FA-5751 / Combinatorics / Open access

Balanced ternary digit value · case 01

Most-significant-first balanced ternary is evaluated backwards.

Verified by executionVariant 1 · 4 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Most-significant-first balanced ternary is evaluated backwards.

VERIFIED REPAIR

Apply the specified mathematical contract directly, preserving all terms and boundary cases: return sum(d*3**i for i,d in enumerate(reversed(digits)))

Unsuccessful approach: A binary place value is used for a ternary numeral.

Case contract

Nonnegative integer counts. Permutation and combination counts are zero when a requested selection exceeds the available objects. Shape sizes satisfy the preconditions stated below. digits is most-significant-first and each digit is -1, 0, or 1; return its signed integer value. Empty digits have value zero. Exact operational definition: sum(d*3**i for i,d in enumerate(reversed(digits)))

Why this case matters

Small exact fixtures expose this error without platform timing, external services, or probabilistic observations. Combinatorics results depend on the stated convention.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
import calendar
import statistics
import itertools
from fractions import Fraction
from datetime import date, datetime, timedelta, timezone
from decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR

N = 1
observations = []
def solve(digits):
    return sum(d*3**i for i,d in enumerate(digits))
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: ([1, 0, -1],)', solve(*([1, 0, -1],)), 8)
check('fixture 2: ([-1, 1],)', solve(*([-1, 1],)), -2)
check('fixture 3: ([0],)', solve(*([0],)), 0)
check('fixture 4: ([1, 1, 1],)', solve(*([1, 1, 1],)), 13)
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
fixture 1: ([1, 0, -1],)	`-8`	`8`	Failed
fixture 2: ([-1, 1],)	`2`	`-2`	Failed
fixture 3: ([0],)	`0`	`0`	Passed
fixture 4: ([1, 1, 1],)	`13`	`13`	Passed

SHA-256 / 39c668ed9a94215f5e46b0e41d0d27a7eaf54af4f593d1829bd7f4884969613b

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
import calendar
import statistics
import itertools
from fractions import Fraction
from datetime import date, datetime, timedelta, timezone
from decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR

N = 1
observations = []
def solve(digits):
    return sum(d*2**i for i,d in enumerate(reversed(digits)))
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: ([1, 0, -1],)', solve(*([1, 0, -1],)), 8)
check('fixture 2: ([-1, 1],)', solve(*([-1, 1],)), -2)
check('fixture 3: ([0],)', solve(*([0],)), 0)
check('fixture 4: ([1, 1, 1],)', solve(*([1, 1, 1],)), 13)
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
fixture 1: ([1, 0, -1],)	`3`	`8`	Failed
fixture 2: ([-1, 1],)	`-1`	`-2`	Failed
fixture 3: ([0],)	`0`	`0`	Passed
fixture 4: ([1, 1, 1],)	`7`	`13`	Failed

SHA-256 / ace298e6fb5e69f9abe0c99658e77ebbdd612b0eab86f2fcfb922dbd7016749e

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json
import math
import calendar
import statistics
import itertools
from fractions import Fraction
from datetime import date, datetime, timedelta, timezone
from decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR

N = 1
observations = []
def solve(digits):
    return sum(d*3**i for i,d in enumerate(reversed(digits)))
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: ([1, 0, -1],)', solve(*([1, 0, -1],)), 8)
check('fixture 2: ([-1, 1],)', solve(*([-1, 1],)), -2)
check('fixture 3: ([0],)', solve(*([0],)), 0)
check('fixture 4: ([1, 1, 1],)', solve(*([1, 1, 1],)), 13)
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
fixture 1: ([1, 0, -1],)	`8`	`8`	Passed
fixture 2: ([-1, 1],)	`-2`	`-2`	Passed
fixture 3: ([0],)	`0`	`0`	Passed
fixture 4: ([1, 1, 1],)	`13`	`13`	Passed

SHA-256 / 34e0c475e7a035828182c39fdcd2b5655f4788098f9d15d7d2d7a8828e700b90

Verification & scope

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 2026-09-29T14:37:53.355029+00:00.

Case digest / 6a9d1ff96d9c19745a380503893154a373dbabe588e2315c7a31686fea46249a