FAILURE MAP
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FA-59461 / Subscription proration billing / Open access

Paused days extending the billing period: overlap merge extent · case 01

A short pause nested inside a longer one shortens the extension.

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

ROOT CAUSE

Merging replaces the merged end with the new end even when it is earlier.

THE FAILURE

Merging replaces the merged end with the new end even when it is earlier.

Unsuccessful approach: The attempt appends the tail from the previous end, which has negative length for nested pauses.

Case contract

Input {start, end (exclusive) day numbers, pauses: [[from, to)]}. Pause intervals are clipped to the period, empty ones dropped, then overlapping ones merged. The period end moves out by the number of distinct paused days. Return [new_end, paused_days].

Why this case matters

Pausing a subscription should extend paid service exactly by the paused time, no more and no less.

1 / The failure

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(x):
    s, e = x['start'], x['end']
    iv = sorted([max(a, s), min(b, e)] for a, b in x['pauses'])
    iv = [p for p in iv if p[0] < p[1]]
    merged = []
    for a, b in iv:
        if merged and a <= merged[-1][1]:
            merged[-1][1] = b
        else:
            merged.append([a, b])
    paused = sum(b - a for a, b in merged)
    return [e + paused, paused]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression', {'start': 73, 'end': 101, 'pauses': [[82, 97], [85, 93], [79, 80], [82, 85]]}, [117, 16]), ('regression', {'start': 98, 'end': 126, 'pauses': [[121, 127], [123, 125]]}, [131, 5]), ('partial-repair probe', {'start': 86, 'end': 116, 'pauses': [[89, 104], [117, 132], [97, 102]]}, [131, 15]), ('partial-repair probe', {'start': 73, 'end': 103, 'pauses': [[70, 72], [68, 79], [74, 86], [77, 84]]}, [116, 13]), ('normal control', {'start': 34, 'end': 65, 'pauses': [[30, 33], [31, 34]]}, [65, 0]), ('normal control', {'start': 20, 'end': 48, 'pauses': [[28, 28], [16, 30], [23, 23]]}, [58, 10]), ('normal control', {'start': 15, 'end': 45, 'pauses': [[20, 34], [22, 25], [25, 35]]}, [60, 15]), ('normal control', {'start': 28, 'end': 56, 'pauses': [[45, 57], [44, 58], [33, 35], [48, 63]]}, [70, 14])], [('regression', {'start': 98, 'end': 126, 'pauses': [[121, 127], [123, 125]]}, [131, 5]), ('regression', {'start': 86, 'end': 116, 'pauses': [[89, 104], [117, 132], [97, 102]]}, [131, 15]), ('partial-repair probe', {'start': 73, 'end': 103, 'pauses': [[70, 72], [68, 79], [74, 86], [77, 84]]}, [116, 13]), ('partial-repair probe', {'start': 91, 'end': 121, 'pauses': [[114, 118], [100, 102], [115, 116]]}, [127, 6]), ('normal control', {'start': 12, 'end': 40, 'pauses': []}, [40, 0]), ('normal control', {'start': 82, 'end': 112, 'pauses': [[76, 78], [84, 98], [94, 101], [102, 113]]}, [139, 27]), ('normal control', {'start': 