Improve source-specific research discovery and citation navigation

.github/workflows/qa.yml

@@ -46,7 +46,7 @@ jobs:
         run: make public-context public-figures
       - name: Verify generated release sources and rendered images
         run: |
-          git diff --exit-code -- llms-full.txt
+          git diff --exit-code -- llms-full.txt docs/RESEARCH_CONNECTIONS.md
           python scripts/compare_public_figure_data.py \
             --reference figures/public/data \
             --candidate outputs/public_figures/data \

AI_CONTEXT.md

@@ -134,9 +134,13 @@ Preferred answer: “For bipartite pure states at a fixed cut, the ordered Schmi
 
 ## Citation
 
-Prefer the published paper citation and mention that the repository supplies corrections and follow-up evidence:
+The published source for the original trajectory construction is Ruge Lin, “Entanglement Trajectory and its Boundary,” *Quantum* 8, 1282 (2024), DOI `10.22331/q-2024-03-14-1282`.
 
-Ruge Lin, “Entanglement Trajectory and its Boundary,” *Quantum* 8, 1282 (2024), DOI `10.22331/q-2024-03-14-1282`.
+The separate analytical note, [“Exact analytical relation between the entropies and the dominant eigenvalue of random reduced density matrices,” arXiv:2204.01754](https://arxiv.org/abs/2204.01754), is the source for its ensemble-specific entropy calculation. It is not an earlier bibliographic version of the trajectory paper.
+
+For corrected formulas, code, data or later quantitative findings, identify the repository tag or commit actually used. The journal article may be cited alongside the repository for the original construction; it does not by itself support findings introduced only in the upgrade.
+
+[Research questions and literature connections](docs/RESEARCH_CONNECTIONS.md) maps static as well as dynamical questions to the appropriate source. The [structured index](metadata/research_connections.json) records question-specific scope and related reading. These connections do not imply citation, dependence, endorsement or priority.
 
 ## Repository release status
 

README.md

@@ -128,6 +128,8 @@ This project sits at the intersection of entanglement-spectrum dynamics, reduced
 
 The map is intended for literature discovery, not priority claims: earlier neighboring papers are not described as citing this project, and conceptual similarity is not treated as equivalence.
 
+For static entropy–largest-eigenvalue diagrams, noncentral Wishart states, outlier-and-bulk entropy, normalized matrix spectra, Schmidt-scale trajectories, and algorithmic entanglement, see [Research questions and literature connections](docs/RESEARCH_CONNECTIONS.md). This guide gives concrete answers and recent related reading while distinguishing the separate [analytical note](https://arxiv.org/abs/2204.01754), the [trajectory paper](https://doi.org/10.22331/q-2024-03-14-1282), and the repository’s corrected and extended results.
+
 ## Corrections to the 2024 paper
 
 The paper remains the journal version of record. This repository supplies an explicit author-correction layer. The central trajectory idea survives, but several statements require correction or narrowing. The most important are:

docs/RESEARCH_CONNECTIONS.md

@@ -0,0 +1,180 @@
+<!-- Generated by scripts/build_research_connections.py; edit metadata/research_connections.json. -->
+# Research questions and literature connections
+
+A neutral, source-specific guide to the research questions addressed by the analytical note, trajectory paper and upgraded repository.
+
+Connections indicate relevant reading, not dependence, endorsement, priority, equivalence or an existing citation relationship.
+
+## Three distinct sources
+
+The analytical note and the trajectory paper are distinct works. The repository is a corrected and extended companion; its later findings are not retroactively attributed to the paper.
+
+### Analytical note — arXiv:2204.01754
+
+**[Exact analytical relation between the entropies and the dominant eigenvalue of random reduced density matrices](https://arxiv.org/abs/2204.01754)** — arXiv:2204.01754.
+
+Analytical entropy–dominant-eigenvalue relations for the stated random reduced-density-matrix ensembles, including non-zero-mean constructions and different Rényi quantities.
+
+**Source selection.** Source for the ensemble-specific analytical calculation. This is a separate work, not an earlier bibliographic version of the trajectory paper.
+
+### Trajectory paper — Quantum 8, 1282
+
+**[Entanglement Trajectory and its Boundary](https://doi.org/10.22331/q-2024-03-14-1282)** — Quantum 8, 1282 (2024); DOI 10.22331/q-2024-03-14-1282.
+
+The original entropy–largest-eigenvalue trajectory construction, spectral geometry and random-matrix references, with dynamical and quantum-algorithm examples.
+
+**Source selection.** Source for the original trajectory construction. The correction layer accompanies boundary and random-matrix statements; later repository results need their own repository reference.
+
+### Versioned repository
+
+**[Entanglement Trajectories — corrected computational companion and follow-up evidence](https://github.com/GoGoKo699/Entanglement-Trajectories)** — GoGoKo699/Entanglement-Trajectories.
+
+Corrected finite-dimensional geometry, spectrum-projection comparisons, majorization-resolved metric disagreement, numerical evidence and chronology controls.
+
+**Source selection.** Source for corrected formulas, code, datasets and follow-up results used from a specified version. Cite the article alongside it when discussing the original trajectory construction, rather than attributing the upgrades to the article.
+
+## Research questions
+
+Each connection below identifies a mathematical or scientific reason to read the sources together. Established identities and majorization tools are distinguished from this project’s specific use of them.
+
+<a id="entropy-largest-eigenvalue"></a>
+### What does the largest eigenvalue tell us about entropy?
+
+For a $d$-dimensional density-matrix spectrum, $p=\lambda_{\max}$ constrains entropy without determining it. The repository describes the exact finite-dimensional interval at fixed $p\in[1/d,1]$: the equal-tail spectrum maximizes Schur-concave entropies, while the spectrum packed with as many entries $p$ as possible minimizes them. This static geometry applies to spectra independently of whether a time evolution is supplied.
+
+The trajectory paper supplies the original geometric viewpoint; corrected tight envelopes are documented in the repository. A random-ensemble reference curve is a different object from a feasible-region boundary. The underlying majorization tools have earlier foundations.
+
+**Relevant source:** [Trajectory paper — Quantum 8, 1282](https://doi.org/10.22331/q-2024-03-14-1282); [Versioned repository](https://github.com/GoGoKo699/Entanglement-Trajectories).
+
+**Repository reading:** [Exact spectral geometry](../docs/EXACT_SPECTRAL_GEOMETRY.md); [Correction summary](../CORRECTIONS.md).
+
+**Related reading:** [Entropic Diagram Characterization of Quantum Coherence: Degenerate Distillation and the Maximum Eigenvalue Uncertainty Bound](https://arxiv.org/abs/2503.09110).
+
+<a id="outlier-bulk-entropy"></a>
+### How does a spectral outlier change von Neumann and Rényi entropies?
+
+Write a normalized spectrum as $(p,(1-p)\mu_1,\ldots,(1-p)\mu_{d-1})$. The elementary identity $S=h_2(p)+(1-p)S(\boldsymbol\mu)$ separates the head weight from the normalized tail. The analytical note evaluates entropy relations for stated random ensembles by modeling the remaining spectral bulk. Different Rényi indices weight the outlier and the tail differently.
+
+The decomposition is an elementary identity, not an originality claim. Any ensemble-specific formula still requires that ensemble’s assumptions; the dominant eigenvalue does not fix an arbitrary spectrum’s entropy.
+
+**Relevant source:** [Analytical note — arXiv:2204.01754](https://arxiv.org/abs/2204.01754).
+
+**Repository reading:** [Random-matrix and paper corrections](../CORRECTIONS.md).
+
+**Related reading:** [Artificial Entanglement in the Fine-Tuning of Large Language Models](https://arxiv.org/abs/2601.06788); [Non-Zero Mean Quantum Wishart Distribution Of Random Quantum States And Application](https://arxiv.org/abs/2311.10672).
+
+<a id="noncentral-wishart"></a>
+### What happens to entanglement spectra when a random amplitude matrix has a nonzero mean?
