Paper 6- Multimode Affinity Geometry for Finite Categorical Systems presents a mathematical framework for studying relationships between systems that have a finite number of possible outcomes. In many datasets, a relationship is summarized by only one number. However, a single number can hide important structure. This work represents the relationship as a small matrix of interaction modes, so different parts of the relationship can be studied separately. What this paper does The framework can: measure the overall strength and shape of an interaction; separate a complex interaction into different mathematical modes; show when a single-number summary is sufficient and when important information is lost; study how hidden or unobserved factors can change the observed interaction; identify which parts of an interaction remain measurable when some hidden effects are allowed; compare interaction patterns across different datasets using matrix and singular-value based quantities. The paper also gives exact mathematical results for combining interactions in parallel and in series, and provides a detailed treatment of the three-outcome (qutrit) case. Where can it be useful? This framework may be useful in problems involving: categorical and contingency-table data; multi-level statistical systems; qutrit and other finite-dimensional quantum data; hidden-variable or latent-factor analysis; comparison of interaction patterns across different experiments or platforms; deciding whether a complex relationship can safely be reduced to one scalar value. The methods are demonstrated using cross-platform qutrit-style datasets, including photonic, superconducting/transmon, and optical-clock examples. Important interpretation This is primarily a mathematical and statistical framework. An observed affinity matrix does not, by itself, identify the physical cause of an interaction or prove a particular hidden mechanism. The paper therefore separates what can be identified directly from the data from what requires additional physical assumptions. Reproducibility The calculations and reproducibility tools for this work are included in QDL Research Suite v1.6.0: Software DOI: 10.5281/zenodo.23032918 Paper DOI: 10.5281/zenodo.23034646
Paper 6- Multimode Affinity Geometry for Finite Categorical Systems presents a mathematical framework for studying relationships between systems that have a finite number of possible outcomes. In many datasets, a relationship is summarized by only one number. However, a single number can hide important structure. This work represents the relationship as a small matrix of interaction modes, so different parts of the relationship can be studied separately. What this paper does The framework can: measure the overall strength and shape of an interaction; separate a complex interaction into different mathematical modes; show when a single-number summary is sufficient and when important information is lost; study how hidden or unobserved factors can change the observed interaction; identify which parts of an interaction remain measurable when some hidden effects are allowed; compare interaction patterns across different datasets using matrix and singular-value based quantities. The paper also gives exact mathematical results for combining interactions in parallel and in series, and provides a detailed treatment of the three-outcome (qutrit) case. Where can it be useful? This framework may be useful in problems involving: categorical and contingency-table data; multi-level statistical systems; qutrit and other finite-dimensional quantum data; hidden-variable or latent-factor analysis; comparison of interaction patterns across different experiments or platforms; deciding whether a complex relationship can safely be reduced to one scalar value. The methods are demonstrated using cross-platform qutrit-style datasets, including photonic, superconducting/transmon, and optical-clock examples. Important interpretation This is primarily a mathematical and statistical framework. An observed affinity matrix does not, by itself, identify the physical cause of an interaction or prove a particular hidden mechanism. The paper therefore separates what can be identified directly from the data from what requires additional physical assumptions. Reproducibility The calculations and reproducibility tools for this work are included in QDL Research Suite v1.6.0: Software DOI: 10.5281/zenodo.23032918 Paper DOI: 10.5281/zenodo.23034646
Paper 9 - Exact General-d Affinity Reversal and Contrast-Space Invariants introduces a compact mathematical framework for understanding a simple but important question: When an interaction is reversed, what changes, what stays the same, and how can that be measured exactly? The paper extends binary affinity to general d-state systems, derives an exact reversal law, and introduces the transformed coordinate Ξd, for which reversal becomes especially simple: ΞR=−ΞF. It also identifies reversal-stable quantities and extends the analysis from a single scalar to the full interaction matrix Θ=HTln(Z)H, allowing richer multi-state structure to be studied through singular values, rank, interaction strength, determinant magnitude, and effective participation. Exact_General_d_Affinity_Revers… Exact_General_d_Affinity_Revers… Why it is useful: the framework can help researchers compare forward and reversed interaction descriptions, study systems with more than two states, test whether a single summary is sufficient, and identify stable geometric features in complex interaction data. The paper includes qutrit, qubit, and many-body validation examples to demonstrate how the method can be used in practice. Exact_General_d_Affinity_Revers… Connected QDL Research This work is part of the broader Quantum Diverter Loop (QDL) research program. Earlier QDL papers develop complementary tools for exact permutation analysis, exact counting and tail probabilities, model identifiability, higher-order interactions, cumulant response, multimode affinity geometry, causal testing, and binary affinity analysis. The methods from Papers 1–9, together with compatibility support for Papers 17–19, are organized in the reproducible QDL Research Suite v1.8.0, making the calculations easier to repeat, test, compare, and independently verify. QDL Research Suite v1.8.0:DOI: 10.5281/zenodo.23161137 All QDL Research Suite versions:DOI: 10.5281/zenodo.22952901 In simple terms, this paper adds a new multi-state reversal layer to a growing QDL toolkit for exact mathematics, reproducible computation, interaction analysis, and independent verification.
