FA-44506 / Data systems / Open access
Dense union child offsets are replaced by row addresses · case 01
Dense union child offsets are replaced by row addresses.
ROOT CAUSE
dense-union-gather: Dense union child offsets are replaced by row addresses.
VERIFIED REPAIR
Preserve the stated physical representation and operation order: Decode a dense tagged union. Tags select named child buffers through a tag map; offsets address those buffers independently of output position. Parent and selected child validity both apply. Emit [child-name,value] for valid parents, None for null parents.
Unsuccessful approach: Always choosing the first child lane loses repeated-child offsets.
Case contract
Decode a dense tagged union. Tags select named child buffers through a tag map; offsets address those buffers independently of output position. Parent and selected child validity both apply. Emit [child-name,value] for valid parents, None for null parents.
Why this case matters
A bounded deterministic data engine model makes representation and changelog faults reproducible.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(d):
try:
tags,offsets,names,children,valid,parent,selection=d
out=[]
for row in selection:
tag=tags[row]
name=names[str(tag)]
offset=min(row,len(children[name])-1)
value=children[name][offset] if valid[name][offset] else None
out.append([name,value] if parent[row] else None)
return out
except (IndexError, KeyError, ValueError, StopIteration) as exc:
return {"representation_error": type(exc).__name__}
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
if N == 1:
check('mixed tags', solve([[7, 9, 7], [1, 0, 0], {'7': 'a', '9': 'b'}, {'a': [1, 2, 3], 'b': [4, 5, 6]}, {'a': [True, True, True], 'b': [True, True, True]}, [True, True, True], [2, 0, 1]]), [['a', 1], ['a', 2], ['b', 4]])
check('child null', solve([[7, 7], [0, 1], {'7': 'a'}, {'a': [1, 2]}, {'a': [False, True]}, [True, True], [0, 1]]), [['a', None], ['a', 2]])
check('parent null', solve([[7], [0], {'7': 'a'}, {'a': [1]}, {'a': [True]}, [False], [0]]), [None])
check('repeat row', solve([[7], [0], {'7': 'a'}, {'a': [1]}, {'a': [True]}, [True], [0, 0]]), [['a', 1], ['a', 1]])
check('empty selection', solve([[7], [0], {'7': 'a'}, {'a': [1]}, {'a': [True]}, [True], []]), [])
check('second tag', solve([[9], [1], {'7': 'a', '9': 'b'}, {'a': [1, 2], 'b': [3, 4]}, {'a': [True, True], 'b': [True, True]}, [True], [0]]), [['b', 4]])
elif N == 2:
check('mixed tags', solve([[7, 9, 7], [1, 0, 0], {'7': 'a', '9': 'b'}, {'a': [2, 3, 4], 'b': [5, 6, 7]}, {'a': [True, True, True], 'b': [True, True, True]}, [True, True, True], [2, 0, 1]]), [['a', 2], ['a', 3], ['b', 5]])
check('child null', solve([[7, 7], [0, 1], {'7': 'a'}, {'a': [2, 3]}, {'a': [False, True]}, [True, True], [0, 1]]), [['a', None], ['a', 3]])
check('parent null', solve([[7], [0], {'7': 'a'}, {'a': [2]}, {'a': [True]}, [False], [0]]), [None])
