FA-91801 / Digital signal filters / Open access

Q15 FIR pushes new samples onto the wrong end of the delay line · case 01

The impulse response comes out reversed for asymmetric taps.

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

ROOT CAUSE

The history is updated as hist[1:] + [v], so the newest sample aligns with the last coefficient.

VERIFIED REPAIR

Insert the new sample at index 0: [v] + hist[:-1].

Unsuccessful approach: The attempted repair inserts at the front but drops the second-newest instead of the oldest sample.

Case contract

Input [coeffs, samples] as Q15 integers. Each output accumulates the full-precision products c_k x[n-k] (zero history) in a wide accumulator, then rounds once (add 2**14, arithmetic shift 15) and saturates to int16. Return {"y": outputs, "saturations": number of clipped outputs}.

Why this case matters

DSP MAC units keep guard bits and round once; per-product rounding or missing overflow accounting degrades fixed-point FIRs.

1 / The failure

Exit 1

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

N = 1
observations = []
def solve(x):
    coefs, xs = x
    hist = [0] * len(coefs)
    out = []
    sat = 0
    for v in xs:
        hist = hist[1:] + [v]
        acc = sum(c * s for c, s in zip(coefs, hist))
        y = (acc + (1 << 14)) >> 15
        if y > 32767:
            y = 32767
            sat += 1
        elif y < -32768:
            y = -32768
            sat += 1
        out.append(y)
    return {'y': out, 'saturations': sat}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: exact rail then negative overflow', [[16384, 16384, 32767], [32767, 32767, -32768, -32768]], {'y': [16384, 32767, 32766, -2], 'saturations': 0}], ['regression: asymmetric taps', [[16384, 8192, 0, -4096], [1000, 0, 0, 0, 0]], {'y': [500, 250, 0, -125, 0], 'saturations': 0}], ['repair check: small products lost', [[1000, 1000, 1000], [100, 100, 100, 100]], {'y': [3, 6, 9, 9], 'saturations': 0}], ['control: random q15 fir 6', [[2221], [-13506, -128, -3471, -275, -20285]], {'y': [-915, -9, -235, -19, -1375], 'saturations': 0}], ['control: random q15 fir 10', [[17726], [-261, 178, -17320, 220]], {'y': [-141, 96, -9369, 119], 'saturations': 0}], ['control: random q15 fir 11', [[-1511], [227, 17400]], {'y': [-10, -802], 'saturations': 0}], ['control: random q15 fir 14', [[2191], [5955, -128]], {'y': [398, -9], 'saturations': 0}]], [['regression: random q15 fir 1', [[-2422, 8115, -26238], [81, -19840, 164, 18, -31318, 26443]], {'y': [-6, 1487, -4990, 15926, 2188, -9725], 'saturations': 0}], ['regression: random q15 fir 2', [[-1074, -846, 29231], [-7102, 287, 18053, 24830, -286, 148]], {'y': [233, 174, -6935, -1024, 15473, 22152], 'saturations': 0}], ['repair check: positive overflow', [[32767, 32767], [32767, 32767]], {'y': [32766, 32767], 'saturations': 1}], ['control: random q15 fir 16', [[-1447], [-227, 108]], {'y': [10, -5], 'saturations': 0}], ['control: random q15 fir 21', [[-28191], [-29871, 2888, 20728, -231, -2825, 26092]], {'y': [25699, -2485, -17833, 199, 2430, -22447], 'saturations': 0}], ['control: random q15 fir 23', [[2603], [-222, 296, 26049]], {'y': [-18, 24, 2069], 'saturations': 0}], ['control: random q15 fir 25', [[-1403], [-217, -76, -13515]], {'y': [9, 3, 579], 'saturations': 0}]], [['regression: random q15 fir 4', [[375, 13267], [120, 1419, -3648]], {'y': [1, 65, 533], 'saturations': 0}], ['regression: random q15 fir 5', [[21007, -2568, -1633], [-267, 32265, 7287, 