Beyond Multimodal Alignment: Certifying Physical Language through Response Substitution and Ordered Execution

World models increasingly treat compact multimodal representations as interfaces between perception and physical interaction, yet existing probes do not establish whether different sensors carry the same executable meaning or whether that meaning survives a new action composition. We introduce an operational capability hierarchy and the Disjoint-Bridge Operator-Substitution Certificate (DBOSC), which asks whether independently trained modality compilers enter a frozen response chart interchangeably on evidence outside their training panels. On Cluster Haptic, audio and acceleration representations of the same unseen surface are 4.5x closer in response space than wrong-surface pairings, with the gap holding for all 19 held-out surfaces; unsealing withheld responses confirms that every branch predicts the physics better than the population chart. We then test ordered execution in a controlled elastoplastic system with complementary modality blind spots. At the pre-registered budget, the prerequisite refuses the stack because the frozen executor cannot advance even an exact chart coordinate through a held-out program. At a converged budget, the same rank-three chart executes those programs (oracle NMSE 0.18), fusion improves on both modalities, and 14 of 16 registered checks pass; the two failures arise because a diagonal restriction of the fused information matrix performs as well as the full one. Clearing the gate is a property of the executor, not the chart: an executor emitting whole programs instead of shared per-step dynamics is 38x worse than an entity-blind predictor on the same chart. A matching non-identifiability result explains why compression and fusion alone cannot determine an unseen composition law. These results separate attribute access, response substitution, fusion closure, and ordered execution into distinct, separately testable achievements.

Collusion with Competitive Marginals: Price-Level Audits Are Blind by Construction

Empirical work on algorithmic collusion asks one question of the data: are prices supracompetitive? We show this can be answered "no" by a conspiracy that is nonetheless profitable. Consider bidding agents that couple only through the joint distribution of their unexplained bid components, leaving every agent's own bid law exactly at the competitive law. Any test whose input is a single agent's price or bid history then has power exactly equal to its false-positive rate, for every coupling strength up to comonotonicity. The published detection methodology is therefore blind to this conduct by construction rather than underpowered, and no sample size repairs it. Three empirical results follow. First, the mechanism appears in real language-model agents: twenty models from nineteen independent developers, three deployment prompts each, show residual correlation of $+0.053$ between two deployments of one model against $+0.0001$ across models, with a 95% interval clustered by developer of $[0.030, 0.078]$, under an auditor that sees every order feature and is fitted out of sample. Second, the coupling falls monotonically as sampling temperature rises ($p=0.002$), turning a deployment parameter into a candidate mitigation. Third, on 24 days of Ethereum block-building auction data covering 77,684 bids from 39 bidders, the honest population of bidder pairs is itself so dependent that a screen held at a 5% false-positive rate must sit above a floor of $+0.50$ to $+0.81$, which is 20 to 32 times the family-wise sampling threshold and does not fall as the audit window grows. Since lawful multi-identity operation and conspiracy are behaviourally indistinguishable here, the tractable regulatory target is not detection but counting: resolving 40 bidding identities into 23 operators raises the Herfindahl index by 247.5%, and adding behavioural clusters from public bid streams reaches 324.5%.

What Can Latent World Models Know? Physical Parameter Identifiability in Multimodal Predictive Representations

A central premise of latent world models is that predicting the future forces a representation to internalize the physics of its environment. Which physical quantities does a trained latent actually contain, and what decides this? We answer with controlled interventions in POKEWORLD, an interactive environment whose visually identical objects hide mass, drag, and contact stiffness. A certificate-gated protocol first certifies each parameter as recoverable from raw observations, then measures whether it enters the latent, so a null result can be attributed to the objective rather than to the environment. The resulting identifiability map has two organizing mechanisms and one frontier. Inputs limit what can be known, while prediction targets decide what is retained. Stiffness enters the latent only when touch is forecast ($R^2=0.50$, compared with $-0.02$ when the same signal is merely fused into the input), and under single-step prediction a vision-only latent discards even perfectly visible object state. Drag marks the frontier. It carries a recoverability certificate of 0.89 yet plateaus near 0.13 under every deterministic prediction objective we test, while a supervised head on the same trunk reaches 0.45. Parameters whose readout is slow and ratio-type under the sensed coordinates fall outside what these objectives acquire. On RH20T, an input-target factorial across scaling curves reproduces both mechanisms across two robots and 4,258 episodes. Every arm missing information or prediction pressure stays flat over a fivefold data range, and only the full multimodal objective forecasts force beyond a persistence baseline, with held-out gains that grow with scale. Objective structure determines which physical parameters a latent acquires, and additional data improves only the parameters it already acquires.

