Add final V15.1 LaTeX manuscript and reproducibility data

manuscript/BUILD_LOG.txt

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+LaTeX toolchain not available in this runtime; source package generated but PDF not compiled here.

manuscript/README.md

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+# Spectral World Models — Final V15.1 Manuscript Package
+
+This package refactors the manuscript around the completed V6–V15.1 experimental program.
+
+## Scientific positioning
+The paper no longer claims that the tested SWM is generally superior. It reports:
+- stability without guaranteed causal fidelity;
+- synthetic V9 directional gains with paired bootstrap intervals;
+- V13 learned axis anisotropy under exact symmetry transformations;
+- V14 external-transfer failure on CartPole-v1, MountainCar-v0, and Acrobot-v1;
+- V15.1 confirmation that the deficit persists in motion, latent, foreground, and state-token diagnostics.
+
+## Frozen reproducibility artifact
+Hugging Face repository:
+https://huggingface.co/kiruluta/Spectral-World-Models-Reproducibility
+
+Exact manuscript revision:
+v15.1-final
+
+Tagged artifact:
+https://huggingface.co/kiruluta/Spectral-World-Models-Reproducibility/tree/v15.1-final
+
+The manuscript BibTeX cites this exact tag.
+
+## Build
+Run:
+    pdflatex main.tex
+    bibtex main
+    pdflatex main.tex
+    pdflatex main.tex
+
+## Included measured data
+The `data/` directory contains the final CSV summaries used to generate the manuscript tables/figures.
+
+## Important
+V15.1 is the stopping point for this experimental series. This package intentionally does not propose or implement a V16 architecture.

manuscript/SHA256SUMS.txt

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+6da3fcceb1217b4ab8922737f9e3419feb38bf599b312423bc9abe6f9d37f4da  references.bib

manuscript/Spectral-World-Models-Manuscript-V15.1-Final.zip

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manuscript/data/v13_forced_collision_summary.csv

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manuscript/data/v14_external_control_summary.csv

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manuscript/data/v15_diagnostics_by_seed.csv

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manuscript/data/v15_diagnostics_summary.csv

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manuscript/data/v6_metrics_summary.csv

