FA-71991 / Error-correcting codes / Open access

RS syndromes evaluate the polynomial reversed · case 01

Error-free codewords report nonzero syndromes.

Verified by executionVariant 1 · 8 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Horner evaluation walks the coefficients lowest degree first.

VERIFIED REPAIR

Walk msg in its stored order (highest degree first).

Unsuccessful approach: Multiplying after adding evaluates x * msg(x), which is nonzero at alpha^0 for clean words.

Case contract

Reed-Solomon syndromes over GF(2^8) (0x11D, alpha = 2, first consecutive root alpha^0). msg lists coefficients from the highest degree down. S_j = msg(alpha^j) for j = 0..nsym-1 by Horner evaluation. Return [syndromes, whether any syndrome is nonzero].

Why this case matters

Storage and broadcast decoders start every Reed-Solomon block with a syndrome check.

1 / The failure

Exit 1

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

N = 1
observations = []
def solve(msg, nsym):
    EXP, LOG = [0] * 512, [0] * 256
    x = 1
    for i in range(255):
        EXP[i] = EXP[i + 255] = x
        LOG[x] = i
        x <<= 1
        if x & 0x100:
            x ^= 0x11D
    def mul(a, b):
        return 0 if a == 0 or b == 0 else EXP[LOG[a] + LOG[b]]
    
