Bibliographic record
Abstract
We propose and experimentally demonstrate the quasi-superposition quantum-inspired system (QSQS)-a conceptual quantum system for randomness generation built on measuring two conjugate observables of a permutation sorting process: the deterministic permutation count n_{p} and the fundamentally nondeterministic sorting time t. By analogy with quantum systems, these observables are linked by an uncertainty-like constraint: algorithmic determinism ensures structural uniformity, while system-level fluctuations introduce irreducible unpredictability. We realize this framework concretely as a quantum permutation pad (QPP) random number generator (RNG) or QPP-RNG, a system-embedded, software-based true random number generator (TRNG). In QPP-RNG, real-time measurements of sorting time t-shaped by CPU pipeline jitter, cache latency, and OS scheduling-dynamically reseed the pseudorandom RNG, driving the permutation sequence. This design fuses deterministic and nondeterministic components, so that entropy emerges organically from the quasisuperposition structure of the system. Crucially, the QSQS transforms initially right-skewed raw distributions of n_{p} and t into nearly uniform outputs after modulo reduction. This effect arises from the system's internal degeneracies: many distinct internal states collapse into the same output symbol, effectively flattening biases and filling out the output space. This transformation from biased measurements to uniform randomness is the core principle of the QSQS. Empirical results show that as the repetition factor m increases, output entropy converges toward theoretical maxima: Shannon and NIST SP 800-90B min-entropy values approach 8 bits, chi-squared statistics stabilize near ideal uniformity, and bell curve plots visually confirm the flattening from skewed to uniform distributions. The convergence to uniformity occurs at a rate inversely proportional to the size of the permutation space, making the system both scalable and theoretically grounded. Beyond practical implications, our findings illustrate how the QSQS unifies deterministic algorithmic processes with nondeterministic physical fluctuations in a single framework, offering a physics-based perspective for engineering randomness. In the quantum-safe era, the QPP-RNG can close the entropy gap by embedding true randomness directly into cryptographic modules, reducing reliance on external entropy sources and enabling entropy-rich, self-contained postquantum cryptographic ecosystems.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".