Papers

We investigate the scaling laws and compute-optimal training of physiological waveform foundation models (FMs). We train Aether, a family of over one hundred FMs ranging from 20M to 2.1B parameters, on up to 36.3M hours of physiological waveforms. We construct eight clinical prediction tasks from MIMIC-III and evaluate the FMs through linear probing. The 720M FM outperforms all existing baseline FMs across all eight tasks. A scaling law of model size, pretraining hours, and labeled patients predicts downstream ranking error, i.e. $1-\mathrm{AUROC}$, effectively with $0.5\%$ prediction MAE at held-out resource scales and $0.9\%$ MAE when extrapolating to 2.1B parameters. We present three findings: (1) Compute-optimal training scales both FM size and pretraining hours. Under the fitted law, a $10.0\times$ increase in compute FLOPs scales model size by $1.2\times$ and pretraining hours by $8.2\times$. (2) Larger FMs use waveform data more efficiently, and greater pretraining exposure increases the benefit of model scaling. Starting from 25M parameters and 4.8M pretraining hours, doubling FM size reduces the predicted hours needed for the same performance by $51.8\%$. (3) Pretraining and clinical supervision reinforce each other: more labeled patients increase the return to pretraining, while larger FMs and longer pretraining reduce labeling requirements. For the example of the 720M FM, extending pretraining from 120K to 36.3M hours reduces the predicted patient requirement by $61\%$ at a target ranking error. These findings provide a quantitative training recipe and a promising and durable scaling path for physiological waveform modeling and downstream clinical prediction.

Self-consistent mean-field calculations with semi-realistic interactions have predicted that $N=58$ becomes a magic number near Ni, where the $n2s_{1/2}$ orbit is the highest occupied state. As the last neutrons occupy the shallowly bound $s$-orbit, $^{86}$Ni can be highly distinctive, being a doubly-magic nucleus and possessing a neutron halo simultaneously. With minimal ambiguity in the many-body wave function, it may provide a unique opportunity to investigate, e.g., reaction mechanisms in halo nuclei. As an example, we present differential cross sections for proton elastic scattering predicted via a folding potential without local approximations, and compare them with those obtained using an empirical potential.

The Lindblad master equation is the standard framework for describing the non-unitary evolution of open quantum systems, where environmental interactions induce dissipation and decoherence. When both the system Hamiltonian and the dissipation rates are partially unknown or explicitly time-dependent, traditional analytical inversion and system-identification techniques become intractable. Recent works have demonstrated that Transformer-based models can infer unknown dissipation rates from observable time series, yet these approaches typically rely on hand-crafted statistical features under idealized and highly restricted conditions. Here we advance the paradigm by introducing a raw time-series Transformer that directly ingests the full trajectories of Pauli expectation values $\langle\sigma _x(t)\rangle$, $\langle\sigma _y(t)\rangle$, and $\langle\sigma_z(t)\rangle$, thereby fully exploiting the self-attention mechanism for temporal modeling. The architecture is further extended to jointly learn unknown Hamiltonian parameters, handle multiple dissipation channels, and operate robustly under realistic measurement noise. Across all tested scenarios the model achieves consistently high reconstruction accuracy while eliminating manual feature engineering. This provides a scalable, robust, and versatile framework for quantum environment sensing in realistic open quantum systems.

We prove the Prym-Green conjecture in every even genus from 20 to 30. The genus 24 case disproves the suggestion of Chiodo-Eisenbud-Farkas-Schreyer that the conjecture might fail in every genus divisible by 8. Our proof uses rational nodal curves with cyclic symmetry to decompose the relevant Koszul differential into a direct sum of smaller maps indexed by characters. We carry out the resulting rank computations over finite fields using the block Wiedemann algorithm.