    synd = []
    for j in range(nsym):
        root = EXP[j]
        v = 0
        for coef in reversed(msg):
            v = mul(v, root) ^ coef
        synd.append(v)
    return [synd, any(synd)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression [[23, 252, 61, 84, 130], 2]', [[23, 252, 61, 84, 130], 2], [[0, 0], False]], ['regression [[23, 252, 61, 64, 130], 2]', [[23, 252, 61, 64, 130], 2], [[20, 40], True]], ['partial-repair [[23, 252, 61, 64, 130], 4]', [[23, 252, 61, 64, 130], 4], [[20, 40, 7, 141], True]], ['control [[0, 0, 0, 0], 2]', [[0, 0, 0, 0], 2], [[0, 0], False]], ['control [[5], 1]', [[5], 1], [[5], True]], ['control [[176, 102, 222, 44, 125, 89], 2]', [[176, 102, 222, 44, 125, 89], 2], [[0, 0], False]], ['control [[176, 102, 222, 61, 125, 89], 2]', [[176, 102, 222, 61, 125, 89], 2], [[17, 68], True]], ['control [[176, 102, 222, 61, 125, 89], 4]', [[176, 102, 222, 61, 125, 89], 4], [[17, 68, 169, 244], True]]], [['regression [[176, 102, 222, 44, 125, 89], 2]', [[176, 102, 222, 44, 125, 89], 2], [[0, 0], False]], ['regression [[176, 102, 222, 61, 125, 89], 2]', [[176, 102, 222, 61, 125, 89], 2], [[17, 68], True]], ['partial-repair [[176, 102, 222, 61, 125, 89], 4]', [[176, 102, 222, 61, 125, 89], 4], [[17, 68, 169, 244], True]], ['partial-repair [[123, 214, 103, 174, 192, 161, 31], 2]', [[123, 214, 103, 174, 192, 161, 31], 2], [[26, 52], True]], ['control [[5], 1]', [[5], 1], [[5], True]], ['control [[0, 0, 0, 0], 2]', [[0, 0, 0, 0], 2], [[0, 0], False]], ['control [[123, 214, 103, 174, 192, 161, 31], 4]', [[123, 214, 103, 174, 192, 161, 31], 4], [[26, 52, 69, 105], True]], ['control [[131, 154, 183, 135, 93, 251, 102, 233], 2]', [[131, 154, 183, 135, 93, 251, 102, 233], 2], [[0, 0], False]]], [['regression [[123, 214, 103, 174, 192, 187, 31], 2]', [[123, 214, 103, 174, 192, 187, 31], 2], [[0, 0], False]], ['regression [[123, 214, 103, 174, 192, 161, 31], 2]', [[123, 214, 103, 174, 192, 161, 31], 2], [[26, 52], True]], ['partial-repair [[131, 154, 183, 135, 93, 136, 102, 233], 2]', [[131, 154, 183, 135, 93, 136, 102, 233], 2], [[115, 209], True]], ['partial-repair [[131, 154, 183, 135, 93, 136, 102, 233], 4]', [[131, 154, 183, 135, 93, 136, 102, 233], 4], [[115, 209, 164, 73], True]], ['control [[0, 0, 0, 0], 2]', [[0, 0, 0, 0], 2], [[0, 0], False]], ['control [[5], 1]', [[5], 1], [[5], True]], ['control [[70, 25, 237, 118, 90, 165, 35, 253, 93, 184], 2]', [[70, 25, 237, 118, 90, 165, 35, 253, 93, 184], 2], [[0, 0], False]], ['control [[70, 25, 237, 118, 90, 32, 35, 253, 93, 184], 2]', [[70, 25, 237, 118, 90, 32, 35, 253, 93, 184], 2], [[133, 184], True]]], [['regression [[131, 154, 183, 135, 93, 251, 102, 233], 2]', [[131, 154, 183, 135, 93, 251, 102, 233], 2], [[0, 0], False]], ['regression [[131, 154, 183, 135, 93, 136, 102, 233], 2]', [[131, 154, 183, 135, 93, 136, 102, 233], 2], [[115, 209], True]], ['partial-repair [[70, 25, 237, 118, 90, 32, 35, 253, 93, 184], 4]', [[70, 25, 237, 118, 90, 32, 35, 253, 93, 184], 4], [[133, 184, 215, 167], True]], ['partial-repair [[178, 65, 204, 132, 27, 119, 170, 156, 109, 21, 94, 12], 2]', [[178, 65, 204, 132, 27, 119, 170, 156, 109, 21, 94, 12], 2], [[203, 88], True]], ['control [[5], 1]', [[5], 1], [[5], True]], ['control [[0, 0, 0, 0], 2]', [[0, 0, 0, 0], 2], [[0, 0], False]], ['control [[178, 65, 204, 132, 27, 119, 170, 156, 109, 21, 94, 12], 4]', [[178, 65, 204, 132, 27, 119, 170, 156, 109, 21, 94, 12], 4], [[203, 88, 8, 229], True]], ['control [[1, 5, 4], 3]', [[1, 5, 4], 3], [[0, 10, 0], True]]], [['regression [[70, 25, 237, 118, 90, 165, 35, 253, 93, 184], 2]', [[70, 25, 237, 118, 90, 165, 35, 253, 93, 184], 2], [[0, 0], False]], ['regression [[70, 25, 237, 118, 90, 32, 35, 253, 93, 184], 2]', [[70, 25, 237, 118, 90, 32, 35, 253, 93, 184], 2], [[133, 184], True]], ['partial-repair [[1, 5, 4], 3]', [[1, 5, 4], 3], [[0, 10, 0], True]], ['partial-repair [[2, 10, 8], 3]', [[2, 10, 8], 3], [[0, 20, 0], True]], ['control [[0, 0, 0, 0], 2]', [[0, 0, 0, 0], 2], [[0, 0], False]], ['control [[5], 1]', [[5], 1], [[5], True]], ['control [[1, 2, 3], 3]', [[1, 2, 3], 3], [[0, 3, 27], True]], ['control [[0, 0, 7], 2]', [[0, 0, 7], 2], [[7, 7], True]]]]
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 [[23, 252, 61, 84, 130], 2]	`[[0, 84], True]`	`[[0, 0], False]`	Failed
regression [[23, 252, 61, 64, 130], 2]	`[[20, 244], True]`	`[[20, 40], True]`	Failed
partial-repair [[23, 252, 61, 64, 130], 4]	`[[20, 244, 230, 164], True]`	`[[20, 40, 7, 141], True]`	Failed
control [[0, 0, 0, 0], 2]	`[[0, 0], False]`	`[[0, 0], False]`	Passed
control [[5], 1]	`[[5], True]`	`[[5], True]`	Passed
control [[176, 102, 222, 44, 125, 89], 2]	`[[0, 50], True]`	`[[0, 0], False]`	Failed
control [[176, 102, 222, 61, 125, 89], 2]	`[[17, 186], True]`	`[[17, 68], True]`	Failed
control [[176, 102, 222, 61, 125, 89], 4]	`[[17, 186, 219, 144], True]`	`[[17, 68, 169, 244], True]`	Failed

