FA-90526 / Garbage collector invariants / Open access

Card marking: cards rebuilt only for newly promoted objects · case 01

Old-to-young references recorded before a minor collection are forgotten afterwards.

Verified by executionVariant 1 · 6 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

After clearing the card table, only promoted objects are rescanned for young references.

VERIFIED REPAIR

Rebuild cards from every old object that still points at a young one.

Unsuccessful approach: Skipping promoted objects forgets references from freshly tenured objects to younger ones.

Case contract

Two generations. objs maps id -> [generation, address, fields]; a field slot i of an old object lives at address + 8*i and belongs to card (slot address // 64). store writes a field and, when an old object receives a young reference, dirties that slot's card. minor: roots plus young referents of old slots in dirty cards seed a trace through young objects; unreached young objects are freed; survivors age by one and are promoted (addresses from 4096 in 64-byte steps) when age >= tenure; the card set is then rebuilt from every old slot that still references a young object. alloc id creates a young object with one null field; root/unroot edit the root list. Return per-minor {freed, promoted, cards}; following a freed object reports {"dangling": id}.

Why this case matters

Minor collections are only correct if the remembered set covers every old-to-young pointer.

1 / The failure

Exit 1

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

N = 1
observations = []
def solve(objs, roots, events, tenure):
    objs = {k: {'gen': v[0], 'addr': v[1], 'fields': list(v[2]), 'age': 0} for k, v in objs.items()}
    roots = list(roots)
    cards = set()
    log = []
    next_addr = 4096
    def slot_card(o, i):
        return (objs[o]['addr'] + 8 * i) // 64
    try:
        for ev in events:
            if ev[0] == 'store':
                _, src, i, dst = ev
                objs[src]['fields'][i] = dst
                if objs[src]['gen'] == 'old' and dst is not None and objs[dst]['gen'] == 'young':
                    cards.add(slot_card(src, i))
            elif ev[0] == 'alloc':
                objs[ev[1]] = {'gen': 'young', 'addr': 0, 'fields': [None], 'age': 0}
            elif ev[0] == 'root':
                roots.append(ev[1])
            elif ev[0] == 'unroot':
                roots.remove(ev[1])
            else:
                grey = [r for r in roots if objs[r]['gen'] == 'young']
                for o, ob in objs.items():
                    if ob['gen'] == 'old':
                        for i, f in enumerate(ob['fields']):
                            if slot_card(o, i) in cards and f is not None and objs[f]['gen'] == 'young':
                                grey.append(f)
                live = set()
                while grey:
                    y = grey.pop()
                    if y in live:
                        continue
                    live.add(y)
                    for f in objs[y]['fields']:
                        if f is not None and objs[f]['gen'] == 'young':
                            grey.append(f)
                dead = sorted(k for k, ob in objs.items() if ob['gen'] == 'young' and k not in live)
                for k in dead:
                    del objs[k]
                promoted = []
                for k in sorted(live):
                    objs[k]['age'] += 1
                    if objs[k]['age'] >= tenure:
                        objs[k]['gen'] = 'old'
                        objs[k]['addr'] = next_addr
                        next_addr += 64
                        promoted.append(k)
                cards = set()
                for o in promoted:
                    for i, f in enumerate(objs[o]['fields']):
                        if f is not None and objs[f]['gen'] == 'young':
                            cards.add(slot_card(o, i))
                log.append({'freed': dead, 'promoted': promoted, 'cards': sorted(cards)})
    except KeyError as e:
        log.append({'dangling': e.args[0]})
    return log
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('regression: old-to-young edge survives two minor collections',
   ({1: ['old', 56, [None, None]],
     2: ['old', 192, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [],
    [['store', 1, 1, 11], ['minor'], ['minor']],
    5),
   [{'cards': [1], 'freed': [13, 14], 'promoted': []}, {'cards': [1], 'freed': [], 'promoted': []}]),
  ('edge stored after the target survived once',
   ({1: ['old', 56, [None, None]],
     2: ['old', 192, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [13],
    [['minor'], ['store', 2, 0, 13], ['unroot', 13], ['minor']],
    5),
   [{'cards': [], 'freed': [11, 12, 14], 'promoted': []}, {'cards': [3], 'freed': [], 'promoted': []}]),
  ('promotion at the tenuring threshold',
   ({1: ['old', 56, [None, None]],
     2: ['old', 192, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [11],
    [['minor'], ['minor'], ['minor']],
    2),
   [{'cards': [], 'freed': [13, 14], 'promoted': []},
    {'cards': [], 'freed': [], 'promoted': [11, 12]},
    {'cards': [], 'freed': [], 'promoted': []}]),