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manuscript/main.tex

@@ -0,0 +1,267 @@
+
+\documentclass[11pt]{article}
+\usepackage[margin=1in]{geometry}
+\usepackage{amsmath,amssymb,amsthm,booktabs,graphicx,microtype,hyperref,xcolor}
+\usepackage{tikz}
+\usetikzlibrary{arrows.meta,positioning,fit}
+\usepackage[numbers,sort&compress]{natbib}
+\usepackage{enumitem}
+\newtheorem{theorem}{Theorem}
+\newtheorem{proposition}{Proposition}
+\newcommand{\Hh}{\mathcal{H}}
+\newcommand{\T}{\mathcal{T}}
+\newcommand{\R}{\mathbb{R}}
+\newcommand{\swm}{\textsc{SWM}}
+\hypersetup{colorlinks=true,linkcolor=blue,citecolor=blue,urlcolor=blue}
+
+\title{\textbf{Spectral World Models: What Structured Operator Dynamics Give---and Do Not Give---for Imagination-Based Prediction}}
+\author{Andrew J. Kiruluta\\UC Berkeley School of Information}
+\date{September 2026}
+
+\begin{document}
+\maketitle
+
+\begin{abstract}
+We study Spectral World Models (SWMs), world models that encode observations into structured spectral coordinates and evolve latent states with action-conditioned operators. The original motivation is attractive: multiresolution coordinates expose scale, operator constraints provide a direct route to bounded rollouts, and counterfactual supervision can make action effects explicit. The completed experimental program, however, gives a more qualified result than the initial proposal. Across a sequence of falsification-oriented studies (V6--V15.1), structured transport remained numerically stable and counterfactual training recovered useful in-distribution action response. Multi-physics trajectory training subsequently improved directional counterfactual alignment over neural-operator and no-transition controls on a synthetic benchmark; paired bootstrap differences in trajectory cosine were positive across interpolation, extrapolation, and structural OOD. Exact rotation and axis-swap audits then exposed a learned coordinate anisotropy: vertical interventions could collapse while symmetry-transformed horizontal interventions recovered, despite an equivariant simulator. Finally, with the V9 architecture frozen, visual Classic Control evaluation on CartPole-v1, MountainCar-v0, and Acrobot-v1 showed substantially worse long-horizon prediction than simpler controls. V15.1 diagnostics demonstrate that this result is not solely a static-background artifact: the deficit persists in foreground, motion-increment, latent-trajectory, and discretized-state diagnostics. We therefore do not claim that spectral/operator structure is a generally superior world-model architecture. Instead, the evidence supports a narrower conclusion: spectral structure offers useful stability and causal-organization tools, but stability does not imply causal fidelity, synthetic causal alignment does not imply coordinate equivariance, and neither guarantees external dynamics transfer. Code, tests, experimental lineage, and measured result tables are frozen in the V15.1 reproducibility artifact \citep{kiruluta2026swmrepo}.
+\end{abstract}
+
+\section{Introduction}
+World models learn internal predictive dynamics that can be rolled forward under candidate actions \citep{ha2018worldmodels,hafner2019planet,hafner2020dream}. Most modern systems use recurrent state-space models, transformer-like predictors, or generic neural transitions. Spectral World Models explore a different design point: represent observations in multiresolution coordinates and learn action-conditioned operators in a shared latent Hilbert space. The idea is related to Koopman lifting \citep{koopman1931,brunton2016koopman}, neural operators \citep{li2021fno,kovachki2023neuraloperator}, and classical multiresolution analysis \citep{mallat2009wavelet}, while targeting action-conditioned predictive modeling rather than PDE solution alone.
+
+The central lesson of this paper is empirical rather than architectural. The completed study does not support the strongest version of the initial hypothesis---that structured spectral dynamics should transfer as a generally competitive world-model mechanism. It instead reveals a hierarchy of properties that must not be conflated:
+\begin{enumerate}[leftmargin=*]
+\item bounded or contractive rollouts are a stability property, not a guarantee of correct action response;
+\item counterfactual response on an in-distribution synthetic simulator is not sufficient evidence of causal generalization;
+\item aggregate causal metrics can hide coordinate-specific failure;
+\item synthetic causal advantages can coexist with poor external dynamics transfer.
+\end{enumerate}
+
