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According to a 927-page document released on Tuesday by the US Office of Government Ethics,
in all, the US president made more than $2.2 billion last year.
He benefited from a vast global network of investments and businesses that range from real estate and golf courses to royalty deals and Trump-branded products such as cologne.
He also took tens of millions of dollars in court settlements.
In his second term, the president and his family have invested heavily in dig…

@NFL@darktundra.xyz
2026-07-04 00:50:48

Travis Kelce Twins With Taylor in Dior nytimes.com/2026/07/03/style/t

@jon@henshaw.social
2026-07-04 03:00:16

Adding files to notes in @… is now live! Now I'm adding bulk editing. So many new features. I can't wait to write about them.

Screenshot of the Files preferences page in Recollect. The main section shows that Recollect is connected to Backblaze B2 cloud storage with key "recollect" and bucket "recollect-notes", connected since 7/3/2026. Below that, the Automated backups section shows a toggle switch that is turned on for "Automatically back up my notes." The backup frequency is set to "Weekly" on "Sunday" at "02:00 AM" in the America/Chicago timezone. A "Back up now" button is displayed, with the last backup timestamp…
Screenshot of a note titled "Note with files?!" containing the text "Heck yeah!" followed by three attached files: ev-etiquette-card.pdf (PDF, 384.8 kilobytes, uploaded July 3, 2026), ev-etiquette-card.ai (AI vector file with description "The vector file that started it all", 390.0 kilobytes, uploaded July 3, 2026), and greatest-of-docs.docx (DOCX, 20.9 kilobytes, uploaded July 3, 2026). Each file has download and link buttons.
@tinoeberl@mastodon.online
2026-07-04 16:18:16

📰 Es ist wichtig, gut informiert zu sein – damit wir Entwicklungen und Erfordernisse zu #Klimaanpassung, #Energiewende und #Gesundheitsschutz verstehen und erkennen, wenn uns

@arXiv_csGT_bot@mastoxiv.page
2026-06-04 08:50:30

Replaced article(s) found for cs.GT. arxiv.org/list/cs.GT/new
[1/1]:
- Breaking $1/\epsilon$ Barrier in Quantum Zero-Sum Games: Generalizing Metric Subregularity for Sp...
Yiheng Su, Emmanouil-Vasileios Vlatakis-Gkaragkounis, Pucheng Xiong
arxiv.org/abs/2509.21570 mastoxiv.page/@arXiv_csGT_bot/
- Shift Bribery over Social Networks
Ashlesha Hota, Susobhan Bandopadhyay, Palash Dey
arxiv.org/abs/2510.21200 mastoxiv.page/@arXiv_csGT_bot/
- Mechanism Design Without Disclosure: Committing to and Running Hidden Mechanisms
Ran Canetti, Amos Fiat, Yannai A. Gonczarowski
arxiv.org/abs/2302.05590 mastoxiv.page/@arXiv_econTH_bo
- Explaining a probabilistic prediction on the simplex with Shapley compositions
Paul-Gauthier No\'e, Miquel Perell\'o-Nieto, Jean-Fran\c{c}ois Bonastre, Peter Flach
arxiv.org/abs/2408.01382 mastoxiv.page/@arXiv_csLG_bot/
- Scheduling in Queueing Systems with Uncertain and Evolving Holding Costs
Caner Gocmen, Thodoris Lykouris, Deeksha Sinha, Wentao Weng
arxiv.org/abs/2505.21331 mastoxiv.page/@arXiv_csDS_bot/
toXiv_bot_toot

@cyrevolt@mastodon.social
2026-07-03 16:32:36

So the Gen 2 ME file system supported page sizes of 0x4000 (i.e. 16K, I figured that from a look at samples), but also 0x10000 (64K), now that I'm analyzing the implementation. :)

@michabbb@social.vivaldi.net
2026-07-04 00:05:07

🔒 Local & private by default — no cloud service, no model API calls, no API keys, and it never writes into your source repos. Includes local docs, man-page generation & signed self-upgrades
github.com/ctxrs/ctx

@arXiv_mathAT_bot@mastoxiv.page
2026-06-04 07:54:59

Universal Assembly and Cellular Loop Spaces on Regular CW Complexes
Serhii Dylda, Tibor Macko
arxiv.org/abs/2606.05051 arxiv.org/pdf/2606.0…

@arXiv_mathCV_bot@mastoxiv.page
2026-06-04 08:40:33

Crosslisted article(s) found for math.CV. arxiv.org/list/math.CV/new
[1/1]:
- Delta-pulse solution in Zener viscoelastic model
Andrea Mentrelli, Juan Luis Gonzalez-Santander, Francesco Mainardi
arxiv.org/abs/2606.04024 mastoxiv.page/@arXiv_mathph_bo
- On the First Caustic of Elliptical Billiards
Aleksandra Uskova
arxiv.org/abs/2606.04132 mastoxiv.page/@arXiv_mathDS_bo
- Combinatorial and analytic aspects of independence polynomials of zero divisor graphs
Bilal Ahmad Rather
arxiv.org/abs/2606.04789 mastoxiv.page/@arXiv_mathCO_bo
- Median porosity is quasiconformally invariant
Tero Kilpel\"ainen, Antti V. V\"ah\"akangas
arxiv.org/abs/2606.05034 mastoxiv.page/@arXiv_mathCA_bo
toXiv_bot_toot

@@arXiv_physicsatomph_bot@mastoxiv.page@mastoxiv.page
2026-07-03 07:39:02

[2026-07-03 Fri (UTC), 2 new articles found for physics.atom-ph Atomic Physics]
toXiv_bot_toot

@Mediagazer@mstdn.social
2026-07-02 22:55:48

Lee Enterprises, which owns the St. Louis Post-Dispatch and more, told its newspapers to run a three-story package on new chairman David Hoffmann on front pages (Angela Fu/Poynter)
poynter.org/rep…