check('repeat row', solve([[7], [0], {'7': 'a'}, {'a': [2]}, {'a': [True]}, [True], [0, 0]]), [['a', 2], ['a', 2]])
check('empty selection', solve([[7], [0], {'7': 'a'}, {'a': [2]}, {'a': [True]}, [True], []]), [])
check('second tag', solve([[9], [1], {'7': 'a', '9': 'b'}, {'a': [2, 3], 'b': [4, 5]}, {'a': [True, True], 'b': [True, True]}, [True], [0]]), [['b', 5]])
elif N == 3:
check('mixed tags', solve([[7, 9, 7], [1, 0, 0], {'7': 'a', '9': 'b'}, {'a': [3, 4, 5], 'b': [6, 7, 8]}, {'a': [True, True, True], 'b': [True, True, True]}, [True, True, True], [2, 0, 1]]), [['a', 3], ['a', 4], ['b', 6]])
check('child null', solve([[7, 7], [0, 1], {'7': 'a'}, {'a': [3, 4]}, {'a': [False, True]}, [True, True], [0, 1]]), [['a', None], ['a', 4]])
check('parent null', solve([[7], [0], {'7': 'a'}, {'a': [3]}, {'a': [True]}, [False], [0]]), [None])
check('repeat row', solve([[7], [0], {'7': 'a'}, {'a': [3]}, {'a': [True]}, [True], [0, 0]]), [['a', 3], ['a', 3]])
check('empty selection', solve([[7], [0], {'7': 'a'}, {'a': [3]}, {'a': [True]}, [True], []]), [])
check('second tag', solve([[9], [1], {'7': 'a', '9': 'b'}, {'a': [3, 4], 'b': [5, 6]}, {'a': [True, True], 'b': [True, True]}, [True], [0]]), [['b', 6]])
elif N == 4:
check('mixed tags', solve([[7, 9, 7], [1, 0, 0], {'7': 'a', '9': 'b'}, {'a': [4, 5, 6], 'b': [7, 8, 9]}, {'a': [True, True, True], 'b': [True, True, True]}, [True, True, True], [2, 0, 1]]), [['a', 4], ['a', 5], ['b', 7]])
check('child null', solve([[7, 7], [0, 1], {'7': 'a'}, {'a': [4, 5]}, {'a': [False, True]}, [True, True], [0, 1]]), [['a', None], ['a', 5]])
check('parent null', solve([[7], [0], {'7': 'a'}, {'a': [4]}, {'a': [True]}, [False], [0]]), [None])
check('repeat row', solve([[7], [0], {'7': 'a'}, {'a': [4]}, {'a': [True]}, [True], [0, 0]]), [['a', 4], ['a', 4]])
check('empty selection', solve([[7], [0], {'7': 'a'}, {'a': [4]}, {'a': [True]}, [True], []]), [])
check('second tag', solve([[9], [1], {'7': 'a', '9': 'b'}, {'a': [4, 5], 'b': [6, 7]}, {'a': [True, True], 'b': [True, True]}, [True], [0]]), [['b', 7]])
elif N == 5:
check('mixed tags', solve([[7, 9, 7], [1, 0, 0], {'7': 'a', '9': 'b'}, {'a': [5, 6, 7], 'b': [8, 9, 10]}, {'a': [True, True, True], 'b': [True, True, True]}, [True, True, True], [2, 0, 1]]), [['a', 5], ['a', 6], ['b', 8]])
check('child null', solve([[7, 7], [0, 1], {'7': 'a'}, {'a': [5, 6]}, {'a': [False, True]}, [True, True], [0, 1]]), [['a', None], ['a', 6]])
check('parent null', solve([[7], [0], {'7': 'a'}, {'a': [5]}, {'a': [True]}, [False], [0]]), [None])
check('repeat row', solve([[7], [0], {'7': 'a'}, {'a': [5]}, {'a': [True]}, [True], [0, 0]]), [['a', 5], ['a', 5]])
check('empty selection', solve([[7], [0], {'7': 'a'}, {'a': [5]}, {'a': [True]}, [True], []]), [])
