FAILURE MAP
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FA-61106 / Bond day-count conventions / Open access

Discount-basis bill price and bond-equivalent yield: a 183-day bill in a 365-day basis year uses the short-dated formula · case 01

Bills just over half a 365-day year report a yield from the simple formula.

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

ROOT CAUSE

The branch hard-codes 183 days, the half year of a 366-day basis.

THE FAILURE

The branch hard-codes 183 days, the half year of a 366-day basis.

Unsuccessful approach: Rounding half the basis up to a whole day still admits 183 days under a 365-day basis.

Case contract

Inputs settlement and maturity [y,m,d] (1 to 364 days apart) and discount rate d. t = days. Price = 100*(1 - d*t/360). Year basis B is 366 if a 29 February lies in (settle, settle+365 days], else 365. For t <= B/2, BEY = B*d/(360 - d*t); otherwise BEY solves the quadratic with a = t/(2B) - 0.25, b = t/B, c = (price-100)/price, taking (-b + sqrt(b^2 - 4ac))/(2a). Return [price rounded 6, BEY rounded 8].

Why this case matters

Bond accrual and pricing systems depend on exact day-count arithmetic; a single-day error changes settlement cash.

1 / The failure

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
import datetime
import math
N = 1
observations = []
def solve(settle, maturity, d):
    S = datetime.date(*settle)
    M = datetime.date(*maturity)
    t = (M - S).days
    def leap(y):
        return (y % 4 == 0 and y % 100 != 0) or y % 400 == 0
    horizon = S + datetime.timedelta(days=365)
    basis = 366 if any(leap(y) and S < datetime.date(y, 2, 29) <= horizon for y in (S.year, S.year + 1)) else 365
    price = 100 * (1 - d * t / 360)
    if t <= 183:
        bey = basis * d / (360 - d * t)
    else:
        a = t / (2 * basis) - 0.25
        b = t / basis
        c = (price - 100) / price
        bey = (-b + math.sqrt(b * b - 4 * a * c)) / (2 * a)
    return [round(price, 6), round(bey, 8)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression half-year threshold 1', [[2066, 5, 30], [2066, 11, 29], 0.08], [95.933333, 0.08453969]], ['regression half-year threshold 2', [[2021, 2, 3], [2021, 8, 5], 0.0525], [97.33125, 0.05468459]], ['partial repair probe 1', [[2099, 12, 15], [2100, 6, 16], 0.08], [95.933333, 0.08453969]], ['partial repair probe 2', [[2005, 5, 30], [2005, 11, 29], 0.025], [98.729167, 0.02567259]], ['boundary control 1', [[2023, 5, 1], [2023, 10, 30], 0.05], [97.472222, 0.05215161]], ['boundary control 2', [[2023, 5, 1], [2023, 10, 31], 0.05], [97.458333, 0.05215904]], ['normal control 1', [[2055, 6, 4], [2055, 12, 3], 0.0435], [97.800833, 0.04521945]], ['normal control 2', [[2028, 1, 1], [2028, 7, 12], 0.025], [98.659722, 0.02574478]]], [['regression half-year threshold 1', [[2001, 12, 28], [2002, 6, 29], 0.01], [99.491667, 0.01019055]], ['regression half-year threshold 2', [[2100, 12, 28], [2101, 6, 29], 0.0525], [97.33125, 0.05468459]], ['partial repair probe 1', [[2014, 1, 31], [2014, 8, 2], 0.08], [95.933333, 0.08453969]], ['partial repair probe 2', [[2102, 8, 20], [2103, 2, 19], 0.025], [98.729167, 0.02567259]], ['boundary control 1', [[2023, 5, 