The scientific question
The experiment asks how well different optimization methods recover a chosen normalized minimum partition. Exhaustive enumeration supplies the reference optimum on the included small instances. The benchmark concerns this exact objective and data generator; it does not establish general AGI or consciousness.
Recovered reproducibility package
The archive includes code, deterministic instance data, protocol, environment record, per-instance results, a CSV table, analysis and a four-page report. The source report and all its formulas have been retained. No quantum hardware run is represented; QAOA is classically simulated.
Method boundaries
Queyranne’s exactness guarantee depends on symmetry and submodularity of the objective. Normalization can change those properties. The source distinguishes the normalized benchmark from an unnormalized diagnostic. Runtime figures need their actual hardware, evaluation budget, objective-table setup and optimizer costs to be interpreted.
Equations in this build
14 linked mathematical records. Each opens its notation, interpretation and source.
Linear Gaussian network and stationary covariance
The next state is a linear transformation of the current state plus independent zero-mean Gaussian noise with identity covariance. At stationarity, the covariance solves the…
Normalized minimum stochastic-interaction partition
For each nontrivial split, the numerator compares the two within-part conditional entropies with the whole-system conditional entropy. K is the smaller marginal entropy, J is…
Gaussian stochastic interaction and marginal differential entropy
Conditional Gaussian entropy is determined by a conditional covariance log determinant. With full-system innovation covariance equal to identity, its log determinant vanishes and…
Simulated QAOA partition-search state
The circuit starts in an equal superposition over m=n−1 partition bits, then alternates a diagonal phase depending on the cost and a mixing rotation generated by Pauli X…
One-step cross-covariance of the linear network
Multiplying W by the stationary covariance gives Cov(Xₜ₊₁,Xₜ). This cross-covariance enters the conditional Gaussian prediction formula. The identity follows because the…
Within-subset prediction residual covariance
The expression subtracts the variance explained by the subset’s own previous state from its next-state marginal covariance. It is a Schur complement and is the conditional…
Annealing temperature initialized from pilot-score spread
The initial temperature is the larger of the standard deviation of 32 random pilot objective values and 0.001. This scales early acceptance of uphill moves to the local…
Remove complement symmetry with one pinned node
A partition and its complement represent the same bipartition. Pinning one of n nodes to the first side leaves m=n−1 freely encoded binary choices. One of the 2ᵐ assignments puts…
p relation
This statement fixes a parameter value for the documented model version. Its effect depends on the equation or update rule that consumes that parameter; it is retained separately…
p relation
This statement fixes a parameter value for the documented model version. Its effect depends on the equation or update rule that consumes that parameter; it is retained separately…
Reported normalized optimum for the representative instance
The saved representative instance has normalized minimum objective approximately 0.2578092851. This number is the ratio J=Φ_SI/K at the minimizing partition. It is dimensionless…
Reported raw information loss at the representative normalized optimum
The unnormalized stochastic-interaction numerator at the selected partition is approximately 2.1867917397 nats. It is saved separately from the dimensionless objective used to…
K relation
This statement fixes a parameter value for the documented model version. Its effect depends on the equation or update rule that consumes that parameter; it is retained separately…
J relation
This statement fixes a parameter value for the documented model version. Its effect depends on the equation or update rule that consumes that parameter; it is retained separately…