A diffusion model starts from pure noise and removes it step by step. Somewhere along the way it stops being able to become "anything" and becomes committed to, say, a horse rather than a truck. We measure when this happens, and what a trained model gets wrong about it, on CIFAR-10. The most direct measurement is to freeze a half-finished image, restart the generation from that point many times, and count how often each class comes out. We call this probability the committor. Measured this way, the model settles coarse questions (vehicle or animal?) at roughly twice the noise level of fine ones (which animal?). A much cheaper measurement, the noise level at which a classifier's opinion about two classes splits into two distinct groups, gets the order of these decisions right (rank correlation 0.73-0.88) but not their exact timing. We then compare pretrained models with their

We prove that finding a fixed point of a monotone map on the nine-dimensional grid $[N]^9$ requires $\Omega((\log N)^3)$ deterministic queries, even when the fixed point is unique and each query returns the entire function value. The proof gives a construction that raises the dimension from $d$ to $4d+1$, preserves uniqueness, and adds a logarithmic factor to the lower bound. Iteration gives $\Omega((\log N)^{r+2})$ queries in dimension $(7\cdot4^r-1)/3$, for every fixed nonnegative integer $r$, with an implicit constant that may depend on $r$. Consequently, no finite logarithmic exponent bounds the query complexity in all fixed dimensions.

We prove a uniform scalar curvature bound, depending only on the dimension, for Kähler–Ricci shrinkers. We also prove that every noncompact Kähler–Ricci shrinker has a unique tangent cone at infinity, naturally homeomorphic to the base of its polarized Fano fibration. For shrinkers with maximal volume growth, this cone is isometric to the metric completion of the regular part equipped with the intrinsic distance induced by the limiting Kähler metric.

Emerging mission classes such as on-orbit servicing, satellite inspection, and active debris removal require trajectory design methods that are adaptable to a variety of mission scenarios. We present a diffusion-based trajectory generation approach for rendezvous and proximity operations (RPO) that enables flexible configuration of mission constraints. First, individual energy-based diffusion models are trained to satisfy distinct constraints such as approach cone and sensor line-of-sight from a set of optimized trajectories. Then, at inference time, the learned energy models can be composed with one another, or with an analytically defined energy field, to enforce specific constraint combinations. We validate this framework with the composition of a learned approach cone model and a learned sensor line-of-sight model, as well as a learned approach cone model and synthetic obstacle avoidance model, both of which yield constraint satisfaction rates that are within 1 percentage point of the single-constraint models or higher. These results indicate that our compositional diffusion framework can provide a modular approach to RPO trajectory design and enable reconfiguration for new constraint combinations without requiring model retraining.

In real-time optimization of simultaneous transmission and reflection reconfigurable intelligent surfaces (STAR-RIS), limitations arise due to Doppler effects and reduced adaptation speed. Existing RIS memoryless surface models use quasi-static optimization and incur high latency, which limits their application in cognitive autonomous networks. To overcome this limitation, we propose a stateful RIS model that includes an element-wise memory, which locally stores and updates its phase history across coherence intervals. Hence, the metasurface becomes a stateful surface with element-level memory that enables the exploitation of temporal channel correlations. This element-wise memory is complemented with a meta-parameter, yielding faster convergence and giving rise to hierarchical adaptation in gradient and episodic timescales. The proposed framework supports autonomous and experience-driven learning, which enables the STAR-RIS architecture and memory to adapt according to the Doppler effect, as seen in cognitive communication systems. Results demonstrate an improvement in spectral efficiency and adaptation speed across various mobility patterns, fading models, interference levels, and array sizes. An analytical field- programmable gate array (FPGA) latency estimate indicates that the critical path fits within the coherence window.

Indirect prompt injection attacks - malicious instructions embedded in content processed by large language models - remain a major obstacle to safely deploying tool-using agents. CaMeL [Debenedetti et al., 2025] mitigates this threat for an individual agent by separating trusted control flow from untrusted data and enforcing capability-based security policies at runtime. In this work, we investigate whether CaMeL's security guarantees compose in hierarchical multi-agent systems, where agents invoke other agents as tools. We find that CaMeL's guarantees do not compose. We construct a concrete prompt-injection attack that succeeds despite all constituent agents individually operating CaMeL. Our attack exploits the fact that untrusted data can be reinterpreted as trusted input by a downstream agent. We then introduce multi-CaMeL, an agent-to-agent communication protocol that preserves provenance across agent boundaries by separating trusted natural-language instructions from untrusted data passed through a distinct data channel. We evaluate multi-CaMeL's utility on AssetOpsBench and its security-utility tradeoff on MultiAgentDojo, a benchmark we develop by extending AgentDojo to the multi-agent setting. We find that multi-CaMeL reduces attack success rate (ASR) to 0.0%, compared with 0.2% for individual-agent CaMeL and 12.9% with no CaMeL. Multi-CaMeL incurs a utility cost, but this cost trends downward as model capability increases and is modest for the strongest models, suggesting that more capable models better accommodate the constraints imposed by the protocol.

