FA-45636 / Data systems / Open access
Session grouping splits events separated by exactly the allowed gap · case 01
Session grouping splits events separated by exactly the allowed gap.
ROOT CAUSE
session-bridge-grouping: Session grouping splits events separated by exactly the allowed gap.
THE FAILURE
session-bridge-grouping: Session grouping splits events separated by exactly the allowed gap.
Unsuccessful approach: Reducing the allowed gap preserves the exact-boundary split.
Case contract
Group [key,time,id] events into sessions independently by key. Sort each key by (time,id); consecutive gaps <=gap belong to one transitive session. Emit [key,first-time,last-time,ordered-ids] ordered by key and session time. An intervening bridge may join otherwise distant endpoints.
Why this case matters
A bounded deterministic data engine model makes representation and changelog faults reproducible.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(d):
try:
events,gap=d
out=[]
for key in sorted(set(k for k,t,i in events)):
rows=sorted((t,i) for k,t,i in events if k==key)
start=last=None; ids=[]
for time,ident in rows:
if ids and time-last>=gap:
out.append([key,start,last,ids]); ids=[]
if not ids: start=time
ids.append(ident); last=time
if ids: out.append([key,start,last,ids])
return out
except (IndexError, KeyError, ValueError, StopIteration) as exc:
return {"representation_error": type(exc).__name__}
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
if N == 1:
check('bridge chain', solve([[['a', 1, 10], ['a', 3, 11], ['a', 5, 12]], 2]), [['a', 1, 5, [10, 11, 12]]])
check('arrival order', solve([[['a', 3, 10], ['a', 1, 11]], 2]), [['a', 1, 3, [11, 10]]])
check('key separation', solve([[['a', 1, 10], ['b', 1, 11]], 2]), [['a', 1, 1, [10]], ['b', 1, 1, [11]]])
check('separate sessions', solve([[['a', 1, 10], ['a', 6, 11]], 2]), [['a', 1, 1, [10]], ['a', 6, 6, [11]]])
check('equal timestamp', solve([[['a', 1, 11], ['a', 1, 10]], 0]), [['a', 1, 1, [10, 11]]])
check('single event', solve([[['a', 1, 10]], 2]), [['a', 1, 1, [10]]])
check('empty stream', solve([[], 2]), [])
elif N == 2:
check('bridge chain', solve([[['a', 2, 10], ['a', 4, 11], ['a', 6, 12]], 2]), [['a', 2, 6, [10, 11, 12]]])
check('arrival order', solve([[['a', 4, 10], ['a', 2, 11]], 2]), [['a', 2, 4, [11, 10]]])
check('key separation', solve([[['a', 2, 10], ['b', 2, 11]], 2]), [['a', 2, 2, [10]], ['b', 2, 2, [11]]])
check('separate sessions', solve([[['a', 2, 10], ['a', 7, 11]], 2]), [['a', 2, 2, [10]], ['a', 7, 7, [11]]])
check('equal timestamp', solve([[['a', 2, 11], ['a', 2, 10]], 0]), [['a', 2, 2, [10, 11]]])
check('single event', solve([[['a', 2, 10]], 2]), [['a', 2, 2, [10]]])
check('empty stream', solve([[], 2]), [])
elif N == 3:
check('bridge chain', solve([[['a', 3, 10], ['a', 5, 11], ['a', 7, 12]], 2]), [['a', 3, 7, [10, 11, 12]]])
check('arrival order', solve([[['a', 5, 10], ['a', 3, 11]], 2]), [['a', 3, 5, [11, 10]]])
check('key separation', solve([[['a', 3, 10], ['b', 3, 11]], 2]), [['a', 3, 3, [10]], ['b', 3, 3, [11]]])
check('separate sessions', solve([[['a', 3, 10], ['a', 8, 11]], 2]), [['a', 3, 3, [10]], ['a', 8, 8, [11]]])
check('equal timestamp', solve([[['a', 3, 11], ['a', 3, 10]], 0]), [['a', 3, 3, [10, 11]]])
check('single event', solve([[['a', 3, 10]], 2]), [['a', 3, 3, [10]]])
check('empty stream', solve([[], 2]), [])
elif N == 4:
check('bridge chain', solve([[['a', 4, 10], ['a', 6, 11], ['a', 8, 12]], 2]), [['a', 4, 8, [10, 11, 12]]])
