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FA-90776 / Garbage collector invariants / Open access

TAMS: object allocated exactly at TAMS judged by marks · case 01

The first object allocated after marking started is freed although it is implicitly live.

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

ROOT CAUSE

The below-TAMS test includes the TAMS address itself.

VERIFIED REPAIR

Only objects strictly below TAMS need a mark.

Unsuccessful approach: Comparing with the current top requires marks for every object allocated during marking.

Case contract

Concurrent marking with per-region top-at-mark-start (TAMS). alloc r size bump-allocates in region r (addresses r*region_size onward; None if it would pass the region end). start snapshots every region's current top as its TAMS (regions never allocated in have TAMS at their bottom) and clears marks. mark addr marks an object. end frees, in address order, every object below its region's TAMS that is not marked; objects at or above TAMS were allocated during marking and are live. Return allocation addresses and the freed list of each end.

Why this case matters

Snapshot collectors treat objects allocated during marking as live using a per-region watermark.

1 / The failure

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

N = 1
observations = []
def solve(region_size, events):
    top = {}
    tams = {}
    marked = set()
    objs = {}
    out = []
    for ev in events:
        op = ev[0]
        if op == 'alloc':
            r = ev[1]
            a = top.get(r, r * region_size)
            if a + ev[2] > (r + 1) * region_size:
                out.append(None)
                continue
            objs[a] = ev[2]
            top[r] = a + ev[2]
            out.append(a)
        elif op == 'start':
            tams = dict(top)
            marked = set()
        elif op == 'mark':
            marked.add(ev[1])
        else:
            dead = []
            for a in sorted(objs):
                r = a // region_size
                if a <= tams.get(r, r * region_size) and a not in marked:
                    dead.append(a)
            for a in dead:
                del objs[a]
            out.append(dead)
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('regression: objects above TAMS are implicitly live',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 21],
     ['alloc', 1, 40],
     ['start'],
     ['alloc', 0, 10],
     ['alloc', 2, 10],
     ['mark', 0],
     ['end']]),
   [0, 30, 100, 51, 200, [30, 100]]),
  ('first object allocated after marking started',
   (100, [['alloc', 0, 30], ['alloc', 0, 21], ['alloc', 1, 40], ['start'], ['alloc', 1, 6], ['end']]),
   [0, 30, 100, 140, [0, 30, 100]]),
  ('region untouched when marking started',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 21],
     ['alloc', 1, 40],
     ['start'],
     ['alloc', 3, 20],
     ['alloc', 3, 5],
     ['end']]),
   [0, 30, 100, 300, 320, [0, 30, 100]]),
  ('second cycle uses fresh TAMS and marks',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 21],
     ['alloc', 1, 40],
     ['start'],
     ['mark', 0],
     ['alloc', 0, 5],
     ['end'],
     ['start'],
     ['mark', 30],
     ['end']]),
   [0, 30, 100, 51, [30, 100], [0, 51]]),
  ('marks from the previous cycle are discarded',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 21],