  ('promoted object pointing at a younger object',
   ({1: ['old', 56, [None, None]],
     2: ['old', 192, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [11],
    [['minor'], ['alloc', 15], ['store', 11, 0, 15], ['minor'], ['minor']],
    2),
   [{'cards': [], 'freed': [13, 14], 'promoted': []},
    {'cards': [64], 'freed': [12], 'promoted': [11]},
    {'cards': [], 'freed': [], 'promoted': [15]}]),
  ('card of a slot in the next card',
   ({1: ['old', 56, [None, None]],
     2: ['old', 192, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [],
    [['store', 1, 0, 13], ['store', 1, 1, 14], ['minor']],
    4),
   [{'cards': [0, 1], 'freed': [11, 12], 'promoted': []}]),
  ('control: unreferenced young objects die',
   ({1: ['old', 56, [None, None]],
     2: ['old', 192, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [12],
    [['minor']],
    3),
   [{'cards': [], 'freed': [11, 13, 14], 'promoted': []}])],
 [('regression: old-to-young edge survives two minor collections',
   ({1: ['old', 120, [None, None]],
     2: ['old', 256, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [],
    [['store', 1, 1, 11], ['minor'], ['minor']],
    5),
   [{'cards': [2], 'freed': [13, 14], 'promoted': []}, {'cards': [2], 'freed': [], 'promoted': []}]),
  ('edge stored after the target survived once',
   ({1: ['old', 120, [None, None]],
     2: ['old', 256, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [13],
    [['minor'], ['store', 2, 0, 13], ['unroot', 13], ['minor']],
    5),
   [{'cards': [], 'freed': [11, 12, 14], 'promoted': []}, {'cards': [4], 'freed': [], 'promoted': []}]),
  ('promotion at the tenuring threshold',
   ({1: ['old', 120, [None, None]],
     2: ['old', 256, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [11],
    [['minor'], ['minor'], ['minor']],
    2),
   [{'cards': [], 'freed': [13, 14], 'promoted': []},
    {'cards': [], 'freed': [], 'promoted': [11, 12]},
    {'cards': [], 'freed': [], 'promoted': []}]),
  ('promoted object pointing at a younger object',
   ({1: ['old', 120, [None, None]],
     2: ['old', 256, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [11],
    [['minor'], ['alloc', 15], ['store', 11, 0, 15], ['minor'], ['minor']],
    2),
   [{'cards': [], 'freed': [13, 14], 'promoted': []},
    {'cards': [64], 'freed': [12], 'promoted': [11]},
    {'cards': [], 'freed': [], 'promoted': [15]}]),
  ('card of a slot in the next card',
   ({1: ['old', 120, [None, None]],
     2: ['old', 256, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [],
    [['store', 1, 0, 13], ['store', 1, 1, 14], ['minor']],
    4),
   [{'cards': [1, 2], 'freed': [11, 12], 'promoted': []}]),
  ('control: unreferenced young objects die',
   ({1: ['old', 120, [None, None]],
     2: ['old', 256, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [12],
    [['minor']],
    3),
   [{'cards': [], 'freed': [11, 13, 14], 'promoted': []}])],
 [('regression: old-to-young edge survives two minor collections',
   ({1: ['old', 184, [None, None]],
     2: ['old', 320, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [],
    [['store', 1, 1, 11], ['minor'], ['minor']],
    5),
   [{'cards': [3], 'freed': [13, 14], 'promoted': []}, {'cards': [3], 'freed': [], 'promoted': []}]),
  ('edge stored after the target survived once',
   ({1: ['old', 184, [None, None]],
     2: ['old', 320, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [13],
    [['minor'], ['store', 2, 0, 13], ['unroot', 13], ['minor']],
    5),
   [{'cards': [], 'freed': [11, 12, 14], 'promoted': []}, {'cards': [5], 'freed': [], 'promoted': []}]),
  ('promotion at the tenuring threshold',
   ({1: ['old', 184, [None, None]],
     2: ['old', 320, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [11],
    [['minor'], ['minor'], ['minor']],
    2),
   [{'cards': [], 'freed': [13, 14], 'promoted': []},
    {'cards': [], 'freed': [], 'promoted': [11, 12]},
    {'cards': [], 'freed': [], 'promoted': []}]),
  ('promoted object pointing at a younger object',
   ({1: ['old', 184, [None, None]],
     2: ['old', 320, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [11],
    [['minor'], ['alloc', 15], ['store', 11, 0, 15], ['minor'], ['minor']],
    2),
   [{'cards': [], 'freed': [13, 14], 'promoted': []},
    {'cards': [64], 'freed': [12], 'promoted': [11]},
    {'cards': [], 'freed': [], 'promoted': [15]}]),
  ('card of a slot in the next card',
   ({1: ['old', 184, [None, None]],
     2: ['old', 320, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [],
    [['store', 1, 0, 13], ['store', 1, 1, 14], ['minor']],
    4),
   [{'cards': [2, 3], 'freed': [11, 12], 'promoted': []}]),
  ('control: unreferenced young objects die',
   ({1: ['old', 184, [None, None]],
     2: ['old', 320, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [12],
    [['minor']],
    3),
   [{'cards': [], 'freed': [11, 13, 14], 'promoted': []}])],
 [('regression: old-to-young edge survives two minor collections',
   ({1: ['old', 248, [None, None]],
     2: ['old', 384, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [],
    [['store', 1, 1, 11], ['minor'], ['minor']],
    5),
   [{'cards': [4], 'freed': [13, 14], 'promoted': []}, {'cards': [4], 'freed': [], 'promoted': []}]),