+Our contributions are therefore revised around completed evidence. First, we retain the mathematical formulation of action-conditioned spectral dynamics and its sufficient stability conditions. Second, we document a sequential V6--V15.1 evaluation program in which each stage was motivated by a failure or ambiguity in the previous one. Third, we provide paired statistical evidence that V9 improves synthetic trajectory-direction alignment over two controls, but exact symmetry audits show that this advantage is coordinate-dependent. Fourth, we evaluate the frozen V9 architecture on three independently defined Classic Control environments and diagnose its failure using full-frame, foreground, motion, latent, and state-token measures. Finally, we release the complete reproducibility artifact at a frozen revision:
+\begin{center}
+\url{https://huggingface.co/kiruluta/Spectral-World-Models-Reproducibility/tree/v15.1-final}.
+\end{center}
+
+\section{Spectral World Model}
+Let the observation at time $t$ contain an image $I_t$, an optional text/state token sequence $W_t$, and action $a_t$. We encode
+\[
+x_t^{\mathrm{img}}=E_{\mathrm{img}}(I_t),\qquad
+x_t^{\mathrm{text}}=E_{\mathrm{text}}(W_t),
+\]
+and form a fused state
+\[
+X_t=F(x_t^{\mathrm{img}},x_t^{\mathrm{text}},m_t)\in\Hh.
+\]
+The implemented family uses a fixed Haar-style multiresolution image transform, a compact spectral/text representation, low-rank multimodal fusion, and an action-conditioned latent transition. A generic semilinear form is
+\[
+X_{t+1}=\T_{a_t}(X_t)=A_{a_t}X_t+N_{a_t}(X_t),
+\]
+where $A_{a_t}$ carries structured transport and $N_{a_t}$ supplies controlled nonlinearity. Decoders map latent states back to observable quantities.
+
+\begin{figure}[t]
+\centering
+\begin{tikzpicture}[node distance=8mm and 11mm, every node/.style={font=\small}, box/.style={draw,rounded corners,align=center,minimum width=28mm,minimum height=9mm}, arr/.style={-{Latex[length=2mm]},thick}]
+\node[box] (img) {Image $I_t$};
+\node[box,below=of img] (txt) {Text/state $W_t$};
+\node[box,right=of img] (ei) {Spectral image\\encoder};
+\node[box,right=of txt] (et) {Spectral text/state\\encoder};
+\node[box,right=18mm of ei,yshift=-9mm] (fuse) {Low-rank fusion\\$X_t\in\Hh$};
+\node[box,right=of fuse] (trans) {Action-conditioned\\spectral transition\\$\T_{a_t}$};
+\node[box,above=of trans] (act) {Action $a_t$};
+\node[box,right=of trans] (future) {Predicted latent\\$\widehat X_{t+1}$};
+\node[box,right=of future] (dec) {Image/state\\decoders};
+\draw[arr] (img)--(ei); \draw[arr] (txt)--(et);
+\draw[arr] (ei)--(fuse); \draw[arr] (et)--(fuse);
+\draw[arr] (fuse)--(trans); \draw[arr] (act)--(trans);
+\draw[arr] (trans)--(future); \draw[arr] (future)--(dec);
+\end{tikzpicture}
+\caption{Implemented SWM abstraction. The experimental program increasingly tests whether a structured transition that is stable also preserves action-conditioned causal effects, symmetry, and external dynamics.}
+\label{fig:arch}
+\end{figure}
+
+\subsection{Training objective}
+The base objective combines observation reconstruction, one-step prediction, multistep rollout consistency, and, in later versions, counterfactual trajectory terms:
+\[
+\mathcal{L}=
+\lambda_{\mathrm{rec}}\mathcal{L}_{\mathrm{rec}}+
+\lambda_{\mathrm{pred}}\mathcal{L}_{\mathrm{pred}}+
+\lambda_{\mathrm{roll}}\mathcal{L}_{\mathrm{roll}}+
+\lambda_{\mathrm{cf}}\mathcal{L}_{\mathrm{cf}}+
+\lambda_{\mathrm{stab}}\mathcal{L}_{\mathrm{stab}}.
+\]
+V6 introduced structured transport; V7 added action-contrastive counterfactual supervision; V9 extended this to multi-physics trajectory counterfactual training. V11 tested explicit causal-gain calibration but did not replace V9 as the frozen external-transfer model.
+
+\section{Stability: What the Operator Constraint Guarantees}
+The main theoretical statement is deliberately narrow.
+
+\begin{theorem}[Sufficient contraction condition]
+Suppose $\T_a(X)=A_aX+N_a(X)$ and, for every admissible action $a$,
+$\|A_a\|_{\mathrm{op}}+L_a\le\rho<1$, where $N_a$ is $L_a$-Lipschitz. Then for any two initial latent states $X,Y$ and any action sequence $a_{t:t+h-1}$,
+\[
+\|\T_{a_{t+h-1}}\circ\cdots\circ\T_{a_t}(X)-
+\T_{a_{t+h-1}}\circ\cdots\circ\T_{a_t}(Y)\|_{\Hh}
+\le \rho^h\|X-Y\|_{\Hh}.
+\]
+\end{theorem}
+\noindent The proof follows by one-step Lipschitz composition. The result guarantees bounded sensitivity in the latent norm. It does \emph{not} guarantee that the learned operator transports the correct action effect. V6 is an empirical demonstration of this distinction: the structured model had effective operator norm $1.05$ with very small orthogonality error, yet its counterfactual effect magnitude ratio was only $0.017$ in the archived one-seed summary. Stability and causal responsiveness are therefore separate axes.