46, 'end': 76, 'pauses': [[72, 81]]}, [80, 4]), ('normal control', {'start': 92, 'end': 122, 'pauses': [[121, 121]]}, [122, 0])], [('regression', {'start': 86, 'end': 116, 'pauses': [[89, 104], [117, 132], [97, 102]]}, [131, 15]), ('regression', {'start': 73, 'end': 103, 'pauses': [[70, 72], [68, 79], [74, 86], [77, 84]]}, [116, 13]), ('partial-repair probe', {'start': 91, 'end': 121, 'pauses': [[114, 118], [100, 102], [115, 116]]}, [127, 6]), ('partial-repair probe', {'start': 62, 'end': 93, 'pauses': [[66, 73], [84, 88], [83, 90]]}, [107, 14]), ('normal control', {'start': 100, 'end': 131, 'pauses': [[127, 128], [119, 120], [97, 98], [120, 128]]}, [140, 9]), ('normal control', {'start': 26, 'end': 56, 'pauses': []}, [56, 0]), ('normal control', {'start': 44, 'end': 72, 'pauses': [[58, 64], [45, 58], [59, 70], [41, 49]]}, [98, 26]), ('normal control', {'start': 92, 'end': 120, 'pauses': [[82, 91]]}, [120, 0])], [('regression', {'start': 73, 'end': 103, 'pauses': [[70, 72], [68, 79], [74, 86], [77, 84]]}, [116, 13]), ('regression', {'start': 91, 'end': 121, 'pauses': [[114, 118], [100, 102], [115, 116]]}, [127, 6]), ('partial-repair probe', {'start': 48, 'end': 78, 'pauses': [[52, 63], [70, 85], [39, 54], [71, 77]]}, [101, 23]), ('partial-repair probe', {'start': 66, 'end': 94, 'pauses': [[63, 73], [69, 72]]}, [101, 7]), ('normal control', {'start': 84, 'end': 115, 'pauses': []}, [115, 0]), ('normal control', {'start': 86, 'end': 114, 'pauses': [[113, 121]]}, [115, 1]), ('normal control', {'start': 0, 'end': 31, 'pauses': [[31, 46], [24, 33], [-7, -3], [-8, 6]]}, [44, 13]), ('normal control', {'start': 96, 'end': 124, 'pauses': [[120, 128], [90, 105], [99, 105], [116, 125]]}, [141, 17])], [('regression', {'start': 91, 'end': 121, 'pauses': [[114, 118], [100, 102], [115, 116]]}, [127, 6]), ('regression', {'start': 62, 'end': 93, 'pauses': [[66, 73], [84, 88], [83, 90]]}, [107, 14]), ('partial-repair probe', {'start': 16, 'end': 46, 'pauses': [[36, 37], [37, 38], [39, 54], [36, 43]]}, [56, 10]), ('partial-repair probe', {'start': 1, 'end': 32, 'pauses': [[-9, 3], [9, 19], [7, 18], [10, 13]]}, [46, 14]), ('normal control', {'start': 28, 'end': 56, 'pauses': [[35, 37], [21, 36]]}, [65, 9]), ('normal control', {'start': 14, 'end': 42, 'pauses': []}, [42, 0]), ('normal control', {'start': 56, 'end': 86, 'pauses': []}, [86, 0]), ('normal control', {'start': 94, 'end': 125, 'pauses': [[103, 112], [94, 95], [111, 118], [87, 100]]}, [146, 21])]]
for i, (label, args, expected) in enumerate(fixtures[N-1]):
    check("%s %d" % (label, i), 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 0[113, 12][117, 16]Failed
regression 1[130, 4][131, 5]Failed
partial-repair probe 2[129, 13][131, 15]Failed
partial-repair probe 3[114, 11][116, 13]Failed
normal control 4[65, 0][65, 0]Passed
normal control 5[58, 10][58, 10]Passed
normal control 6[60, 15][60, 15]Passed
normal control 7[70, 14][70, 14]Passed