  ('edge stored after the target survived once',
   ({1: ['old', 248, [None, None]],
     2: ['old', 384, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [13],
    [['minor'], ['store', 2, 0, 13], ['unroot', 13], ['minor']],
    5),
   [{'cards': [], 'freed': [11, 12, 14], 'promoted': []}, {'cards': [6], 'freed': [], 'promoted': []}]),
  ('promotion at the tenuring threshold',
   ({1: ['old', 248, [None, None]],
     2: ['old', 384, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [11],
    [['minor'], ['minor'], ['minor']],
    2),
   [{'cards': [], 'freed': [13, 14], 'promoted': []},
    {'cards': [], 'freed': [], 'promoted': [11, 12]},
    {'cards': [], 'freed': [], 'promoted': []}]),
  ('promoted object pointing at a younger object',
   ({1: ['old', 248, [None, None]],
     2: ['old', 384, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [11],
    [['minor'], ['alloc', 15], ['store', 11, 0, 15], ['minor'], ['minor']],
    2),
   [{'cards': [], 'freed': [13, 14], 'promoted': []},
    {'cards': [64], 'freed': [12], 'promoted': [11]},
    {'cards': [], 'freed': [], 'promoted': [15]}]),
  ('card of a slot in the next card',
   ({1: ['old', 248, [None, None]],
     2: ['old', 384, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [],
    [['store', 1, 0, 13], ['store', 1, 1, 14], ['minor']],
    4),
   [{'cards': [3, 4], 'freed': [11, 12], 'promoted': []}]),
  ('control: unreferenced young objects die',
   ({1: ['old', 248, [None, None]],
     2: ['old', 384, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [12],
    [['minor']],
    3),
   [{'cards': [], 'freed': [11, 13, 14], 'promoted': []}])],
 [('regression: old-to-young edge survives two minor collections',
   ({1: ['old', 312, [None, None]],
     2: ['old', 448, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [],
    [['store', 1, 1, 11], ['minor'], ['minor']],
    5),
   [{'cards': [5], 'freed': [13, 14], 'promoted': []}, {'cards': [5], 'freed': [], 'promoted': []}]),
  ('edge stored after the target survived once',
   ({1: ['old', 312, [None, None]],
     2: ['old', 448, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [13],
    [['minor'], ['store', 2, 0, 13], ['unroot', 13], ['minor']],
    5),
   [{'cards': [], 'freed': [11, 12, 14], 'promoted': []}, {'cards': [7], 'freed': [], 'promoted': []}]),
  ('promotion at the tenuring threshold',
   ({1: ['old', 312, [None, None]],
     2: ['old', 448, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [11],
    [['minor'], ['minor'], ['minor']],
    2),
   [{'cards': [], 'freed': [13, 14], 'promoted': []},
    {'cards': [], 'freed': [], 'promoted': [11, 12]},
    {'cards': [], 'freed': [], 'promoted': []}]),
  ('promoted object pointing at a younger object',
   ({1: ['old', 312, [None, None]],
     2: ['old', 448, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [11],
    [['minor'], ['alloc', 15], ['store', 11, 0, 15], ['minor'], ['minor']],
    2),
   [{'cards': [], 'freed': [13, 14], 'promoted': []},
    {'cards': [64], 'freed': [12], 'promoted': [11]},
    {'cards': [], 'freed': [], 'promoted': [15]}]),
  ('card of a slot in the next card',
   ({1: ['old', 312, [None, None]],
     2: ['old', 448, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [],
    [['store', 1, 0, 13], ['store', 1, 1, 14], ['minor']],
    4),
   [{'cards': [4, 5], 'freed': [11, 12], 'promoted': []}]),
  ('control: unreferenced young objects die',
   ({1: ['old', 312, [None, None]],
     2: ['old', 448, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [12],
    [['minor']],
    3),
   [{'cards': [], 'freed': [11, 13, 14], 'promoted': []}])]]
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 fixture	Actual	Expected	Outcome
regression: old-to-young edge survives two minor collections	`[{'cards': [], 'freed': [13, 14], 'promoted': []}, {'cards': [], 'freed': [11, 12], 'promoted': []}]`	`[{'cards': [1], 'freed': [13, 14], 'promoted': []}, {'cards': [1], 'freed': [], 'promoted': []}]`	Failed
edge stored after the target survived once	`[{'cards': [], 'freed': [11, 12, 14], 'promoted': []}, {'cards': [], 'freed': [], 'promoted': []}]`	`[{'cards': [], 'freed': [11, 12, 14], 'promoted': []}, {'cards': [3], 'freed': [], 'promoted': []}]`	Failed
promotion at the tenuring threshold	`[{'cards': [], 'freed': [13, 14], 'promoted': []}, {'cards': [], 'freed': [], 'promoted': [11, 12]}, {'cards': [], 'freed': [], 'promoted': []}]`	`[{'cards': [], 'freed': [13, 14], 'promoted': []}, {'cards': [], 'freed': [], 'promoted': [11, 12]}, {'cards': [], 'freed': [], 'promoted': []}]`	Passed
promoted object pointing at a younger object	`[{'cards': [], 'freed': [13, 14], 'promoted': []}, {'cards': [64], 'freed': [12], 'promoted': [11]}, {'cards': [], 'freed': [], 'promoted': [15]}]`	`[{'cards': [], 'freed': [13, 14], 'promoted': []}, {'cards': [64], 'freed': [12], 'promoted': [11]}, {'cards': [], 'freed': [], 'promoted': [15]}]`	Passed
card of a slot in the next card	`[{'cards': [], 'freed': [11, 12], 'promoted': []}]`	`[{'cards': [0, 1], 'freed': [11, 12], 'promoted': []}]`	Failed
control: unreferenced young objects die	`[{'cards': [], 'freed': [11, 13, 14], 'promoted': []}]`	`[{'cards': [], 'freed': [11, 13, 14], 'promoted': []}]`	Passed