+
+\section{Experimental Program}
+Rather than tune a single benchmark until favorable, the study evolved as a sequence of attempted falsifications.
+
+\begin{table}[t]
+\centering\small
+\begin{tabular}{p{1.1cm}p{4.2cm}p{8.1cm}}
+\toprule
+Stage & Question & Outcome used to motivate the next stage\\
+\midrule
+V6 & Can structured transport remain stable? & Stable transport, but action-effect magnitude was strongly suppressed.\\
+V7 & Can counterfactual supervision restore action response? & In-distribution response recovered; OOD causal transfer remained untested.\\
+V8 & Does the recovered response survive shifted physics? & Predictive stability survived better than causal response; counterfactual transfer degraded.\\
+V9--V10 & Can multi-physics trajectory training improve causal generalization, and is the benchmark valid? & Directional response improved; audit confirmed distinct physics/trajectories and exposed endpoint-cosine insensitivity.\\
+V11--V12 & Is causal gain calibrated, and where does response fail? & Gain calibration could overcorrect; decomposition showed aggregate V9 directional gains but severe intervention-specific failure.\\
+V13 & Is the failure simulator physics or learned anisotropy? & Exact rotations/swaps localized the failure to learned axis anisotropy.\\
+V14 & Does frozen V9 transfer externally? & It lost substantially on visual Classic Control long-horizon MSE.\\
+V15.1 & Is V14 mostly a static-background metric artifact? & No: deficits persist in motion, latent, foreground, and state-token diagnostics.\\
+\bottomrule
+\end{tabular}
+\caption{Falsification-oriented progression. V15.1 is the stopping point; no architecture changes were made after the external diagnostic.}
+\label{tab:program}
+\end{table}
+
+\subsection{Synthetic causal evaluation}
+The synthetic benchmark uses controlled moving-shape dynamics with intervention programs and multiple physics regimes. V12 evaluates matched episodes under interpolation, extrapolation, and structural OOD. The primary directional statistic is trajectory cosine; magnitude is analyzed separately. Paired bootstrap resampling uses 640 episodes and 2000 bootstrap draws per regime/control comparison.
+
+\subsection{Axis-equivariance audit}
+V13 applies exact $90^\circ$ rotations, $x/y$ swaps, and reflections to matched interventions. Because the simulator transformation is known, the audit asks whether model response transforms consistently. Oracle equivariance error is effectively zero in the archived audit, allowing model anisotropy to be separated from simulator asymmetry.
+
+\subsection{External benchmark}
+V14 freezes the V9 architecture and trains models from scratch on visual CartPole-v1, MountainCar-v0, and Acrobot-v1. Each environment uses 32$\times$32 grayscale observations and 10 seeds. The comparison is against a neural-operator model and a no-spectral-transition control. Horizons are H5, H10, H20, and H30.
+
+V15.1 then evaluates the V14 checkpoints with full-frame MSE, static-frame baseline, foreground-weighted MSE, motion-increment MSE, PSNR/SSIM, latent cosine, and discretized environment-state token accuracy. This stage changes the diagnostic, not the architecture.
+
+\section{Results}
+\subsection{V6: stability is not causal fidelity}
+The archived V6 summary contains one seed and should be treated as diagnostic rather than confirmatory. The structured model achieved H5 rollout MSE $0.02998$ versus $0.02946$ for no-transition, with latent cosine $0.813$ versus $0.905$. Its counterfactual effect-vector cosine was $0.970$, but the effect magnitude ratio was only $0.017$. Thus a directionally aligned but nearly suppressed intervention can coexist with controlled rollout dynamics.
+
+\subsection{V12: synthetic directional gains are statistically detectable}
+Table~\ref{tab:v12} reports paired bootstrap differences for V9 trajectory cosine. Every 95\% interval is above zero. This supports stronger directional alignment for V9 on this synthetic benchmark, not a general superiority claim.
+
+\begin{table}[t]
+\centering
+\begin{tabular}{llrr}
+\toprule
+Regime & Control & $\Delta$ trajectory cosine & 95\% CI\\
+\midrule
+Interpolation & Neural operator & 0.141 & [0.118, 0.165]\\
+Extrapolation & Neural operator & 0.148 & [0.126, 0.173]\\
+Structural OOD & Neural operator & 0.123 & [0.103, 0.146]\\
+Interpolation & No transition & 0.080 & [0.053, 0.109]\\
+Extrapolation & No transition & 0.081 & [0.053, 0.110]\\
+Structural OOD & No transition & 0.058 & [0.031, 0.085]\\
+\bottomrule
+\end{tabular}
+\caption{V12 paired bootstrap results for V9 minus control trajectory cosine.}