@arXiv_csDB_bot@mastoxiv.page
2026-06-04 07:48:41

GraphAlg Playground: An Online Platform for Learning and Experimenting with the GraphAlg Language
Daan de Graaf, Robert Brijder, Soham Chakraborty, George Fletcher, Bram van de Wall, Nikolay Yakovets
arxiv.org/abs/2606.04813

@grahamperrin@bsd.cafe
2026-07-02 17:19:49

@…
Foot of the page, the info@ email address should be good enough.
IIRC the page was OK in the past. <web.…

@arXiv_mathGN_bot@mastoxiv.page
2026-06-04 07:48:53

[2026-06-04 Thu (UTC), no new articles found for math.GN General Topology]
toXiv_bot_toot

@Techmeme@techhub.social
2026-07-01 22:56:18

Higharc, which uses AI to assist house builders in design and construction, raised a $95M Series C led by Insight Partners, bringing its total funding to $170M (Lauren Ohnesorge/Triangle Business Journal)
bizjournals.com/triangle/news/

@arXiv_mathAT_bot@mastoxiv.page
2026-06-04 07:48:43

Slices of the special linear algebraic cobordism spectrum
Ahina Nandy, Oliver R\"ondigs, Egor Zolotarev
arxiv.org/abs/2606.05020 arxiv…

@arXiv_mathCV_bot@mastoxiv.page
2026-06-03 09:05:10

Replaced article(s) found for math.CV. arxiv.org/list/math.CV/new
[1/1]:
- Tur\'an type oscillation inequalities in $L^q$ norm on the boundary of convex polygonal domains
Polina Glazyrina, Szil\'ard Gy. R\'ev\'esz
arxiv.org/abs/2407.18404 mastoxiv.page/@arXiv_mathCV_bo
- Subtlety of oscillation indices of oscillatory integrals of real analytic functions
In-Kyun Kim, Morihiko Saito
arxiv.org/abs/2511.16257 mastoxiv.page/@arXiv_mathCV_bo
- On elliptic and quasiregularly elliptic manifolds
Fedor Manin, Eden Prywes
arxiv.org/abs/2410.19121 mastoxiv.page/@arXiv_mathDG_bo
- Linear Reservoir: A Diagonalization-Based Optimization
Romain de Coudenhove, Yannis Bendi-Ouis, Anthony Strock, Xavier Hinaut
arxiv.org/abs/2602.19802 mastoxiv.page/@arXiv_csDC_bot/
toXiv_bot_toot

@zudn@theres.life
2026-07-02 21:17:41

Not *real*. But I still ate one.
#blogging #Now

@arXiv_csGT_bot@mastoxiv.page
2026-06-04 08:38:12

Crosslisted article(s) found for cs.GT. arxiv.org/list/cs.GT/new
[1/1]:
- What Makes Majority Illusion Easy to Detect?
\v{S}imon Schierreich, Ildik\'o Schlotter
arxiv.org/abs/2606.04260 mastoxiv.page/@arXiv_csSI_bot/
- Episodic Memory Temporal Consistency for Cooperative Multi-Agent Reinforcement Learning
Zicheng Zhao, Yu Lan, Chengzhengxu Li, Zhaohan Zhang, Xiaoming Liu
arxiv.org/abs/2606.04492 mastoxiv.page/@arXiv_csLG_bot/
- Mean-based algorithms: A lower bound and regret
Julius Durmann, Amelie Kleber
arxiv.org/abs/2606.04931 mastoxiv.page/@arXiv_csLG_bot/
toXiv_bot_toot

@arXiv_condmatstrel_bot@mastoxiv.page
2026-06-04 08:55:47

Replaced article(s) found for cond-mat.str-el. arxiv.org/list/cond-mat.str-el
[1/1]:
- Comparing Symmetrized Determinant Neural Quantum States for the Hubbard Model
Louis Sharma, Ahmedeo Shokry, Rajah Nutakki, Olivier Simard, Michel Ferrero, Filippo Vicentini

@arXiv_csMA_bot@mastoxiv.page
2026-06-04 07:43:28

Channel Fracture: Architectural Blind Spots in Scheduled Cross-Agent Memory Injection for Multi-Agent Orchestration Systems
Levent Liu
arxiv.org/abs/2606.04896

@arXiv_csOS_bot@mastoxiv.page
2026-06-04 07:41:41

GNStor: Design of GPU-Native High-Performance Remote All-Flash Array
Shushu Yi, Wenbo Wu, Guoci Chen, Junrong Zhu, Shengwen Liang, Mao Bo, Chenying Huan, Chen Tian, Jie Zhang
arxiv.org/abs/2606.04908 arxiv.org/pdf/2606.04908 arxiv.org/html/2606.04908
arXiv:2606.04908v1 Announce Type: new
Abstract: GPU has become the leading computing device for a wide range of data-intensive applications, which tightly collaborates with remote all-flash array (AFA) to accommodate ever-expanding datasets, facilitate multi-client data sharing, and guarantee fault tolerance. Although GPU is the center of computation, all I/O processes in existing GPU-AFA systems are still CPU-centric. CPU orchestrates remote I/O requests and executes a centralized AFA engine to take charge of AFA-level functionalities (e.g., access control and metadata persistence). This design disparity suffers from substantial CPU-GPU interaction overhead and I/O traffic amplification, compromising end-to-end I/O performance.
In this work, we present \emph{GNStor}, a GPU-native AFA system that enables GPU to directly access remote AFA without CPU intervention in the I/O path, thereby fully exploiting the performance of AFA. Specifically, GNStor first proposes a GPU-centric NVMe over RDMA (NoR) software stack (named \emph{GNoR}), paving a fast path for GPUs to directly initiate NoR I/O requests to SSDs within remote AFA. GNoR employs an atomic-operation-based I/O orchestration design and follows the single-instruction-multiple-thread (SIMT) execution model of GPU, fully exploiting the massive parallelism of GPU architectures. To facilitate essential AFA functionalities in a CPU-bypass I/O path, GNStor further designs \emph{deEngine}, a decentralized AFA engine that seamlessly decomposes and integrates AFA-level tasks into each SSD firmware, thereby achieving efficient AFA access at low cost. Evaluation results show that GNStor achieves 3.2$\times$ higher I/O throughput and reduces application execution time by 31.1\%, compared to state-of-the-art AFA systems.
toXiv_bot_toot