49]], {'y': [-171, 20705, 2156, -2148], 'saturations': 0}], ['regression: exact rail then negative overflow', [[16384, 16384, 32767], [32767, 32767, -32768, -32768]], {'y': [16384, 32767, 32766, -2], 'saturations': 0}], ['control: random q15 fir 30', [[-1704], [264, 265, -20482, -11272]], {'y': [-14, -14, 1065, 586], 'saturations': 0}], ['control: random q15 fir 31', [[-3085], [-26725, -134, 160, 76]], {'y': [2516, 13, -15, -7], 'saturations': 0}], ['control: random q15 fir 32', [[-531], [-184, 26, -95, 27147, -17595, -11363]], {'y': [3, 0, 2, -440, 285, 184], 'saturations': 0}], ['control: random q15 fir 39', [[6030], [48, -8, -16638, -41, -299]], {'y': [9, -1, -3062, -8, -55], 'saturations': 0}]], [['regression: random q15 fir 8', [[-249, 2187, 304], [24116, 6453, 6219, -174, -23699]], {'y': [-183, 1561, 607, 476, 226], 'saturations': 0}], ['regression: random q15 fir 9', [[-2404, -24823], [-43, 254, -254, -25264]], {'y': [3, 14, -174, 2046], 'saturations': 0}], ['regression: random q15 fir 0', [[-32619, -22239, 2111], [244, -26104, -17179, -16]], {'y': [-243, 25820, 32767, 9993], 'saturations': 1}], ['control: random q15 fir 41', [[1560], [-107, 23988, 110, -204]], {'y': [-5, 1142, 5, -10], 'saturations': 0}], ['control: random q15 fir 48', [[-4769], [-272, 210, 31, -12840, -276, 18842]], {'y': [40, -31, -5, 1869, 40, -2742], 'saturations': 0}], ['control: random q15 fir 6', [[2221], [-13506, -128, -3471, -275, -20285]], {'y': [-915, -9, -235, -19, -1375], 'saturations': 0}], ['control: random q15 fir 10', [[17726], [-261, 178, -17320, 220]], {'y': [-141, 96, -9369, 119], 'saturations': 0}]], [['regression: random q15 fir 13', [[-2749, -1952, 11064], [29305, 10126]], {'y': [-2458, -2595], 'saturations': 0}], ['regression: random q15 fir 15', [[7820, -2373, 744], [14902, 174, -178, 7258, -26936]], {'y': [3556, -1038, 283, 1749, -6958], 'saturations': 0}], ['regression: random q15 fir 2', [[-1074, -846, 29231], [-7102, 287, 18053, 24830, -286, 148]], {'y': [233, 174, -6935, -1024, 15473, 22152], 'saturations': 0}], ['control: random q15 fir 11', [[-1511], [227, 17400]], {'y': [-10, -802], 'saturations': 0}], ['control: random q15 fir 14', [[2191], [5955, -128]], {'y': [398, -9], 'saturations': 0}], ['control: random q15 fir 16', [[-1447], [-227, 108]], {'y': [10, -5], 'saturations': 0}], ['control: random q15 fir 21', [[-28191], [-29871, 2888, 20728, -231, -2825, 26092]], {'y': [25699, -2485, -17833, 199, 2430, -22447], 'saturations': 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 fixture	Actual	Expected	Outcome
regression: exact rail then negative overflow	`{'saturations': 1, 'y': [32766, 32767, 0, -32767]}`	`{'saturations': 0, 'y': [16384, 32767, 32766, -2]}`	Failed
regression: asymmetric taps	`{'saturations': 0, 'y': [-125, 0, 250, 500, 0]}`	`{'saturations': 0, 'y': [500, 250, 0, -125, 0]}`	Failed
repair check: small products lost	`{'saturations': 0, 'y': [3, 6, 9, 9]}`	`{'saturations': 0, 'y': [3, 6, 9, 9]}`	Passed
control: random q15 fir 6	`{'saturations': 0, 'y': [-915, -9, -235, -19, -1375]}`	`{'saturations': 0, 'y': [-915, -9, -235, -19, -1375]}`	Passed
control: random q15 fir 10	`{'saturations': 0, 'y': [-141, 96, -9369, 119]}`	`{'saturations': 0, 'y': [-141, 96, -9369, 119]}`	Passed
control: random q15 fir 11	`{'saturations': 0, 'y': [-10, -802]}`	`{'saturations': 0, 'y': [-10, -802]}`	Passed
control: random q15 fir 14	`{'saturations': 0, 'y': [398, -9]}`	`{'saturations': 0, 'y': [398, -9]}`	Passed

