FAILURE MAP
← Case archive

FA-90391 / Garbage collector invariants / Open access

Trial deletion: edges into already-gray objects not subtracted · case 01

Garbage cycles keep a phantom count from the edge that closes the cycle and are never collected.

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

ROOT CAUSE

The decrement is skipped when the child is already gray, so back-edges are never removed.

THE FAILURE

The decrement is skipped when the child is already gray, so back-edges are never removed.

Unsuccessful approach: Skipping only self-edges still leaks self-referencing garbage.

Case contract

Synchronous trial-deletion cycle collection. Reference counts are external references plus heap in-edges. For each candidate, mark gray: colour gray and, for every out-edge, decrement the child count and recurse. Then scan each candidate: a gray object with positive count is re-blackened together with everything it reaches, restoring one count per traversed edge; a gray object with zero count turns white and its children are scanned. White objects are garbage. Return the garbage and the counts of the surviving objects.

Why this case matters

Cycle collectors for reference-counted heaps depend on exact decrement/restore bookkeeping.

1 / The failure

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

N = 1
observations = []
def solve(heap, external, candidates):
    rc = {o: external.get(o, 0) for o in heap}
    for o, kids in heap.items():
        for c in kids:
            rc[c] += 1
    color = {o: 'black' for o in heap}
    def mark_gray(o):
        if color[o] != 'gray':
            color[o] = 'gray'
            for c in heap[o]:
                if color[c] != 'gray':
                    rc[c] -= 1
                mark_gray(c)
    def scan(o):
        if color[o] == 'gray':
            if rc[o] > 0:
                scan_black(o)
            else:
                color[o] = 'white'
                for c in heap[o]:
                    scan(c)
    def scan_black(o):
        color[o] = 'black'
        for c in heap[o]:
            rc[c] += 1
            if color[c] != 'black':
                scan_black(c)
    for o in candidates:
        mark_gray(o)
    for o in candidates:
        scan(o)
    garbage = sorted(o for o in heap if color[o] == 'white')
    return {'garbage': garbage, 'rc': {str(o): rc[o] for o in sorted(heap) if color[o] != 'white'}}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('regression: three-object garbage cycle',
   ({11: [12], 12: [13], 13: [11]}, {}, [11]),
   {'garbage': [11, 12, 13], 'rc': {}}),
  ('garbage cycle pointing at a live object',
   ({11: [12], 12: [11, 13], 13: []}, {13: 1}, [11]),
   {'garbage': [11, 12], 'rc': {'13': 1}}),
  ('externally held cycle restores its counts',
   ({11: [12], 12: [11]}, {12: 1}, [11]),
   {'garbage': [], 'rc': {'11': 1, '12': 2}}),
  ('candidate sharing a child with a live object',
   ({15: [16], 16: [], 17: [16]}, {15: 1}, [17]),
   {'garbage': [17], 'rc': {'15': 1, '16': 1}}),
  ('self-referencing garbage', ({14: [14], 19: []}, {19: 1}, [14]), {'garbage': [14], 'rc': {'19': 1}}),
  ('object with two external references',
   ({18: [19], 19: []}, {18: 2}, [18]),
   {'garbage': [], 'rc': {'18': 2, '19': 1}}),
  ('control: acyclic live candidate',
   ({11: [12], 12: []}, {11: 1}, [11, 12]),
   {'garbage': [], 'rc': {'11': 1, '12': 1}})],
 [('regression: three-object garbage cycle',
   ({21: [22], 22: [23], 23: [21]}, {}, [21]),
   {'garbage': [21, 22, 23], 'rc': {}}),
  ('garbage cycle pointing at a live object',
   ({21: [22], 22: [21, 23], 23: []}, {23: 1}, [21]),
   {'garbage': [21, 22], 'rc': {'23': 1}}),
  ('externally held cycle restores its counts',
   ({21: [22], 22: [21]}, {22: 1}, [21]),
   {'garbage': [], 'rc': {'21': 1, '22': 2}}),
  ('candidate sharing a child with a live object',
   ({25: [26], 26: [], 27: [26]}, {25: 1}, [27]),
   {'garbage': [27], 'rc': {'25': 1, '26': 1}}),
  ('self-referencing garbage', ({24: [24], 29: []}, {29: 1}, [24]), {'garbage': [24], 'rc': {'29': 1}}),