     ['alloc', 1, 40],
     ['start'],
     ['mark', 0],
     ['mark', 100],
     ['end'],
     ['start'],
     ['end']]),
   [0, 30, 100, [30], [0, 100]]),
  ('control: allocation beyond the region',
   (100, [['alloc', 0, 90], ['alloc', 0, 21], ['start'], ['end']]),
   [0, None, [0]])],
 [('regression: objects above TAMS are implicitly live',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 22],
     ['alloc', 1, 40],
     ['start'],
     ['alloc', 0, 10],
     ['alloc', 2, 10],
     ['mark', 0],
     ['end']]),
   [0, 30, 100, 52, 200, [30, 100]]),
  ('first object allocated after marking started',
   (100, [['alloc', 0, 30], ['alloc', 0, 22], ['alloc', 1, 40], ['start'], ['alloc', 1, 7], ['end']]),
   [0, 30, 100, 140, [0, 30, 100]]),
  ('region untouched when marking started',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 22],
     ['alloc', 1, 40],
     ['start'],
     ['alloc', 3, 20],
     ['alloc', 3, 5],
     ['end']]),
   [0, 30, 100, 300, 320, [0, 30, 100]]),
  ('second cycle uses fresh TAMS and marks',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 22],
     ['alloc', 1, 40],
     ['start'],
     ['mark', 0],
     ['alloc', 0, 5],
     ['end'],
     ['start'],
     ['mark', 30],
     ['end']]),
   [0, 30, 100, 52, [30, 100], [0, 52]]),
  ('marks from the previous cycle are discarded',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 22],
     ['alloc', 1, 40],
     ['start'],
     ['mark', 0],
     ['mark', 100],
     ['end'],
     ['start'],
     ['end']]),
   [0, 30, 100, [30], [0, 100]]),
  ('control: allocation beyond the region',
   (100, [['alloc', 0, 90], ['alloc', 0, 22], ['start'], ['end']]),
   [0, None, [0]])],
 [('regression: objects above TAMS are implicitly live',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 23],
     ['alloc', 1, 40],
     ['start'],
     ['alloc', 0, 10],
     ['alloc', 2, 10],
     ['mark', 0],
     ['end']]),
   [0, 30, 100, 53, 200, [30, 100]]),
  ('first object allocated after marking started',
   (100, [['alloc', 0, 30], ['alloc', 0, 23], ['alloc', 1, 40], ['start'], ['alloc', 1, 8], ['end']]),
   [0, 30, 100, 140, [0, 30, 100]]),
  ('region untouched when marking started',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 23],
     ['alloc', 1, 40],
     ['start'],
     ['alloc', 3, 20],
     ['alloc', 3, 5],
     ['end']]),
   [0, 30, 100, 300, 320, [0, 30, 100]]),
  ('second cycle uses fresh TAMS and marks',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 23],
     ['alloc', 1, 40],
     ['start'],
     ['mark', 0],
     ['alloc', 0, 5],
     ['end'],
     ['start'],
     ['mark', 30],
     ['end']]),
   [0, 30, 100, 53, [30, 100], [0, 53]]),
  ('marks from the previous cycle are discarded',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 23],
     ['alloc', 1, 40],
     ['start'],
     ['mark', 0],
     ['mark', 100],
     ['end'],
     ['start'],
     ['end']]),
   [0, 30, 100, [30], [0, 100]]),
  ('control: allocation beyond the region',
   (100, [['alloc', 0, 90], ['alloc', 0, 23], ['start'], ['end']]),
   [0, None, [0]])],
 [('regression: objects above TAMS are implicitly live',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 24],
     ['alloc', 1, 40],
     ['start'],
     ['alloc', 0, 10],