SHA-256 / 852197009172600636e860b5cfa31f38216b0a57037a9f465c4a89687dd99b81

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(x):
    coefs, xs = x
    hist = [0] * len(coefs)
    out = []
    sat = 0
    for v in xs:
        hist = [v] + hist[1:]
        acc = sum(c * s for c, s in zip(coefs, hist))
        y = (acc + (1 << 14)) >> 15
        if y > 32767:
            y = 32767
            sat += 1
        elif y < -32768:
            y = -32768
            sat += 1
        out.append(y)
    return {'y': out, 'saturations': sat}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: exact rail then negative overflow', [[16384, 16384, 32767], [32767, 32767, -32768, -32768]], {'y': [16384, 32767, 32766, -2], 'saturations': 0}], ['regression: asymmetric taps', [[16384, 8192, 0, -4096], [1000, 0, 0, 0, 0]], {'y': [500, 250, 0, -125, 0], 'saturations': 0}], ['repair check: small products lost', [[1000, 1000, 1000], [100, 100, 100, 100]], {'y': [3, 6, 9, 9], 'saturations': 0}], ['control: random q15 fir 6', [[2221], [-13506, -128, -3471, -275, -20285]], {'y': [-915, -9, -235, -19, -1375], 'saturations': 0}], ['control: random q15 fir 10', [[17726], [-261, 178, -17320, 220]], {'y': [-141, 96, -9369, 119], 'saturations': 0}], ['control: random q15 fir 11', [[-1511], [227, 17400]], {'y': [-10, -802], 'saturations': 0}], ['control: random q15 fir 14', [[2191], [5955, -128]], {'y': [398, -9], 'saturations': 0}]], [['regression: random q15 fir 1', [[-2422, 8115, -26238], [81, -19840, 164, 18, -31318, 26443]], {'y': [-6, 1487, -4990, 15926, 2188, -9725], 'saturations': 0}], ['regression: random q15 fir 2', [[-1074, -846, 29231], [-7102, 287, 18053, 24830, -286, 148]], {'y': [233, 174, -6935, -1024, 15473, 22152], 'saturations': 0}], ['repair check: positive overflow', [[32767, 32767], [32767, 32767]], {'y': [32766, 32767], 'saturations': 1}], ['control: random q15 fir 16', [[-1447], [-227, 108]], {'y': [10, -5], 'saturations': 0}], ['control: random q15 fir 21', [[-28191], [-29871, 2888, 20728, -231, -2825, 26092]], {'y': [25699, -2485, -17833, 199, 2430, -22447], 'saturations': 0}], ['control: random q15 fir 23', [[2603], [-222, 296, 26049]], {'y': [-18, 24, 2069], 'saturations': 0}], ['control: random q15 fir 25', [[-1403], [-217, -76, -13515]], {'y': [9, 3, 579], 'saturations': 0}]], [['regression: random q15 fir 4', [[375, 13267], [120, 1419, -3648]], {'y': [1, 65, 533], 'saturations': 0}], ['regression: random q15 fir 5', [[21007, -2568, -1633], [-267, 32265, 7287, 49]], {'y': [-171, 20705, 2156, -2148], 'saturations': 0}], ['regression: exact rail then negative overflow', [[16384, 16384, 32767], [32767, 32767, -32768, -32768]], {'y': [16384, 32767, 32766, -2], 'saturations': 0}], ['control: random q15 fir 30', [[-1704], [264, 265, -20482, -11272]], {'y': [-14, -14, 1065, 586], 'saturations': 0}], ['control: random q15 fir 31', [[-3085], [-26725, -134, 160, 76]], {'y': [2516, 13, -15, -7], 'saturations': 0}], ['control: random q15 fir 