check('second tag', solve([[9], [1], {'7': 'a', '9': 'b'}, {'a': [5, 6], 'b': [7, 8]}, {'a': [True, True], 'b': [True, True]}, [True], [0]]), [['b', 8]])
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 |
|---|---|---|---|
| mixed tags | [['a', 3], ['a', 1], ['b', 5]] | [['a', 1], ['a', 2], ['b', 4]] | Failed |
| child null | [['a', None], ['a', 2]] | [['a', None], ['a', 2]] | Passed |
| parent null | [None] | [None] | Passed |
| repeat row | [['a', 1], ['a', 1]] | [['a', 1], ['a', 1]] | Passed |
| empty selection | [] | [] | Passed |
| second tag | [['b', 3]] | [['b', 4]] | Failed |
SHA-256 / bb75ab09e489d047726be3e49aeaf9784b092ce63730471fbaf906e7c53444e6
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(d):
try:
tags,offsets,names,children,valid,parent,selection=d
out=[]
for row in selection:
tag=tags[row]
name=names[str(tag)]
offset=0
value=children[name][offset] if valid[name][offset] else None
out.append([name,value] if parent[row] else None)
return out
except (IndexError, KeyError, ValueError, StopIteration) as exc:
return {"representation_error": type(exc).__name__}
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
if N == 1:
check('mixed tags', solve([[7, 9, 7], [1, 0, 0], {'7': 'a', '9': 'b'}, {'a': [1, 2, 3], 'b': [4, 5, 6]}, {'a': [True, True, True], 'b': [True, True, True]}, [True, True, True], [2, 0, 1]]), [['a', 1], ['a', 2], ['b', 4]])
check('child null', solve([[7, 7], [0, 1], {'7': 'a'}, {'a': [1, 2]}, {'a': [False, True]}, [True, True], [0, 1]]), [['a', None], ['a', 2]])
check('parent null', solve([[7], [0], {'7': 'a'}, {'a': [1]}, {'a': [True]}, [False], [0]]), [None])
check('repeat row', solve([[7], [0], {'7': 'a'}, {'a': [1]}, {'a': [True]}, [True], [0, 0]]), [['a', 1], ['a', 1]])
check('empty selection', solve([[7], [0], {'7': 'a'}, {'a': [1]}, {'a': [True]}, [True], []]), [])
check('second tag', solve([[9], [1], {'7': 'a', '9': 'b'}, {'a': [1, 2], 'b': [3, 4]}, {'a': [True, True], 'b': [True, True]}, [True], [0]]), [['b', 4]])
elif N == 2:
check('mixed tags', solve([[7, 9, 7], [1, 0, 0], {'7': 'a', '9': 'b'}, {'a': [2, 3, 4], 'b': [5, 6, 7]}, {'a': [True, True, True], 'b': [True, True, True]}, [True, True, True], [2, 0, 1]]), [['a', 2], ['a', 3], ['b', 5]])
check('child null', solve([[7, 7], [0, 1], {'7': 'a'}, {'a': [2, 3]}, {'a': [False, True]}, [True, True], [0, 1]]), [['a', None], ['a', 3]])
check('parent null', solve([[7], [0], {'7': 'a'}, {'a': [2]}, {'a': [True]}, [False], [0]]), [None])
check('repeat row', solve([[7], [0], {'7': 'a'}, {'a': [2]}, {'a': [True]}, [True], [0, 0]]), [['a', 2], ['a', 2]])
check('empty selection', solve([[7], [0], {'7': 'a'}, {'a': [2]}, {'a': [True]}, [True], []]), [])
check('second tag', solve([[9], [1], {'7': 'a', '9': 'b'}, {'a': [2, 3], 'b': [4, 5]}, {'a': [True, True], 'b': [True, True]}, [True], [0]]), [['b', 5]])
elif N == 3:
check('mixed tags', solve([[7, 9, 7], [1, 0, 0], {'7': 'a', '9': 'b'}, {'a': [3, 4, 5], 'b': [6, 7, 8]}, {'a': [True, True, True], 'b': [True, True, True]}, [True, True, True], [2, 0, 1]]), [['a', 3], ['a', 4], ['b', 6]])
check('child null', solve([[7, 7], [0, 1], {'7': 'a'}, {'a': [3, 4]}, {'a': [False, True]}, [True, True], [0, 1]]), [['a', None], ['a', 4]])
check('parent null', solve([[7], [0], {'7': 'a'}, {'a': [3]}, {'a': [True]}, [False], [0]]), [None])
check('repeat row', solve([[7], [0], {'7': 'a'}, {'a': [3]}, {'a': [True]}, [True], [0, 0]]), [['a', 3], ['a', 3]])
check('empty selection', solve([[7], [0], {'7': 'a'}, {'a': [3]}, {'a': [True]}, [True], []]), [])
check('second tag', solve([[9], [1], {'7': 'a', '9': 'b'}, {'a': [3, 4], 'b': [5, 6]}, {'a': [True, True], 'b': [True, True]}, [True], [0]]), [['b', 6]])
elif N == 4:
check('mixed tags', solve([[7, 9, 7], [1, 0, 0], {'7': 'a', '9': 'b'}, {'a': [4, 5, 6], 'b': [7, 8, 9]}, {'a': [True, True, True], 'b': [True, True, True]}, [True, True, True], [2, 0, 1]]), [['a', 4], ['a', 5], ['b', 7]])
check('child null', solve([[7, 7], [0, 1], {'7': 'a'}, {'a': [4, 5]}, {'a': [False, True]}, [True, True], [0, 1]]), [['a', None], ['a', 5]])
check('parent null', solve([[7], [0], {'7': 'a'}, {'a': [4]}, {'a': [True]}, [False], [0]]), [None])
check('repeat row', solve([[7], [0], {'7': 'a'}, {'a': [4]}, {'a': [True]}, [True], [0, 0]]), [['a', 4], ['a', 4]])
check('empty selection', solve([[7], [0], {'7': 'a'}, {'a': [4]}, {'a': [True]}, [True], []]), [])
check('second tag', solve([[9], [1], {'7': 'a', '9': 'b'}, {'a': [4, 5], 'b': [6, 7]}, {'a': [True, True], 'b': [True, True]}, [True], [0]]), [['b', 7]])
elif N == 5:
check('mixed tags', solve([[7, 9, 7], [1, 0, 0], {'7': 'a', '9': 'b'}, {'a': [5, 6, 7], 'b': [8, 9, 10]}, {'a': [True, True, True], 'b': [True, True, True]}, [True, True, True], [2, 0, 1]]), [['a', 5], ['a', 6], ['b', 8]])
check('child null', solve([[7, 7], [0, 1], {'7': 'a'}, {'a': [5, 6]}, {'a': [False, True]}, [True, True], [0, 1]]), [['a', None], ['a', 6]])
check('parent null', solve([[7], [0], {'7': 'a'}, {'a': [5]}, {'a': [True]}, [False], [0]]), [None])
check('repeat row', solve([[7], [0], {'7': 'a'}, {'a': [5]}, {'a': [True]}, [True], [0, 0]]), [['a', 5], ['a', 5]])
check('empty selection', solve([[7], [0], {'7': 'a'}, {'a': [5]}, {'a': [True]}, [True], []]), [])
check('second tag', solve([[9], [1], {'7': 'a', '9': 'b'}, {'a': [5, 6], 'b': [7, 8]}, {'a': [True, True], 'b': [True, True]}, [True], [0]]), [['b', 8]])
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 |
|---|---|---|---|
| mixed tags | [['a', 1], ['a', 1], ['b', 4]] | [['a', 1], ['a', 2], ['b', 4]] | Failed |
| child null | [['a', None], ['a', None]] | [['a', None], ['a', 2]] | Failed |
| parent null | [None] | [None] | Passed |
| repeat row | [['a', 1], ['a', 1]] | [['a', 1], ['a', 1]] | Passed |