  ('object with two external references',
   ({28: [29], 29: []}, {28: 2}, [28]),
   {'garbage': [], 'rc': {'28': 2, '29': 1}}),
  ('control: acyclic live candidate',
   ({21: [22], 22: []}, {21: 1}, [21, 22]),
   {'garbage': [], 'rc': {'21': 1, '22': 1}})],
 [('regression: three-object garbage cycle',
   ({31: [32], 32: [33], 33: [31]}, {}, [31]),
   {'garbage': [31, 32, 33], 'rc': {}}),
  ('garbage cycle pointing at a live object',
   ({31: [32], 32: [31, 33], 33: []}, {33: 1}, [31]),
   {'garbage': [31, 32], 'rc': {'33': 1}}),
  ('externally held cycle restores its counts',
   ({31: [32], 32: [31]}, {32: 1}, [31]),
   {'garbage': [], 'rc': {'31': 1, '32': 2}}),
  ('candidate sharing a child with a live object',
   ({35: [36], 36: [], 37: [36]}, {35: 1}, [37]),
   {'garbage': [37], 'rc': {'35': 1, '36': 1}}),
  ('self-referencing garbage', ({34: [34], 39: []}, {39: 1}, [34]), {'garbage': [34], 'rc': {'39': 1}}),
  ('object with two external references',
   ({38: [39], 39: []}, {38: 2}, [38]),
   {'garbage': [], 'rc': {'38': 2, '39': 1}}),
  ('control: acyclic live candidate',
   ({31: [32], 32: []}, {31: 1}, [31, 32]),
   {'garbage': [], 'rc': {'31': 1, '32': 1}})],
 [('regression: three-object garbage cycle',
   ({41: [42], 42: [43], 43: [41]}, {}, [41]),
   {'garbage': [41, 42, 43], 'rc': {}}),
  ('garbage cycle pointing at a live object',
   ({41: [42], 42: [41, 43], 43: []}, {43: 1}, [41]),
   {'garbage': [41, 42], 'rc': {'43': 1}}),
  ('externally held cycle restores its counts',
   ({41: [42], 42: [41]}, {42: 1}, [41]),
   {'garbage': [], 'rc': {'41': 1, '42': 2}}),
  ('candidate sharing a child with a live object',
   ({45: [46], 46: [], 47: [46]}, {45: 1}, [47]),
   {'garbage': [47], 'rc': {'45': 1, '46': 1}}),
  ('self-referencing garbage', ({44: [44], 49: []}, {49: 1}, [44]), {'garbage': [44], 'rc': {'49': 1}}),
  ('object with two external references',
   ({48: [49], 49: []}, {48: 2}, [48]),
   {'garbage': [], 'rc': {'48': 2, '49': 1}}),
  ('control: acyclic live candidate',
   ({41: [42], 42: []}, {41: 1}, [41, 42]),
   {'garbage': [], 'rc': {'41': 1, '42': 1}})],
 [('regression: three-object garbage cycle',
   ({51: [52], 52: [53], 53: [51]}, {}, [51]),
   {'garbage': [51, 52, 53], 'rc': {}}),
  ('garbage cycle pointing at a live object',
   ({51: [52], 52: [51, 53], 53: []}, {53: 1}, [51]),
   {'garbage': [51, 52], 'rc': {'53': 1}}),
  ('externally held cycle restores its counts',
   ({51: [52], 52: [51]}, {52: 1}, [51]),
   {'garbage': [], 'rc': {'51': 1, '52': 2}}),
  ('candidate sharing a child with a live object',
   ({55: [56], 56: [], 57: [56]}, {55: 1}, [57]),
   {'garbage': [57], 'rc': {'55': 1, '56': 1}}),
  ('self-referencing garbage', ({54: [54], 59: []}, {59: 1}, [54]), {'garbage': [54], 'rc': {'59': 1}}),
  ('object with two external references',
   ({58: [59], 59: []}, {58: 2}, [58]),
   {'garbage': [], 'rc': {'58': 2, '59': 1}}),
  ('control: acyclic live candidate',
   ({51: [52], 52: []}, {51: 1}, [51, 52]),
   {'garbage': [], 'rc': {'51': 1, '52': 1}})]]
for label, args, expected in cases[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: three-object garbage cycle{'garbage': [], 'rc': {'11': 2, '12': 1, '13': 1}}{'garbage': [11, 12, 13], 'rc': {}}Failed
garbage cycle pointing at a live object{'garbage': [], 'rc': {'11': 2, '12': 1, '13': 2}}{'garbage': [11, 12], 'rc': {'13': 1}}Failed
externally held cycle restores its counts{'garbage': [], 'rc': {'11': 2, '12': 2}}{'garbage': [], 'rc': {'11': 1, '12': 2}}Failed
candidate sharing a child with a live object{'garbage': [17], 'rc': {'15': 1, '16': 1}}{'garbage': [17], 'rc': {'15': 1, '16': 1}}Passed
self-referencing garbage{'garbage': [], 'rc': {'14': 2, '19': 1}}{'garbage': [14], 'rc': {'19': 1}}Failed
object with two external references{'garbage': [], 'rc': {'18': 2, '19': 1}}{'garbage': [], 'rc': {'18': 2, '19': 1}}Passed
control: acyclic live candidate{'garbage': [], 'rc': {'11': 1, '12': 1}}{'garbage': [], 'rc': {'11': 1, '12': 1}}Passed