32', [[-531], [-184, 26, -95, 27147, -17595, -11363]], {'y': [3, 0, 2, -440, 285, 184], 'saturations': 0}], ['control: random q15 fir 39', [[6030], [48, -8, -16638, -41, -299]], {'y': [9, -1, -3062, -8, -55], 'saturations': 0}]], [['regression: random q15 fir 8', [[-249, 2187, 304], [24116, 6453, 6219, -174, -23699]], {'y': [-183, 1561, 607, 476, 226], 'saturations': 0}], ['regression: random q15 fir 9', [[-2404, -24823], [-43, 254, -254, -25264]], {'y': [3, 14, -174, 2046], 'saturations': 0}], ['regression: random q15 fir 0', [[-32619, -22239, 2111], [244, -26104, -17179, -16]], {'y': [-243, 25820, 32767, 9993], 'saturations': 1}], ['control: random q15 fir 41', [[1560], [-107, 23988, 110, -204]], {'y': [-5, 1142, 5, -10], 'saturations': 0}], ['control: random q15 fir 48', [[-4769], [-272, 210, 31, -12840, -276, 18842]], {'y': [40, -31, -5, 1869, 40, -2742], 'saturations': 0}], ['control: random q15 fir 6', [[2221], [-13506, -128, -3471, -275, -20285]], {'y': [-915, -9, -235, -19, -1375], 'saturations': 0}], ['control: random q15 fir 10', [[17726], [-261, 178, -17320, 220]], {'y': [-141, 96, -9369, 119], 'saturations': 0}]], [['regression: random q15 fir 13', [[-2749, -1952, 11064], [29305, 10126]], {'y': [-2458, -2595], 'saturations': 0}], ['regression: random q15 fir 15', [[7820, -2373, 744], [14902, 174, -178, 7258, -26936]], {'y': [3556, -1038, 283, 1749, -6958], 'saturations': 0}], ['regression: random q15 fir 2', [[-1074, -846, 29231], [-7102, 287, 18053, 24830, -286, 148]], {'y': [233, 174, -6935, -1024, 15473, 22152], 'saturations': 0}], ['control: random q15 fir 11', [[-1511], [227, 17400]], {'y': [-10, -802], 'saturations': 0}], ['control: random q15 fir 14', [[2191], [5955, -128]], {'y': [398, -9], 'saturations': 0}], ['control: random q15 fir 16', [[-1447], [-227, 108]], {'y': [10, -5], 'saturations': 0}], ['control: random q15 fir 21', [[-28191], [-29871, 2888, 20728, -231, -2825, 26092]], {'y': [25699, -2485, -17833, 199, 2430, -22447], 'saturations': 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 fixture	Actual	Expected	Outcome
regression: exact rail then negative overflow	`{'saturations': 0, 'y': [16384, 16384, -16384, -16384]}`	`{'saturations': 0, 'y': [16384, 32767, 32766, -2]}`	Failed
regression: asymmetric taps	`{'saturations': 0, 'y': [500, 0, 0, 0, 0]}`	`{'saturations': 0, 'y': [500, 250, 0, -125, 0]}`	Failed
repair check: small products lost	`{'saturations': 0, 'y': [3, 3, 3, 3]}`	`{'saturations': 0, 'y': [3, 6, 9, 9]}`	Failed
control: random q15 fir 6	`{'saturations': 0, 'y': [-915, -9, -235, -19, -1375]}`	`{'saturations': 0, 'y': [-915, -9, -235, -19, -1375]}`	Passed
control: random q15 fir 10	`{'saturations': 0, 'y': [-141, 96, -9369, 119]}`	`{'saturations': 0, 'y': [-141, 96, -9369, 119]}`	Passed
control: random q15 fir 11	`{'saturations': 0, 'y': [-10, -802]}`	`{'saturations': 0, 'y': [-10, -802]}`	Passed
control: random q15 fir 14	`{'saturations': 0, 'y': [398, -9]}`	`{'saturations': 0, 'y': [398, -9]}`	Passed