+\label{tab:v12}
+\end{table}
+
+\begin{figure}[t]
+\centering\includegraphics[width=.88\linewidth]{figures/v12_bootstrap_trajectory_cosine.pdf}
+\caption{V12 paired differences. Positive intervals establish a synthetic directional-alignment advantage under the tested protocol.}
+\end{figure}
+
+\subsection{V13: aggregate gains hide learned axis anisotropy}
+The symmetry audit changes the interpretation of V12. In the archived experiment, V9 horizontal left/right response had trajectory cosine about $0.386$, while rotating that intervention into the vertical axis reduced the response to approximately zero. Conversely, an original vertical up/down intervention near zero recovered to about $0.387$ when rotated into the horizontal axis. Oracle transformation errors were effectively zero. The causal deficit therefore follows the model coordinate system rather than the simulator physics. Collision-enriched tests preserve the same qualitative conclusion.
+
+This is an important negative result: counterfactual trajectory training can improve aggregate causal metrics while leaving a strong coordinate-specific shortcut.
+
+\subsection{V14: frozen V9 does not transfer competitively}
+Table~\ref{tab:v14} gives H30 full-frame MSE. V9 is worse than both controls in all three environments and has substantially larger across-seed variance.
+
+\begin{table}[t]
+\centering
+\begin{tabular}{lrrr}
+\toprule
+Environment & Neural operator & No transition & V9 SWM\\
+\midrule
+CartPole-v1 & $0.001631$ & $0.001567$ & $0.036374$\\
+MountainCar-v0 & $0.001155$ & $0.003346$ & $0.028382$\\
+Acrobot-v1 & $0.001739$ & $0.002563$ & $0.022414$\\
+\bottomrule
+\end{tabular}
+\caption{V14 H30 full-frame rollout MSE, mean over 10 seeds. Lower is better.}
+\label{tab:v14}
+\end{table}
+
+\begin{figure}[t]
+\centering\includegraphics[width=.88\linewidth]{figures/v14_h30_mse.pdf}
+\caption{External-control H30 rollout MSE. The frozen V9 model is not competitive on the primary V14 endpoint.}
+\end{figure}
+
+Full-frame MSE can reward static-background prediction, so V14 alone cannot distinguish transition failure from a rendering/metric confound. V15.1 was designed specifically to resolve that ambiguity.
+
+\subsection{V15.1: the external deficit persists on dynamics-sensitive metrics}
+Table~\ref{tab:v15motion} reports H30 motion-increment MSE. Relative to the neural operator, V9's mean error is about $12.6\times$ larger on CartPole, $66.5\times$ on MountainCar, and $3.3\times$ on Acrobot. This cannot be explained by static background alone.
+
+\begin{table}[t]
+\centering
+\begin{tabular}{lrrr}
+\toprule
+Environment & Neural operator & No transition & V9 SWM\\
+\midrule
+CartPole-v1 & $0.000343$ & $0.000364$ & $0.004322$\\
+MountainCar-v0 & $0.000130$ & $0.000122$ & $0.008650$\\
+Acrobot-v1 & $0.001930$ & $0.001937$ & $0.006325$\\
+\bottomrule
+\end{tabular}
+\caption{V15.1 H30 motion-increment MSE. Lower is better.}
+\label{tab:v15motion}
+\end{table}
+
+\begin{figure}[t]
+\centering\includegraphics[width=.88\linewidth]{figures/v15_h30_motion_mse.pdf}
+\caption{Dynamics-sensitive H30 motion error. The V9 deficit survives removal of much of the static-background advantage.}
+\end{figure}
+
+Latent diagnostics point in the same direction. H30 latent cosine for V9 is $0.184$ on CartPole, $0.370$ on MountainCar, and $0.480$ on Acrobot, compared with neural-operator values $0.716$, $0.505$, and $0.774$. The no-transition values are $0.699$, $0.558$, and $0.712$.
+
+\begin{figure}[t]
+\centering\includegraphics[width=.88\linewidth]{figures/v15_h30_latent_cosine.pdf}
+\caption{H30 latent cosine. The external deficit is present in latent trajectories, not only decoded pixels.}
+\end{figure}
+
+The discretized state-token diagnostic is also lower for V9 at H30: $0.358$ versus $0.488/0.504$ on CartPole, $0.554$ versus $0.683/0.676$ on MountainCar, and $0.546$ versus $0.727/0.724$ on Acrobot (neural operator/no transition). Foreground MSE narrows some gaps, confirming that static image structure does influence full-frame metrics, but it does not reverse the broader dynamics-sensitive conclusion.
+
+\section{Discussion}
+\subsection{What the evidence supports}
+The experiments support three positive but bounded claims. First, explicit operator constraints provide a transparent mechanism for controlling latent rollout growth. Second, counterfactual trajectory supervision can improve directional action-effect alignment on a controlled synthetic benchmark. Third, symmetry and decomposition audits are effective at revealing failure modes that aggregate endpoint metrics obscure.
+
+\subsection{What the evidence does not support}