| empty selection | [] | [] | Passed |
| second tag | [['b', 3]] | [['b', 4]] | Failed |
SHA-256 / ae649b00b86591ef7ae0e0d2e45dd76045e779b0396f4c1efcc3c627b3b12787
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(d):
try:
tags,offsets,names,children,valid,parent,selection=d
out=[]
for row in selection:
tag=tags[row]
name=names[str(tag)]
offset=offsets[row]
value=children[name][offset] if valid[name][offset] else None
out.append([name,value] if parent[row] else None)
return out
except (IndexError, KeyError, ValueError, StopIteration) as exc:
return {"representation_error": type(exc).__name__}
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
if N == 1:
check('mixed tags', solve([[7, 9, 7], [1, 0, 0], {'7': 'a', '9': 'b'}, {'a': [1, 2, 3], 'b': [4, 5, 6]}, {'a': [True, True, True], 'b': [True, True, True]}, [True, True, True], [2, 0, 1]]), [['a', 1], ['a', 2], ['b', 4]])
check('child null', solve([[7, 7], [0, 1], {'7': 'a'}, {'a': [1, 2]}, {'a': [False, True]}, [True, True], [0, 1]]), [['a', None], ['a', 2]])
check('parent null', solve([[7], [0], {'7': 'a'}, {'a': [1]}, {'a': [True]}, [False], [0]]), [None])
check('repeat row', solve([[7], [0], {'7': 'a'}, {'a': [1]}, {'a': [True]}, [True], [0, 0]]), [['a', 1], ['a', 1]])
check('empty selection', solve([[7], [0], {'7': 'a'}, {'a': [1]}, {'a': [True]}, [True], []]), [])
check('second tag', solve([[9], [1], {'7': 'a', '9': 'b'}, {'a': [1, 2], 'b': [3, 4]}, {'a': [True, True], 'b': [True, True]}, [True], [0]]), [['b', 4]])
elif N == 2:
check('mixed tags', solve([[7, 9, 7], [1, 0, 0], {'7': 'a', '9': 'b'}, {'a': [2, 3, 4], 'b': [5, 6, 7]}, {'a': [True, True, True], 'b': [True, True, True]}, [True, True, True], [2, 0, 1]]), [['a', 2], ['a', 3], ['b', 5]])
check('child null', solve([[7, 7], [0, 1], {'7': 'a'}, {'a': [2, 3]}, {'a': [False, True]}, [True, True], [0, 1]]), [['a', None], ['a', 3]])
check('parent null', solve([[7], [0], {'7': 'a'}, {'a': [2]}, {'a': [True]}, [False], [0]]), [None])
check('repeat row', solve([[7], [0], {'7': 'a'}, {'a': [2]}, {'a': [True]}, [True], [0, 0]]), [['a', 2], ['a', 2]])
check('empty selection', solve([[7], [0], {'7': 'a'}, {'a': [2]}, {'a': [True]}, [True], []]), [])
check('second tag', solve([[9], [1], {'7': 'a', '9': 'b'}, {'a': [2, 3], 'b': [4, 5]}, {'a': [True, True], 'b': [True, True]}, [True], [0]]), [['b', 5]])
elif N == 3:
check('mixed tags', solve([[7, 9, 7], [1, 0, 0], {'7': 'a', '9': 'b'}, {'a': [3, 4, 5], 'b': [6, 7, 8]}, {'a': [True, True, True], 'b': [True, True, True]}, [True, True, True], [2, 0, 1]]), [['a', 3], ['a', 4], ['b', 6]])
check('child null', solve([[7, 7], [0, 1], {'7': 'a'}, {'a': [3, 4]}, {'a': [False, True]}, [True, True], [0, 1]]), [['a', None], ['a', 4]])
check('parent null', solve([[7], [0], {'7': 'a'}, {'a': [3]}, {'a': [True]}, [False], [0]]), [None])