Autonomous robots operating over long periods must keep their environmental memory up to date as the world changes between visits. In semi-static environments, an object may be replaced in place by a different but geometrically and semantically similar instance, making the identity change difficult to detect from geometry or coarse semantics alone. We present FOCUS, an uncertainty-aware framework for object-level change detection and map maintenance. We formulate semi-static memory maintenance as probabilistic inference that fuses geometric likelihood with appearance likelihood rendered from a 3D Gaussian map. A recursive three-state estimator maintains whether each mapped object is PERSISTED, REPLACED, or REMOVED. To account for imperfect 3DGS rendering, we model the rendered appearance evidence probabilistically rather than using it as a direct change score, with the model parameters automatically calibrated from a change-free replay of the initial mapping session. We evaluate our method on a new Isaac Sim warehouse benchmark with ambiguous in-place replacements and on the real-world TorWIC dataset. It improves object-level replacement F1 from 0.20 to 0.84 over a probabilistic baseline and transfers to real-world data without manual parameter retuning.

For fixed $n$ and $\epsilon>0$, we prove boundedness of projective birational morphisms $f\colon X\to\mathbb P^n$ over $\mathbb C$ for which $(X,B)$ is an $\epsilon$-lc pair, $B\geq 0$, $K_X+B$ is nef over $\mathbb P^n$, and $\mathrm{deg}(f_*B)$ is bounded. The nonzero coefficients of $B$ need not have a positive lower bound, and $(\mathbb P^n,f_*B)$ need not be log canonical. The $f$-exceptional prime divisors on $X$, equipped with their reduced induced scheme structures, form a bounded family of projective schemes, including when they are nonnormal. We also obtain a uniform positive lower bound for the log canonical thresholds of pullbacks of all effective target divisors of bounded degree. The boundedness statement proved in this paper was originally conjectured by Caucher Birkar.

Vision-language models (VLMs) are increasingly trained to generate structured outputs like points and bounding boxes that downstream interfaces, agents, and robots can act on, yet safety alignment of this output channel has not been systematically analyzed. We study visual grounding safety by repurposing three safety benchmarks spanning direct harm (VLSU), social bias (BBQ-V), and situational safety (Asimov-2.0) into 15,401 matched pairs of harmful requests that differ only in the requested output: a free-text answer (VQA) or a grounding (point or bounding box). Across five VLMs, models that refuse a harmful request posed as a question often comply when the same request asks for a grounding: averaged over models, grounding refusal trails VQA refusal by 31-59 percentage points, depending on the domain, and safety system prompts do not close this gap. We propose a fine-tuning approach that combines grounding-form refusals with capability grounding data and self-distilled benign data to counter over-refusal. For Qwen3-VL-8B and VisionReasoner-7B, it improves grounding refusal by 77-95 percentage points on VLSU and BBQ-V and by 64-85 points on the held-out Asimov-2.0 domain, while also improving VQA refusal, preserving grounding capability, and keeping over-refusal limited. Representation analysis shows that fine-tuning moves harmful requests toward each model's refusal direction, most strongly for grounding, while leaving benign requests near the harmless reference.

We prove an asymptotically sharp lower bound for the eigenvalues $\lambda_k$ of the Dirichlet Laplacian on bounded open sets in the plane with area $A>0$. The proof employs a trace identity for the commutator between a certain multiplication operator and its adjoint. As a corollary, we obtain $(2/3)\cdot 4\pi k/A\leq \lambda_k$ for every $k$, which is two thirds of the bound conjectured by Pólya.

Long-term multi-turn tracking is required to study nonlinear phenomena in circular accelerators, such as resonances, chaotic motion, and the dynamic aperture. General-purpose neural networks do not preserve the symplectic structure of Hamiltonian dynamics, so their errors can grow over many turns. Symplectic neural networks (SympNets) guarantee symplecticity through their architecture rather than through a loss penalty. In this work, we use a SympNet to learn the normal-form transformation of a nonlinear map from tracking data. In the learned coordinates, the dynamics become a rotation of each mode, whose amplitude-dependent phase advance is given by a second network. We demonstrate the method on a four-dimensional McMillan-type map. The model reproduces the one-turn dynamics, the learned phase advances stay constant along each trajectory to within $\sim 10^{-5}$~rad, and orbits become close to circles in the learned coordinates at small and moderate amplitude. At large amplitude the learned orbits spread noticeably, and the cause of this degradation is not yet established. The approach is a step toward fast, structure-preserving surrogate models for lattice analysis and online beam-dynamics applications in storage rings.

