	Failed
constant stream	`[1, [1, 1]]`	`[1, [1, 1]]`	Passed
long queue	`[0, [0, -1, 2]]`	`[1, [0, -1, 2]]`	Failed

SHA-256 / 025416d2fd7c1362849def56935516fc777a6bcc8d536d31cce6555dba77c09f

3 / The verified repair

Exit 0

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

N = 1
observations = []
def solve(queue, command):
    return [queue[0],queue[1:]+[command]]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('single delay', solve([0], N), [0,[N]])
check('two delay', solve([N,2*N], 3*N), [N,[2*N,3*N]])
check('negative history', solve([-N,0], N), [-N,[0,N]])
check('zero command', solve([N], 0), [N,[0]])
check('constant stream', solve([N,N], N), [N,[N,N]])
check('long queue', solve([N,0,-N], 2*N), [N,[0,-N,2*N]])
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
single delay	`[0, [1]]`	`[0, [1]]`	Passed
two delay	`[1, [2, 3]]`	`[1, [2, 3]]`	Passed
negative history	`[-1, [0, 1]]`	`[-1, [0, 1]]`	Passed
zero command	`[1, [0]]`	`[1, [0]]`	Passed
constant stream	`[1, [1, 1]]`	`[1, [1, 1]]`	Passed
long queue	`[1, [0, -1, 2]]`	`[1, [0, -1, 2]]`	Passed

SHA-256 / 9617650965f5938d1a2af7b6897df0fa2a1856a78161dc88c1687f841d6f80ae

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 2026-09-29T14:38:52.824223+00:00.

Case digest / 69d3ee04014bf2d05a1925f402ab345c7f0c844619ae182158bc4ceb9e903cf3