     ['alloc', 2, 10],
     ['mark', 0],
     ['end']]),
   [0, 30, 100, 54, 200, [30, 100]]),
  ('first object allocated after marking started',
   (100, [['alloc', 0, 30], ['alloc', 0, 24], ['alloc', 1, 40], ['start'], ['alloc', 1, 9], ['end']]),
   [0, 30, 100, 140, [0, 30, 100]]),
  ('region untouched when marking started',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 24],
     ['alloc', 1, 40],
     ['start'],
     ['alloc', 3, 20],
     ['alloc', 3, 5],
     ['end']]),
   [0, 30, 100, 300, 320, [0, 30, 100]]),
  ('second cycle uses fresh TAMS and marks',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 24],
     ['alloc', 1, 40],
     ['start'],
     ['mark', 0],
     ['alloc', 0, 5],
     ['end'],
     ['start'],
     ['mark', 30],
     ['end']]),
   [0, 30, 100, 54, [30, 100], [0, 54]]),
  ('marks from the previous cycle are discarded',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 24],
     ['alloc', 1, 40],
     ['start'],
     ['mark', 0],
     ['mark', 100],
     ['end'],
     ['start'],
     ['end']]),
   [0, 30, 100, [30], [0, 100]]),
  ('control: allocation beyond the region',
   (100, [['alloc', 0, 90], ['alloc', 0, 24], ['start'], ['end']]),
   [0, None, [0]])],
 [('regression: objects above TAMS are implicitly live',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 25],
     ['alloc', 1, 40],
     ['start'],
     ['alloc', 0, 10],
     ['alloc', 2, 10],
     ['mark', 0],
     ['end']]),
   [0, 30, 100, 55, 200, [30, 100]]),
  ('first object allocated after marking started',
   (100, [['alloc', 0, 30], ['alloc', 0, 25], ['alloc', 1, 40], ['start'], ['alloc', 1, 10], ['end']]),
   [0, 30, 100, 140, [0, 30, 100]]),
  ('region untouched when marking started',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 25],
     ['alloc', 1, 40],
     ['start'],
     ['alloc', 3, 20],
     ['alloc', 3, 5],
     ['end']]),
   [0, 30, 100, 300, 320, [0, 30, 100]]),
  ('second cycle uses fresh TAMS and marks',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 25],
     ['alloc', 1, 40],
     ['start'],
     ['mark', 0],
     ['alloc', 0, 5],
     ['end'],
     ['start'],
     ['mark', 30],
     ['end']]),
   [0, 30, 100, 55, [30, 100], [0, 55]]),
  ('marks from the previous cycle are discarded',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 25],
     ['alloc', 1, 40],
     ['start'],
     ['mark', 0],
     ['mark', 100],
     ['end'],
     ['start'],
     ['end']]),
   [0, 30, 100, [30], [0, 100]]),
  ('control: allocation beyond the region',
   (100, [['alloc', 0, 90], ['alloc', 0, 25], ['start'], ['end']]),
   [0, None, [0]])]]
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: objects above TAMS are implicitly live[0, 30, 100, 51, 200, [30, 51, 100, 200]][0, 30, 100, 51, 200, [30, 100]]Failed
first object allocated after marking started[0, 30, 100, 140, [0, 30, 100, 140]][0, 30, 100, 140, [0, 30, 100]]Failed
region untouched when marking started[0, 30, 100, 300, 320, [0, 30, 100, 300]][0, 30, 100, 300, 320, [0, 30, 100]]Failed
second cycle uses fresh TAMS and marks[0, 30, 100, 51, [30, 51, 100], [0]][0, 30, 100, 51, [30, 100], [0, 51]]Failed
marks from the previous cycle are discarded[0, 30, 100, [30], [0, 100]][0, 30, 100, [30], [0, 100]]Passed
control: allocation beyond the region[0, None, [0]][0, None, [0]]Passed