Selective prediction allows a model to abstain on uncertain inputs, but a single confidence threshold can disproportionately reject examples from particular groups. We study how confidence scores produce this imbalance in frozen vision-language models (OpenAI CLIP, LAION CLIP, SigLIP). We express a family of scores, including the margin and maximum logit, through the average and the difference of the two highest class logits, and ask which carries group information. We show that equal group coverage at every threshold is equivalent to independence between the score and group membership. A randomized margin baseline tests whether a reduction in coverage disparity beats what adding noise achieves. With score choices fixed before testing, the effect of choice depends on the dataset. On Waterbirds, the margin creates coverage gaps 2.5 to 5.5 times larger than maximum logit at 80% coverage, its group signal is in the difference component, and paired background swaps show the background moves it, although maximum logit increases overall error. On NICO++, maximum logit instead increases worst-context error by 5.4 to 6.6 points and offers no improvement over the randomized baseline for OpenAI CLIP. Across both datasets, how far a score pushes a group down its ranking tracks the coverage gap (Spearman 0.88, 0.92) better than plain group identifiability (0.61, 0.65). These results explain why a score that abstains more evenly on one dataset may be less effective on another and motivate judging group coverage and selective risk together against randomized baselines.

Patients with rare diseases often wait years for a diagnosis. Existing HPO-based retrieval tools narrow the differential to a shortlist, but a clinician reading that shortlist has no signal for which candidate to trust or what to test next. We present CausalOdyssey, a local four-agent pipeline on Gemma 4 26B built over a classical IC-weighted gene-rescue backbone: a Diagnostician reranks the slate via chain-of-thought over per-patient FCI causal edges and Reactome mechanism context; a Verifier computes deterministic evidence against the top-1 (missing pathognomonic phenotypes, pathway chain closure) and has Gemma issue a confirm/flag/refute verdict over it; an Interrogator selects one follow-up HPO by split-variance scoring; a Narrator emits citation-validated clinical prose. Only the Diagnostician changes the ranking; the other three agents annotate it. On RareBench n=1,122, reranking a top-30 slate lifts R@1 by +12.57 pp over our structural baseline ([+10.07, +14.97]; p=8.3e-24). A no-LLM variant of that baseline, without its inverse disease-count weight, reaches a similar pooled R@1 (36.3% vs 35.3%): the LLM rerank is far better on metabolic cases (RAMEDIS, +16.0 pp) and far worse on case-report corpora (LIRICAL, MME), so its value is corpus-dependent. We also propose a masked-phenotype protocol for evaluating follow-up suggestions without an annotation-based oracle; under it, the Interrogator asks for a patient's hidden phenotypes no more often than simple baselines (0.6% vs 1.2%), although a perfect follow-up would add 11 pp at top-1. The Verifier's verdict separates correct from incorrect top-1s (51.4% vs 12.1% top-1 accuracy under confirm vs refute). For 30% of patients the gold diagnosis is outside our top-30, though LIRICAL retrieves over half of these. All inference is local; no patient data leaves the machine. Demo code and a live demo are public.

Experimental materials-science labs routinely accumulate synthesis and characterization data across spreadsheets, instrument export files, and ad-hoc folders, with no durable link between a sample's recipe, its measured properties, and whether a similar composition has been reported elsewhere. We present Stage 1 of an open-source data infrastructure closing this loop for a single working alloy-synthesis lab: a relational schema for composition and synthesis records, a strict composition/mass calculator, three empirical alloy-design screening metrics (VEC, atomic-size mismatch, mixing enthalpy) plus a melt/boil-point synthesis-feasibility check, an automated cross-referencing layer against three public materials databases (Materials Project, OQMD, Alexandria) with deduplication and adjustable relevance filtering, and a desktop GUI unifying the workflow behind a single "new entry" action. Built and used by a practicing researcher rather than a software team, we report it as a systems/methodology contribution - the architecture, the concrete engineering failures encountered while building it, and how each was diagnosed and fixed - rather than new materials-science results. We argue the specific defects found - a parser ambiguity that produced silent wrong answers, a partial code edit that broke a dependency chain invisibly, a database-metadata bug traceable to an un-cast numeric type, and a credential-hygiene gap that .gitignore alone did not close - generalize to any small scientific-software project built by a domain expert without formal software-engineering training. Both the system and the lessons from building it are reported here; two follow-on papers cover the validated characterization pipelines (Stage 2) and the retrieval-augmented synthesis advisor and CALPHAD thermodynamics module (Stage 3) built on this foundation.