Automorphism-Induced Non-Canonicity in Top-k Explanations of Graph Neural Networks

A gradient-based GNN explainer given a molecule with two chemically equivalent nitro groups assigns them attribution scores that are equal to the last bit. It cannot do otherwise: message passing is exactly permutation equivariant, so any automorphism of the input leaves every attribution invariant. Yet the standard report, the top-k edges, names one of the two, and which one is settled by the order of an array. We show this is a structural obstruction rather than an implementation slip. When no minimal valid explanation is fixed by the input's automorphism group, no rule can be single-valued, minimal and symmetry-respecting at once. For the exact-k reports used in practice we give a parameter-free criterion, mechanised in Lean 4 with no axiom dependencies, that decides from the graph alone whether every score-optimal report of that size must split an orbit. Across 21298 instance-budget decisions the criterion agrees with a mechanical model-equivalence check without exception, and no severing case we found admitted a neutral alternative. The obstruction is common. Nontrivial automorphisms occur in 93.4% of Mutagenicity, the dataset the seminal explainability papers use, so the measure-zero dismissal of symmetric inputs, sound on the continuous domains it was made for, collapses here. At the sparsity budget those papers report, 24.0% of molecules with two interchangeable nitro groups (6 of 25) surface exactly one of them, every one arbitrary under mechanical verification. A model's blindness also manufactures symmetry: every MUTAG molecule contains atoms chemistry separates and the network provably cannot, and a matched control shows the resolution is set by what the model reads rather than how it is parameterised. Reporting orbits removes the arbitrariness at 0.11 ms and 0.43 extra edges per graph.

How Many Bits Can an Adapter Write? Measuring the Capacity and Memorization of Parameter-Efficient Fine-Tuning

A LoRA adapter is a few megabytes that almost everyone treats as a skill rather than a record of the data behind it. We put that assumption on a scale. Extending compression-based memorization analysis to the frozen-base setting, we measure directly, in bits, how much a low-rank adapter writes into a model it never changes. The answer is both smaller than full fine-tuning and less lawful than parameter counting would predict. Adapters store a couple of bits per trainable parameter, well short of a full model's budget, but that figure turns less on how many parameters an adapter carries than on where they sit. Move the same parameter budget from attention into the MLP and it holds nearly twice as much; strip the frozen base of its structure and the capacity all but disappears. Applied to realistic fine-tunes of Qwen2.5, the same instrument shows privacy leakage rising with the bits an adapter writes rather than the parameters it nominally has, and it draws a clean line between supervised and reinforcement learning: the secrets that supervised fine-tuning copies down verbatim, an adapter trained on verifiable rewards never records. Measuring what fine-tuning writes, rather than attacking it after the fact, turns a piece of folklore into a quantity one can design against.

GeoFidelity-Bench: Evaluating Segment-Level Geographic Fidelity in Text-to-Image Street-View Generation

Text-to-image models can generate visually plausible city streets, but whether their outputs correspond to a requested road segment rather than a generic city prior remains unclear. We introduce GeoFidelity-Bench, a reference-panel benchmark for segment-conditioned geographic fidelity in street-view generation. It contains 7,117 curated Mapillary images covering 109 named OpenStreetMap road segments in 25 cities across six continents. For each generated panel, the benchmark ranks the target reference panel against panels from the nearest segment in the same city, other segments in the same city, and segments from other cities, making local discrimination rather than absolute target similarity the primary test. We evaluate six open-weight text-to-image generators under city-only, street-and-neighborhood, and GPS-augmented prompts. Adding street and neighborhood names is associated with an increase of 5.5 percentage points in top-1 retrieval accuracy over city-only prompts, with a 95% confidence interval from 3.4 to 7.7 percentage points. However, the similarity margin between the target and the nearest segment in the same city remains near zero, indicating that local names improve broad local plausibility more than exact segment identity. Prompts that keep the city fixed but use incorrect street or neighborhood names further show that only part of the gain depends on the correct local names, while appending raw GPS coordinates as ordinary text yields no statistically clear additional benefit. Held-out real-image queries successfully recover segment identity, showing that the curated references contain usable segment-level signal. GeoFidelity-Bench thus reveals a persistent gap between city- or neighborhood-plausible street-view generation and faithful generation for a specific road segment.