SHA-256 / 21db7021bc2025f7a77bdca85ff3ede77ab3231417e44f9009157b5170d603a2

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(region_size, events):
    top = {}
    tams = {}
    marked = set()
    objs = {}
    out = []
    for ev in events:
        op = ev[0]
        if op == 'alloc':
            r = ev[1]
            a = top.get(r, r * region_size)
            if a + ev[2] > (r + 1) * region_size:
                out.append(None)
                continue
            objs[a] = ev[2]
            top[r] = a + ev[2]
            out.append(a)
        elif op == 'start':
            tams = dict(top)
            marked = set()
        elif op == 'mark':
            marked.add(ev[1])
        else:
            dead = []
            for a in sorted(objs):
                r = a // region_size
                if a < top.get(r, r * region_size) and a not in marked:
                    dead.append(a)
            for a in dead:
                del objs[a]
            out.append(dead)
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('regression: objects above TAMS are implicitly live',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 21],
     ['alloc', 1, 40],
     ['start'],
     ['alloc', 0, 10],
     ['alloc', 2, 10],
     ['mark', 0],
     ['end']]),
   [0, 30, 100, 51, 200, [30, 100]]),
  ('first object allocated after marking started',
   (100, [['alloc', 0, 30], ['alloc', 0, 21], ['alloc', 1, 40], ['start'], ['alloc', 1, 6], ['end']]),
   [0, 30, 100, 140, [0, 30, 100]]),
  ('region untouched when marking started',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 21],
     ['alloc', 1, 40],
     ['start'],
     ['alloc', 3, 20],
     ['alloc', 3, 5],
     ['end']]),
   [0, 30, 100, 300, 320, [0, 30, 100]]),
  ('second cycle uses fresh TAMS and marks',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 21],
     ['alloc', 1, 40],
     ['start'],
     ['mark', 0],
     ['alloc', 0, 5],
     ['end'],
     ['start'],
     ['mark', 30],
     ['end']]),
   [0, 30, 100, 51, [30, 100], [0, 51]]),
  ('marks from the previous cycle are discarded',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 21],
     ['alloc', 1, 40],
     ['start'],
     ['mark', 0],
     ['mark', 100],
     ['end'],
     ['start'],
     ['end']]),
   [0, 30, 100, [30], [0, 100]]),
  ('control: allocation beyond the region',
   (100, [['alloc', 0, 90], ['alloc', 0, 21], ['start'], ['end']]),
   [0, None, [0]])],
 [('regression: objects above TAMS are implicitly live',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 22],
     ['alloc', 1, 40],
     ['start'],
     ['alloc', 0, 10],
     ['alloc', 2, 10],
     ['mark', 0],
     ['end']]),
   [0, 30, 100, 52, 200, [30, 100]]),
  ('first object allocated after marking started',
   (100, [['alloc', 0, 30], ['alloc', 0, 22], ['alloc', 1, 40], ['start'], ['alloc', 1, 7], ['end']]),
   [0, 30, 100, 140, [0, 30, 100]]),
  ('region untouched when marking started',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 22],
     ['alloc', 1, 40],
     ['start'],
     ['alloc', 3, 20],
     ['alloc', 3, 5],
     ['end']]),
   [0, 30, 100, 300, 320, [0, 30, 100]]),
  ('second cycle uses fresh TAMS and marks',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 22],
     ['alloc', 1, 40],
     ['start'],
     ['mark', 0],
     ['alloc', 0, 5],
     ['end'],
     ['start'],
     ['mark', 30],
     ['end']]),
   [0, 30, 100, 52, [30, 100], [0, 52]]),
  ('marks from the previous cycle are discarded',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 22],
     ['alloc', 1, 40],
     ['start'],
     ['mark', 0],
     ['mark', 100],
     ['end'],
     ['start'],
     ['end']]),
   [0, 30, 100, [30], [0, 100]]),
  ('control: allocation beyond the region',
   (100, [['alloc', 0, 90], ['alloc', 0, 22], ['start'], ['end']]),
   [0, None, [0]])],
 [('regression: objects above TAMS are implicitly live',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 23],
     ['alloc', 1, 40],
     ['start'],
     ['alloc', 0, 10],
     ['alloc', 2, 10],
     ['mark', 0],
     ['end']]),
   [0, 30, 100, 53, 200, [30, 100]]),
  ('first object allocated after marking started',
   (100, [['alloc', 0, 30], ['alloc', 0, 23], ['alloc', 1, 40], ['start'], ['alloc', 1, 8], ['end']]),
   [0, 30, 100, 140, [0, 30, 100]]),
  ('region untouched when marking started',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 23],