SHA-256 / 51cc57c6b2a3ca9b8c4bab75b412ccef23134aba17b98c5916c8661245821a3c

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(msg, nsym):
    EXP, LOG = [0] * 512, [0] * 256
    x = 1
    for i in range(255):
        EXP[i] = EXP[i + 255] = x
        LOG[x] = i
        x <<= 1
        if x & 0x100:
            x ^= 0x11D
    def mul(a, b):
        return 0 if a == 0 or b == 0 else EXP[LOG[a] + LOG[b]]
    
    synd = []
    for j in range(nsym):
        root = EXP[j]
        v = 0
        for coef in msg:
            v = mul(v ^ coef, root)
        synd.append(v)
    return [synd, any(synd)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression [[23, 252, 61, 84, 130], 2]', [[23, 252, 61, 84, 130], 2], [[0, 0], False]], ['regression [[23, 252, 61, 64, 130], 2]', [[23, 252, 61, 64, 130], 2], [[20, 40], True]], ['partial-repair [[23, 252, 61, 64, 130], 4]', [[23, 252, 61, 64, 130], 4], [[20, 40, 7, 141], True]], ['control [[0, 0, 0, 0], 2]', [[0, 0, 0, 0], 2], [[0, 0], False]], ['control [[5], 1]', [[5], 1], [[5], True]], ['control [[176, 102, 222, 44, 125, 89], 2]', [[176, 102, 222, 44, 125, 89], 2], [[0, 0], False]], ['control [[176, 102, 222, 61, 125, 89], 2]', [[176, 102, 222, 61, 125, 89], 2], [[17, 68], True]], ['control [[176, 102, 222, 61, 125, 89], 4]', [[176, 102, 222, 61, 125, 89], 4], [[17, 68, 169, 244], True]]], [['regression [[176, 102, 222, 44, 125, 89], 2]', [[176, 102, 222, 44, 125, 89], 2], [[0, 0], False]], ['regression [[176, 102, 222, 61, 125, 89], 2]', [[176, 102, 222, 61, 125, 89], 2], [[17, 68], True]], ['partial-repair [[176, 102, 222, 61, 125, 89], 4]', [[176, 102, 222, 61, 125, 89], 4], [[17, 68, 169, 244], True]], ['partial-repair [[123, 214, 103, 174, 192, 161, 31], 2]', [[123, 214, 103, 174, 192, 161, 31], 2], [[26, 52], True]], ['control [[5], 1]', [[5], 1], [[5], True]], ['control [[0, 0, 0, 0], 2]', [[0, 0, 0, 0], 2], [[0, 0], False]], ['control [[123, 214, 103, 174, 192, 161, 31], 4]', [[123, 214, 103, 174, 192, 161, 31], 4], [[26, 52, 69, 105], True]], ['control [[131, 154, 183, 135, 93, 251, 102, 233], 2]', [[131, 154, 183, 135, 93, 251, 102, 233], 2], [[0, 0], False]]], [['regression [[123, 214, 103, 174, 192, 187, 31], 2]', [[123, 214, 103, 174, 192, 187, 31], 2], [[0, 0], False]], ['regression [[123, 214, 103, 174, 192, 161, 31], 2]', [[123, 214, 103, 174, 192, 161, 31], 2], [[26, 52], True]], ['partial-repair [[131, 154, 183, 135, 93, 136, 102, 233], 2]', [[131, 154, 183, 135, 93, 136, 102, 233], 2], [[115, 209], True]], ['partial-repair [[131, 154, 183, 135, 93, 136, 102, 233], 4]', [[131, 154, 183, 135, 93, 136, 102, 233], 4], [[115, 209, 164, 73], True]], ['control [[0, 0, 0, 0], 2]', [[0, 0, 0, 0], 2], [[0, 0], False]], ['control [[5], 1]', [[5], 1], [[5], True]], ['control [[70, 25, 237, 118, 90, 165, 35, 253, 93, 184], 2]', [[70, 25, 237, 118, 90, 165, 35, 253, 93, 184], 2], [[0, 0], False]], ['control [[70, 25, 237, 118, 90, 32, 35, 253, 93, 184], 2]', [[70, 25, 237, 118, 90, 32, 35, 253, 93, 184], 2], [[133, 184], True]]], [['regression [[131, 154, 183, 135, 93, 251, 102, 233], 2]', [[131, 154, 183, 135, 93, 251, 102, 233], 2], [[0, 0], False]], ['regression [[131, 154, 183, 135, 93, 136, 102, 233], 2]', [[131, 154, 183, 135, 93, 136, 102, 233], 2], [[115, 209], True]], ['partial-repair [[70, 25, 237, 118, 90, 32, 35, 253, 93, 184], 4]', [[70, 25, 237, 118, 90, 32, 35, 253, 93, 184], 4], [[133, 184, 215, 167], True]], ['partial-repair [[178, 65, 204, 132, 27, 119, 170, 156, 109, 21, 94, 12], 2]', [[178, 65, 204, 132, 27, 119, 170, 156, 109, 21, 94, 12], 2], [[203, 88], True]], ['control [[5], 1]', [[5], 1], [[5], True]], ['control [[0, 0, 0, 0], 2]', [[0, 0, 0, 0], 2], [[0, 0], False]], ['control [[178, 65, 204, 132, 27, 119, 170, 156, 109, 21, 94, 12], 4]', [[178, 65, 204, 132, 27, 119, 170, 156, 109, 21, 94, 12], 4], [[203, 88, 8, 229], True]], ['control [[1, 5, 4], 3]', [[1, 5, 4], 3], [[0, 10, 0], True]]], [['regression [[70, 25, 237, 118, 90, 165, 35, 253, 93, 184], 2]', [[70, 25, 237, 118, 90, 165, 35, 253, 93, 184], 2], [[0, 0], False]], ['regression [[70, 25, 237, 118, 90, 32, 35, 253, 93, 184], 2]', [[70, 25, 237, 118, 90, 32, 35, 253, 93, 184], 2], [[133, 184], True]], ['partial-repair [[1, 5, 4], 3]', [[1, 5, 4], 3], [[0, 10, 0], True]], ['partial-repair [[2, 10, 8], 3]', [[2, 10, 8], 3], [[0, 20, 0], True]], ['control [[0, 0, 0, 0], 2]', [[0, 0, 0, 0], 2], [[0, 0], False]], ['control [[5], 1]', [[5], 1], [[5], True]], ['control [[1, 2, 3], 3]', [[1, 2, 3], 3], [[0, 3, 27], True]], ['control [[0, 0, 7], 2]', [[0, 0, 7], 2], [[7, 7], True]]]]
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 [[23, 252, 61, 84, 130], 2]	`[[0, 0], False]`	`[[0, 0], False]`	Passed
regression [[23, 252, 61, 64, 130], 2]	`[[20, 80], True]`	`[[20, 40], True]`	Failed
partial-repair [[23, 252, 61, 64, 130], 4]	`[[20, 80, 28, 28], True]`	`[[20, 40, 7, 141], True]`	Failed
control [[0, 0, 0, 0], 2]	`[[0, 0], False]`	`[[0, 0], False]`	Passed
control [[5], 1]	`[[5], True]`	`[[5], True]`	Passed
control [[176, 102, 222, 44, 125, 89], 2]	`[[0, 0], False]`	`[[0, 0], False]`	Passed
control [[176, 102, 222, 61, 125, 89], 2]	`[[17, 136], True]`	`[[17, 68], True]`	Failed
control [[176, 102, 222, 61, 125, 89], 4]	`[[17, 136, 158, 243], True]`	`[[17, 68, 169, 244], True]`	Failed