1], [2023, 10, 31], 0.05], [97.458333, 0.05215904]], ['boundary control 2', [[2023, 5, 1], [2023, 10, 30], 0.05], [97.472222, 0.05215161]], ['normal control 1', [[2027, 1, 1], [2027, 7, 1], 0.025], [98.743056, 0.02566988]], ['normal control 2', [[2096, 4, 10], [2096, 10, 8], 0.0435], [97.812917, 0.04509033]]], [['regression half-year threshold 1', [[2056, 11, 28], [2057, 5, 30], 0.0435], [97.78875, 0.04509869]], ['regression half-year threshold 2', [[2022, 7, 7], [2023, 1, 6], 0.025], [98.729167, 0.02567259]], ['partial repair probe 1', [[2008, 11, 1], [2009, 5, 3], 0.08], [95.933333, 0.08453969]], ['partial repair probe 2', [[2037, 4, 29], [2037, 10, 29], 0.025], [98.729167, 0.02567259]], ['boundary control 1', [[2023, 1, 1], [2023, 1, 2], 0.05], [99.986111, 0.05070149]], ['boundary control 2', [[2023, 5, 1], [2023, 10, 30], 0.05], [97.472222, 0.05215161]], ['normal control 1', [[2051, 9, 19], [2052, 9, 17], 0.0525], [94.691667, 0.0555986]], ['normal control 2', [[2081, 6, 16], [2081, 9, 15], 0.0525], [98.672917, 0.05394506]]], [['regression half-year threshold 1', [[2041, 8, 21], [2042, 2, 20], 0.025], [98.729167, 0.02567259]], ['regression half-year threshold 2', [[2100, 3, 1], [2100, 8, 31], 0.0525], [97.33125, 0.05468459]], ['partial repair probe 1', [[2024, 3, 15], [2024, 9, 14], 0.08], [95.933333, 0.08453969]], ['partial repair probe 2', [[2036, 5, 1], [2036, 10, 31], 0.0435], [97.78875, 0.04509869]], ['boundary control 1', [[2023, 5, 1], [2023, 10, 31], 0.05], [97.458333, 0.05215904]], ['boundary control 2', [[2023, 5, 1], [2023, 10, 30], 0.05], [97.472222, 0.05215161]], ['normal control 1', [[2033, 4, 9], [2033, 7, 9], 0.0435], [98.900417, 0.04459452]], ['normal control 2', [[2024, 12, 1], [2025, 5, 31], 0.0435], [97.812917, 0.04509033]]], [['regression half-year threshold 1', [[2053, 11, 23], [2054, 5, 25], 0.01], [99.491667, 0.01019055]], ['regression half-year threshold 2', [[2053, 5, 31], [2053, 11, 30], 0.08], [95.933333, 0.08453969]], ['partial repair probe 1', [[2100, 3, 1], [2100, 8, 31], 0.0525], [97.33125, 0.05468459]], ['partial repair probe 2', [[2099, 1, 15], [2099, 7, 17], 0.025], [98.729167, 0.02567259]], ['boundary control 1', [[2023, 5, 1], [2023, 10, 31], 0.05], [97.458333, 0.05215904]], ['boundary control 2', [[2023, 3, 1], [2024, 2, 28], 0.05], [94.944444, 0.05284575]], ['normal control 1', [[2002, 1, 7], [2002, 7, 8], 0.0525], [97.345833, 0.05468048]], ['normal control 2', [[2034, 1, 31], [2034, 5, 2], 0.025], [99.368056, 0.02550842]]]]
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 fixtureActualExpectedOutcome
regression half-year threshold 1[95.933333, 0.08454946][95.933333, 0.08453969]Failed
regression half-year threshold 2[97.33125, 0.05468867][97.33125, 0.05468459]Failed
partial repair probe 1[95.933333, 0.08454946][95.933333, 0.08453969]Failed
partial repair probe 2[98.729167, 0.02567349][98.729167, 0.02567259]Failed
boundary control 1[97.472222, 0.05215161][97.472222, 0.05215161]Passed
boundary control 2[97.458333, 0.05215904][97.458333, 0.05215904]Passed
normal control 1[97.800833, 0.04521945][97.800833, 0.04521945]Passed
normal control 2[98.659722, 0.02574478][98.659722, 0.02574478]Passed