@arXiv_qfinRM_bot@mastoxiv.page
2026-06-04 07:48:55

A Certified Higher Order Quantum Framework for CSA and Margin-Aware Collateral Optimization
Tao Jin, Stuart Florescu
arxiv.org/abs/2606.04235

@tinoeberl@mastodon.online
2026-06-04 07:55:20

📰 Vielen Dank für Eure #Spenden zur Unterstützung der Technikkosten, um alles am Laufen zu halten. Shoutout an alle #Steady-Förderer! 👍
Über 30 Seiten wurden bereits von den vermaledeiten Amazon-Affiliate-Links befreit.
Hier kann man Steady-Mäzen werden:

@@arXiv_physicsatomph_bot@mastoxiv.page@mastoxiv.page
2026-07-03 07:43:11

Microwave shielding of ultracold polar molecules on the transition $\boldsymbol{n=1 \rightarrow 2}$
Joy Dutta, Jeremy M. Hutson
arxiv.org/abs/2607.02470

@arXiv_mathAT_bot@mastoxiv.page
2026-06-04 07:47:20

The Hochschild Homology of Reedy Categories
Alexandra Ballow
arxiv.org/abs/2606.04297 arxiv.org/pdf/2606.04297

@arXiv_csDB_bot@mastoxiv.page
2026-06-04 07:42:37

Indexicon: A Spatial Indexing Library
Panagiotis Simatis, Panagiotis Bouros, Nikos Mamoulis
arxiv.org/abs/2606.04676 arxiv.org/pdf/2606.046…

@arXiv_mathGN_bot@mastoxiv.page
2026-06-03 07:44:44

Planar extensions in o-minimal structures
Dinh Si Tiep, Nhan Nguyen
arxiv.org/abs/2606.03155 arxiv.org/pdf/2606.03155

@@arXiv_physicsatomph_bot@mastoxiv.page@mastoxiv.page
2026-07-03 07:41:05

Identical-Particle Symmetry-Enabled Complete Coherent Control of Ultracold Atomic and Molecular Collisions
Jing-Chen Zhang, Adrien Devolder, Timur V. Tscherbul, Paul Brumer, Yu Liu
arxiv.org/abs/2607.01620

@grahamperrin@bsd.cafe
2026-07-02 21:44:13

@… oh, thanks!
Sorry, I should have been clearer: FreeBSD-ports-kmods should also be before, not after, the first boot of 15.1 …
… this is also missing from the official upgrading page at <

@arXiv_mathAT_bot@mastoxiv.page
2026-06-04 07:35:49

Left exact monoidal localizations from tidy maps
Mathieu Anel, Georg Biedermann, Eric Finster, Andr\'e Joyal
arxiv.org/abs/2606.04263 a…

@arXiv_mathCV_bot@mastoxiv.page
2026-06-04 08:52:55

Replaced article(s) found for math.CV. arxiv.org/list/math.CV/new
[1/1]:
- On the boundary behavior of bounded analytic functions in the unit disc
Spyros Pasias
arxiv.org/abs/2305.10870 mastoxiv.page/@arXiv_mathCV_bo
- Criteria for a fiberwise Fujiki/Kahler family to be locally Moishezon/projective
Jian Chen
arxiv.org/abs/2503.07548 mastoxiv.page/@arXiv_mathAG_bo
toXiv_bot_toot

@arXiv_csGT_bot@mastoxiv.page
2026-06-04 07:57:46

Fairness and Strategy-Proofness in Automated Market Makers
Frank M. V. Feys
arxiv.org/abs/2606.04959 arxiv.org/pdf/2606.04959 arxiv.org/html/2606.04959
arXiv:2606.04959v1 Announce Type: new
Abstract: No deployed automated market maker lets its liquidity providers vote on the trading function. We show this is structural, not an oversight. On the weighted-product family with $n \geq 3$ assets, no aggregation rule is at once fair and strategy-proof. Arrovian fairness forces a unique form, the weighted Aitchison centroid, the weighted geometric mean of the providers' preferred pools. But fairness forces mean-type aggregation and strategy-proofness forces median-type, and the only rule that is both is a single-provider dictator. The obstruction is sharp: it vanishes at $n = 2$, where a fair strategy-proof rule exists. Under the Frongillo--Papireddygari--Waggoner equivalence, the centroid is Genest's logarithmic opinion pool, and the impossibility transfers to externally Bayesian pooling.
toXiv_bot_toot

@arXiv_condmatstrel_bot@mastoxiv.page
2026-06-04 08:43:51

Crosslisted article(s) found for cond-mat.str-el. arxiv.org/list/cond-mat.str-el
[1/1]:
- Emergence of Macroscopic Quantum Order via Translational Zero Modes
Kenan Gundogdu

@arXiv_csMA_bot@mastoxiv.page
2026-06-04 07:39:46

Organizational Control Layer: Governance Infrastructure at the Execution Boundary of LLM Agent Systems
Tianyu Shi, Yang Mo, Yiou Liu, Zhuonan Hao, Yin Wang, Wenzhuo Hu, Nan Yu, Meng Zhou, Jiangbo Yu
arxiv.org/abs/2606.04306

@arXiv_csOS_bot@mastoxiv.page
2026-06-04 07:32:59

[2026-06-04 Thu (UTC), 1 new article found for cs.OS Operating Systems]
toXiv_bot_toot