     ['alloc', 1, 40],
     ['start'],
     ['alloc', 3, 20],
     ['alloc', 3, 5],
     ['end']]),
   [0, 30, 100, 300, 320, [0, 30, 100]]),
  ('second cycle uses fresh TAMS and marks',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 23],
     ['alloc', 1, 40],
     ['start'],
     ['mark', 0],
     ['alloc', 0, 5],
     ['end'],
     ['start'],
     ['mark', 30],
     ['end']]),
   [0, 30, 100, 53, [30, 100], [0, 53]]),
  ('marks from the previous cycle are discarded',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 23],
     ['alloc', 1, 40],
     ['start'],
     ['mark', 0],
     ['mark', 100],
     ['end'],
     ['start'],
     ['end']]),
   [0, 30, 100, [30], [0, 100]]),
  ('control: allocation beyond the region',
   (100, [['alloc', 0, 90], ['alloc', 0, 23], ['start'], ['end']]),
   [0, None, [0]])],
 [('regression: objects above TAMS are implicitly live',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 24],
     ['alloc', 1, 40],
     ['start'],
     ['alloc', 0, 10],
     ['alloc', 2, 10],
     ['mark', 0],
     ['end']]),
   [0, 30, 100, 54, 200, [30, 100]]),
  ('first object allocated after marking started',
   (100, [['alloc', 0, 30], ['alloc', 0, 24], ['alloc', 1, 40], ['start'], ['alloc', 1, 9], ['end']]),
   [0, 30, 100, 140, [0, 30, 100]]),
  ('region untouched when marking started',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 24],
     ['alloc', 1, 40],
     ['start'],
     ['alloc', 3, 20],
     ['alloc', 3, 5],
     ['end']]),
   [0, 30, 100, 300, 320, [0, 30, 100]]),
  ('second cycle uses fresh TAMS and marks',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 24],
     ['alloc', 1, 40],
     ['start'],
     ['mark', 0],
     ['alloc', 0, 5],
     ['end'],
     ['start'],
     ['mark', 30],
     ['end']]),
   [0, 30, 100, 54, [30, 100], [0, 54]]),
  ('marks from the previous cycle are discarded',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 24],
     ['alloc', 1, 40],
     ['start'],
     ['mark', 0],
     ['mark', 100],
     ['end'],
     ['start'],
     ['end']]),
   [0, 30, 100, [30], [0, 100]]),
  ('control: allocation beyond the region',
   (100, [['alloc', 0, 90], ['alloc', 0, 24], ['start'], ['end']]),
   [0, None, [0]])],
 [('regression: objects above TAMS are implicitly live',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 25],
     ['alloc', 1, 40],
     ['start'],
     ['alloc', 0, 10],
     ['alloc', 2, 10],
     ['mark', 0],
     ['end']]),
   [0, 30, 100, 55, 200, [30, 100]]),
  ('first object allocated after marking started',
   (100, [['alloc', 0, 30], ['alloc', 0, 25], ['alloc', 1, 40], ['start'], ['alloc', 1, 10], ['end']]),
   [0, 30, 100, 140, [0, 30, 100]]),
  ('region untouched when marking started',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 25],
     ['alloc', 1, 40],
     ['start'],
     ['alloc', 3, 20],
     ['alloc', 3, 5],
     ['end']]),
   [0, 30, 100, 300, 320, [0, 30, 100]]),
  ('second cycle uses fresh TAMS and marks',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 25],
     ['alloc', 1, 40],
     ['start'],
     ['mark', 0],
     ['alloc', 0, 5],
     ['end'],
     ['start'],
     ['mark', 30],
     ['end']]),
   [0, 30, 100, 55, [30, 100], [0, 55]]),
  ('marks from the previous cycle are discarded',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 25],
     ['alloc', 1, 40],
     ['start'],
     ['mark', 0],
     ['mark', 100],
     ['end'],
     ['start'],
     ['end']]),
   [0, 30, 100, [30], [0, 100]]),
  ('control: allocation beyond the region',
   (100, [['alloc', 0, 90], ['alloc', 0, 25], ['start'], ['end']]),
   [0, None, [0]])]]
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: objects above TAMS are implicitly live[0, 30, 100, 51, 200, [30, 51, 100, 200]][0, 30, 100, 51, 200, [30, 100]]Failed
first object allocated after marking started[0, 30, 100, 140, [0, 30, 100, 140]][0, 30, 100, 140, [0, 30, 100]]Failed
region untouched when marking started[0, 30, 100, 300, 320, [0, 30, 100, 300, 320]][0, 30, 100, 300, 320, [0, 30, 100]]Failed
second cycle uses fresh TAMS and marks[0, 30, 100, 51, [30, 51, 100], [0]][0, 30, 100, 51, [30, 100], [0, 51]]Failed
marks from the previous cycle are discarded[0, 30, 100, [30], [0, 100]][0, 30, 100, [30], [0, 100]]Passed
control: allocation beyond the region[0, None, [0]][0, None, [0]]Passed