SHA-256 / e1dda233bbcc4e919a528a735be34e4ac534a04197e905339b0f35cd0165ae77

3 / The verified repair

Exit 0

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

N = 1
observations = []
def solve(x):
    coefs, xs = x
    hist = [0] * len(coefs)
    out = []
    sat = 0
    for v in xs:
        hist = [v] + hist[:-1]
        acc = sum(c * s for c, s in zip(coefs, hist))
        y = (acc + (1 << 14)) >> 15
        if y > 32767:
            y = 32767
            sat += 1
        elif y < -32768:
            y = -32768
            sat += 1
        out.append(y)
    return {'y': out, 'saturations': sat}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: exact rail then negative overflow', [[16384, 16384, 32767], [32767, 32767, -32768, -32768]], {'y': [16384, 32767, 32766, -2], 'saturations': 0}], ['regression: asymmetric taps', [[16384, 8192, 0, -4096], [1000, 0, 0, 0, 0]], {'y': [500, 250, 0, -125, 0], 'saturations': 0}], ['repair check: small products lost', [[1000, 1000, 1000], [100, 100, 100, 100]], {'y': [3, 6, 9, 9], 'saturations': 0}], ['control: random q15 fir 6', [[2221], [-13506, -128, -3471, -275, -20285]], {'y': [-915, -9, -235, -19, -1375], 'saturations': 0}], ['control: random q15 fir 10', [[17726], [-261, 178, -17320, 220]], {'y': [-141, 96, -9369, 119], 'saturations': 0}], ['control: random q15 fir 11', [[-1511], [227, 17400]], {'y': [-10, -802], 'saturations': 0}], ['control: random q15 fir 14', [[2191], [5955, -128]], {'y': [398, -9], 'saturations': 0}]], [['regression: random q15 fir 1', [[-2422, 8115, -26238], [81, -19840, 164, 18, -31318, 26443]], {'y': [-6, 1487, -4990, 15926, 2188, -9725], 'saturations': 0}], ['regression: random q15 fir 2', [[-1074, -846, 29231], [-7102, 287, 18053, 24830, -286, 148]], {'y': [233, 174, -6935, -1024, 15473, 22152], 'saturations': 0}], ['repair check: positive overflow', [[32767, 32767], [32767, 32767]], {'y': [32766, 32767], 'saturations': 1}], ['control: random q15 fir 16', [[-1447], [-227, 108]], {'y': [10, -5], 'saturations': 0}], ['control: random q15 fir 21', [[-28191], [-29871, 2888, 20728, -231, -2825, 26092]], {'y': [25699, -2485, -17833, 199, 2430, -22447], 'saturations': 0}], ['control: random q15 fir 23', [[2603], [-222, 296, 26049]], {'y': [-18, 24, 2069], 'saturations': 0}], ['control: random q15 fir 25', [[-1403], [-217, -76, -13515]], {'y': [9, 3, 579], 'saturations': 0}]], [['regression: random q15 fir 4', [[375, 13267], [120, 1419, -3648]], {'y': [1, 65, 533], 'saturations': 0}], ['regression: random q15 fir 5', [[21007, -2568, -1633], [-267, 32265, 7287, 49]], {'y': [-171, 20705, 2156, -2148], 'saturations': 0}], ['regression: exact rail then negative overflow', [[16384, 16384, 32767], [32767, 32767, -32768, -32768]], {'y': [16384, 32767, 32766, -2], 'saturations': 0}], ['control: random q15 fir 30', [[-1704], [264, 265, -20482, -11272]], {'y': [-14, -14, 1065, 586], 'saturations': 0}], ['control: random q15 fir 31', [[-3085], [-26725, -134, 160, 76]], {'y': [2516, 13, -15, -7], 'saturations': 0}], ['control: random q15 fir 32', [[-531], [-184, 26, -95, 27147, -17595, -11363]], {'y': [3, 0, 2, -440, 285, 184], 'saturations': 0}], ['control: random q15 fir 39', [[6030], [48, -8, -16638, -41, -299]], {'y': [9, -1, -3062, -8, -55], 'saturations': 