@arXiv_csDB_bot@mastoxiv.page
2026-06-04 07:38:19

Bridge the Last-Mile Gap to Semantic Analytics: Compiling Natural-Language Queries into Semantic Operator Pipelines
Wenkai Dong, Ruyu Li, Sairam Gurajada, Yifan Wang
arxiv.org/abs/2606.04641

@arXiv_mathAT_bot@mastoxiv.page
2026-06-04 07:34:26

[2026-06-04 Thu (UTC), 4 new articles found for math.AT Algebraic Topology]
toXiv_bot_toot

@arXiv_mathGN_bot@mastoxiv.page
2026-06-03 07:35:32

[2026-06-03 Wed (UTC), 1 new article found for math.GN General Topology]
toXiv_bot_toot

@arXiv_csGT_bot@mastoxiv.page
2026-06-04 07:57:38

Welfare Maximization in Bilateral Trade: Improved Approximation Guarantees Beyond the Fixed Price Barrier
Shahar Dobzinski, Ariel Shaulker
arxiv.org/abs/2606.04890 arxiv.org/pdf/2606.04890 arxiv.org/html/2606.04890
arXiv:2606.04890v1 Announce Type: new
Abstract: We study the setting of welfare maximization in bilateral trade, where the values of both the buyer and the seller are drawn from independent distributions. Our goal is to maximize social welfare. In this setting, fixed price mechanisms have been extensively studied. In a fixed price mechanism, there is a price $p$ that depends only on the distributions of the buyer and the seller. Trade occurs if and only if the buyer's value is at least $p$ and the seller's value is at most $p$. A long line of work has culminated in determining almost exactly the approximation ratios achievable by fixed price mechanisms: there exists a fixed price mechanism that obtains at least a $0.72$ fraction of the social welfare, but no fixed price mechanism can guarantee more than a $0.7381$ fraction of it [Cai and Wu, STOC'23; Liu, Ren, and Wang, STOC'23]. No other incentive-compatible mechanism is known to beat the performance of fixed-price mechanisms in this setting.
This paper shows how to achieve a larger fraction of the optimal welfare with other classes of mechanisms. Specifically, we study the buyer-offering mechanism with a reserve price. In this mechanism, the buyer observes its value and makes a take-it-or-leave-it offer to the seller, where the offer is at least the reserve price. Beyond its simplicity, this natural mechanism is attractive because the seller always has a dominant strategy: accept the offer if its value is at most the offer, and otherwise reject it. We show that there always exists a reserve price that guarantees a $0.746$ fraction of the social welfare. This not only improves upon the best previously known approximation guarantee for the problem, but also demonstrates that fixed-price mechanisms are not optimal in this setting.
toXiv_bot_toot

@arXiv_mathAT_bot@mastoxiv.page
2026-06-03 07:58:35

Loop Space Splittings for Codimensional Sphere Bundles
Wen Shen
arxiv.org/abs/2606.03072 arxiv.org/pdf/2606.03072

@@arXiv_physicsatomph_bot@mastoxiv.page@mastoxiv.page
2026-07-03 09:03:19

Replaced article(s) found for physics.atom-ph. arxiv.org/list/physics.atom-ph
[1/1]:
- Cryogenic source of atomic tritium for neutrino-mass measurements and precision spectroscopy
Aleksei Semakin, et al.

@arXiv_csDB_bot@mastoxiv.page
2026-06-04 07:34:46

Selectivity Estimation for Semantic Filters on Image Data
Matthias Urban, Vu Huy Nguyen, Gabriele Sanmartino, Paolo Papotti, Carsten Binnig
arxiv.org/abs/2606.04610

@arXiv_mathCV_bot@mastoxiv.page
2026-06-04 07:52:25

Extension of Lohwater-Pommerenke's Theorem for strongly-normal Maps
Gopal Datt, Rahul Gogoi
arxiv.org/abs/2606.04800 arxiv.org/pdf/2606.04800 arxiv.org/html/2606.04800
arXiv:2606.04800v1 Announce Type: new
Abstract: We introduce strong normality for holomorphic curves and logharmonic mappings, extending classical normality concepts. We establish an extension of the rescaling characterization due to Lohwater and Pommerenke for not strongly-normal maps. In addition, we also study the Bloch mappings, little-Bloch mappings and prove Zalcman-Pang type rescaling results for them. The framework is further extended to strongly $\varphi$-normal mappings, yielding a unified treatment across these settings.
toXiv_bot_toot

@arXiv_csMA_bot@mastoxiv.page
2026-06-04 07:36:43

Exploring the Topology and Memory of Consensus: How LLM Agents Agree, Fragment, or Settle When Forming Conventions
Aliakbar Mehdizadeh, Martin Hilbert
arxiv.org/abs/2606.04197

@arXiv_csOS_bot@mastoxiv.page
2026-06-03 07:36:32

Agent libOS: A Library-OS-Inspired Runtime for Long-Running, Capability-Controlled LLM Agents
Yingqi Zhang
arxiv.org/abs/2606.03895 arxiv.org/pdf/2606.03895 arxiv.org/html/2606.03895
arXiv:2606.03895v1 Announce Type: new
Abstract: Large language model (LLM) agents are evolving from request-response assistants into long-running software actors: they maintain state across model calls, fork subtasks, wait for external events, request human authority, generate tools, and perform side effects that must be resumed and audited. This paper presents Agent libOS, a library-OS-inspired runtime substrate for LLM agents. Agent libOS runs above a conventional host operating system; it does not implement hardware drivers, kernel-mode isolation, or a POSIX-compatible operating system. Instead, it treats an agent as an AgentProcess: a schedulable execution subject with process identity, parent-child lineage, lifecycle state, a tool table derived from an AgentImage, typed Object Memory, explicit capabilities, human queues, checkpoints, events, and audit records. Its central design rule is tools are libc-like wrappers; runtime primitives are the authority boundary. Filesystem access, object access, sleeps, human approval, JIT tool registration, and external side effects are checked at primitive boundaries under explicit capabilities and policy.
We describe the design, threat model, Python prototype, and safety-oriented evaluation. The current prototype implements async scheduling, namespace-local Object Memory, runtime-integrated human approval, one-shot permission grants, per-process working directories, shell and image-registration primitives, Deno/TypeScript JIT tools over a libOS syscall broker, filesystem/object bridge tools, an injectable Resource Provider Substrate, deterministic demos, real-model smoke scripts, and 123 regression tests at the time of writing. Rather than improving planner accuracy, Agent libOS demonstrates a runtime substrate in which long-running LLM agents can be scheduled, authorized, resumed, and audited without treating tool dispatch as the trust boundary.
toXiv_bot_toot