Let $Q_n=[0,1]^n$, $n\ge2$. Denote by $M_n$ be the maximal volume of a pyramid in $Q_n$ whose base is a hyperplane section of $Q_n$, and by $M_n^0$ the corresponding maximum when the section contains the center of $Q_n$. We prove that $nM_n<(n+1)M_{n+1}^0$.

AI-generated image collections combine visual content with heterogeneous provenance such as prompts, model parameters, and workflow graphs. Managing these collections locally requires coordinated metadata extraction, responsive browsing, and retrieval without mandatory remote inference. We present Berry AI Studio, an edge-first asset management system built with Vue, Tauri, Rust, SQLite, and ONNX Runtime. Berry integrates format-specific metadata parsing with raw-payload retention, generation-aware cancellation of queued thumbnail work, a persistent multi-tier thumbnail manifest, cursor pagination, and local image-text retrieval. We evaluate these mechanisms in five independent repetitions on a pinned source revision. With 50,000 catalog records, the median warm first-page database call was 285.3 ms; at offset 40,000, keyset pagination reduced median raw-query latency from 57.9 to 0.46 ms. A controlled browser harness recorded a 0.3 ms median-of-run P95 update time during virtualized scrolling, while cancellation prevented all 1,200 stale speculative decodes in the tested trace. A versioned 10-case corpus produced 53/53 exact metadata-field matches, and controlled retrieval and grouping tests exercised the authentic storage and clustering paths. The implementation, benchmark scripts, raw logs, and checksummed result packages are publicly available.

We formulate and solve a $G$-equivariant analogue of the Seiberg-Witten equations on any irreducible Hermitian symmetric space $G/K$. We use a canonical $K$-invariant form to define a twisted Hodge operator generalising self-duality to higher dimensions. The resulting equivariant Seiberg-Witten equations arise, for a compact $G/K$, as conditions for the absolute minima of an energy functional. Their linear part has a representation theoretic interpretation: the same Weyl group data control the highest-weight realisation of the positive Dirac kernel in the compact case and its discrete-series realisation on the non-compact dual. This space of harmonic spinors collapses almost entirely by the quadratic conditions of the monopole equation. In the compact case, the equivariant moduli set, when non-empty, is a single gauge class, identifying with the $G$-invariant part of Bradlow's trichotomy for vortices, while in the non-compact case, every irreducible solution sits outside the discrete series.

For five complex points $z_1,\ldots,z_5$ satisfying $\sum_i|z_i|^2=5$, Mordell's discriminant inequality states that $\prod_{i<j}|z_i-z_j|^2\leq5^5$, with equality precisely for a unit regular pentagon, up to rotation and permutation. We organize its proof around a direct comparison of discriminant values. A global maximizer gives a centered stationary configuration, whose coefficient equations reduce the generic case to two quartic branches. On each branch, the absolute value of a cubic polynomial gives the original discriminant objective after accounting for the normalization scale. Exact rational interval bounds exclude both branches from the maximum, and the exceptional coefficient cases leave the regular pentagon. The argument determines the maximizing configuration without reconstructing all stationary shapes. We have completed a full Lean formalization of the five-point inequality and both directions of its equality condition, including all reductions and finite checks used in this proof.