SHA-256 / 14ff3fdfa02517480bf0235b56b73f473e1a2456bd084e34f9a007855d8139c6

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(objs, roots, events, tenure):
    objs = {k: {'gen': v[0], 'addr': v[1], 'fields': list(v[2]), 'age': 0} for k, v in objs.items()}
    roots = list(roots)
    cards = set()
    log = []
    next_addr = 4096
    def slot_card(o, i):
        return (objs[o]['addr'] + 8 * i) // 64
    try:
        for ev in events:
            if ev[0] == 'store':
                _, src, i, dst = ev
                objs[src]['fields'][i] = dst
                if objs[src]['gen'] == 'old' and dst is not None and objs[dst]['gen'] == 'young':
                    cards.add(slot_card(src, i))
            elif ev[0] == 'alloc':
                objs[ev[1]] = {'gen': 'young', 'addr': 0, 'fields': [None], 'age': 0}
            elif ev[0] == 'root':
                roots.append(ev[1])
            elif ev[0] == 'unroot':
                roots.remove(ev[1])
            else:
                grey = [r for r in roots if objs[r]['gen'] == 'young']
                for o, ob in objs.items():
                    if ob['gen'] == 'old':
                        for i, f in enumerate(ob['fields']):
                            if slot_card(o, i) in cards and f is not None and objs[f]['gen'] == 'young':
                                grey.append(f)
                live = set()
                while grey:
                    y = grey.pop()
                    if y in live:
                        continue
                    live.add(y)
                    for f in objs[y]['fields']:
                        if f is not None and objs[f]['gen'] == 'young':
                            grey.append(f)
                dead = sorted(k for k, ob in objs.items() if ob['gen'] == 'young' and k not in live)
                for k in dead:
                    del objs[k]
                promoted = []
                for k in sorted(live):
                    objs[k]['age'] += 1
                    if objs[k]['age'] >= tenure:
                        objs[k]['gen'] = 'old'
                        objs[k]['addr'] = next_addr
                        next_addr += 64
                        promoted.append(k)
                cards = set()
                for o in [k for k, ob in objs.items() if ob['gen'] == 'old' and k not in promoted]:
                    for i, f in enumerate(objs[o]['fields']):
                        if f is not None and objs[f]['gen'] == 'young':
                            cards.add(slot_card(o, i))
                log.append({'freed': dead, 'promoted': promoted, 'cards': sorted(cards)})
    except KeyError as e:
        log.append({'dangling': e.args[0]})
    return log
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('regression: old-to-young edge survives two minor collections',
   ({1: ['old', 56, [None, None]],
     2: ['old', 192, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [],
    [['store', 1, 1, 11], ['minor'], ['minor']],
    5),
   [{'cards': [1], 'freed': [13, 14], 'promoted': []}, {'cards': [1], 'freed': [], 'promoted': []}]),
  ('edge stored after the target survived once',
   ({1: ['old', 56, [None, None]],
     2: ['old', 192, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [13],
    [['minor'], ['store', 2, 0, 13], ['unroot', 13], ['minor']],
    5),
   [{'cards': [], 'freed': [11, 12, 14], 'promoted': []}, {'cards': [3], 'freed': [], 'promoted': []}]),
  ('promotion at the tenuring threshold',
   ({1: ['old', 56, [None, None]],
     2: ['old', 192, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [11],
    [['minor'], ['minor'], ['minor']],
    2),
   [{'cards': [], 'freed': [13, 14], 'promoted': []},
    {'cards': [], 'freed': [], 'promoted': [11, 12]},
    {'cards': [], 'freed': [], 'promoted': []}]),
  ('promoted object pointing at a younger object',
   ({1: ['old', 56, [None, None]],
     2: ['old', 192, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [11],
    [['minor'], ['alloc', 15], ['store', 11, 0, 15], ['minor'], ['minor']],
    2),
   [{'cards': [], 'freed': [13, 14], 'promoted': []},
    {'cards': [64], 'freed': [12], 'promoted': [11]},
    {'cards': [], 'freed': [], 'promoted': [15]}]),
  ('card of a slot in the next card',
   ({1: ['old', 56, [None, None]],
     2: ['old', 192, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [],
    [['store', 1, 0, 13], ['store', 1, 1, 14], ['minor']],
    4),
   [{'cards': [0, 1], 'freed': [11, 12], 'promoted': []}]),
  ('control: unreferenced young objects die',
   ({1: ['old', 56, [None, None]],
     2: ['old', 192, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [12],
    [['minor']],
    3),
   [{'cards': [], 'freed': [11, 13, 14], 'promoted': []}])],
 [('regression: old-to-young edge survives two minor collections',
   ({1: ['old', 120, [None, None]],
     2: ['old', 256, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [],
    [['store', 1, 1, 11], ['minor'], ['minor']],
    5),
   [{'cards': [2], 'freed': [13, 14], 'promoted': []}, {'cards': [2], 'freed': [], 'promoted': []}]),
  ('edge stored after the target survived once',
   ({1: ['old', 120, [None, None]],
     2: ['old', 256, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [13],
    [['minor'], ['store', 2, 0, 13], ['unroot', 13], ['minor']],
    5),
   [{'cards': [], 'freed': [11, 12, 14], 'promoted': []}, {'cards': [4], 'freed': [], 'promoted': []}]),
  ('promotion at the tenuring threshold',
   ({1: ['old', 120, [None, None]],
     2: ['old', 256, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [11],
    [['minor'], ['minor'], ['minor']],
    2),
   [{'cards': [], 'freed': [13, 14], 'promoted': []},
    {'cards': [], 'freed': [], 'promoted': [11, 12]},
    {'cards': [], 'freed': [], 'promoted': []}]),
  ('promoted object pointing at a younger object',
   ({1: ['old', 120, [None, None]],
     2: ['old', 256, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [11],
    [['minor'], ['alloc', 15], ['store', 11, 0, 15], ['minor'], ['minor']],
    2),
   [{'cards': [], 'freed': [13, 14], 'promoted': []},
    {'cards': [64], 'freed': [12], 'promoted': [11]},
    {'cards': [], 'freed': [], 'promoted': [15]}]),
  ('card of a slot in the next card',
   ({1: ['old', 120, [None, None]],
     2: ['old', 256, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [],
    [['store', 1, 0, 13], ['store', 1, 1, 14], ['minor']],
    4),
   [{'cards': [1, 2], 'freed': [11, 12], 'promoted': []}]),
  ('control: unreferenced young objects die',
   ({1: ['old', 120, [None, None]],
     2: ['old', 256, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [12],
    [['minor']],
    3),
   [{'cards': [], 'freed': [11, 13, 14], 'promoted': []}])],
 [('regression: old-to-young edge survives two minor collections',
   ({1: ['old', 184, [None, None]],
     2: ['old', 320, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [],
    [['store', 1, 1, 11], ['minor'], ['minor']],
    5),
   [{'cards': [3], 'freed': [13, 14], 'promoted': []}, {'cards': [3], 'freed': [], 'promoted': []}]),
  ('edge stored after the target survived once',