@arXiv_mathAT_bot@mastoxiv.page
2026-06-03 07:44:29

Cheeger Inequalities for the Persistent Laplacian
Magnus Bakke Botnan, Rui Dong
arxiv.org/abs/2606.02846 arxiv.org/pdf/2606.02846

@arXiv_csGT_bot@mastoxiv.page
2026-06-04 07:33:52

Extending the El Farol Bar Game with Partial Observability and Incentive Design
Iosif Polenakis, Kalliopi Kastampolidou, Theodore Andronikos
arxiv.org/abs/2606.04753 arxiv.org/pdf/2606.04753 arxiv.org/html/2606.04753
arXiv:2606.04753v1 Announce Type: new
Abstract: The El Farol Bar game is a classic model of coordination under uncertainty, traditionally treating the venue as a passive constraint. In this work, we re-conceptualize the problem by modeling the bar as a strategic player equipped with AI-driven learning capabilities. We extend the original framework to include partial observability, i.e., agents observe only subsets of past attendees, and transform the bar from a passive capacity threshold into an active mechanism designer that adjusts pricing policies to balance revenue, utilization, and sustainability constraints. Agents employ AI-based learning to form beliefs and adapt attendance strategies under incomplete information, while the bar uses policy learning to optimize dynamic pricing. The resulting two-sided learning system frames coordination as a co-evolutionary process between boundedly rational agents and an adaptive institution, offering insights into congestion management, resource allocation, and mechanism design in complex adaptive systems.
toXiv_bot_toot

@@arXiv_physicsatomph_bot@mastoxiv.page@mastoxiv.page
2026-07-03 08:51:26

Crosslisted article(s) found for physics.atom-ph. arxiv.org/list/physics.atom-ph
[1/1]:
- Stark-Broadened Profiles for Ionized Helium Lines Using Computer Simulations
Patrick Tremblay, Alain Beauchamp, Pierre Bergeron

@arXiv_mathAT_bot@mastoxiv.page
2026-06-03 07:42:53

Burklund-Lin-Wang-Xu Methods in the Cofiber-of-Tau Formalism and Applications to Equivariant Slice Differentials
Yuchen Wu
arxiv.org/abs/2606.02779

@arXiv_csDB_bot@mastoxiv.page
2026-06-04 07:34:13

GraftDB: Dynamic Folding of Concurrent Analytical Queries
Genki Kimura, Kazuo Goda
arxiv.org/abs/2606.04303 arxiv.org/pdf/2606.04303

@arXiv_mathCV_bot@mastoxiv.page
2026-06-04 07:51:58

On the fundamental solutions of two nonlocal parabolic equations related to logarithmic Laplacians
Bart Rosenzweig, Jonathan Stanfill
arxiv.org/abs/2606.04225 arxiv.org/pdf/2606.04225 arxiv.org/html/2606.04225
arXiv:2606.04225v1 Announce Type: new
Abstract: We answer in the affirmative a question posed by V. Maz'ya of whether one can continue as a meromorphic function of $t$ the series representation of the fundamental solution of a certain nonlocal parabolic equation associated to a logarithmic Laplacian on the circle, which arises in the study of boundary value problems associated to the ordinary Laplacian on domains with thin cavities. The $a\ln(n) O(1)$ growth of the eigenvalues of the integral operator, together with explicit formulas for the eigenfunctions and the subleading asymptotic behavior of the eigenvalues, allows us to show that the fundamental solution is reminiscent of a sum of shifted Riemann zeta functions or polylogarithms, depending on the spatial variable. We show an analogous result for an operator related to a different logarithmic Laplacian on the interval, whose structure is similar. Along the way we are led to prove and to conjecture a number of curious identities involving Bell polynomials and Bernoulli numbers related to the exponential of the digamma function which are of independent interest.
toXiv_bot_toot

@arXiv_csGT_bot@mastoxiv.page
2026-06-04 07:33:46

Improved Approximation Guarantees for Groupwise Maximin Share Fairness
Georgios Amanatidis, Anna Korfiati, Evangelos Markakis, Christodoulos Santorinaios
arxiv.org/abs/2606.04731 arxiv.org/pdf/2606.04731 arxiv.org/html/2606.04731
arXiv:2606.04731v1 Announce Type: new
Abstract: We study the problem of fairly allocating a set of indivisible goods to a set of $n$ agents with additive valuation functions. We focus on the very demanding notion of \textit{groupwise maximin share fairness} (GMMS), which requires that each agent $i$ receives value comparable to their maximin share, where the latter is computed \textit{with respect to any subset of agents that contains $i$}. We show that it is possible to compute $(\phi-1)$-approximate GMMS allocations in polynomial time, where $\phi \approx 1.618$ is the golden ratio). This improves on the previously known guarantee of $4/7$ of Chaudhury et al. [SICOMP; 2021] and Amanatidis et al. [TCS; 2020]. We propose a simple algorithm that maintains the same main properties as the Draft-and-Eliminate algorithm of Amanatidis et al. [TCS, 2020] and we improve on the approximation guarantee analysis by carefully bounding the relevant value within any subinstance induced by the restriction of our allocation to a subset of agents. Our analysis is asymptotically tight for algorithms that share these properties and has the additional benefit of giving improved guarantees for restricted settings; in particular, when the agents agree on the top $n$ goods or when the number of agents is small. To illustrate the challenges of going beyond the guarantees of our algorithm, we also present a variant with an improved approximation of $(\sqrt{10}-1)/3 \approx 0.72$ for the case of three agents. To achieve this improvement we partially characterize the maximin share guarantees of short picking sequences for a small number of goods.
toXiv_bot_toot