SHA-256 / bd816f6335659673b61ebc2770b552a0af9b148a0eba1dde43fd43f9938d8811

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(x):
    s, e = x['start'], x['end']
    iv = sorted([max(a, s), min(b, e)] for a, b in x['pauses'])
    iv = [p for p in iv if p[0] < p[1]]
    merged = []
    for a, b in iv:
        if merged and a <= merged[-1][1]:
            merged.append([merged[-1][1], b])
        else:
            merged.append([a, b])
    paused = sum(b - a for a, b in merged)
    return [e + paused, paused]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression', {'start': 73, 'end': 101, 'pauses': [[82, 97], [85, 93], [79, 80], [82, 85]]}, [117, 16]), ('regression', {'start': 98, 'end': 126, 'pauses': [[121, 127], [123, 125]]}, [131, 5]), ('partial-repair probe', {'start': 86, 'end': 116, 'pauses': [[89, 104], [117, 132], [97, 102]]}, [131, 15]), ('partial-repair probe', {'start': 73, 'end': 103, 'pauses': [[70, 72], [68, 79], [74, 86], [77, 84]]}, [116, 13]), ('normal control', {'start': 34, 'end': 65, 'pauses': [[30, 33], [31, 34]]}, [65, 0]), ('normal control', {'start': 20, 'end': 48, 'pauses': [[28, 28], [16, 30], [23, 23]]}, [58, 10]), ('normal control', {'start': 15, 'end': 45, 'pauses': [[20, 34], [22, 25], [25, 35]]}, [60, 15]), ('normal control', {'start': 28, 'end': 56, 'pauses': [[45, 57], [44, 58], [33, 35], [48, 63]]}, [70, 14])], [('regression', {'start': 98, 'end': 126, 'pauses': [[121, 127], [123, 125]]}, [131, 5]), ('regression', {'start': 86, 'end': 116, 'pauses': [[89, 104], [117, 132], [97, 102]]}, [131, 15]), ('partial-repair probe', {'start': 73, 'end': 103, 'pauses': [[70, 72], [68, 79], [74, 86], [77, 84]]}, [116, 13]), ('partial-repair probe', {'start': 91, 'end': 121, 'pauses': [[114, 118], [100, 102], [115, 116]]}, [127, 6]), ('normal control', {'start': 12, 'end': 40, 'pauses': []}, [40, 0]), ('normal control', {'start': 82, 'end': 112, 'pauses': [[76, 78], [84, 98], [94, 101], [102, 113]]}, [139, 27]), ('normal control', {'start': 46, 'end': 76, 'pauses': [[72, 81]]}, [80, 4]), ('normal control', {'start': 92, 'end': 122, 'pauses': [[121, 121]]}, [122, 0])], [('regression', {'start': 86, 'end': 116, 'pauses': [[89, 104], [117, 132], [97, 102]]}, [131, 15]), ('regression', {'start': 73, 'end': 103, 'pauses': [[70, 72], [68, 79], [74, 86], [77, 84]]}, [116, 13]), ('partial-repair probe', {'start': 91, 'end': 121, 'pauses': [[114, 118], [100, 102], [115, 116]]}, [127, 6]), ('partial-repair probe', {'start': 62, 'end': 93, 'pauses': [[66, 73], [84, 88], [83, 90]]}, [107, 14]), ('normal control', {'start': 100, 'end': 131, 'pauses': [[127, 128], [119, 120], [97, 98], [120, 128]]}, [140, 9]), ('normal control', {'start': 26, 'end': 56, 'pauses': []}, [56, 0]), ('normal control', {'start': 44, 'end': 72, 'pauses': [[58, 64], [45, 58], [59, 70], [41, 49]]}, [98, 26]), ('normal control', {'start': 92, 'end': 120, 'pauses': [[82, 91]]}, [120, 0])], [('regression', {'start': 73, 'end': 103, 'pauses': [[70, 72], [68, 79], [74, 86], [77, 84]]}, [116, 13]), ('regression', {'start': 91, 'end': 121, 'pauses': [[114, 118], [100, 102], [115, 116]]}, [127, 6]), ('partial-repair probe', {'start': 48, 'end': 78, 'pauses': [[52, 63], [70, 85], [39, 54], [71, 77]]}, [101, 23]), ('partial-repair probe', {'start': 66, 'end': 94, 'pauses': [[63, 73], [69, 72]]}, [101, 7]), ('normal control', {'start': 84, 'end': 115, 'pauses': []}, [115, 0]), ('normal control', {'start': 86, 'end': 114, 'pauses': [[113, 121]]}, [115, 1]), ('normal control', {'start': 0, 'end': 31, 'pauses': [[31, 46], [24, 33], [-7, -3], [-8, 6]]}, [44, 13]), ('normal control', {'start': 96, 'end': 124, 'pauses': [[120, 128], [90, 105], [99, 105], [116, 125]]}, [141, 17])], [('regression', {'start': 91, 'end': 121, 'pauses': [[114, 118], [100, 102], [115, 116]]}, [127, 6]), ('regression', {'start': 62, 'end': 93, 'pauses': [[66, 73], [84, 88], [83, 90]]}, [107, 14]), ('partial-repair probe', {'start': 16, 'end': 46, 'pauses': [[36, 37], [37, 38], [39, 54], [36, 43]]}, [56, 10]), ('partial-repair probe', {'start': 1, 'end': 32, 'pauses': [[-9, 3], [9, 19], [7, 18], [10, 13]]}, [46, 14]), ('normal control', {'start': 28, 'end': 56, 'pauses': [[35, 37], [21, 36]]}, [65, 9]), ('normal control', {'start': 14, 'end': 42, 'pauses': []}, [42, 0]), ('normal control', {'start': 56, 'end': 86, 'pauses': []}, [86, 0]), ('normal control', {'start': 94, 'end': 125, 'pauses': [[103, 112], [94, 95], [111, 118], [87, 100]]}, [146, 21])]]
for i, (label, args, expected) in enumerate(fixtures[N-1]):
    check("%s %d" % (label, i), 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 0[113, 12][117, 16]Failed
regression 1[130, 4][131, 5]Failed
partial-repair probe 2[129, 13][131, 15]Failed
partial-repair probe 3[114, 11][116, 13]Failed
normal control 4[65, 0][65, 0]Passed
normal control 5[58, 10][58, 10]Passed
normal control 6[60, 15][60, 15]Passed
normal control 7[70, 14][70, 14]Passed

SHA-256 / f58418b79e3cd8cb6034337647952de70c05b704c734dc41c2fc92b9f5cb4487

HELD IN THE MEMBER ARCHIVE

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

This mechanism has 8 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

A deterministic teaching model of a stipulated billing rule. It makes no claim to reproduce any billing provider's exact behaviour and is not billing software. 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 2026-09-29T14:46:36.563363+00:00.

Case digest / 01110b532312fa3a8ed924b1f7c61ef1d46b2c18d4b12d5e714b511723e93522