   ({1: ['old', 184, [None, None]],
     2: ['old', 320, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [13],
    [['minor'], ['store', 2, 0, 13], ['unroot', 13], ['minor']],
    5),
   [{'cards': [], 'freed': [11, 12, 14], 'promoted': []}, {'cards': [5], 'freed': [], 'promoted': []}]),
  ('promotion at the tenuring threshold',
   ({1: ['old', 184, [None, None]],
     2: ['old', 320, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [11],
    [['minor'], ['minor'], ['minor']],
    2),
   [{'cards': [], 'freed': [13, 14], 'promoted': []},
    {'cards': [], 'freed': [], 'promoted': [11, 12]},
    {'cards': [], 'freed': [], 'promoted': []}]),
  ('promoted object pointing at a younger object',
   ({1: ['old', 184, [None, None]],
     2: ['old', 320, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [11],
    [['minor'], ['alloc', 15], ['store', 11, 0, 15], ['minor'], ['minor']],
    2),
   [{'cards': [], 'freed': [13, 14], 'promoted': []},
    {'cards': [64], 'freed': [12], 'promoted': [11]},
    {'cards': [], 'freed': [], 'promoted': [15]}]),
  ('card of a slot in the next card',
   ({1: ['old', 184, [None, None]],
     2: ['old', 320, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [],
    [['store', 1, 0, 13], ['store', 1, 1, 14], ['minor']],
    4),
   [{'cards': [2, 3], 'freed': [11, 12], 'promoted': []}]),
  ('control: unreferenced young objects die',
   ({1: ['old', 184, [None, None]],
     2: ['old', 320, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [12],
    [['minor']],
    3),
   [{'cards': [], 'freed': [11, 13, 14], 'promoted': []}])],
 [('regression: old-to-young edge survives two minor collections',
   ({1: ['old', 248, [None, None]],
     2: ['old', 384, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [],
    [['store', 1, 1, 11], ['minor'], ['minor']],
    5),
   [{'cards': [4], 'freed': [13, 14], 'promoted': []}, {'cards': [4], 'freed': [], 'promoted': []}]),
  ('edge stored after the target survived once',
   ({1: ['old', 248, [None, None]],
     2: ['old', 384, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [13],
    [['minor'], ['store', 2, 0, 13], ['unroot', 13], ['minor']],
    5),
   [{'cards': [], 'freed': [11, 12, 14], 'promoted': []}, {'cards': [6], 'freed': [], 'promoted': []}]),
  ('promotion at the tenuring threshold',
   ({1: ['old', 248, [None, None]],
     2: ['old', 384, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [11],
    [['minor'], ['minor'], ['minor']],
    2),
   [{'cards': [], 'freed': [13, 14], 'promoted': []},
    {'cards': [], 'freed': [], 'promoted': [11, 12]},
    {'cards': [], 'freed': [], 'promoted': []}]),
  ('promoted object pointing at a younger object',
   ({1: ['old', 248, [None, None]],
     2: ['old', 384, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [11],
    [['minor'], ['alloc', 15], ['store', 11, 0, 15], ['minor'], ['minor']],
    2),
   [{'cards': [], 'freed': [13, 14], 'promoted': []},
    {'cards': [64], 'freed': [12], 'promoted': [11]},
    {'cards': [], 'freed': [], 'promoted': [15]}]),
  ('card of a slot in the next card',
   ({1: ['old', 248, [None, None]],
     2: ['old', 384, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [],
    [['store', 1, 0, 13], ['store', 1, 1, 14], ['minor']],
    4),
   [{'cards': [3, 4], 'freed': [11, 12], 'promoted': []}]),
  ('control: unreferenced young objects die',
   ({1: ['old', 248, [None, None]],
     2: ['old', 384, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [12],
    [['minor']],
    3),
   [{'cards': [], 'freed': [11, 13, 14], 'promoted': []}])],
 [('regression: old-to-young edge survives two minor collections',
   ({1: ['old', 312, [None, None]],
     2: ['old', 448, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [],
    [['store', 1, 1, 11], ['minor'], ['minor']],
    5),
   [{'cards': [5], 'freed': [13, 14], 'promoted': []}, {'cards': [5], 'freed': [], 'promoted': []}]),
  ('edge stored after the target survived once',
   ({1: ['old', 312, [None, None]],
     2: ['old', 448, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [13],
    [['minor'], ['store', 2, 0, 13], ['unroot', 13], ['minor']],
    5),
   [{'cards': [], 'freed': [11, 12, 14], 'promoted': []}, {'cards': [7], 'freed': [], 'promoted': []}]),
  ('promotion at the tenuring threshold',
   ({1: ['old', 312, [None, None]],
     2: ['old', 448, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [11],
    [['minor'], ['minor'], ['minor']],
    2),
   [{'cards': [], 'freed': [13, 14], 'promoted': []},
    {'cards': [], 'freed': [], 'promoted': [11, 12]},
    {'cards': [], 'freed': [], 'promoted': []}]),
  ('promoted object pointing at a younger object',
   ({1: ['old', 312, [None, None]],
     2: ['old', 448, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [11],
    [['minor'], ['alloc', 15], ['store', 11, 0, 15], ['minor'], ['minor']],
    2),
   [{'cards': [], 'freed': [13, 14], 'promoted': []},
    {'cards': [64], 'freed': [12], 'promoted': [11]},
    {'cards': [], 'freed': [], 'promoted': [15]}]),
  ('card of a slot in the next card',
   ({1: ['old', 312, [None, None]],
     2: ['old', 448, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [],
    [['store', 1, 0, 13], ['store', 1, 1, 14], ['minor']],
    4),
   [{'cards': [4, 5], 'freed': [11, 12], 'promoted': []}]),
  ('control: unreferenced young objects die',
   ({1: ['old', 312, [None, None]],
     2: ['old', 448, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [12],
    [['minor']],
    3),
   [{'cards': [], 'freed': [11, 13, 14], 'promoted': []}])]]
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 fixture	Actual	Expected	Outcome
regression: old-to-young edge survives two minor collections	`[{'cards': [1], 'freed': [13, 14], 'promoted': []}, {'cards': [1], 'freed': [], 'promoted': []}]`	`[{'cards': [1], 'freed': [13, 14], 'promoted': []}, {'cards': [1], 'freed': [], 'promoted': []}]`	Passed
edge stored after the target survived once	`[{'cards': [], 'freed': [11, 12, 14], 'promoted': []}, {'cards': [3], 'freed': [], 'promoted': []}]`	`[{'cards': [], 'freed': [11, 12, 14], 'promoted': []}, {'cards': [3], 'freed': [], 'promoted': []}]`	Passed
promotion at the tenuring threshold	`[{'cards': [], 'freed': [13, 14], 'promoted': []}, {'cards': [], 'freed': [], 'promoted': [11, 12]}, {'cards': [], 'freed': [], 'promoted': []}]`	`[{'cards': [], 'freed': [13, 14], 'promoted': []}, {'cards': [], 'freed': [], 'promoted': [11, 12]}, {'cards': [], 'freed': [], 'promoted': []}]`	Passed
promoted object pointing at a younger object	`[{'cards': [], 'freed': [13, 14], 'promoted': []}, {'cards': [], 'freed': [12], 'promoted': [11]}, {'dangling': 15}]`	`[{'cards': [], 'freed': [13, 14], 'promoted': []}, {'cards': [64], 'freed': [12], 'promoted': [11]}, {'cards': [], 'freed': [], 'promoted': [15]}]`	Failed
card of a slot in the next card	`[{'cards': [0, 1], 'freed': [11, 12], 'promoted': []}]`	`[{'cards': [0, 1], 'freed': [11, 12], 'promoted': []}]`	Passed
control: unreferenced young objects die	`[{'cards': [], 'freed': [11, 13, 14], 'promoted': []}]`	`[{'cards': [], 'freed': [11, 13, 14], 'promoted': []}]`	Passed