@arXiv_mathAT_bot@mastoxiv.page
2026-06-03 07:36:20

A structural reduction for the symmetric hit problem in four variables
Dang Vo Phuc
arxiv.org/abs/2606.02626 arxiv.org/pdf/2606.02626

@arXiv_csMA_bot@mastoxiv.page
2026-06-04 07:35:32

[2026-06-04 Thu (UTC), 3 new articles found for cs.MA Multiagent Systems]
toXiv_bot_toot

@arXiv_csOS_bot@mastoxiv.page
2026-06-03 07:32:56

[2026-06-03 Wed (UTC), 1 new article found for cs.OS Operating Systems]
toXiv_bot_toot

@arXiv_csDB_bot@mastoxiv.page
2026-06-04 07:31:22

Puffin-Backed Vector Indexes: Attaching Approximate Nearest Neighbor Indexes to Apache Iceberg Snapshots for Compute-Disaggregated Query Engines
Artur Borycki
arxiv.org/abs/2606.04196

@arXiv_mathCV_bot@mastoxiv.page
2026-06-04 07:48:14

[2026-06-04 Thu (UTC), 2 new articles found for math.CV Complex Variables]
toXiv_bot_toot

@arXiv_mathAT_bot@mastoxiv.page
2026-06-03 07:34:23

[2026-06-03 Wed (UTC), 5 new articles found for math.AT Algebraic Topology]
toXiv_bot_toot

@arXiv_csGT_bot@mastoxiv.page
2026-06-04 07:57:46

Fairness and Strategy-Proofness in Automated Market Makers
Frank M. V. Feys
arxiv.org/abs/2606.04959 arxiv.org/pdf/2606.04959

@arXiv_csDB_bot@mastoxiv.page
2026-06-04 07:31:05

[2026-06-04 Thu (UTC), 6 new articles found for cs.DB Databases]
toXiv_bot_toot

@arXiv_csMA_bot@mastoxiv.page
2026-06-03 07:58:14

MeDxAgent: Multi-Agent Consultation for Interactive Medical Diagnosis
Akshat Sanghvi, Naren Akash, Raza Imam, Amit Sharma, Mohit Jain
arxiv.org/abs/2606.03416

@arXiv_mathCV_bot@mastoxiv.page
2026-06-03 07:46:20

First-order Schwartian derivative and some classes of univalent functions
Milutin Obradovic, Nikola Tuneski
arxiv.org/abs/2606.03433 arxiv.org/pdf/2606.03433 arxiv.org/html/2606.03433
arXiv:2606.03433v1 Announce Type: new
Abstract: In this paper we give estimate of $|S'_{f}(0)|$, where $S_{f}(z)= \left(\frac{f''(z)}{f'(z)}\right)'-\frac{1}{2}\left(\frac{f''(z)}{f'(z)}\right)^{2}$ is the Schwartian derivative, and $f$ belongs to different classes of functions univalent in the open unit disc $\ID$.
toXiv_bot_toot

@arXiv_csGT_bot@mastoxiv.page
2026-06-04 07:57:38

Welfare Maximization in Bilateral Trade: Improved Approximation Guarantees Beyond the Fixed Price Barrier
Shahar Dobzinski, Ariel Shaulker
arxiv.org/abs/2606.04890

@arXiv_csGT_bot@mastoxiv.page
2026-06-04 07:33:52

Extending the El Farol Bar Game with Partial Observability and Incentive Design
Iosif Polenakis, Kalliopi Kastampolidou, Theodore Andronikos
arxiv.org/abs/2606.04753

@arXiv_mathCV_bot@mastoxiv.page
2026-06-03 07:45:50

Area Theorems and Quasiconformal Extensions of Harmonic Mappings with a Pole
Zhijun Chen, Limei Wang
arxiv.org/abs/2606.03306 arxiv.org/pdf/2606.03306 arxiv.org/html/2606.03306
arXiv:2606.03306v1 Announce Type: new
Abstract: In this paper, we study the class \Sigma_{H}^{k}(p) of sense-preserving univalent harmonic mappings in the unit disk \mathbb{D} that possess a simple pole at p\in[0,1) and admit a k-quasiconformal extension to the extended complex plane for k\in[0,1). In 2024, Bhowmik and Satpati established an area theorem and derived a sufficient condition for the k-quasiconformal extension of harmonic mappings belonging to \Sigma_{H}^{k}(p) without logarithmic terms. Motivated by their work, we investigate the corresponding problem when a logarithmic singularity is present. Our main contributions are two-fold: we first prove a generalized area theorem for all mappings in \Sigma_{H}^{k}(p); we then obtain a sufficient condition for sense-preserving univalent harmonic mappings in \mathbb{D} to admit explicit k-quasiconformal extensions. These results extend the aforementioned work to the setting where logarithmic singularities are allowed.
toXiv_bot_toot

@arXiv_csDB_bot@mastoxiv.page
2026-06-03 08:07:47

MLSkip: Data Skipping for ML Filters via Lightweight Metadata
Mihail Stoian, Mark Gerarts, Pascal Ginter, Andreas Zimmerer, Jan Van den Bussche, Andreas Kipf
arxiv.org/abs/2606.03946

@arXiv_csMA_bot@mastoxiv.page
2026-06-03 07:44:02

OpenAgenet/OAN: Technical Architecture for Trust-Governed Agent Identity and Discovery
Jinliang Xu
arxiv.org/abs/2606.03163 arxiv.org/pdf/2…