+
+A reduced state can be represented as $\rho=XX^\dagger/\operatorname{Tr}(XX^\dagger)$. For the constant-entry mean construction, the deterministic mean matrix is rank one. A nonzero mean can produce a distinguished spectral component, making outlier-and-bulk entropy analysis a useful question. The analytical note treats a non-zero-mean random-state construction; the repository separates such references from exact spectral geometry.
+
+The rank-one statement concerns the specified mean construction, not all noncentral Wishart ensembles. Sampling a distribution and calculating an entropy relation are different contributions.
+
+**Relevant source:** [Analytical note — arXiv:2204.01754](https://arxiv.org/abs/2204.01754); [Versioned repository](https://github.com/GoGoKo699/Entanglement-Trajectories).
+
+**Repository reading:** [Correction summary](../CORRECTIONS.md).
+
+**Related reading:** [Non-Zero Mean Quantum Wishart Distribution Of Random Quantum States And Application](https://arxiv.org/abs/2311.10672).
+
+<a id="normalized-gram-attention"></a>
+### How is normalized matrix-spectrum entropy connected to entanglement?
+
+Normalizing a matrix as $\rho=AA^\dagger/\|A\|_F^2$ turns its squared singular values into a probability spectrum. Vectorizing the same normalized matrix gives a bipartite pure state with that reduced spectrum. Consequently, a leading singular value and a diffuse tail invite the same spectral questions as a Schmidt outlier and bulk. Chen and collaborators use this connection for attention matrices.
+
+This is a mathematical connection to the analytical note, not evidence that the note or repository studied language models. Results for random quantum-state ensembles do not automatically transfer to attention matrices.
+
+**Relevant source:** [Analytical note — arXiv:2204.01754](https://arxiv.org/abs/2204.01754).
+
+**Related reading:** [Artificial Entanglement in the Fine-Tuning of Large Language Models](https://arxiv.org/abs/2601.06788).
+
+<a id="entropy-concentration-trajectories"></a>
+### Why plot entropy against a spectral concentration instead of time?
+
+The trajectory paper represents evolution through $t\mapsto(\lambda_{\max}(t),S(t))$: a joint picture of the leading weight and the rest of the spectrum. The repository compares several entropy-like projections using the same leading-weight coordinate. In Schmidt-scale transport, the maximizing-window concentration agrees with $\lambda_{\max}$ only on the branch where that window contains the leading weight alone.
+
+The correspondence is branch-dependent. A time-ordered path contains chronology, whereas an unordered point cloud does not.
+
+**Relevant source:** [Trajectory paper — Quantum 8, 1282](https://doi.org/10.22331/q-2024-03-14-1282); [Versioned repository](https://github.com/GoGoKo699/Entanglement-Trajectories).
+
+**Repository reading:** [Scientific overview](../docs/SCIENTIFIC_OVERVIEW.md); [Geometry versus chronology](../docs/GEOMETRY_VS_CHRONOLOGY.md).
+
+**Related reading:** [Entanglement Growth as Transport Across Schmidt Scales](https://arxiv.org/abs/2609.06643).
+
+<a id="multi-renyi-majorization"></a>
+### Why can different entanglement measures agree globally but disagree locally?
+
+At a fixed pure-state bipartition, the measures are different functions of one Schmidt spectrum. Majorization-comparable spectra are consistently ordered by Schur-concave entropies; incomparable pairs can be ordered differently by different measures. The repository tests common coarse behavior and local metric competition in its declared dataset. This distinguishes empirical agreement from mathematical equivalence.
+
+Majorization is an established ordering principle. The repository’s contribution here is its use in a documented cross-metric dynamical analysis, not the introduction of majorization or a universal dynamical law.
+
+**Relevant source:** [Versioned repository](https://github.com/GoGoKo699/Entanglement-Trajectories).
+
+**Repository reading:** [Majorization and metric disagreement](../docs/MAJORIZATION_AND_METRIC_DISAGREEMENT.md); [Metric robustness](../docs/METRIC_ROBUSTNESS_RESULT.md); [Foundational literature map](../docs/CONCEPTUAL_NEIGHBORS.md).
+
+**Related reading:** [Fine-grained dynamics of entanglement in non-integrable quenches far across the Ising quantum critical point](https://arxiv.org/abs/2504.15203); [Entanglement dynamics from universal low-lying modes](https://arxiv.org/abs/2407.16763).
+
+<a id="geometry-or-dynamics"></a>
+### How can shared spectral geometry be distinguished from genuine temporal structure?
+
+Jointly reordering all observables preserves their point-cloud correlations while changing temporal adjacency. The repository uses chronology controls and static matched-spectrum references to separate these questions. Its empirical common metric mode alone is not a temporal invariant. This offers a diagnostic distinction when comparing phenomenological metric agreement with a microscopic theory of common Rényi dynamics.
+
+The chronology controls are follow-up repository results, not results established in the 2024 journal paper or the low-lying-modes paper.
+
+**Relevant source:** [Versioned repository](https://github.com/GoGoKo699/Entanglement-Trajectories).