SHA-256 / c896412f3b3567846720f2ff28b613f120048923b01f7ea08f9e93208b068f0a

3 / The verified repair

Exit 0

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

N = 1
observations = []
def solve(objs, roots, events, tenure):
    objs = {k: {'gen': v[0], 'addr': v[1], 'fields': list(v[2]), 'age': 0} for k, v in objs.items()}
    roots = list(roots)
    cards = set()
    log = []
    next_addr = 4096
    def slot_card(o, i):
        return (objs[o]['addr'] + 8 * i) // 64
    try:
        for ev in events:
            if ev[0] == 'store':
                _, src, i, dst = ev
                objs[src]['fields'][i] = dst
                if objs[src]['gen'] == 'old' and dst is not None and objs[dst]['gen'] == 'young':
                    cards.add(slot_card(src, i))
            elif ev[0] == 'alloc':
                objs[ev[1]] = {'gen': 'young', 'addr': 0, 'fields': [None], 'age': 0}
            elif ev[0] == 'root':
                roots.append(ev[1])
            elif ev[0] == 'unroot':
                roots.remove(ev[1])
            else:
                grey = [r for r in roots if objs[r]['gen'] == 'young']
                for o, ob in objs.items():
                    if ob['gen'] == 'old':
                        for i, f in enumerate(ob['fields']):
                            if slot_card(o, i) in cards and f is not None and objs[f]['gen'] == 'young':
                                grey.append(f)
                live = set()
                while grey:
                    y = grey.pop()
                    if y in live:
                        continue
                    live.add(y)
                    for f in objs[y]['fields']:
                        if f is not None and objs[f]['gen'] == 'young':
                            grey.append(f)
                dead = sorted(k for k, ob in objs.items() if ob['gen'] == 'young' and k not in live)
                for k in dead:
                    del objs[k]
                promoted = []
                for k in sorted(live):
                    objs[k]['age'] += 1
                    if objs[k]['age'] >= tenure:
                        objs[k]['gen'] = 'old'
                        objs[k]['addr'] = next_addr
                        next_addr += 64
                        promoted.append(k)
                cards = set()
                for o in [k for k, ob in objs.items() if ob['gen'] == 'old']:
                    for i, f in enumerate(objs[o]['fields']):
                        if f is not None and objs[f]['gen'] == 'young':
                            cards.add(slot_card(o, i))
                log.append({'freed': dead, 'promoted': promoted, 'cards': sorted(cards)})
    except KeyError as e:
        log.append({'dangling': e.args[0]})
    return log
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('regression: old-to-young edge survives two minor collections',
   ({1: ['old', 56, [None, None]],
     2: ['old', 192, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [],
    [['store', 1, 1, 11], ['minor'], ['minor']],
    5),
   [{'cards': [1], 'freed': [13, 14], 'promoted': []}, {'cards': [1], 'freed': [], 'promoted': []}]),
  ('edge stored after the target survived once',
   ({1: ['old', 56, [None, None]],
     2: ['old', 192, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [13],
    [['minor'], ['store', 2, 0, 13], ['unroot', 13], ['minor']],
    5),
   [{'cards': [], 'freed': [11, 12, 14], 'promoted': []}, {'cards': [3], 'freed': [], 'promoted': []}]),
  ('promotion at the tenuring threshold',
   ({1: ['old', 56, [None, None]],
     2: ['old', 192, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [11],
    [['minor'], ['minor'], ['minor']],
    2),
   [{'cards': [], 'freed': [13, 14], 'promoted': []},
    {'cards': [], 'freed': [], 'promoted': [11, 12]},
    {'cards': [], 'freed': [], 'promoted': []}]),
  ('promoted object pointing at a younger object',
   ({1: ['old', 56, [None, None]],
     2: ['old', 192, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [11],
    [['minor'], ['alloc', 15], ['store', 11, 0, 15], ['minor'], ['minor']],
    2),
   [{'cards': [], 'freed': [13, 14], 'promoted': []},
    {'cards': [64], 'freed': [12], 'promoted': [11]},
    {'cards': [], 'freed': [], 'promoted': [15]}]),
  ('card of a slot in the next card',
   ({1: ['old', 56, [None, None]],
     2: ['old', 192, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [],
    [['store', 1, 0, 13], ['store', 1, 1, 14], ['minor']],
    4),
   [{'cards': [0, 1], 'freed': [11, 12], 'promoted': []}]),
  ('control: unreferenced young objects die',
   ({1: ['old', 56, [None, None]],
     2: ['old', 192, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [12],
    [['minor']],
    3),
   [{'cards': [], 'freed': [11, 13, 14], 'promoted': []}])],
 [('regression: old-to-young edge survives two minor collections',
   ({1: ['old', 120, [None, None]],