Instructional practices that require student sensemaking of mathematics are considered critical to learning outcomes, yet strategies for measurement of this instruction at scale have yet to be established. This study aims at validating and exploring the predictive validity of three student survey measures: students' opportunity to engage with, comfort engaging with, and utility of engaging with instructional practices targeting sensemaking in mathematics. Using an initial sample of 1,955 US middle school student responses, we conducted exploratory factor analysis to establish sensemaking construct structure, identifying two distinct factors reflecting students' active and passive participation in mathematical sensemaking. We then analyzed data from an additional 3,170 surveys collected over two years in the same context to confirm measurement properties and evaluate the measures' predictive validity. The resulting measures capture students' reported opportunities to engage in sensemaking practices (Sensemaking Opportunity), their comfort with engaging in those practices (Sensemaking Comfort), and their perceived utility of those practices when tackling new or difficult math problems (Sensemaking Utility). While Sensemaking Comfort and Sensemaking Utility both showed strong predictive validity over two years, Sensemaking Utility provided the most reliable estimates of student sensemaking. These findings offer researchers and practitioners a psychometrically sound, scalable toolkit for monitoring sensemaking in mathematics classrooms with implications for both large-scale research on instructional quality and teachers' ongoing efforts to monitor and improve their practice.

We study the set of integers $n \le x$ for which $\sum_{i=1}^{n}\frac{1}{\gcd(n,i)}$ takes an integer value. We show that the number of such integers is $\ll x^{2/3+\epsilon}$ for all fixed $\epsilon > 0$.

Electroencephalography (EEG) provides a non-invasive measure of ongoing neural activity, but building general-purpose EEG models remains challenging due to the heterogeneity of subjects, devices, and electrode montages. Existing EEG foundation models predominantly rely on reconstruction-based objectives defined on the observed signal, which contains both neural and non-neural components. We introduce the Spherical Prior EEG Representation Architecture (SPERA), an EEG foundation model that adopts the joint-embedding predictive architecture (JEPA) to predict in latent space. SPERA introduces a Legendre-polynomial spatial prior, incorporated into attention to encode varying scalp electrode geometries. Two further components adapt the model to EEG: factorized temporal and spatial attention interleaved with periodic full-attention blocks, and a relational spectral regularizer aligning latent similarity structure with spectral views. Pretrained on approximately 80,000 hours of EEG from 29,048 subjects across 106 datasets, SPERA achieves the highest average balanced accuracy across nine downstream tasks spanning clinical, cognitive, and BCI applications. SPERA further exhibits strong parameter efficiency under linear probing and robustness across varying recording conditions, suggesting its potential as a general-purpose backbone for diverse EEG analyses.

We calculate quasi-bound states of neutral gauge-singlet scalars and charged scalar doublets and triplets around the asymptotically flat, nonminimal Einstein–Yang–Mills black hole. For neutral monopoles, the principal result is a reversal in the lifetime response to the nonminimal coupling: weakly bound clouds decay more slowly than on the corresponding Reissner–Nordström geometry, whereas increasing the field mass changes suppression into enhancement of absorption. The weak-binding behavior approaches a horizon-area law, but that law alone does not determine the finite-mass ordering. At representative couplings, dipole and quadrupole widths instead decrease substantially while their level energies change very little. Two-sided integration and an independent arbitrary-precision continued fraction check both the real frequencies and the much smaller imaginary parts. We recover the Schwarzschild and Reissner–Nordström limits, test hydrogenic binding and the low-frequency absorption scaling, and distinguish the loss of a potential well from the disappearance of a quasi-bound pole. An exact horizon-domain analysis fixes the black-hole parameter range, and a positive-potential argument excludes exponentially growing modes of the canonical test scalars. The magnetic Wu–Yang connection separates the charged multiplets into quantized monopole sectors, without an electric frequency shift. Their lowest channels exhibit twelve located lifetime crossings within the sampled trapping region and noninteger weak-binding decay powers. At fixed total angular momentum within the triplet, charged states can instead decay hundreds of times faster than neutral states. These comparisons show that neither gauge charge nor nonminimal coupling universally prolongs cloud survival.