check('arrival order', solve([[['a', 6, 10], ['a', 4, 11]], 2]), [['a', 4, 6, [11, 10]]])
check('key separation', solve([[['a', 4, 10], ['b', 4, 11]], 2]), [['a', 4, 4, [10]], ['b', 4, 4, [11]]])
check('separate sessions', solve([[['a', 4, 10], ['a', 9, 11]], 2]), [['a', 4, 4, [10]], ['a', 9, 9, [11]]])
check('equal timestamp', solve([[['a', 4, 11], ['a', 4, 10]], 0]), [['a', 4, 4, [10, 11]]])
check('single event', solve([[['a', 4, 10]], 2]), [['a', 4, 4, [10]]])
check('empty stream', solve([[], 2]), [])
elif N == 5:
check('bridge chain', solve([[['a', 5, 10], ['a', 7, 11], ['a', 9, 12]], 2]), [['a', 5, 9, [10, 11, 12]]])
check('arrival order', solve([[['a', 7, 10], ['a', 5, 11]], 2]), [['a', 5, 7, [11, 10]]])
check('key separation', solve([[['a', 5, 10], ['b', 5, 11]], 2]), [['a', 5, 5, [10]], ['b', 5, 5, [11]]])
check('separate sessions', solve([[['a', 5, 10], ['a', 10, 11]], 2]), [['a', 5, 5, [10]], ['a', 10, 10, [11]]])
check('equal timestamp', solve([[['a', 5, 11], ['a', 5, 10]], 0]), [['a', 5, 5, [10, 11]]])
check('single event', solve([[['a', 5, 10]], 2]), [['a', 5, 5, [10]]])
check('empty stream', solve([[], 2]), [])
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 |
|---|---|---|---|
| bridge chain | [['a', 1, 1, [10]], ['a', 3, 3, [11]], ['a', 5, 5, [12]]] | [['a', 1, 5, [10, 11, 12]]] | Failed |
| arrival order | [['a', 1, 1, [11]], ['a', 3, 3, [10]]] | [['a', 1, 3, [11, 10]]] | Failed |
| key separation | [['a', 1, 1, [10]], ['b', 1, 1, [11]]] | [['a', 1, 1, [10]], ['b', 1, 1, [11]]] | Passed |
| separate sessions | [['a', 1, 1, [10]], ['a', 6, 6, [11]]] | [['a', 1, 1, [10]], ['a', 6, 6, [11]]] | Passed |
| equal timestamp | [['a', 1, 1, [10]], ['a', 1, 1, [11]]] | [['a', 1, 1, [10, 11]]] | Failed |
| single event | [['a', 1, 1, [10]]] | [['a', 1, 1, [10]]] | Passed |
| empty stream | [] | [] | Passed |
SHA-256 / 577585dd02c3c797b4e488c2cde259d362fdad81a5533062082500111909abf5
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(d):
try:
events,gap=d
out=[]
for key in sorted(set(k for k,t,i in events)):
rows=sorted((t,i) for k,t,i in events if k==key)
start=last=None; ids=[]
for time,ident in rows:
if ids and time-last>gap-1:
out.append([key,start,last,ids]); ids=[]
if not ids: start=time
ids.append(ident); last=time
if ids: out.append([key,start,last,ids])
return out
except (IndexError, KeyError, ValueError, StopIteration) as exc:
return {"representation_error": type(exc).__name__}
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
if N == 1:
check('bridge chain', solve([[['a', 1, 10], ['a', 3, 11], ['a', 5, 12]], 2]), [['a', 1, 5, [10, 11, 12]]])
check('arrival order', solve([[['a', 3, 10], ['a', 1, 11]], 2]), [['a', 1, 3, [11, 10]]])
check('key separation', solve([[['a', 1, 10], ['b', 1, 11]], 2]), [['a', 1, 1, [10]], ['b', 1, 1, [11]]])
check('separate sessions', solve([[['a', 1, 10], ['a', 6, 11]], 2]), [['a', 1, 1, [10]], ['a', 6, 6, [11]]])
check('equal timestamp', solve([[['a', 1, 11], ['a', 1, 10]], 0]), [['a', 1, 1, [10, 11]]])
check('single event', solve([[['a', 1, 10]], 2]), [['a', 1, 1, [10]]])
check('empty stream', solve([[], 2]), [])
elif N == 2:
check('bridge chain', solve([[['a', 2, 10], ['a', 4, 11], ['a', 6, 12]], 2]), [['a', 2, 6, [10, 11, 12]]])
check('arrival order', solve([[['a', 4, 10], ['a', 2, 11]], 2]), [['a', 2, 4, [11, 10]]])
check('key separation', solve([[['a', 2, 10], ['b', 2, 11]], 2]), [['a', 2, 2, [10]], ['b', 2, 2, [11]]])