     2: ['old', 256, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [],
    [['store', 1, 1, 11], ['minor'], ['minor']],
    5),
   [{'cards': [2], 'freed': [13, 14], 'promoted': []}, {'cards': [2], 'freed': [], 'promoted': []}]),
  ('edge stored after the target survived once',
   ({1: ['old', 120, [None, None]],
     2: ['old', 256, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [13],
    [['minor'], ['store', 2, 0, 13], ['unroot', 13], ['minor']],
    5),
   [{'cards': [], 'freed': [11, 12, 14], 'promoted': []}, {'cards': [4], 'freed': [], 'promoted': []}]),
  ('promotion at the tenuring threshold',
   ({1: ['old', 120, [None, None]],
     2: ['old', 256, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [11],
    [['minor'], ['minor'], ['minor']],
    2),
   [{'cards': [], 'freed': [13, 14], 'promoted': []},
    {'cards': [], 'freed': [], 'promoted': [11, 12]},
    {'cards': [], 'freed': [], 'promoted': []}]),
  ('promoted object pointing at a younger object',
   ({1: ['old', 120, [None, None]],
     2: ['old', 256, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [11],
    [['minor'], ['alloc', 15], ['store', 11, 0, 15], ['minor'], ['minor']],
    2),
   [{'cards': [], 'freed': [13, 14], 'promoted': []},
    {'cards': [64], 'freed': [12], 'promoted': [11]},
    {'cards': [], 'freed': [], 'promoted': [15]}]),
  ('card of a slot in the next card',
   ({1: ['old', 120, [None, None]],
     2: ['old', 256, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [],
    [['store', 1, 0, 13], ['store', 1, 1, 14], ['minor']],
    4),
   [{'cards': [1, 2], 'freed': [11, 12], 'promoted': []}]),
  ('control: unreferenced young objects die',
   ({1: ['old', 120, [None, None]],
     2: ['old', 256, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [12],
    [['minor']],
    3),
   [{'cards': [], 'freed': [11, 13, 14], 'promoted': []}])],
 [('regression: old-to-young edge survives two minor collections',
   ({1: ['old', 184, [None, None]],
     2: ['old', 320, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [],
    [['store', 1, 1, 11], ['minor'], ['minor']],
    5),
   [{'cards': [3], 'freed': [13, 14], 'promoted': []}, {'cards': [3], 'freed': [], 'promoted': []}]),
  ('edge stored after the target survived once',
   ({1: ['old', 184, [None, None]],
     2: ['old', 320, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [13],
    [['minor'], ['store', 2, 0, 13], ['unroot', 13], ['minor']],
    5),
   [{'cards': [], 'freed': [11, 12, 14], 'promoted': []}, {'cards': [5], 'freed': [], 'promoted': []}]),
  ('promotion at the tenuring threshold',
   ({1: ['old', 184, [None, None]],
     2: ['old', 320, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [11],
    [['minor'], ['minor'], ['minor']],
    2),
   [{'cards': [], 'freed': [13, 14], 'promoted': []},
    {'cards': [], 'freed': [], 'promoted': [11, 12]},
    {'cards': [], 'freed': [], 'promoted': []}]),
  ('promoted object pointing at a younger object',
   ({1: ['old', 184, [None, None]],
     2: ['old', 320, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [11],
    [['minor'], ['alloc', 15], ['store', 11, 0, 15], ['minor'], ['minor']],
    2),
   [{'cards': [], 'freed': [13, 14], 'promoted': []},
    {'cards': [64], 'freed': [12], 'promoted': [11]},
    {'cards': [], 'freed': [], 'promoted': [15]}]),
  ('card of a slot in the next card',
   ({1: ['old', 184, [None, None]],
     2: ['old', 320, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [],
    [['store', 1, 0, 13], ['store', 1, 1, 14], ['minor']],
    4),
   [{'cards': [2, 3], 'freed': [11, 12], 'promoted': []}]),
  ('control: unreferenced young objects die',
   ({1: ['old', 184, [None, None]],
     2: ['old', 320, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [12],
    [['minor']],
    3),
   [{'cards': [], 'freed': [11, 13, 14], 'promoted': []}])],
 [('regression: old-to-young edge survives two minor collections',
   ({1: ['old', 248, [None, None]],
     2: ['old', 384, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [],
    [['store', 1, 1, 11], ['minor'], ['minor']],
    5),
   [{'cards': [4], 'freed': [13, 14], 'promoted': []}, {'cards': [4], 'freed': [], 'promoted': []}]),
  ('edge stored after the target survived once',
   ({1: ['old', 248, [None, None]],
     2: ['old', 384, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [13],
    [['minor'], ['store', 2, 0, 13], ['unroot', 13], ['minor']],
    5),
   [{'cards': [], 'freed': [11, 12, 14], 'promoted': []}, {'cards': [6], 'freed': [], 'promoted': []}]),
  ('promotion at the tenuring threshold',
   ({1: ['old', 248, [None, None]],
     2: ['old', 384, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [11],
    [['minor'], ['minor'], ['minor']],
    2),
   [{'cards': [], 'freed': [13, 14], 'promoted': []},
    {'cards': [], 'freed': [], 'promoted': [11, 12]},