SHA-256 / 0d8561c03129a7f1a26c1dc76a16dca0d3885c483e405751403daf7c58b18b16

3 / The verified repair

Exit 0
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(region_size, events):
    top = {}
    tams = {}
    marked = set()
    objs = {}
    out = []
    for ev in events:
        op = ev[0]
        if op == 'alloc':
            r = ev[1]
            a = top.get(r, r * region_size)
            if a + ev[2] > (r + 1) * region_size:
                out.append(None)
                continue
            objs[a] = ev[2]
            top[r] = a + ev[2]
            out.append(a)
        elif op == 'start':
            tams = dict(top)
            marked = set()
        elif op == 'mark':
            marked.add(ev[1])
        else:
            dead = []
            for a in sorted(objs):
                r = a // region_size
                if a < tams.get(r, r * region_size) and a not in marked:
                    dead.append(a)
            for a in dead:
                del objs[a]
            out.append(dead)
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('regression: objects above TAMS are implicitly live',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 21],
     ['alloc', 1, 40],
     ['start'],
     ['alloc', 0, 10],
     ['alloc', 2, 10],
     ['mark', 0],
     ['end']]),
   [0, 30, 100, 51, 200, [30, 100]]),
  ('first object allocated after marking started',
   (100, [['alloc', 0, 30], ['alloc', 0, 21], ['alloc', 1, 40], ['start'], ['alloc', 1, 6], ['end']]),
   [0, 30, 100, 140, [0, 30, 100]]),
  ('region untouched when marking started',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 21],
     ['alloc', 1, 40],
     ['start'],
     ['alloc', 3, 20],
     ['alloc', 3, 5],
     ['end']]),
   [0, 30, 100, 300, 320, [0, 30, 100]]),
  ('second cycle uses fresh TAMS and marks',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 21],
     ['alloc', 1, 40],
     ['start'],
     ['mark', 0],
     ['alloc', 0, 5],
     ['end'],
     ['start'],
     ['mark', 30],
     ['end']]),
   [0, 30, 100, 51, [30, 100], [0, 51]]),
  ('marks from the previous cycle are discarded',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 21],
     ['alloc', 1, 40],
     ['start'],
     ['mark', 0],
     ['mark', 100],
     ['end'],
     ['start'],
     ['end']]),
   [0, 30, 100, [30], [0, 100]]),
  ('control: allocation beyond the region',
   (100, [['alloc', 0, 90], ['alloc', 0, 21], ['start'], ['end']]),
   [0, None, [0]])],
 [('regression: objects above TAMS are implicitly live',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 22],
     ['alloc', 1, 40],
     ['start'],
     ['alloc', 0, 10],
     ['alloc', 2, 10],
     ['mark', 0],
     ['end']]),
   [0, 30, 100, 52, 200, [30, 100]]),
  ('first object allocated after marking started',
   (100, [['alloc', 0, 30], ['alloc', 0, 22], ['alloc', 1, 40], ['start'], ['alloc', 1, 7], ['end']]),
   [0, 30, 100, 140, [0, 30, 100]]),
  ('region untouched when marking started',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 22],
     ['alloc', 1, 40],
     ['start'],
     ['alloc', 3, 20],
     ['alloc', 3, 5],
     ['end']]),
   [0, 30, 100, 300, 320, [0, 30, 100]]),
  ('second cycle uses fresh TAMS and marks',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 22],
     ['alloc', 1, 40],
     ['start'],
     ['mark', 0],
     ['alloc', 0, 5],
     ['end'],
     ['start'],
     ['mark', 30],
     ['end']]),
   [0, 30, 100, 52, [30, 100], [0, 52]]),
  ('marks from the previous cycle are discarded',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 22],
     ['alloc', 1, 40],
     ['start'],
     ['mark', 0],
     ['mark', 100],
     ['end'],
     ['start'],
     ['end']]),
   [0, 30, 100, [30], [0, 100]]),
  ('control: allocation beyond the region',
   (100, [['alloc', 0, 90], ['alloc', 0, 22], ['start'], ['end']]),
   [0, None, [0]])],
 [('regression: objects above TAMS are implicitly live',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 23],
     ['alloc', 1, 40],
     ['start'],
     ['alloc', 0, 10],
     ['alloc', 2, 10],
     ['mark', 0],
     ['end']]),
   [0, 30, 100, 53, 200, [30, 100]]),
  ('first object allocated after marking started',
   (100, [['alloc', 0, 30], ['alloc', 0, 23], ['alloc', 1, 40], ['start'], ['alloc', 1, 8], ['end']]),
   [0, 30, 100, 140, [0, 30, 100]]),
  ('region untouched when marking started',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 23],
     ['alloc', 1, 40],
     ['start'],
     ['alloc', 3, 20],