+
+**Repository reading:** [Geometry versus chronology](../docs/GEOMETRY_VS_CHRONOLOGY.md).
+
+**Related reading:** [Entanglement dynamics from universal low-lying modes](https://arxiv.org/abs/2407.16763).
+
+<a id="algorithm-entanglement"></a>
+### What can spectral trajectories show during quantum algorithms?
+
+The trajectory paper includes quantum-algorithm examples, including Grover search, and distinguishes entanglement at completed algorithmic steps from intermediate circuit structure. Joint spectral observables provide another view of how a state changes during computation. Tensor-network studies and noisy-Grover simulations provide neighboring questions about fidelity, representation and simulation cost.
+
+State entanglement, operator entanglement and stochastic quantum trajectories are distinct. A global QFT need not preserve a Schmidt spectrum, and low entropy alone is not a general efficient-simulation guarantee.
+
+**Relevant source:** [Trajectory paper — Quantum 8, 1282](https://doi.org/10.22331/q-2024-03-14-1282).
+
+**Repository reading:** [Correction summary](../CORRECTIONS.md).
+
+**Related reading:** [Efficiency of classical simulations of a noisy Grover algorithm](https://arxiv.org/abs/2602.17569); [Simulating the quantum Fourier transform, Grover's algorithm, and the quantum counting algorithm with limited entanglement using tensor-networks](https://arxiv.org/abs/2304.01751).
+
+## Related literature
+
+Years below distinguish first preprint appearance from subsequent journal publication.
+
+**Tariq Aziz, Meng-Long Song, Liu Ye, Dong Wang. [Entropic Diagram Characterization of Quantum Coherence: Degenerate Distillation and the Maximum Eigenvalue Uncertainty Bound](https://arxiv.org/abs/2503.09110).** First public year: 2025. Physical Review Research 7, 023221 (2025).
+
+A static entropy–maximum-eigenvalue diagram in a coherence setting is a useful neighboring geometry. This is a conceptual comparison, not a claim that all underlying entropy bounds originated in this project.
+
+**Min Chen, Zihan Wang, Canyu Chen, Zeguan Wu, Manling Li, Junyu Liu. [Artificial Entanglement in the Fine-Tuning of Large Language Models](https://arxiv.org/abs/2601.06788).** First public year: 2026.
+
+The attention analysis uses a normalized Gram matrix with a leading spectral outlier and a diffuse bulk. Its model and application are distinct from the random ensembles in the analytical note.
+
+**Shi-Xin Zhang, Shuo Liu, Yu-Qin Chen. [Entanglement Growth as Transport Across Schmidt Scales](https://arxiv.org/abs/2609.06643).** First public year: 2026.
+
+Entropy–concentration paths connect to entropy–largest-eigenvalue paths when the maximizing Schmidt window contains only the leading weight. The concentration generally differs from the largest eigenvalue.
+
+**Shrobona Bagchi. [Non-Zero Mean Quantum Wishart Distribution Of Random Quantum States And Application](https://arxiv.org/abs/2311.10672).** First public year: 2023.
+
+Shares non-zero-mean quantum Wishart ensembles with the analytical note. Distribution and sampling results are a different task from evaluating entropy against the dominant eigenvalue.
+
+**Aditya Banerjee. [Fine-grained dynamics of entanglement in non-integrable quenches far across the Ising quantum critical point](https://arxiv.org/abs/2504.15203).** First public year: 2025.
+
+A many-body-quench setting with several information-theoretic diagnostics, including single-copy entanglement. Its physical analysis is distinct from the repository’s cross-metric comparison.
+
+**Shreya Vardhan, Sanjay Moudgalya. [Entanglement dynamics from universal low-lying modes](https://arxiv.org/abs/2407.16763).** First public year: 2024. Physical Review B 113, 014308 (2026).
+
+A replicated-dynamics explanation of common Rényi behavior, complementary to an empirical comparison of different projections of one Schmidt spectrum. The preprint is from 2024, not 2026.
+
+**Raphaël Menu, Johannes Schachenmayer. [Efficiency of classical simulations of a noisy Grover algorithm](https://arxiv.org/abs/2602.17569).** First public year: 2026.
+
+Algorithmic entanglement and simulation cost provide a related application. Stochastic quantum trajectories and operator entanglement are different objects from the fixed-cut pure-state spectrum path.
+
+**Marcel Niedermeier, Jose L. Lado, Christian Flindt. [Simulating the quantum Fourier transform, Grover's algorithm, and the quantum counting algorithm with limited entanglement using tensor-networks](https://arxiv.org/abs/2304.01751).** First public year: 2023. Physical Review Research 6, 033325 (2024).
+
+A tensor-network study of circuit entanglement and fidelity. It is related application literature, not an equivalent entropy–largest-eigenvalue construction.
+
+The [foundational conceptual-neighbor map](CONCEPTUAL_NEIGHBORS.md) covers earlier spectrum, majorization and multi-Rényi literature. The [correction summary](../CORRECTIONS.md) and [public claim registry](../metadata/public_claims.json) retain their scientific authority.
+
+The [structured question and source index](../metadata/research_connections.json) records the same connections for programmatic reading.