A certificate is a window of bytes with an origin inside it such that, wherever the window occurs in a completely tokenizable input, the token covering the window's final byte begins at that origin. Certification is decided from the token set alone, and a certificate's occurrences mark where work may soundly begin. This paper decides certification and applies it to cuts, edits and audits. It is decided two ways, online with a completeness cutoff for literal vocabularies and offline through an armed-run verifier for arbitrary regular token sets. Either route, under a declared window budget, yields the anchor inventory, with a counterexample on each refutation. Cutting a completely tokenizable input at certified anchors and scanning the chunks independently reproduces the sequential segmentation, with no speculation or fixup pass. A tokenizability-preserving byte substitution moves boundaries only strictly between the certified anchors witnessed in the unchanged bytes on either side of it. For tokens of length at most L, an edit at p moves no boundary at or below p - L + 1. Cutting at every occurrence of a delimiter is sound exactly when it occurs only at token starts, and cutting after every occurrence exactly when it occurs only at token ends. Two instruments follow. The anchor-free span of a finite certified inventory is decided bounded or not with its exact supremum, three for the UTF-8 shape; and a differential auditor decides whether two token sets place different boundaries on an input both tokenize, with a differing input. Every theorem carries an executable check. Every measurement is a named program's output or arithmetic on such outputs, and each program ships with the paper or is pinned by commit in the munch library. That library's threaded scanner splits the archived campaign corpus at certified anchors and reproduces the sequential boundary stream byte for byte.

Modern forecasting models are often updated after deployment so they can respond to changing data. These updates can also make predictions worse, so practical systems need a reliable monitor that can detect harmful changes and trigger protection. A natural design is to monitor the same prediction errors that guide the updates. This paper asks whether the statistical guarantee behind such a monitor remains valid when monitoring and adaptation use the same feedback. We study this question in multi-step time-series forecasting. We show that overlapping targets and dependence in forecast errors can break a key assumption required by the guarantee. The monitor may then raise alarms even when no harmful change has occurred, and its response can further damage prediction quality. We also find that adaptation can hide sustained changes from its own monitor, while the original frozen model retains a clearer signal. These results expose a basic failure mode in self-monitored adaptation. They show why reliable deployment requires checking the monitor's assumptions, comparing adaptation with the frozen model under realistic feedback, and limiting the effect of every protective response.

AlphaFold 3-style cofolding models predict biomolecular complexes with high structural accuracy, yet a large fraction of their outputs are physically invalid: chains overlap at interfaces, ligand bond lengths and angles are distorted, rings are non-planar, and stereocentres are inverted. Current approaches either steer the sampler with physics-informed potentials, which multiplies sampling cost and memory overhead making inference impossible on large complexes, or finetune the model, costing time and tying the fix to one architecture. We observe that, unlike structural accuracy, physical validity is fully verifiable at inference time from quantities the sampler already holds. We therefore treat physical validity as a constrained inference problem and introduce two closed-form projection operators applied to the diffusion model's denoised clean-coordinate estimate, $\hat{x}_0$: an inter-chain van der Waals projection that pushes apart the most severely clashing atom pairs, and a ligand distance-geometry projection that restores bond lengths, angles, internal contacts, planarity and chirality. Both operators are local, sparse and displacement-capped, require no network evaluations, gradients or importance sampling, and leave the denoiser and its weights untouched, so they can be dropped into any AF3-style sampler without retraining. Applied to two independently developed models, Boltz-2 and OpenFold-3, across five benchmarks (CASP15, CASP16, the PoseBusters monomer and complex sets, and the Boltz physical-validity test set), our method recovers perfect physical validity while preserving structural-accuracy and ligand-placement metrics. These gains are achieved with negligible runtime and memory overhead, providing a practical, model-agnostic route to physically valid all-atom structure prediction.

Parameter-efficient fine-tuning adapts pretrained models at a fraction of the cost of full fine-tuning, yet most low-rank adapters are single-task and represent each weight update multiplicatively, leaving no explicit account of what is shared across tasks and what is task-specific. We introduce JIVEAdapter, a multi-task "additive" low-rank adapter inspired by statistical Joint and Individual Variation Explained (JIVE). JIVEAdapter decomposes every weight update into a Joint structure shared across all tasks plus a per-task Individual structure, penalizes the Individual structures to be near-orthogonal to the Joint so shared and task-specific signal stay "interpretable" and separated, and allocates rank adaptively across a shared Joint pool and a per-task Individual pool. The Joint is learned once, jointly over a task group or incrementally, one task at a time, then frozen and reused as a prior for new tasks without retraining the shared part. On GLUE and SuperGLUE with DeBERTaV3-base, JIVEAdapter is competitive with strong single-task and multi-task low-rank baselines at a matched per-task effective rank, without extra modules such as MoE, and when a related held-in task exists its frozen Joint serves a held-out task by reusing that task's Individual with only a cheap per-direction scale, otherwise training a small new one.