@arXiv_mathAT_bot@mastoxiv.page
2026-06-04 08:52:37

Replaced article(s) found for math.AT. arxiv.org/list/math.AT/new
[1/1]:
- A Structural Characterization of the Hit Image in the Motivic Steenrod Algebra
Dang Vo Phuc

@arXiv_csGT_bot@mastoxiv.page
2026-06-04 07:33:46

Improved Approximation Guarantees for Groupwise Maximin Share Fairness
Georgios Amanatidis, Anna Korfiati, Evangelos Markakis, Christodoulos Santorinaios
arxiv.org/abs/2606.04731

@arXiv_mathCV_bot@mastoxiv.page
2026-06-03 07:41:29

Linearisation problem under finite \'etale cover
Xiaojun Wu
arxiv.org/abs/2606.03039 arxiv.org/pdf/2606.03039 arxiv.org/html/2606.03039
arXiv:2606.03039v1 Announce Type: new
Abstract: In this article, we study the (full or vertical) linearisation problem under a finite Galois \'etale cover. As an application, we give sufficient conditions for full linearisation near Hopf manifolds and for vertical or full linearisation near hyperelliptic manifolds.
toXiv_bot_toot

@arXiv_mathAT_bot@mastoxiv.page
2026-06-04 08:40:10

Crosslisted article(s) found for math.AT. arxiv.org/list/math.AT/new
[1/1]:
- Forman--Ricci Curvature for Irregular Convex Mosaics
Abhyudaya Gupta, Sayak Mukherjee, Kuldeep Saha

@arXiv_csMA_bot@mastoxiv.page
2026-06-03 07:39:50

OpenAgenet/OAN: Open Infrastructure for Trusted Agent Interconnection
Jinliang Xu
arxiv.org/abs/2606.03161 arxiv.org/pdf/2606.03161

@arXiv_mathCV_bot@mastoxiv.page
2026-06-03 07:41:23

Bohr, Bohr-Rogosinski, and Landau-Type Results for a Generalized Class of Harmonic Mappings
Xiaoyuan Wang, Xintong Han, Rajesh Hossain, Molla Basir Ahamed
arxiv.org/abs/2606.02612 arxiv.org/pdf/2606.02612 arxiv.org/html/2606.02612
arXiv:2606.02612v1 Announce Type: new
Abstract: In this paper, we study the Bohr phenomenon for a generalized subclass of harmonic mappings defined by a second-order differential inequality in the unit disk. Specifically, we consider the class $\mathcal{BH}_0(\gamma, \delta)$, which extends several known subclasses of harmonic and analytic functions. By employing sharp coefficient estimates and growth results, we establish improved versions of Bohr-type inequalities, including refined Bohr radii and Bohr--Rogosinski radii for this class. Furthermore, we derive generalized inequalities involving higher-order coefficient sums and area terms, thereby extending classical Bohr inequalities in a harmonic setting. The sharpness of the obtained results is verified through extremal functions. In addition, we obtain Landau-type theorems for the class $\mathcal{BH}_0(\gamma, \delta)$, providing explicit bounds for the radius of univalence and the size of schlicht disks contained in the image domain. Our results not only unify and extend several earlier works but also provide new insights into the geometric behavior of harmonic mappings under differential constraints.
toXiv_bot_toot

@arXiv_mathAT_bot@mastoxiv.page
2026-06-03 09:04:44

Replaced article(s) found for math.AT. arxiv.org/list/math.AT/new
[1/1]:
- The geometric diagonal of the special linear algebraic cobordism
Egor Zolotarev

@arXiv_mathAT_bot@mastoxiv.page
2026-06-03 08:53:02

Crosslisted article(s) found for math.AT. arxiv.org/list/math.AT/new
[1/1]:
- Learning Coherent Representations: A Topological Approach to Interpretability
Sigurd Gaukstad, Melvin Vaupel, Valdemar Karg{\aa}rd Olsen, Erik Hermansen, Benjamin Dunn

@arXiv_mathCV_bot@mastoxiv.page
2026-06-03 07:36:53

[2026-06-03 Wed (UTC), 4 new articles found for math.CV Complex Variables]
toXiv_bot_toot

@arXiv_csMA_bot@mastoxiv.page
2026-06-03 07:35:11

Capability Advertisement as a Market for Lemons: A Trust Layer for Heterogeneous Agent Networks
Gaurav Naresh Mittal
arxiv.org/abs/2606.03034

@arXiv_mathAT_bot@mastoxiv.page
2026-06-03 08:01:47

Composition of bispans of $G$-sets and plethysm
Nathan Cornelius, Evan Franchere, Usman Hafeez, Jesse Keyes, David Mehrle, Lakshay Modi, Nathaniel Stapleton
arxiv.org/abs/2606.03649

@arXiv_csDB_bot@mastoxiv.page
2026-06-04 08:49:48

Replaced article(s) found for cs.DB. arxiv.org/list/cs.DB/new
[1/1]:
- Don't Stir the Pot! Authorized Vector Data Retrieval via Access-Aware Indexing
Shanshan Han, Vishal Chakraborty, Sharad Mehrotra

@arXiv_mathCV_bot@mastoxiv.page
2026-06-03 08:52:53

Crosslisted article(s) found for math.CV. arxiv.org/list/math.CV/new
[1/1]:
- On the geometry of non-collapsed polarized cscK surfaces
Junsheng Zhang, Keshu Zhou
arxiv.org/abs/2606.02816 mastoxiv.page/@arXiv_mathDG_bo
toXiv_bot_toot