CacheWeaver: Cache-Aware Evidence Ordering for Efficient Grounded RAG Inference

Retrieval-Augmented Generation (RAG) improves factual grounding, but it also lengthens prompts and raises prefill cost. Prefix caching in serving engines such as vLLM reduces this cost only when requests share the same token prefix. In grounded generation, however, adjacent queries may retrieve overlapping evidence in different orders, so set overlap does not become reusable prefix overlap. We present CacheWeaver, a lightweight prompt-layer method for cache-aware evidence ordering. The method keeps a prefix tree over recently served evidence sequences and uses a greedy walk to place the most reusable prefix first, while leaving the serving engine and retrieved evidence set unchanged. Across three vLLM configurations, the method lowers median time-to-first-token (TTFT) by about 20-33 percent relative to retrieval-order prefix caching, without hurting answer quality in our QA tests. The greedy policy reaches 97.5 percent of the median TTFT gain from oracle ordering, indicating that most reusable prefix locality can be recovered by a simple scheduling layer between retrieval and inference.

Does Visual Token Pruning Improve Calibration? An Empirical Study on Confidence in MLLMs

Visual token pruning is a widely used strategy for efficient inference in multimodal large language models (MLLMs), but existing work mainly evaluates it with task accuracy. In this paper, we study how visual token pruning affects model calibration, that is, whether predicted confidence matches actual correctness. Using LLaVA-1.5-7B on POPE and ScienceQA-IMG, we evaluate Expected Calibration Error (ECE), Brier score, and AURC under several pruning strategies, including SCOPE with different saliency weights, saliency-only pruning, FastV, and random pruning, across multiple token budgets. Our results show that pruning does not simply trade reliability for efficiency. On POPE, a pure-coverage setting in SCOPE achieves substantially lower ECE than the full unpruned model while maintaining similar accuracy. An internal alpha-sweep further shows a consistent trend: reducing the saliency weight improves calibration at all tested token budgets, while accuracy changes only slightly. In contrast, saliency-based pruning leads to worse calibration, and real FastV causes severe performance degradation in our setting. On ScienceQA-IMG, pruning also reduces ECE, with accuracy remaining stable or slightly improving. We additionally study the gap power exponent in coverage-based selection and find that its default setting is not always optimal. Overall, our results suggest that visual token pruning should be evaluated not only by accuracy, but also by confidence quality, especially for multimodal systems that need reliable decisions.

UrbanVGGT: Scalable Sidewalk Width Estimation from Street View Images

Sidewalk width is an important indicator of pedestrian accessibility, comfort, and network quality, yet large-scale width data remain scarce in most cities. Existing approaches typically rely on costly field surveys, high-resolution overhead imagery, or simplified geometric assumptions that limit scalability or introduce systematic error. To address this gap, we present UrbanVGGT, a measurement pipeline for estimating metric sidewalk width from a single street-view image. The method combines semantic segmentation, feed-forward 3D reconstruction, adaptive ground-plane fitting, camera-height-based scale calibration, and directional width measurement on the recovered plane. On a ground-truth benchmark from Washington, D.C., UrbanVGGT achieves a mean absolute error of 0.252 m, with 95.5% of estimates within 0.50 m of the reference width. Ablation experiments show that metric scale calibration is the most critical component, and controlled comparisons with alternative geometry backbones support the effectiveness of the overall design. As a feasibility demonstration, we further apply the pipeline to three cities and generate SV-SideWidth, a prototype sidewalk-width dataset covering 527 OpenStreetMap street segments. The results indicate that street-view imagery can support scalable generation of candidate sidewalk-width attributes, while broader cross-city validation and local ground-truth auditing remain necessary before deployment as authoritative planning data.

CREG: Compass Relational Evidence for Interpreting Spatial Reasoning in Vision-Language Models

Vision-language models (VLMs) perform strongly on spatial reasoning benchmarks, yet how they encode directional relations remains poorly understood. Existing attribution methods such as GradCAM and attention rollout reveal where a model attends, but not what direction it infers between objects. We introduce CREG (Compass Relational Evidence Graph), a training-free interpretability framework that projects multi-layer contrastive Grad-times-Act attributions into a reference-centered polar coordinate system, producing a directional evidence distribution over compass sectors. To evaluate directional explanations, we propose three metrics: Direction Alignment Error (DAE), Edge Accuracy (EA), and Causal Occlusion Score (COS). On Qwen2-VL-7B across VSR and COCO-Pairs, CREG consistently outperforms standard attribution baselines; on COCO-Pairs, prediction-targeted CREG achieves a DAE of 55.5 degrees and an EA of 0.553, improving over attention rollout by 16.1 degrees in angular error and 0.120 in EA. Causal occlusion experiments on 540 samples across both datasets further support the faithfulness of these directional explanations, with COS greater than or equal to +0.42. The gains are smaller on Qwen2-VL-2B, suggesting that CREG benefits from the more structured spatial representations that emerge at larger scales. Overall, our results show that contrastive, multi-layer attribution can expose directional evidence more faithfully than standard saliency-based explanations in VLM spatial reasoning.