SHA-256 / a600955bffcd4c0add270040623dfacaff2d9f63da262a8f966102e8a178c72e

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(heap, external, candidates):
    rc = {o: external.get(o, 0) for o in heap}
    for o, kids in heap.items():
        for c in kids:
            rc[c] += 1
    color = {o: 'black' for o in heap}
    def mark_gray(o):
        if color[o] != 'gray':
            color[o] = 'gray'
            for c in heap[o]:
                rc[c] -= 1 if c != o else 0
                mark_gray(c)
    def scan(o):
        if color[o] == 'gray':
            if rc[o] > 0:
                scan_black(o)
            else:
                color[o] = 'white'
                for c in heap[o]:
                    scan(c)
    def scan_black(o):
        color[o] = 'black'
        for c in heap[o]:
            rc[c] += 1
            if color[c] != 'black':
                scan_black(c)
    for o in candidates:
        mark_gray(o)
    for o in candidates:
        scan(o)
    garbage = sorted(o for o in heap if color[o] == 'white')
    return {'garbage': garbage, 'rc': {str(o): rc[o] for o in sorted(heap) if color[o] != 'white'}}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('regression: three-object garbage cycle',
   ({11: [12], 12: [13], 13: [11]}, {}, [11]),
   {'garbage': [11, 12, 13], 'rc': {}}),
  ('garbage cycle pointing at a live object',
   ({11: [12], 12: [11, 13], 13: []}, {13: 1}, [11]),
   {'garbage': [11, 12], 'rc': {'13': 1}}),
  ('externally held cycle restores its counts',
   ({11: [12], 12: [11]}, {12: 1}, [11]),
   {'garbage': [], 'rc': {'11': 1, '12': 2}}),
  ('candidate sharing a child with a live object',
   ({15: [16], 16: [], 17: [16]}, {15: 1}, [17]),
   {'garbage': [17], 'rc': {'15': 1, '16': 1}}),
  ('self-referencing garbage', ({14: [14], 19: []}, {19: 1}, [14]), {'garbage': [14], 'rc': {'19': 1}}),
  ('object with two external references',
   ({18: [19], 19: []}, {18: 2}, [18]),
   {'garbage': [], 'rc': {'18': 2, '19': 1}}),
  ('control: acyclic live candidate',
   ({11: [12], 12: []}, {11: 1}, [11, 12]),
   {'garbage': [], 'rc': {'11': 1, '12': 1}})],
 [('regression: three-object garbage cycle',
   ({21: [22], 22: [23], 23: [21]}, {}, [21]),
   {'garbage': [21, 22, 23], 'rc': {}}),
  ('garbage cycle pointing at a live object',
   ({21: [22], 22: [21, 23], 23: []}, {23: 1}, [21]),
   {'garbage': [21, 22], 'rc': {'23': 1}}),
  ('externally held cycle restores its counts',
   ({21: [22], 22: [21]}, {22: 1}, [21]),
   {'garbage': [], 'rc': {'21': 1, '22': 2}}),
  ('candidate sharing a child with a live object',
   ({25: [26], 26: [], 27: [26]}, {25: 1}, [27]),
   {'garbage': [27], 'rc': {'25': 1, '26': 1}}),
  ('self-referencing garbage', ({24: [24], 29: []}, {29: 1}, [24]), {'garbage': [24], 'rc': {'29': 1}}),
  ('object with two external references',
   ({28: [29], 29: []}, {28: 2}, [28]),
   {'garbage': [], 'rc': {'28': 2, '29': 1}}),
  ('control: acyclic live candidate',
   ({21: [22], 22: []}, {21: 1}, [21, 22]),
   {'garbage': [], 'rc': {'21': 1, '22': 1}})],
 [('regression: three-object garbage cycle',
   ({31: [32], 32: [33], 33: [31]}, {}, [31]),
   {'garbage': [31, 32, 33], 'rc': {}}),
  ('garbage cycle pointing at a live object',
   ({31: [32], 32: [31, 33], 33: []}, {33: 1}, [31]),
   {'garbage': [31, 32], 'rc': {'33': 1}}),
  ('externally held cycle restores its counts',
   ({31: [32], 32: [31]}, {32: 1}, [31]),
   {'garbage': [], 'rc': {'31': 1, '32': 2}}),
  ('candidate sharing a child with a live object',
   ({35: [36], 36: [], 37: [36]}, {35: 1}, [37]),
   {'garbage': [37], 'rc': {'35': 1, '36': 1}}),
  ('self-referencing garbage', ({34: [34], 39: []}, {39: 1}, [34]), {'garbage': [34], 'rc': {'39': 1}}),
  ('object with two external references',
