QDL Research Suite v1.10.0

Abstract

Overview QDL Research Suite is an integrated scientific software package developed under the Quantum Diverter Loop (QDL) research program. The software brings mathematical, statistical, and computational methods from multiple research papers into one organized and reproducible framework. Its main purpose is to make scientific calculations easier to perform, repeat, compare, test, and independently verify. Version 1.10.0 includes computational modules for Papers 1–9, 11, 13, and 17–19, covering 14 research papers. Included Research Papers and Calculations Paper 1 — Exact Permutation Moments What it studies: Exact statistical properties of Walsh interaction-order energies under permutations of observed data. Calculations: Exact permutation means, variances, covariances, cross-order dependence, and finite-sample statistical comparisons, using Walsh transforms and structured computation. Use: Helps evaluate interaction patterns and their statistical significance without relying only on Monte Carlo approximations. Paper 2 — Exact Distribution and Counting What it studies: Exact probability distributions and structured combinatorial counting. Calculations: Exact outcome counts, structured distribution reductions, lower-order counting methods, and finite-case verification. Use: Helps solve probability and counting problems where approximate methods may not provide sufficient precision. Paper 3 — Exact Tail Probability What it studies: Exact probabilities of rare or extreme statistical outcomes. Calculations: Exact tail counts, structured combinatorial reductions, symmetry-based enumeration, and certified finite-case probabilities. Use: Helps determine how unusual an observed result is using mathematically verified probability calculations. Paper 4 — Model Identification and Testing What it studies: Mathematical model identification, statistical testing, and the limits of inference from available observations. Calculations: Model-specific statistical quantities, identifiability checks, numerical validation, and reproducibility tests. Use: Helps determine whether an observed dataset supports a proposed model and whether important ambiguities remain. Paper 5 — Johnson-Harmonic Pattern Analysis What it studies: Structured interaction patterns using Johnson-scheme, harmonic, and symmetry-based mathematical methods. Calculations: Harmonic decomposition, interaction-layer analysis, symmetry-based transformations, and selected quantum-system applications. Use: Helps identify and compare organized interaction structures in complex, high-dimensional systems. Paper 6 — Four-Sector Affinity and Cumulant Response What it studies: How statistical relationships change under exponential tilting and higher-order response. Calculations: Four-sector affinity, partition functions, cumulant expansions, response derivatives, and related statistical identities. Use: Helps separate changes associated with means, variances, and higher-order statistical effects. Paper 7 — Multimode Affinity Geometry What it studies: Mathematical descriptions of interactions involving multiple states, variables, and structured modes. Calculations: Multimode affinity matrices, forward and reverse transformations, hidden-variable reductions, mode composition, and selected higher-dimensional examples. Use: Helps analyze complex interactions without reducing all their information to a single scalar measurement. Paper 8 — Fresh-Later Complete-Nonselection Testing What it studies: A framework for testing whether an earlier completed outcome is statistically associated with a genuinely later measurement choice. Calculations: Four-sector statistics, forward and reverse relations, selection-effect bounds, nonselection controls, and experimental eligibility checks. Use: Helps design and evaluate scientifically controlled tests while distinguishing genuine statistical evidence from selection, filtering, and experimental artifacts. Scientific scope: This is a testing and falsification framework. It does not establish backwards-time influence or a new physical mechanism. Paper 9 — General-d Affinity Reversal and Contrast-Space Invariants What it studies: Affinity relationships and mathematical reversals in binary and multi-state systems. Calculations: Forward and inverse affinity transformations, symmetric general-d extensions, contrast-space matrices, singular values, rank, matrix norms, and geometric invariants. Use: Helps compare interaction descriptions across different state spaces and identify mathematical properties preserved by specified transformations. Scientific scope: These are mathematical and statistical results, not evidence of retrocausality. Paper 11 — Reproducible Evidence Framework for Fresh-Later Quantum Tests What it studies: How to evaluate quantum experimental data using clearly defined event identities, measurement chronology, complete event selection, statistical