+The completed study does not support a claim that the tested SWM is a generally superior world-model architecture. V13 shows that the synthetic causal advantage is coordinate-dependent, and V14--V15.1 show that the frozen V9 transition/training recipe does not transfer competitively to the three tested external visual-control environments. The external result is not reducible to a full-frame pixel-MSE artifact because it persists in motion and latent metrics.
+
+The study also does not falsify spectral representations, neural operators, Koopman-style lifting, or operator-theoretic world models as broad research directions. It falsifies a narrower empirical hypothesis about this specific structured V9 transition and training recipe under the tested transfer protocol.
+
+\subsection{Stability, causality, symmetry, and transfer are distinct}
+A recurring mistake in structured world-model research is to treat mathematical regularity as a proxy for predictive correctness. The completed sequence shows why these properties must be measured separately. Stability asks whether repeated application remains bounded. Causal fidelity asks whether actions produce the correct differential effect. Equivariance asks whether that effect transforms consistently under known symmetries. Transfer asks whether the learned mechanism survives a change of environment family. None follows automatically from the previous one.
+
+\subsection{Why stop at V15.1}
+The external diagnostic was predeclared as a stopping experiment rather than another tuning target. Because V9 loses on multiple dynamics-sensitive diagnostics, the appropriate scientific response is to report the limitation, freeze the architecture, and avoid post-hoc benchmark-specific repair. A future paper may investigate symmetry-aware spectral transitions or richer nonlinear operators, but such work constitutes a new hypothesis rather than V16 of the present experiment.
+
+\section{Limitations}
+The synthetic causal study is deliberately small and structured, so its directional gains should not be generalized to natural video or robotics. V6 has only one archived seed. V11 changed calibration behavior and is informative diagnostically, but it is not treated as a clean replacement for the frozen V9 baseline. Classic Control provides independent environment definitions but remains visually and dynamically simple relative to real-world embodied tasks. The external benchmark evaluates predictive transfer rather than closed-loop planning performance. The discretized state-token metric in V15.1 is a coarse diagnostic, not continuous-state regression. Finally, only three external environments are tested, so the result establishes a concrete failure of transfer under this suite rather than a universal impossibility result.
+
+\section{Reproducibility}
+The final source code, 32-test validation suite, experiment documentation, measured result tables, and V6--V15.1 lineage are frozen in the Hugging Face artifact \citep{kiruluta2026swmrepo}:
+\begin{center}
+\url{https://huggingface.co/kiruluta/Spectral-World-Models-Reproducibility/tree/v15.1-final}.
+\end{center}
+The final package was locally validated with \texttt{32 passed} tests; one non-fatal PyTorch warning concerns scalar conversion of a gradient-tracked tensor inside a test assertion. The repository preserves measured CSVs where available and does not synthesize missing historical raw results.
+
+For archival citation we recommend citing the exact tag rather than the moving \texttt{main} branch. The BibTeX entry is included in \texttt{references.bib}.
+
+\section{Conclusion}
+Spectral World Models remain an appealing way to expose multiscale structure and operator constraints inside a world model, but the completed evidence changes the paper's thesis. Structured spectral dynamics can be stable without being causally faithful; counterfactual supervision can improve aggregate synthetic causal alignment without producing coordinate equivariance; and synthetic causal advantages can fail to transfer to independently defined external dynamics. The frozen V9 SWM is not competitive with simpler controls on the tested Classic Control suite, and V15.1 shows that the deficit persists beyond static-background pixel metrics.
+
+The resulting contribution is therefore a falsification-oriented account of what structured spectral dynamics provide and where they fail. This narrower conclusion is more useful than an unqualified architecture claim: it identifies stability, causal response, symmetry, and external transfer as separate requirements that future operator-based world models should test explicitly.
+
+\bibliographystyle{plainnat}
+\bibliography{references}
+\end{document}