Overview This work presents a simple and unified mathematical framework for binary affinity. For a binary variable with states (+1) and (-1), the observable response (X) and the affinity coordinate (\theta) are linked exactly by [X=\tanh(\theta),\qquad\theta=\operatorname{atanh}(X).] Within this defined binary exponential-affinity family, these forward and reverse relations are called the Universal Mathematical Law and the Reverse Universal Affinity Law. Main Results The paper also derives an exact balanced-count probability law for binary trials and a related normalized quantity whose large-sample limit approaches (\pi). The (\pi) limit comes from standard central-binomial asymptotics and is not claimed as a new physical derivation of (\pi). Physical Checks The same tanh structure is compared with: thermal spin polarization, the one-dimensional Ising model, a probabilistic Ising-machine system, and a 2026 photonic quantum-switch dataset. The quantum-switch reanalysis reconstructs a Bell-like causal witness of 1.808954375, while six spacelike-marginal affinity diagnostics remain statistically consistent with zero. This shows an important point: a strong correlation or causal witness should not automatically be interpreted as a generic affinity or new causal effect. In Simple Terms Paper 18 provides a clear forward-and-reverse mathematical language for binary relationships. It shows how to convert between an underlying affinity (\theta) and an observed normalized response (X), compares the same structure across several physical systems, and clearly separates exact mathematics from broader physical claims.
Paper-5 develops a reproducible symmetry-resolved method for analyzing the internal structure of fixed-order many-body quantum correlator fields using Johnson-harmonic decomposition. Instead of compressing a large collection of labelled correlators into a single overall number, the method keeps the subset structure of the data and separates the centered correlator field into different harmonic layers. This makes it possible to see how correlations are organized inside a quantum system, not only how large the total correlation is. J742_Paper5_Main_Manuscript_DOI… This work is part of the broader QDL five-paper progression: Paper-1 — Exact Permutation Moments: develops exact finite-sample mean, variance, and covariance formulas for Walsh interaction-order energies under permutation. Paper-2 — Exact Distribution Laws: extends the framework to structured exact distributions, Krawtchouk-based reductions, computational-complexity boundaries, and continuation-horizon classification. Paper-3 — Exact Certified Tail Computation: develops certified deterministic counting methods for difficult exact tail probabilities in a structured finite Walsh/Clebsch problem. Paper-4 — Identifiability, Contrast Closure, and Frozen External Testing: studies restricted four-variable log-linear interaction models, rank, identifiability, contrast closure, and a frozen external statistical test. Paper-5 — Johnson-Harmonic Correlator Profiles: applies a symmetry-resolved framework to complete labelled quantum correlator fields and studies how their internal correlation structure is distributed across Johnson-harmonic layers. The central challenge in Paper-5 is that a many-body experiment can produce hundreds or thousands of labelled correlators. If these are reduced to one aggregate norm, important structural information can be lost. Paper-5 preserves the full labelled subset geometry and resolves the correlator field into interpretable harmonic components. What Paper-5 does: reconstructs complete fixed-order labelled correlator fields from public experimental data; removes the common-mode component and decomposes the remaining structure into Johnson-harmonic layers; computes layer energies and normalized structural statistics; uses exact finite-population projector calibration; preserves subset-label information instead of reducing everything to a single total norm; propagates uncertainty using source-native randomized experimental replicates; applies an exact finite-shot bias correction to quadratic layer energies; compares the physical signal with a source-defined noise-reference cohort; provides a reproducible computational route through QDL Research Suite v1.3.0. The mathematical Johnson/slice decomposition itself is established mathematics; the contribution of Paper-5 is