FAILURE MAP
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FA-90411 / Garbage collector invariants / Open access

Trial deletion: external references ignored · case 01

Every candidate subgraph is collected, including ones held by the mutator.

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

ROOT CAUSE

Counts are seeded with zero instead of the external reference counts.

THE FAILURE

Counts are seeded with zero instead of the external reference counts.

Unsuccessful approach: Clamping external references to one loses counts for objects held by several roots.

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: 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
                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, 13], 'rc': {}}{'garbage': [11, 12], 'rc': {'13': 1}}Failed
externally held cycle restores its counts{'garbage': [11, 12], 'rc': {}}{'garbage': [], 'rc': {'11': 1, '12': 2}}Failed
candidate sharing a child with a live object{'garbage': [17], 'rc': {'15': 0, '16': 1}}{'garbage': [17], 'rc': {'15': 1, '16': 1}}Failed
self-referencing garbage{'garbage': [14], 'rc': {'19': 0}}{'garbage': [14], 'rc': {'19': 1}}Failed
object with two external references{'garbage': [18, 19], 'rc': {}}{'garbage': [], 'rc': {'18': 2, '19': 1}}Failed
control: acyclic live candidate{'garbage': [11, 12], 'rc': {}}{'garbage': [], 'rc': {'11': 1, '12': 1}}Failed

SHA-256 / e34217e5aac432739ef66b2147ed423774dd058997d0f4b92dac0c26100b523c

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: min(external.get(o, 0), 1) 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
                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': [14], 'rc': {'19': 1}}{'garbage': [14], 'rc': {'19': 1}}Passed
object with two external references{'garbage': [], 'rc': {'18': 1, '19': 1}}{'garbage': [], 'rc': {'18': 2, '19': 1}}Failed
control: acyclic live candidate{'garbage': [], 'rc': {'11': 1, '12': 1}}{'garbage': [], 'rc': {'11': 1, '12': 1}}Passed

SHA-256 / ec4ef8b766b5b15d4110dbd5b32d8b05b57399bac50c82b585dfdad21aff0548

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.

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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 / 4077c559c580e11de6bc905cda2255d64c19a8ee4b4044d22fd13fde88051b38