     ['alloc', 3, 5],
     ['end']]),
   [0, 30, 100, 300, 320, [0, 30, 100]]),
  ('second cycle uses fresh TAMS and marks',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 23],
     ['alloc', 1, 40],
     ['start'],
     ['mark', 0],
     ['alloc', 0, 5],
     ['end'],
     ['start'],
     ['mark', 30],
     ['end']]),
   [0, 30, 100, 53, [30, 100], [0, 53]]),
  ('marks from the previous cycle are discarded',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 23],
     ['alloc', 1, 40],
     ['start'],
     ['mark', 0],
     ['mark', 100],
     ['end'],
     ['start'],
     ['end']]),
   [0, 30, 100, [30], [0, 100]]),
  ('control: allocation beyond the region',
   (100, [['alloc', 0, 90], ['alloc', 0, 23], ['start'], ['end']]),
   [0, None, [0]])],
 [('regression: objects above TAMS are implicitly live',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 24],
     ['alloc', 1, 40],
     ['start'],
     ['alloc', 0, 10],
     ['alloc', 2, 10],
     ['mark', 0],
     ['end']]),
   [0, 30, 100, 54, 200, [30, 100]]),
  ('first object allocated after marking started',
   (100, [['alloc', 0, 30], ['alloc', 0, 24], ['alloc', 1, 40], ['start'], ['alloc', 1, 9], ['end']]),
   [0, 30, 100, 140, [0, 30, 100]]),
  ('region untouched when marking started',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 24],
     ['alloc', 1, 40],
     ['start'],
     ['alloc', 3, 20],
     ['alloc', 3, 5],
     ['end']]),
   [0, 30, 100, 300, 320, [0, 30, 100]]),
  ('second cycle uses fresh TAMS and marks',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 24],
     ['alloc', 1, 40],
     ['start'],
     ['mark', 0],
     ['alloc', 0, 5],
     ['end'],
     ['start'],
     ['mark', 30],
     ['end']]),
   [0, 30, 100, 54, [30, 100], [0, 54]]),
  ('marks from the previous cycle are discarded',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 24],
     ['alloc', 1, 40],
     ['start'],
     ['mark', 0],
     ['mark', 100],
     ['end'],
     ['start'],
     ['end']]),
   [0, 30, 100, [30], [0, 100]]),
  ('control: allocation beyond the region',
   (100, [['alloc', 0, 90], ['alloc', 0, 24], ['start'], ['end']]),
   [0, None, [0]])],
 [('regression: objects above TAMS are implicitly live',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 25],
     ['alloc', 1, 40],
     ['start'],
     ['alloc', 0, 10],
     ['alloc', 2, 10],
     ['mark', 0],
     ['end']]),
   [0, 30, 100, 55, 200, [30, 100]]),
  ('first object allocated after marking started',
   (100, [['alloc', 0, 30], ['alloc', 0, 25], ['alloc', 1, 40], ['start'], ['alloc', 1, 10], ['end']]),
   [0, 30, 100, 140, [0, 30, 100]]),
  ('region untouched when marking started',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 25],
     ['alloc', 1, 40],
     ['start'],
     ['alloc', 3, 20],
     ['alloc', 3, 5],
     ['end']]),
   [0, 30, 100, 300, 320, [0, 30, 100]]),
  ('second cycle uses fresh TAMS and marks',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 25],
     ['alloc', 1, 40],
     ['start'],
     ['mark', 0],
     ['alloc', 0, 5],
     ['end'],
     ['start'],
     ['mark', 30],
     ['end']]),
   [0, 30, 100, 55, [30, 100], [0, 55]]),
  ('marks from the previous cycle are discarded',
   (100,
    [['alloc', 0, 30],
     ['alloc', 0, 25],
     ['alloc', 1, 40],
     ['start'],
     ['mark', 0],
     ['mark', 100],
     ['end'],
     ['start'],
     ['end']]),
   [0, 30, 100, [30], [0, 100]]),
  ('control: allocation beyond the region',
   (100, [['alloc', 0, 90], ['alloc', 0, 25], ['start'], ['end']]),
   [0, None, [0]])]]
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: objects above TAMS are implicitly live[0, 30, 100, 51, 200, [30, 100]][0, 30, 100, 51, 200, [30, 100]]Passed
first object allocated after marking started[0, 30, 100, 140, [0, 30, 100]][0, 30, 100, 140, [0, 30, 100]]Passed
region untouched when marking started[0, 30, 100, 300, 320, [0, 30, 100]][0, 30, 100, 300, 320, [0, 30, 100]]Passed
second cycle uses fresh TAMS and marks[0, 30, 100, 51, [30, 100], [0, 51]][0, 30, 100, 51, [30, 100], [0, 51]]Passed
marks from the previous cycle are discarded[0, 30, 100, [30], [0, 100]][0, 30, 100, [30], [0, 100]]Passed
control: allocation beyond the region[0, None, [0]][0, None, [0]]Passed

SHA-256 / 08733f1667198471e1e446d147e2172eea74560fe0cd79ca20982aef24699465

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 2026-09-29T14:51:29.780705+00:00.

Case digest / 377abb54fa40466833bb6734cab392d5cc8a2f2e1bf255b3ad4c64cdedd4ff48