the combined experimental-analysis workflow and its application to two independent public quantum datasets. J742_Paper5_Main_Manuscript_DOI… Main locked results: For the six-qubit tomography dataset, each setting contains 20 three-body correlators with harmonic dimensions 20 = 1 + 5 + 9 + 5. Across 28 source measurement settings, the pooled centered correlation structure is: H1 = 48.4133% H2 = 36.7277% H3 = 14.8590% This shows a distributed harmonic profile rather than concentration in a single layer. J742_Paper5_Main_Manuscript_DOI… For the independent 32-qubit hardware dataset, each seed contains 4,960 three-body correlators, decomposed as 4,960 = 1 + 31 + 464 + 4,464. Across nine frozen seeds, the pooled profile is: H1 = 0.341937% H2 = 0.123369% H3 = 99.534694% showing an extremely strong H3-dominant structure. J742_Paper5_Main_Manuscript_DOI… The H3-dominant result remains stable across 675 source-randomized physical twirls. A seed-blocked bootstrap gives a pooled H3 95% interval of approximately: 99.5301% – 99.5388%. J742_Paper5_Main_Manuscript_DOI… After exact finite-shot correction, the pooled H3 fraction changes only from approximately 99.53469% → 99.53486%, showing that ordinary finite-shot sampling bias is extremely small relative to the observed structure. J742_Paper5_Main_Manuscript_DOI… A source-defined noise-renormalization reference cohort gives the opposite profile: Physical corrected H3: 99.534860% Noise-reference corrected H3: 0.138145% providing a strong diagnostic contrast between the physical cohort and the source-defined reference data. J742_Paper5_Main_Manuscript_DOI… How Paper-5 connects to the earlier papers:Paper-1 provides exact permutation-moment tools. Paper-2 studies structured exact distributions. Paper-3 develops certified exact-tail computation. Paper-4 focuses on identifiability and restricted interaction models. Paper-5 moves to a different but related application layer: it uses structured mathematical tools to analyze the internal organization of many-body quantum correlation fields. Why it is useful:The method is useful when a quantum experiment produces many labelled multi-qubit or many-body correlators and researchers want to understand where the structure is located inside that large correlation field. Potential applications include: quantum-state tomography; randomized-measurement analysis; many-body quantum experiments; multi-qubit correlation analysis; quantum-hardware characterization; comparison of correlation structures across devices or experiments; finite-shot robustness checks; structured analysis of subset-indexed data; reproducibility and independent verification of quantum experiments. Rather than asking only: “How much correlation is present?” Paper-5 also asks: “How is that correlation organized across different symmetry layers?” This makes the method useful as a structure scanner for complex quantum correlation data. Reproducibility:The computational implementation for Paper-5 is included in QDL Research Suite v1.3.0, DOI 10.5281/zenodo.22972830. The software provides the Paper-5 computational reproduction route while preserving the original public datasets as the source authority. J742_Paper5_Main_Manuscript_DOI… Paper-5 Preprint DOI:10.5281/zenodo.22974172 J742_Paper5_Main_Manuscript_DOI… Scope:Paper-5 provides a structural and statistical diagnostic workflow. The Johnson decomposition itself is established mathematics. The paper does not claim a new universal Johnson theorem, Bell nonlocality, neutrino thermalization from the H3 statistic, a new physical mechanism, causation, retrocausality, future-state prediction, or a nonzero physical intervention parameter. J742_Paper5_Main_Manuscript_DOI… In simple terms:Paper-5 takes a large set of quantum correlations and breaks it into meaningful symmetry layers. Instead of giving only one total correlation number, it shows where the correlation structure lives inside the data. In the six-qubit experiment, the structure is spread across several layers. In the 32-qubit dataset, almost all of the centered structure appears in the highest Johnson layer, and this pattern remains stable after randomized-twirl analysis and finite-shot correction. In one sentence:Paper-5 is a reproducible structure-analysis framework for complex quantum correlation data that shows not only how much correlation exists, but how that correlation is organized inside the system.