SHA-256 / 479cf6cf78338eda0c712fdef689c9004fdcb54c0277160c9a0d0d5c1fc1a8dd

3 / The verified repair

Exit 0

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

N = 1
observations = []
def solve(msg, nsym):
    EXP, LOG = [0] * 512, [0] * 256
    x = 1
    for i in range(255):
        EXP[i] = EXP[i + 255] = x
        LOG[x] = i
        x <<= 1
        if x & 0x100:
            x ^= 0x11D
    def mul(a, b):
        return 0 if a == 0 or b == 0 else EXP[LOG[a] + LOG[b]]
    
    synd = []
    for j in range(nsym):
        root = EXP[j]
        v = 0
        for coef in msg:
            v = mul(v, root) ^ coef
        synd.append(v)
    return [synd, any(synd)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression [[23, 252, 61, 84, 130], 2]', [[23, 252, 61, 84, 130], 2], [[0, 0], False]], ['regression [[23, 252, 61, 64, 130], 2]', [[23, 252, 61, 64, 130], 2], [[20, 40], True]], ['partial-repair [[23, 252, 61, 64, 130], 4]', [[23, 252, 61, 64, 130], 4], [[20, 40, 7, 141], True]], ['control [[0, 0, 0, 0], 2]', [[0, 0, 0, 0], 2], [[0, 0], False]], ['control [[5], 1]', [[5], 1], [[5], True]], ['control [[176, 102, 222, 44, 125, 89], 2]', [[176, 102, 222, 44, 125, 89], 2], [[0, 0], False]], ['control [[176, 102, 222, 61, 125, 89], 2]', [[176, 102, 222, 61, 125, 89], 2], [[17, 68], True]], ['control [[176, 102, 222, 61, 125, 89], 4]', [[176, 102, 222, 61, 125, 89], 4], [[17, 68, 169, 244], True]]], [['regression [[176, 102, 222, 44, 125, 89], 2]', [[176, 102, 222, 44, 125, 89], 2], [[0, 0], False]], ['regression [[176, 102, 222, 61, 125, 89], 2]', [[176, 102, 222, 61, 125, 89], 2], [[17, 68], True]], ['partial-repair [[176, 102, 222, 61, 125, 89], 4]', [[176, 102, 222, 61, 125, 89], 4], [[17, 68, 169, 244], True]], ['partial-repair [[123, 214, 103, 174, 192, 161, 31], 2]', [[123, 214, 103, 174, 192, 161, 31], 2], [[26, 52], True]], ['control [[5], 1]', [[5], 1], [[5], True]], ['control [[0, 0, 0, 0], 2]', [[0, 0, 0, 0], 2], [[0, 0], False]], ['control [[123, 214, 103, 174, 192, 161, 31], 4]', [[123, 214, 103, 174, 192, 161, 31], 4], [[26, 52, 69, 105], True]], ['control [[131, 154, 183, 135, 93, 251, 102, 233], 2]', [[131, 154, 183, 135, 93, 251, 102, 233], 2], [[0, 0], False]]], [['regression [[123, 214, 103, 174, 192, 187, 31], 2]', [[123, 214, 103, 174, 192, 187, 31], 2], [[0, 0], False]], ['regression [[123, 214, 103, 174, 192, 161, 31], 2]', [[123, 214, 103, 174, 192, 161, 31], 2], [[26, 52], True]], ['partial-repair [[131, 154, 183, 135, 93, 136, 102, 233], 2]', [[131, 154, 183, 135, 93, 136, 102, 233], 2], [[115, 209], True]], ['partial-repair [[131, 154, 183, 135, 93, 136, 102, 233], 4]', [[131, 154, 183, 135, 93, 136, 102, 233], 4], [[115, 209, 164, 73], True]], ['control [[0, 0, 0, 0], 2]', [[0, 0, 0, 0], 2], [[0, 0], False]], ['control [[5], 1]', [[5], 1], [[5], True]], ['control [[70, 25, 237, 118, 90, 165, 35, 