    {'cards': [], 'freed': [], 'promoted': []}]),
  ('promoted object pointing at a younger object',
   ({1: ['old', 248, [None, None]],
     2: ['old', 384, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [11],
    [['minor'], ['alloc', 15], ['store', 11, 0, 15], ['minor'], ['minor']],
    2),
   [{'cards': [], 'freed': [13, 14], 'promoted': []},
    {'cards': [64], 'freed': [12], 'promoted': [11]},
    {'cards': [], 'freed': [], 'promoted': [15]}]),
  ('card of a slot in the next card',
   ({1: ['old', 248, [None, None]],
     2: ['old', 384, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [],
    [['store', 1, 0, 13], ['store', 1, 1, 14], ['minor']],
    4),
   [{'cards': [3, 4], 'freed': [11, 12], 'promoted': []}]),
  ('control: unreferenced young objects die',
   ({1: ['old', 248, [None, None]],
     2: ['old', 384, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [12],
    [['minor']],
    3),
   [{'cards': [], 'freed': [11, 13, 14], 'promoted': []}])],
 [('regression: old-to-young edge survives two minor collections',
   ({1: ['old', 312, [None, None]],
     2: ['old', 448, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [],
    [['store', 1, 1, 11], ['minor'], ['minor']],
    5),
   [{'cards': [5], 'freed': [13, 14], 'promoted': []}, {'cards': [5], 'freed': [], 'promoted': []}]),
  ('edge stored after the target survived once',
   ({1: ['old', 312, [None, None]],
     2: ['old', 448, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [13],
    [['minor'], ['store', 2, 0, 13], ['unroot', 13], ['minor']],
    5),
   [{'cards': [], 'freed': [11, 12, 14], 'promoted': []}, {'cards': [7], 'freed': [], 'promoted': []}]),
  ('promotion at the tenuring threshold',
   ({1: ['old', 312, [None, None]],
     2: ['old', 448, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [11],
    [['minor'], ['minor'], ['minor']],
    2),
   [{'cards': [], 'freed': [13, 14], 'promoted': []},
    {'cards': [], 'freed': [], 'promoted': [11, 12]},
    {'cards': [], 'freed': [], 'promoted': []}]),
  ('promoted object pointing at a younger object',
   ({1: ['old', 312, [None, None]],
     2: ['old', 448, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [11],
    [['minor'], ['alloc', 15], ['store', 11, 0, 15], ['minor'], ['minor']],
    2),
   [{'cards': [], 'freed': [13, 14], 'promoted': []},
    {'cards': [64], 'freed': [12], 'promoted': [11]},
    {'cards': [], 'freed': [], 'promoted': [15]}]),
  ('card of a slot in the next card',
   ({1: ['old', 312, [None, None]],
     2: ['old', 448, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [],
    [['store', 1, 0, 13], ['store', 1, 1, 14], ['minor']],
    4),
   [{'cards': [4, 5], 'freed': [11, 12], 'promoted': []}]),
  ('control: unreferenced young objects die',
   ({1: ['old', 312, [None, None]],
     2: ['old', 448, [None]],
     11: ['young', 0, [12]],
     12: ['young', 0, []],
     13: ['young', 0, []],
     14: ['young', 0, [None]]},
    [12],
    [['minor']],
    3),
   [{'cards': [], 'freed': [11, 13, 14], 'promoted': []}])]]
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 fixture	Actual	Expected	Outcome
regression: old-to-young edge survives two minor collections	`[{'cards': [1], 'freed': [13, 14], 'promoted': []}, {'cards': [1], 'freed': [], 'promoted': []}]`	`[{'cards': [1], 'freed': [13, 14], 'promoted': []}, {'cards': [1], 'freed': [], 'promoted': []}]`	Passed
edge stored after the target survived once	`[{'cards': [], 'freed': [11, 12, 14], 'promoted': []}, {'cards': [3], 'freed': [], 'promoted': []}]`	`[{'cards': [], 'freed': [11, 12, 14], 'promoted': []}, {'cards': [3], 'freed': [], 'promoted': []}]`	Passed
promotion at the tenuring threshold	`[{'cards': [], 'freed': [13, 14], 'promoted': []}, {'cards': [], 'freed': [], 'promoted': [11, 12]}, {'cards': [], 'freed': [], 'promoted': []}]`	`[{'cards': [], 'freed': [13, 14], 'promoted': []}, {'cards': [], 'freed': [], 'promoted': [11, 12]}, {'cards': [], 'freed': [], 'promoted': []}]`	Passed
promoted object pointing at a younger object	`[{'cards': [], 'freed': [13, 14], 'promoted': []}, {'cards': [64], 'freed': [12], 'promoted': [11]}, {'cards': [], 'freed': [], 'promoted': [15]}]`	`[{'cards': [], 'freed': [13, 14], 'promoted': []}, {'cards': [64], 'freed': [12], 'promoted': [11]}, {'cards': [], 'freed': [], 'promoted': [15]}]`	Passed
card of a slot in the next card	`[{'cards': [0, 1], 'freed': [11, 12], 'promoted': []}]`	`[{'cards': [0, 1], 'freed': [11, 12], 'promoted': []}]`	Passed
control: unreferenced young objects die	`[{'cards': [], 'freed': [11, 13, 14], 'promoted': []}]`	`[{'cards': [], 'freed': [11, 13, 14], 'promoted': []}]`	Passed

SHA-256 / 368786931ca48a50ec0f2c4b6eb27f930ea9fb21625955d14701473326201cf7

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 2026-09-29T14:51:27.660472+00:00.

Case digest / 710e0662c6dbf1379e7c5e41b5771424fc6e3d6a1982b9d82190c293d49ad1cd