manuscript/references.bib

@@ -0,0 +1,52 @@
+
+@article{ha2018worldmodels,
+  title={World Models}, author={Ha, David and Schmidhuber, J{\"u}rgen},
+  journal={arXiv preprint arXiv:1803.10122}, year={2018}
+}
+@inproceedings{hafner2019planet,
+  title={Learning Latent Dynamics for Planning from Pixels},
+  author={Hafner, Danijar and Lillicrap, Timothy and Fischer, Ian and Villegas, Ruben and Ha, David and Lee, Honglak and Davidson, James},
+  booktitle={International Conference on Machine Learning}, year={2019}
+}
+@inproceedings{hafner2020dream,
+  title={Dream to Control: Learning Behaviors by Latent Imagination},
+  author={Hafner, Danijar and Lillicrap, Timothy and Ba, Jimmy and Norouzi, Mohammad},
+  booktitle={International Conference on Learning Representations}, year={2020}
+}
+@article{koopman1931,
+  title={Hamiltonian Systems and Transformation in Hilbert Space},
+  author={Koopman, Bernard O.}, journal={Proceedings of the National Academy of Sciences},
+  volume={17}, number={5}, pages={315--318}, year={1931}
+}
+@article{brunton2016koopman,
+  title={Discovering Governing Equations from Data by Sparse Identification of Nonlinear Dynamical Systems},
+  author={Brunton, Steven L. and Proctor, Joshua L. and Kutz, J. Nathan},
+  journal={Proceedings of the National Academy of Sciences}, volume={113}, number={15},
+  pages={3932--3937}, year={2016}
+}
+@inproceedings{li2021fno,
+  title={Fourier Neural Operator for Parametric Partial Differential Equations},
+  author={Li, Zongyi and Kovachki, Nikola and Azizzadenesheli, Kamyar and Liu, Burigede and Bhattacharya, Kaushik and Stuart, Andrew and Anandkumar, Anima},
+  booktitle={International Conference on Learning Representations}, year={2021}
+}
+@article{kovachki2023neuraloperator,
+  title={Neural Operator: Learning Maps Between Function Spaces with Applications to PDEs},
+  author={Kovachki, Nikola and Li, Zongyi and Liu, Burigede and Azizzadenesheli, Kamyar and Bhattacharya, Kaushik and Stuart, Andrew and Anandkumar, Anima},
+  journal={Journal of Machine Learning Research}, volume={24}, number={89}, pages={1--97}, year={2023}
+}
+@book{mallat2009wavelet,
+  title={A Wavelet Tour of Signal Processing: The Sparse Way},
+  author={Mallat, St{\'e}phane}, edition={3}, publisher={Academic Press}, year={2009}
+}
+@inproceedings{vaswani2017attention,
+  title={Attention Is All You Need},
+  author={Vaswani, Ashish and others}, booktitle={Advances in Neural Information Processing Systems}, year={2017}
+}
+@misc{kiruluta2026swmrepo,
+  author={Kiruluta, Andrew J.},
+  title={Spectral World Models: V15.1 Final Reproducibility Artifact},
+  year={2026},
+  howpublished={Hugging Face model repository, tag v15.1-final},
+  url={https://huggingface.co/kiruluta/Spectral-World-Models-Reproducibility/tree/v15.1-final},
+  note={Frozen code, tests, experimental lineage, and measured result tables}
+}