SPECIMEN REPORT · 001 · DEPENDENCE / PROBABILITY / EVIDENCE
PROOF OF EXIT
When a maze shows two doors, do they really represent two independent chances? A 4×4 maze, one real completed Atlas graph-v1 job, one exhaustive classical proof — and an honest mismatch between what was requested and what the engine returned.REQUESTED vs OBSERVED
16 QUBITS
17 EDGES
4096 SHOTS
EMU / AER
65 536 WORLDS CHECKED
JOB a03509aa…4514f
QGE-16 · WORLD VIEWERLIVE
BRIDGE EDGES (3,7) · (10,14)PATH 0→15
01 · INDEPENDENT-DOOR INTUITION
0%
Two doors, each open half the time, assumed independent.
02 · BALANCED TARGET PREDICTION
0%
Ideal dependent model — bridge doors move together.
03 · OBSERVED ATLAS EMULATION
0%
4,096/4,096 shots → all-zero world → certified path.
01
Why intuition fails
ASSUMPTION ≠ VISUAL FACT▚ THE COMFORTABLE ANSWER
For two independent doors that each open with probability ½, the chance that at least one opens is ¾. Familiar, tidy — and completely reliant on an assumption the picture does not prove.
1 − (½)² = 75%VALID ONLY IF THE DOORS ARE INDEPENDENT
▚ WHAT THE MAZE ACTUALLY ENCODES
Under this maze's ideal corridor constraints, the two bridge doors must agree — they open and close together. Exhaustive classical proof checked all 65,536 sixteen-bit worlds: four satisfy the ideal constraints, and none has exactly one open bridge.
P(escape) = 50% · but only with a balanced bridge correlationTHE EQUALITY THEOREM ALONE DOES NOT PROVE THAT PROBABILITY
▚ THREE NUMBERS, THREE DIFFERENT STORIES
▚ THE PROBABILITY DIAGNOSTIC
| INDEPENDENT INTUITION | BALANCED TARGET | OBSERVED EMULATION | |
|---|---|---|---|
| ESCAPE PROBABILITY | 75% | 50% | 100.0% |
| UNDERLYING MODEL | naive assumption | ideal dependent | real Aer emulation |
| BRIDGE LOGIC | independent variables | correlated · ZZ=0 target | perfect agreement · ZZ=1 actual |
| RESULTING WORLD | theoretical | 4 valid 16-bit states | 0000000000000000 only |
02
The real Atlas job
NOT A MOCK RESULT▚ WHAT CAME BACK
The completed job returned 0000000000000000 in all 4,096 shots. That world has a certified path to the exit, so the observed escape fraction is 100%. Tomography reports ZZ = 1 on both bridge edges — the requested zero bridge correlations were not reached. The reason for the mismatch is unresolved; the request, status and raw result are preserved below, unedited.
The conditional finite theorem still holds: when all non-bridge equality constraints hold, the bridge doors agree. The all-zero world satisfies them. Endianness can't change this run's certificate — every returned bit is zero.
03
The mismatch is the result
REQUESTED ≠ OBSERVEDZZ = 0REQUESTED · BRIDGE EDGES (3,7) & (10,14)
TOMOGRAPHY
ZZ = 1OBSERVED · PERFECT AGREEMENT · TARGET NOT REALISED
The intended 50% balanced-bridge target was not realised — and the page says so in the open. Quantum outputs must be validated, not interpreted from intent alone.
04
Sampled world certificate
CLASSICAL REACHABILITYEXIT · p = 1.000
S---o---o---o
| | |
o o---o o
| | |
o---o o---o
| | |
o---o---o E
CERTIFIED PATH 0-1-2-3-7-11-15
▚ WHY A CERTIFICATE?
Every sampled world receives a deterministic path or sealed-region certificate — classical reachability over the returned bits. The engine proposes; classical logic disposes. Readers can tell apart three different things: the intended model, the actual engine output, and the classical explanation of what it means.
samples: 4096/4096 → one world → one certificateEDGE AGREEMENT SCORE 1.00
05
What is quantum here?
HONEST LIMITATIONSThe completed Atlas graph-v1 job used mode emu, backend aer — quantum-circuit emulation on a classical simulator, no physical QPU. The returned distribution is real Atlas job evidence; the finite proof and path certificates are classical. This demo does not claim quantum advantage or experimental confirmation of the balanced 50% target.
What survives the honesty cut: a graph engine asked to prepare a 16-qubit state whose measured edges match requested Pauli expectations, a real job lifecycle with saved request / status / raw JSON, and a lesson in dependence — the same reason quantum correlation is not just "two independent chances" either. That is the real teaching core: probability you can see.
06
Reproducibility evidence
CREDENTIAL-FREE · RAWCREDENTIAL-FREE REQUEST
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}COMPLETED JOB STATUS
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"updated_at": "2026-10-01T15:44:02Z"
}FULL RAW ATLAS RESULT
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