253, 93, 184], 2]', [[70, 25, 237, 118, 90, 165, 35, 253, 93, 184], 2], [[0, 0], False]], ['control [[70, 25, 237, 118, 90, 32, 35, 253, 93, 184], 2]', [[70, 25, 237, 118, 90, 32, 35, 253, 93, 184], 2], [[133, 184], True]]], [['regression [[131, 154, 183, 135, 93, 251, 102, 233], 2]', [[131, 154, 183, 135, 93, 251, 102, 233], 2], [[0, 0], False]], ['regression [[131, 154, 183, 135, 93, 136, 102, 233], 2]', [[131, 154, 183, 135, 93, 136, 102, 233], 2], [[115, 209], True]], ['partial-repair [[70, 25, 237, 118, 90, 32, 35, 253, 93, 184], 4]', [[70, 25, 237, 118, 90, 32, 35, 253, 93, 184], 4], [[133, 184, 215, 167], True]], ['partial-repair [[178, 65, 204, 132, 27, 119, 170, 156, 109, 21, 94, 12], 2]', [[178, 65, 204, 132, 27, 119, 170, 156, 109, 21, 94, 12], 2], [[203, 88], True]], ['control [[5], 1]', [[5], 1], [[5], True]], ['control [[0, 0, 0, 0], 2]', [[0, 0, 0, 0], 2], [[0, 0], False]], ['control [[178, 65, 204, 132, 27, 119, 170, 156, 109, 21, 94, 12], 4]', [[178, 65, 204, 132, 27, 119, 170, 156, 109, 21, 94, 12], 4], [[203, 88, 8, 229], True]], ['control [[1, 5, 4], 3]', [[1, 5, 4], 3], [[0, 10, 0], True]]], [['regression [[70, 25, 237, 118, 90, 165, 35, 253, 93, 184], 2]', [[70, 25, 237, 118, 90, 165, 35, 253, 93, 184], 2], [[0, 0], False]], ['regression [[70, 25, 237, 118, 90, 32, 35, 253, 93, 184], 2]', [[70, 25, 237, 118, 90, 32, 35, 253, 93, 184], 2], [[133, 184], True]], ['partial-repair [[1, 5, 4], 3]', [[1, 5, 4], 3], [[0, 10, 0], True]], ['partial-repair [[2, 10, 8], 3]', [[2, 10, 8], 3], [[0, 20, 0], True]], ['control [[0, 0, 0, 0], 2]', [[0, 0, 0, 0], 2], [[0, 0], False]], ['control [[5], 1]', [[5], 1], [[5], True]], ['control [[1, 2, 3], 3]', [[1, 2, 3], 3], [[0, 3, 27], True]], ['control [[0, 0, 7], 2]', [[0, 0, 7], 2], [[7, 7], True]]]]
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 [[23, 252, 61, 84, 130], 2]	`[[0, 0], False]`	`[[0, 0], False]`	Passed
regression [[23, 252, 61, 64, 130], 2]	`[[20, 40], True]`	`[[20, 40], True]`	Passed
partial-repair [[23, 252, 61, 64, 130], 4]	`[[20, 40, 7, 141], True]`	`[[20, 40, 7, 141], True]`	Passed
control [[0, 0, 0, 0], 2]	`[[0, 0], False]`	`[[0, 0], False]`	Passed
control [[5], 1]	`[[5], True]`	`[[5], True]`	Passed
control [[176, 102, 222, 44, 125, 89], 2]	`[[0, 0], False]`	`[[0, 0], False]`	Passed
control [[176, 102, 222, 61, 125, 89], 2]	`[[17, 68], True]`	`[[17, 68], True]`	Passed
control [[176, 102, 222, 61, 125, 89], 4]	`[[17, 68, 169, 244], True]`	`[[17, 68, 169, 244], True]`	Passed

SHA-256 / 978815099db6e26400fc86442e5070209fd6fc3bdf1860c7f42c6c7e15bbeca2

Verification & scope

A deterministic, bounded teaching model of the named code under the stated contract; not a production codec. 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 2026-09-29T14:48:34.598398+00:00.

Case digest / fc70c4ea89e07c28c250e76d72f78e7b1be6f6e7df1d85bf7138060c9382e534