A Reproducible Method for Checking Earlier Events and Later Choices in Quantum Experiments QDL Research Program — Paper 11 | Version V1.0.0 DOI: https://doi.org/10.5281/zenodo.23261100 Overview Quantum experiments can produce surprising results. Sometimes, an event is recorded first, and a measurement choice is made later. If these two events appear connected, an important question arises: Is this connection supported by the experimental data, or could it be explained by statistical variation, event selection, or measurement conditions? This paper presents a clear and reproducible method for investigating that question. It combines real experimental data, exact statistical calculations, source verification, and computer-based testing. The main goal is simple: make quantum-data calculations easier to understand, repeat, and independently check. What Does This Paper Study? The study examines how researchers can correctly compare an earlier recorded event with a later measurement setting. It focuses on five important questions: Were the earlier events and later settings correctly identified? Were all eligible events included using the original experimental rules? Do the observed numbers show a meaningful statistical relationship? Could selection effects, detection differences, or data-matching errors explain the result? Can another researcher reproduce the same calculations using the available sources? The paper provides mathematical formulas, numerical examples, source checks, and reproducible software for these questions. Three Main Research Applications 1. Munich Event-Ready Bell Experiment The first application studies data from a published quantum Bell experiment involving entangled atoms. The published dataset contains 55,568 events. We independently recalculated four-sector statistics from the published count tables. The main results are: Measurement Odds Ratio Fisher p-value Lab 1 0.997122 0.8653 Lab 2 0.980578 0.2486 These results do not provide stable evidence of an association between the selected variables in the full published counts. We also analyzed original event-level records from two experimental runs in April and June 2016. These files contain 20,403 valid paired events. By applying the original selection rule of 5,000 events per Bell-state class, we exactly reproduced the historical results. All 16 published sector counts matched, with zero differences. This demonstrates why correct event selection and source verification are important for reliable scientific calculations. 2. Photonic Quantum-Switch Experiment The second application examines published data from a 2026 photonic quantum-switch experiment. The original study reported a Bell-like causal-inequality value of approximately 1.8090 ± 0.0024, compared with a fixed-order bound of 1.75. We independently recalculated the relevant quantity using 256 published probability entries. Our calculated value was: 1.808954375 This agrees with the reported result at its published precision. We also examined six statistical comparisons involving measurement settings and marginal probabilities. These checks help distinguish an experimental causal-inequality result from a possible statistical relationship between an earlier event and a later setting. The two questions are different and should not be confused. 3. Testing the Method with 80,000 Synthetic Trials The third application uses 80,000 computer-generated trials, divided into four controlled scenarios. The scenarios represent: A system with no inserted effect. A system with a deliberately inserted statistical difference. A system affected by detection-efficiency differences. A system with information leakage before the earlier result was fully recorded. The software reproduced the expected numerical results for all four scenarios. These tests show how the method can identify known statistical patterns and distinguish them from possible experimental artifacts. The synthetic trials are software-validation data, not new laboratory observations. Main Contributions This paper brings together several important elements in one reproducible research workflow. 1. Clear event identification It defines which event happened earlier, which setting was chosen later, and how the records should be matched. 2. Exact statistical calculations It uses four-sector count tables, odds ratios, log-affinity measures, uncertainty estimates, and Fisher's exact tests. 3. Original-data verification It demonstrates how the correct historical event-selection rule can reproduce published results exactly. 4. Independent source comparisons It uses different quantum datasets without incorrectly treating their measurements as equivalent. 