SHA-256 / dfacb0c09da6f4d3d30e0adb83e5b0ed6f94cdb1cab1b3f1dba2cf103807f8cf

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
import datetime
import math
N = 1
observations = []
def solve(settle, maturity, d):
    S = datetime.date(*settle)
    M = datetime.date(*maturity)
    t = (M - S).days
    def leap(y):
        return (y % 4 == 0 and y % 100 != 0) or y % 400 == 0
    horizon = S + datetime.timedelta(days=365)
    basis = 366 if any(leap(y) and S < datetime.date(y, 2, 29) <= horizon for y in (S.year, S.year + 1)) else 365
    price = 100 * (1 - d * t / 360)
    if t <= math.ceil(basis / 2):
        bey = basis * d / (360 - d * t)
    else:
        a = t / (2 * basis) - 0.25
        b = t / basis
        c = (price - 100) / price
        bey = (-b + math.sqrt(b * b - 4 * a * c)) / (2 * a)
    return [round(price, 6), round(bey, 8)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression half-year threshold 1', [[2066, 5, 30], [2066, 11, 29], 0.08], [95.933333, 0.08453969]], ['regression half-year threshold 2', [[2021, 2, 3], [2021, 8, 5], 0.0525], [97.33125, 0.05468459]], ['partial repair probe 1', [[2099, 12, 15], [2100, 6, 16], 0.08], [95.933333, 0.08453969]], ['partial repair probe 2', [[2005, 5, 30], [2005, 11, 29], 0.025], [98.729167, 0.02567259]], ['boundary control 1', [[2023, 5, 1], [2023, 10, 30], 0.05], [97.472222, 0.05215161]], ['boundary control 2', [[2023, 5, 1], [2023, 10, 31], 0.05], [97.458333, 0.05215904]], ['normal control 1', [[2055, 6, 4], [2055, 12, 3], 0.0435], [97.800833, 0.04521945]], ['normal control 2', [[2028, 1, 1], [2028, 7, 12], 0.025], [98.659722, 0.02574478]]], [['regression half-year threshold 1', [[2001, 12, 28], [2002, 6, 29], 0.01], [99.491667, 0.01019055]], ['regression half-year threshold 2', [[2100, 12, 28], [2101, 6, 29], 0.0525], [97.33125, 0.05468459]], ['partial repair probe 1', [[2014, 1, 31], [2014, 8, 2], 0.08], [95.933333, 0.08453969]], ['partial repair probe 2', [[2102, 8, 20], [2103, 2, 19], 0.025], [98.729167, 0.02567259]], ['boundary control 1', [[2023, 5, 1], [2023, 10, 31], 0.05], [97.458333, 0.05215904]], ['boundary control 2', [[2023, 5, 1], [2023, 10, 30], 0.05], [97.472222, 0.05215161]], ['normal control 1', [[2027, 1, 1], [2027, 7, 1], 0.025], [98.743056, 0.02566988]], ['normal control 2', [[2096, 4, 10], [2096, 10, 8], 0.0435], [97.812917, 0.04509033]]], [['regression half-year threshold 1', [[2056, 11, 28], [2057, 5, 30], 0.0435], [97.78875, 0.04509869]], ['regression half-year threshold 2', [[2022, 7, 7], [2023, 1, 6], 0.025], [98.729167, 0.02567259]], ['partial repair probe 1', [[2008, 11, 1], [2009, 5, 3], 0.08], [95.933333, 0.08453969]], ['partial repair probe 2', [[2037, 4, 29], [2037, 10, 29], 0.025], [98.729167, 0.02567259]], ['boundary control 1', [[2023, 1, 1], [2023, 1, 2], 0.05], [99.986111, 0.05070149]], ['boundary control 2', [[2023, 5, 1], [2023, 10, 30], 0.05], [97.472222, 0.05215161]], ['normal control 1', [[2051, 9, 19], [2052, 9, 17], 0.0525], [94.691667, 0.0555986]], ['normal control 2', [[2081, 6, 16], [2081, 9, 15], 0.0525], [98.672917, 0.05394506]]], [['regression half-year threshold 1', [[2041, 8, 21], [2042, 2, 20], 0.025], [98.729167, 0.02567259]], ['regression half-year threshold 2', [[2100, 3, 1], [2100, 8, 31], 0.0525], [97.33125, 0.05468459]], ['partial repair probe 1', [[2024, 3, 15], [2024, 9, 14], 0.08], [95.933333, 0.08453969]], ['partial repair probe 2', [[2036, 5, 1], [2036, 10, 31], 0.0435], [97.78875, 0.04509869]], ['boundary control 1', [[2023, 5, 1], [2023, 10, 31], 0.05], [97.458333, 0.05215904]], ['boundary control 2', [[2023, 5, 1], [2023, 10, 30], 0.05], [97.472222, 0.05215161]], ['normal control 1', [[2033, 4, 9], [2033, 7, 9], 0.0435], [98.900417, 0.04459452]], ['normal control 2', [[2024, 12, 1], [2025, 5, 31], 0.0435], [97.812917, 0.04509033]]], [['regression half-year threshold 1', [[2053, 11, 23], [2054, 5, 25], 0.01], [99.491667, 0.01019055]], ['regression half-year threshold 2', [[2053, 5, 31], [2053, 11, 30], 0.08], [95.933333, 0.08453969]], ['partial repair probe 1', [[2100, 3, 1], [2100, 8, 31], 0.0525], [97.33125, 0.05468459]], ['partial repair probe 2', [[2099, 1, 15], [2099, 7, 17], 0.025], [98.729167, 0.02567259]], ['boundary control 1', [[2023, 5, 1], [2023, 10, 31], 0.05], [97.458333, 0.05215904]], ['boundary control 2', [[2023, 3, 1], [2024, 2, 28], 0.05], [94.944444, 0.05284575]], ['normal control 1', [[2002, 1, 7], [2002, 7, 8], 0.0525], [97.345833, 0.05468048]], ['normal control 2', [[2034, 1, 31], [2034, 5, 2], 0.025], [99.368056, 0.02550842]]]]
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 fixtureActualExpectedOutcome
regression half-year threshold 1[95.933333, 0.08454946][95.933333, 0.08453969]Failed
regression half-year threshold 2[97.33125, 0.05468867][97.33125, 0.05468459]Failed
partial repair probe 1[95.933333, 0.08454946][95.933333, 0.08453969]Failed
partial repair probe 2[98.729167, 0.02567349][98.729167, 0.02567259]Failed
boundary control 1[97.472222, 0.05215161][97.472222, 0.05215161]Passed
boundary control 2[97.458333, 0.05215904][97.458333, 0.05215904]Passed
normal control 1[97.800833, 0.04521945][97.800833, 0.04521945]Passed
normal control 2[98.659722, 0.02574478][98.659722, 0.02574478]Passed

SHA-256 / 9762806d88621cb9a1cb18a75dab80b541c5788024d48e92654bc10664fa381a

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 toy contract stated explicitly in the contract field; no claim of conformance to any published convention text. 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 2026-09-29T14:46:52.102775+00:00.

Case digest / 7eae3ae82cf01abf954751ec3d0bc7bd2198fc517eca9d07454a479073107e9f