check('separate sessions', solve([[['a', 2, 10], ['a', 7, 11]], 2]), [['a', 2, 2, [10]], ['a', 7, 7, [11]]])
check('equal timestamp', solve([[['a', 2, 11], ['a', 2, 10]], 0]), [['a', 2, 2, [10, 11]]])
check('single event', solve([[['a', 2, 10]], 2]), [['a', 2, 2, [10]]])
check('empty stream', solve([[], 2]), [])
elif N == 3:
check('bridge chain', solve([[['a', 3, 10], ['a', 5, 11], ['a', 7, 12]], 2]), [['a', 3, 7, [10, 11, 12]]])
check('arrival order', solve([[['a', 5, 10], ['a', 3, 11]], 2]), [['a', 3, 5, [11, 10]]])
check('key separation', solve([[['a', 3, 10], ['b', 3, 11]], 2]), [['a', 3, 3, [10]], ['b', 3, 3, [11]]])
check('separate sessions', solve([[['a', 3, 10], ['a', 8, 11]], 2]), [['a', 3, 3, [10]], ['a', 8, 8, [11]]])
check('equal timestamp', solve([[['a', 3, 11], ['a', 3, 10]], 0]), [['a', 3, 3, [10, 11]]])
check('single event', solve([[['a', 3, 10]], 2]), [['a', 3, 3, [10]]])
check('empty stream', solve([[], 2]), [])
elif N == 4:
check('bridge chain', solve([[['a', 4, 10], ['a', 6, 11], ['a', 8, 12]], 2]), [['a', 4, 8, [10, 11, 12]]])
check('arrival order', solve([[['a', 6, 10], ['a', 4, 11]], 2]), [['a', 4, 6, [11, 10]]])
check('key separation', solve([[['a', 4, 10], ['b', 4, 11]], 2]), [['a', 4, 4, [10]], ['b', 4, 4, [11]]])
check('separate sessions', solve([[['a', 4, 10], ['a', 9, 11]], 2]), [['a', 4, 4, [10]], ['a', 9, 9, [11]]])
check('equal timestamp', solve([[['a', 4, 11], ['a', 4, 10]], 0]), [['a', 4, 4, [10, 11]]])
check('single event', solve([[['a', 4, 10]], 2]), [['a', 4, 4, [10]]])
check('empty stream', solve([[], 2]), [])
elif N == 5:
check('bridge chain', solve([[['a', 5, 10], ['a', 7, 11], ['a', 9, 12]], 2]), [['a', 5, 9, [10, 11, 12]]])
check('arrival order', solve([[['a', 7, 10], ['a', 5, 11]], 2]), [['a', 5, 7, [11, 10]]])
check('key separation', solve([[['a', 5, 10], ['b', 5, 11]], 2]), [['a', 5, 5, [10]], ['b', 5, 5, [11]]])
check('separate sessions', solve([[['a', 5, 10], ['a', 10, 11]], 2]), [['a', 5, 5, [10]], ['a', 10, 10, [11]]])
check('equal timestamp', solve([[['a', 5, 11], ['a', 5, 10]], 0]), [['a', 5, 5, [10, 11]]])
check('single event', solve([[['a', 5, 10]], 2]), [['a', 5, 5, [10]]])
check('empty stream', solve([[], 2]), [])
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 |
|---|---|---|---|
| bridge chain | [['a', 1, 1, [10]], ['a', 3, 3, [11]], ['a', 5, 5, [12]]] | [['a', 1, 5, [10, 11, 12]]] | Failed |
| arrival order | [['a', 1, 1, [11]], ['a', 3, 3, [10]]] | [['a', 1, 3, [11, 10]]] | Failed |
| key separation | [['a', 1, 1, [10]], ['b', 1, 1, [11]]] | [['a', 1, 1, [10]], ['b', 1, 1, [11]]] | Passed |
| separate sessions | [['a', 1, 1, [10]], ['a', 6, 6, [11]]] | [['a', 1, 1, [10]], ['a', 6, 6, [11]]] | Passed |
| equal timestamp | [['a', 1, 1, [10]], ['a', 1, 1, [11]]] | [['a', 1, 1, [10, 11]]] | Failed |
| single event | [['a', 1, 1, [10]]] | [['a', 1, 1, [10]]] | Passed |
| empty stream | [] | [] | Passed |
SHA-256 / ec52c566e04b11f4bd226be3009f37115fb1fa113b98cb5ececc878d82f91286
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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Sign in to the archive ↗Verification & scope
Offline stipulated semantics over valid small inputs; no performance, concurrency, or production-engine conformance claim. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.
Observations recorded using Python 3.12.14 at 2026-09-29T14:44:24.438853+00:00.
Case digest / 7fbf7ed502cf5683053002d495dc496f4bf4e1df3f758d4e972ab0f6f3a75c33