5. Reproducible software It provides a computational framework for repeating the calculations, checking results, and recording source limitations. Why Is This Work Useful? Scientific results become more valuable when other researchers can independently verify them. This paper offers a practical way to investigate complex quantum-data questions without depending only on interpretations or assumptions. The method can help researchers: Recheck published quantum experiments. Find problems caused by event selection or data matching. Compare statistical results across experimental runs. Separate real experimental measurements from simulated examples. Design more reliable tests for future quantum experiments. Understand which conclusions are supported by the available evidence. Scientific Scope This work is primarily about statistical verification, experimental-data interpretation, and reproducibility. It does not establish backwards-time signalling or a new fundamental physical law. The Munich published-count analysis and the two recovered original runs have different levels of source access. The quantum-switch experiment measures a different physical quantity. The synthetic trials are used only to test the software. These distinctions are maintained throughout the study. Data and Software Availability The calculations are supported by QDL Research Suite, a Python-based scientific software package containing tools for reproducible mathematical and statistical analysis. QDL Research Suite — All Versions: https://doi.org/10.5281/zenodo.22952901 QDL Research Suite v1.10.0 — Version Used: https://doi.org/10.5281/zenodo.23256494 The software provides calculation modules, reproducibility tools, automated tests, and verification outputs. The study also identifies the original experimental publications and available source datasets so that the calculations can be checked against their sources. Conclusion The central contribution of Paper 11 is a clear, source-linked method for checking quantum experimental data. It combines published experimental results, original event records, exact statistical methods, and controlled software tests. The work shows how careful data selection, transparent calculations, and independent verification can improve confidence in scientific analysis. Its purpose is to help make complex quantum research more understandable, reproducible, and reliable, while keeping mathematical results, experimental evidence, and physical interpretations clearly separated. Author: Roshankumar Chandaliya Research Program: Quantum Diverter Loop (QDL) Paper: 11 Version: V1.0.0 DOI: https://doi.org/10.5281/zenodo.23261100
This article introduces a quantum-inspired framework for modeling LLM conversational behavior using qutrit SU(3) embeddings, leveraging the mathematical structure of three-level quantum systems as an interpretable space for conversational stance dynamics. The framework defines Sincerity, Irony, and Ambiguity as orthogonal qutrit basis states and models conversational transitions through SU(3) unitary operators derived from the Gell–Mann matrices. qutrit_embeddings The paper details methods for projecting high-dimensional LLM embeddings into a three-dimensional complex Hilbert space via dimensionality reduction, state normalization, and latent clustering. The resulting qutrit state |ψ⟩ encodes the stance composition of each conversational turn, with |α|², |β|², and |γ|² representing the likelihood of each stance. The article further outlines hybrid validation methodologies using both synthetic data and real LLM conversational outputs, including fidelity measurement, purity analysis, ternary probability plots, and process-tomography-inspired state tracking. qutrit_embeddings Applications include style modulation via operator-based stance biasing, improved interpretability through qutrit state visualization, and multi-agent interaction modeling through quantum-inspired correlation analysis reminiscent of entanglement effects. The paper concludes with a critical discussion of limitations—including oversimplification risks and mapping challenges—and proposes pathways toward higher-dimensional qudit models and advanced visualization frameworks. qutrit_embeddings Overall, this work establishes a rigorous, cross-disciplinary foundation for applying SU(3) operator theory, quantum cognition concepts, and high-dimensional geometry to next-generation AI behavior modeling.
Manipulation et caractérisation de la lumière quantique multimode dans les systèmes photoniques Cette thèse fait progresser l'optique quantique multimode à travers deux contributions théoriques et pratiques majeures.Premièrement, nous introduisons les cavités temporelles comme une nouvelle approche pour le filtrage des modes temporels, en exploitant les principes de dualité espace-temps pour transposer les principes des cavités de nettoyage de modes spatiaux au domaine temporel. Contrairement aux approches existantes, cette opération de filtrage ne repose pas sur des interactions non linéaires ou sur l'accord de phase, préserve la fréquence porteuse et maintient intacte la structure des modes temporels. Nous démontrons la faisabilité d'une implémentation pratique utilisant des lentilles temporelles électro-optiques et des réseaux de diffraction, avec des stratégies complètes d'optimisation des paramètres pour les applications classiques et quantiques.Deuxièmement, nous abordons les limitations fondamentales de la détection d'états quantiques à travers les interféromètres à effet mémoire (IME). Nous établissons de nouveaux critères pour prédire la compression cachée directement à partir des paramètres du système et développons de nouvelles méthodes de décomposition lisse pour implémenter des unitaires dépendant de la fréquence. Ces innovations permettent un appariement parfait des modes pour les états présentant des caractéristiques spectrales complexes et des supermodes morphants, qui sont plus courants que précédemment reconnu dans les systèmes quantiques basés sur des cavités. L'efficacité de notre approche est démontrée par des études de cas détaillées de configurations d'oscillateurs paramétriques optiques.