controls, and reproducible source records. Calculations and verification: Four-sector count tables, odds ratios, log-affinity estimates, uncertainty measures, and Fisher's exact tests. Published aggregate analysis of 55,568 events from the Munich event-ready Bell experiment. Event-level analysis of two available Munich experimental runs containing 20,403 valid paired records. Exact reconstruction of the historical 10,000-event selection for each run, reproducing all 16 archived sector counts. Independent calculations using 256 probability entries from the Qu 2026 photonic quantum-switch study. Statistical validation using 80,000 explicitly synthetic trials across four controlled software-test scenarios. Source-integrity, event-selection, robustness, and reproducibility checks. Use: Helps researchers reproduce published quantum-data calculations, check selection rules, compare statistical evidence, identify experimental artifacts, and distinguish mathematical associations from physical interpretations. Scientific scope: The published 55,568-event Munich aggregate is analyzed from reported counts; only the two available original runs are independently replayed at event level. The synthetic trials are software tests, not experimental observations. Paper 11 does not claim backwards-time signalling or a newly established physical QDL effect. Paper 13 — Cross-Device and Cross-Temperature Gibbs-State Noise Analysis What it studies: Noise and errors in quantum Gibbs-state preparation across different devices and temperatures. Calculations: Two-qubit Hamiltonian models, 15-Pauli tomography, Hilbert-Schmidt distance, purity, Pauli-channel baselines, generalized amplitude damping, cross-device comparisons, and cross-temperature validation. Use: Helps compare quantum noise models, quantify deviations from target states, and test whether a model developed under one condition remains useful under other conditions. Scientific scope: The results are specific to the studied models and datasets. They do not establish universal hardware-noise parameters. Paper 17 — Four-Variable Binary Affinity What it studies: Interactions among four binary variables through a complete mathematical representation. Calculations: Sixteen-state probability representations, 15 Walsh/log-linear coordinates, interaction reconstruction, conditional forward and inverse laws, and one-event updates. Use: Helps separate individual-variable, pairwise, three-variable, and four-variable interaction effects. Paper 18 — Binary Affinity Framework What it studies: Exact mathematical relationships between binary affinity, probability balance, and forward/reverse transformations. Calculations: Hyperbolic tangent transformations, inverse affinity, four-sector cross-ratios, probability balance, normalization, and symmetric multi-state extensions. Use: Provides a direct mathematical method for measuring and transforming binary affinity relationships. Scientific scope: The term Universal Mathematical Law refers to the defined mathematical family, not a universal physical law. Paper 19 — Affinity Geometry, Transfer Laws, and π Invariants What it studies: Mathematical relationships between affinity transformations, limiting geometry, and information-geometric quantities. Calculations: Exact Q_n sequences, recurrence relations, Richardson acceleration, affinity-transfer functions, odds-ratio powers, Fisher information, Fisher–Rao distances, π-related geometric identities, and cross-dimensional transformations. Use: Helps analyze how mathematical affinity and geometric quantities behave under defined transformations and across different dimensions. Scientific scope: The results apply within their specified mathematical models and do not establish a universal physical mechanism. Main Software Capabilities QDL Research Suite provides a unified collection of tools for: Exact permutation statistics and probability calculations. Combinatorial counting and rare-event analysis. Model identification and statistical validation. Harmonic decomposition and high-dimensional interaction analysis. Four-sector affinity and higher-order response. Multimode and multi-state mathematical transformations. Controlled quantum-data testing and source verification. Quantum Gibbs-state noise analysis. Binary affinity, contrast-space geometry, and transfer laws. Reproducible numerical experiments and verification. Reproducibility and Verification The software includes Python source code, an installable package, command-line calculation tools, automated tests, reference calculations, documentation, and machine-readable verification outputs. Version 1.10.0 has passed 125 automated regression tests. The source installation and built package also reproduce matching results across the 14 included paper modules. Paper 11 additionally includes reproducibility checks using available original experimental records, published probability data