   ({38: [39], 39: []}, {38: 2}, [38]),
   {'garbage': [], 'rc': {'38': 2, '39': 1}}),
  ('control: acyclic live candidate',
   ({31: [32], 32: []}, {31: 1}, [31, 32]),
   {'garbage': [], 'rc': {'31': 1, '32': 1}})],
 [('regression: three-object garbage cycle',
   ({41: [42], 42: [43], 43: [41]}, {}, [41]),
   {'garbage': [41, 42, 43], 'rc': {}}),
  ('garbage cycle pointing at a live object',
   ({41: [42], 42: [41, 43], 43: []}, {43: 1}, [41]),
   {'garbage': [41, 42], 'rc': {'43': 1}}),
  ('externally held cycle restores its counts',
   ({41: [42], 42: [41]}, {42: 1}, [41]),
   {'garbage': [], 'rc': {'41': 1, '42': 2}}),
  ('candidate sharing a child with a live object',
   ({45: [46], 46: [], 47: [46]}, {45: 1}, [47]),
   {'garbage': [47], 'rc': {'45': 1, '46': 1}}),
  ('self-referencing garbage', ({44: [44], 49: []}, {49: 1}, [44]), {'garbage': [44], 'rc': {'49': 1}}),
  ('object with two external references',
   ({48: [49], 49: []}, {48: 2}, [48]),
   {'garbage': [], 'rc': {'48': 2, '49': 1}}),
  ('control: acyclic live candidate',
   ({41: [42], 42: []}, {41: 1}, [41, 42]),
   {'garbage': [], 'rc': {'41': 1, '42': 1}})],
 [('regression: three-object garbage cycle',
   ({51: [52], 52: [53], 53: [51]}, {}, [51]),
   {'garbage': [51, 52, 53], 'rc': {}}),
  ('garbage cycle pointing at a live object',
   ({51: [52], 52: [51, 53], 53: []}, {53: 1}, [51]),
   {'garbage': [51, 52], 'rc': {'53': 1}}),
  ('externally held cycle restores its counts',
   ({51: [52], 52: [51]}, {52: 1}, [51]),
   {'garbage': [], 'rc': {'51': 1, '52': 2}}),
  ('candidate sharing a child with a live object',
   ({55: [56], 56: [], 57: [56]}, {55: 1}, [57]),
   {'garbage': [57], 'rc': {'55': 1, '56': 1}}),
  ('self-referencing garbage', ({54: [54], 59: []}, {59: 1}, [54]), {'garbage': [54], 'rc': {'59': 1}}),
  ('object with two external references',
   ({58: [59], 59: []}, {58: 2}, [58]),
   {'garbage': [], 'rc': {'58': 2, '59': 1}}),
  ('control: acyclic live candidate',
   ({51: [52], 52: []}, {51: 1}, [51, 52]),
   {'garbage': [], 'rc': {'51': 1, '52': 1}})]]
for label, args, expected in cases[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: three-object garbage cycle{'garbage': [11, 12, 13], 'rc': {}}{'garbage': [11, 12, 13], 'rc': {}}Passed
garbage cycle pointing at a live object{'garbage': [11, 12], 'rc': {'13': 1}}{'garbage': [11, 12], 'rc': {'13': 1}}Passed
externally held cycle restores its counts{'garbage': [], 'rc': {'11': 1, '12': 2}}{'garbage': [], 'rc': {'11': 1, '12': 2}}Passed
candidate sharing a child with a live object{'garbage': [17], 'rc': {'15': 1, '16': 1}}{'garbage': [17], 'rc': {'15': 1, '16': 1}}Passed
self-referencing garbage{'garbage': [], 'rc': {'14': 2, '19': 1}}{'garbage': [14], 'rc': {'19': 1}}Failed
object with two external references{'garbage': [], 'rc': {'18': 2, '19': 1}}{'garbage': [], 'rc': {'18': 2, '19': 1}}Passed
control: acyclic live candidate{'garbage': [], 'rc': {'11': 1, '12': 1}}{'garbage': [], 'rc': {'11': 1, '12': 1}}Passed

SHA-256 / ad2200e8b7cb3c7b88ad1cfd1634ab5d37f66f75806b7f9a55c1a5bae98bb2a8

HELD IN THE MEMBER ARCHIVE

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

This mechanism has 7 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.

Member access is invitation-based. Sign in with your invited account to inspect the repair.

Sign in to the archive ↗

Verification & scope

A deterministic, bounded teaching model of one garbage-collector mechanism with stipulated rules; it is not a production collector and claims no conformance to any particular runtime. 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 2026-09-29T14:51:26.468411+00:00.

Case digest / db8afb32a4dc2a1fe0e3922169ebec58832a37def1028afe9383a8b5add52002