check('repeat row', solve([[7], [0], {'7': 'a'}, {'a': [3]}, {'a': [True]}, [True], [0, 0]]), [['a', 3], ['a', 3]])
check('empty selection', solve([[7], [0], {'7': 'a'}, {'a': [3]}, {'a': [True]}, [True], []]), [])
check('second tag', solve([[9], [1], {'7': 'a', '9': 'b'}, {'a': [3, 4], 'b': [5, 6]}, {'a': [True, True], 'b': [True, True]}, [True], [0]]), [['b', 6]])
elif N == 4:
check('mixed tags', solve([[7, 9, 7], [1, 0, 0], {'7': 'a', '9': 'b'}, {'a': [4, 5, 6], 'b': [7, 8, 9]}, {'a': [True, True, True], 'b': [True, True, True]}, [True, True, True], [2, 0, 1]]), [['a', 4], ['a', 5], ['b', 7]])
check('child null', solve([[7, 7], [0, 1], {'7': 'a'}, {'a': [4, 5]}, {'a': [False, True]}, [True, True], [0, 1]]), [['a', None], ['a', 5]])
check('parent null', solve([[7], [0], {'7': 'a'}, {'a': [4]}, {'a': [True]}, [False], [0]]), [None])
check('repeat row', solve([[7], [0], {'7': 'a'}, {'a': [4]}, {'a': [True]}, [True], [0, 0]]), [['a', 4], ['a', 4]])
check('empty selection', solve([[7], [0], {'7': 'a'}, {'a': [4]}, {'a': [True]}, [True], []]), [])
check('second tag', solve([[9], [1], {'7': 'a', '9': 'b'}, {'a': [4, 5], 'b': [6, 7]}, {'a': [True, True], 'b': [True, True]}, [True], [0]]), [['b', 7]])
elif N == 5:
check('mixed tags', solve([[7, 9, 7], [1, 0, 0], {'7': 'a', '9': 'b'}, {'a': [5, 6, 7], 'b': [8, 9, 10]}, {'a': [True, True, True], 'b': [True, True, True]}, [True, True, True], [2, 0, 1]]), [['a', 5], ['a', 6], ['b', 8]])
check('child null', solve([[7, 7], [0, 1], {'7': 'a'}, {'a': [5, 6]}, {'a': [False, True]}, [True, True], [0, 1]]), [['a', None], ['a', 6]])
check('parent null', solve([[7], [0], {'7': 'a'}, {'a': [5]}, {'a': [True]}, [False], [0]]), [None])
check('repeat row', solve([[7], [0], {'7': 'a'}, {'a': [5]}, {'a': [True]}, [True], [0, 0]]), [['a', 5], ['a', 5]])
check('empty selection', solve([[7], [0], {'7': 'a'}, {'a': [5]}, {'a': [True]}, [True], []]), [])
check('second tag', solve([[9], [1], {'7': 'a', '9': 'b'}, {'a': [5, 6], 'b': [7, 8]}, {'a': [True, True], 'b': [True, True]}, [True], [0]]), [['b', 8]])
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 |
|---|---|---|---|
| mixed tags | [['a', 1], ['a', 2], ['b', 4]] | [['a', 1], ['a', 2], ['b', 4]] | Passed |
| child null | [['a', None], ['a', 2]] | [['a', None], ['a', 2]] | Passed |
| parent null | [None] | [None] | Passed |
| repeat row | [['a', 1], ['a', 1]] | [['a', 1], ['a', 1]] | Passed |
| empty selection | [] | [] | Passed |
| second tag | [['b', 4]] | [['b', 4]] | Passed |
SHA-256 / 3f0bc15811ad816b24c65a25481b1b0fcefbaf9ef4e6c2e5894c647c0e734390
Verification & scope
Offline stipulated semantics over valid small inputs; no performance, concurrency, or production-engine conformance claim. 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 2026-09-29T14:44:12.880548+00:00.
Case digest / 6f7d319c13c3e19070a3d5f29458c1d7b03b0fcd719d694d44db2452872fbff1