0}]], [['regression: random q15 fir 8', [[-249, 2187, 304], [24116, 6453, 6219, -174, -23699]], {'y': [-183, 1561, 607, 476, 226], 'saturations': 0}], ['regression: random q15 fir 9', [[-2404, -24823], [-43, 254, -254, -25264]], {'y': [3, 14, -174, 2046], 'saturations': 0}], ['regression: random q15 fir 0', [[-32619, -22239, 2111], [244, -26104, -17179, -16]], {'y': [-243, 25820, 32767, 9993], 'saturations': 1}], ['control: random q15 fir 41', [[1560], [-107, 23988, 110, -204]], {'y': [-5, 1142, 5, -10], 'saturations': 0}], ['control: random q15 fir 48', [[-4769], [-272, 210, 31, -12840, -276, 18842]], {'y': [40, -31, -5, 1869, 40, -2742], 'saturations': 0}], ['control: random q15 fir 6', [[2221], [-13506, -128, -3471, -275, -20285]], {'y': [-915, -9, -235, -19, -1375], 'saturations': 0}], ['control: random q15 fir 10', [[17726], [-261, 178, -17320, 220]], {'y': [-141, 96, -9369, 119], 'saturations': 0}]], [['regression: random q15 fir 13', [[-2749, -1952, 11064], [29305, 10126]], {'y': [-2458, -2595], 'saturations': 0}], ['regression: random q15 fir 15', [[7820, -2373, 744], [14902, 174, -178, 7258, -26936]], {'y': [3556, -1038, 283, 1749, -6958], 'saturations': 0}], ['regression: random q15 fir 2', [[-1074, -846, 29231], [-7102, 287, 18053, 24830, -286, 148]], {'y': [233, 174, -6935, -1024, 15473, 22152], 'saturations': 0}], ['control: random q15 fir 11', [[-1511], [227, 17400]], {'y': [-10, -802], 'saturations': 0}], ['control: random q15 fir 14', [[2191], [5955, -128]], {'y': [398, -9], 'saturations': 0}], ['control: random q15 fir 16', [[-1447], [-227, 108]], {'y': [10, -5], 'saturations': 0}], ['control: random q15 fir 21', [[-28191], [-29871, 2888, 20728, -231, -2825, 26092]], {'y': [25699, -2485, -17833, 199, 2430, -22447], 'saturations': 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 fixture	Actual	Expected	Outcome
regression: exact rail then negative overflow	`{'saturations': 0, 'y': [16384, 32767, 32766, -2]}`	`{'saturations': 0, 'y': [16384, 32767, 32766, -2]}`	Passed
regression: asymmetric taps	`{'saturations': 0, 'y': [500, 250, 0, -125, 0]}`	`{'saturations': 0, 'y': [500, 250, 0, -125, 0]}`	Passed
repair check: small products lost	`{'saturations': 0, 'y': [3, 6, 9, 9]}`	`{'saturations': 0, 'y': [3, 6, 9, 9]}`	Passed
control: random q15 fir 6	`{'saturations': 0, 'y': [-915, -9, -235, -19, -1375]}`	`{'saturations': 0, 'y': [-915, -9, -235, -19, -1375]}`	Passed
control: random q15 fir 10	`{'saturations': 0, 'y': [-141, 96, -9369, 119]}`	`{'saturations': 0, 'y': [-141, 96, -9369, 119]}`	Passed
control: random q15 fir 11	`{'saturations': 0, 'y': [-10, -802]}`	`{'saturations': 0, 'y': [-10, -802]}`	Passed
control: random q15 fir 14	`{'saturations': 0, 'y': [398, -9]}`	`{'saturations': 0, 'y': [398, -9]}`	Passed

SHA-256 / ad7e620592ebbdb7e86a75e97599f45e9f900612c650eb5941712cce622538e2

Verification & scope

A deterministic bounded teaching model with a stipulated toy contract; exact rational arithmetic or fixed-decimal rounding keeps outputs strict JSON. It is not a production DSP library and claims no standards conformance. 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 2026-09-29T14:51:39.437723+00:00.

Case digest / dbeb170406820a0aec59063f8db7eb26696df818774bb4a9c7643eeecfa16901