@arXiv_csGT_bot@mastoxiv.page
2026-06-04 08:12:50

Gradient Dynamics in First-Price Auctions: Iterative Strategy Elimination via Cubic Potentials
Mete \c{S}eref Ahunbay, Weiqiang Zheng, Tao Lin
arxiv.org/abs/2606.05108 arxiv.org/pdf/2606.05108 arxiv.org/html/2606.05108
arXiv:2606.05108v1 Announce Type: new
Abstract: We show that in discretised first-price auctions with complete information, if the buyers learn to bid with online gradient ascent, in time-average the outcome is (almost) the efficient outcome of the second-price auction. Our proof rests on two novel innovations in the analysis of online gradient ascent in normal-form games, which may be useful in a wider range of applications. First, we develop a potential-function-based argument for the analysis of gradient ascent in normal-form games, allowing us to deduce that certain strategies will not be played in time-average. We provide sufficient conditions which ensure this argument can be applied iteratively, resulting in a procedure reminiscent of iterative elimination of dominated strategies. Second, we develop a novel class of cubic "candidate potential functions", classifying a family of quadratic strategy modifications on the probability simplex against which online gradient ascent incurs no regret.
toXiv_bot_toot

@arXiv_csDB_bot@mastoxiv.page
2026-06-04 08:37:11

Crosslisted article(s) found for cs.DB. arxiv.org/list/cs.DB/new
[1/1]:
- ANN Search: Recall What Matters
Dimitris Dimitropoulos, Nikos Mamoulis

@arXiv_csGT_bot@mastoxiv.page
2026-06-04 08:06:11

Non-obvious Manipulability in the Additively Separable Group Activity Selection Problem
Maria Fomenko (Gran Sasso Science Institute), Giovanna Varricchio (University of Calabria)
arxiv.org/abs/2606.05048 arxiv.org/pdf/2606.05048 arxiv.org/html/2606.05048
arXiv:2606.05048v1 Announce Type: new
Abstract: In this work, we study the additively separable Group Activity Selection Problem (AS-GASP) in an imperfect information setting, where agents have private preferences over activities and weights over other agents. Our goal is to design mechanisms that assign agents to activities based on their declared preferences and weights, with the objective of maximizing social welfare while ensuring truthful reporting. We, therefore, focus on the notion of non-obvious manipulability (NOM), a form of resilience to manipulation. We first investigate the relationship between NOM and social welfare optimality. In this regard, our main result shows that, when preferences and weights are arbitrary or non-negative, any optimal mechanism is non-obviously manipulable. In contrast, when either preferences or weights are binary, we show that optimality and NOM may be incompatible. We then turn to computational aspects. While it is known that computing an optimal outcome for the AS-GASP is NP-hard even in restricted settings, we establish a strong inapproximability result showing that no polynomial-time algorithm can guarantee a bounded approximation ratio when preferences and weights may take arbitrary values. In turn, when preferences are non-negative, we show that a bounded approximation is possible, and we present two asymptotically optimal approximation mechanisms that are also guaranteed to satisfy NOM.
toXiv_bot_toot

@arXiv_csDB_bot@mastoxiv.page
2026-06-03 09:02:03

Replaced article(s) found for cs.DB. arxiv.org/list/cs.DB/new
[1/1]:
- Test-Time Optimization of Physical Query Plans with LLMs
Mehmet Hamza Erol, Xiangpeng Hao, Federico Bianchi, Ciro Greco, Jacopo Tagliabue, James Zou

@arXiv_mathAT_bot@mastoxiv.page
2026-06-04 07:48:43

Slices of the special linear algebraic cobordism spectrum
Ahina Nandy, Oliver R\"ondigs, Egor Zolotarev
arxiv.org/abs/2606.05020 arxiv.org/pdf/2606.05020 arxiv.org/html/2606.05020
arXiv:2606.05020v1 Announce Type: new
Abstract: Let $F$ be a field of exponential characteristic $e$. We compute the slices of $\mathbf{MSL}[e^{-1}]$, where $\mathbf{MSL}$ is the special linear algebraic cobordism spectrum defined by Panin and Walter. The answer is expressed in terms of the second page of the Adams-Novikov spectral sequence for the special unitary cobordism spectrum, which was explicitly determined by Novikov. Its applicability is demonstrated by computations with the slice spectral sequence for $\mathbf{MSL}$, which determine the first few Milnor-Witt stems of its homotopy groups (up to the third) in terms of very effective hermitian $K$-theory. We also establish a decomposition of the rational special linear algebraic cobordism spectrum over an arbitrary qcqs scheme.
toXiv_bot_toot

@arXiv_csGT_bot@mastoxiv.page
2026-06-04 08:50:30

Replaced article(s) found for cs.GT. arxiv.org/list/cs.GT/new
[1/1]:
- Breaking $1/\epsilon$ Barrier in Quantum Zero-Sum Games: Generalizing Metric Subregularity for Sp...
Yiheng Su, Emmanouil-Vasileios Vlatakis-Gkaragkounis, Pucheng Xiong

@arXiv_csDB_bot@mastoxiv.page
2026-06-03 08:49:10

Crosslisted article(s) found for cs.DB. arxiv.org/list/cs.DB/new
[1/1]:
- Inference Cost Attacks for Retrieval-Augmented Large Language Models
Chengliang Liu, Liangbo Ning, Yujuan Ding, Wenqi Fan

@arXiv_csGT_bot@mastoxiv.page
2026-06-04 08:38:12

Crosslisted article(s) found for cs.GT. arxiv.org/list/cs.GT/new
[1/1]:
- What Makes Majority Illusion Easy to Detect?
\v{S}imon Schierreich, Ildik\'o Schlotter

@arXiv_csGT_bot@mastoxiv.page
2026-06-04 08:12:50

Gradient Dynamics in First-Price Auctions: Iterative Strategy Elimination via Cubic Potentials
Mete \c{S}eref Ahunbay, Weiqiang Zheng, Tao Lin
arxiv.org/abs/2606.05108

@arXiv_mathAT_bot@mastoxiv.page
2026-06-04 07:54:59

Universal Assembly and Cellular Loop Spaces on Regular CW Complexes
Serhii Dylda, Tibor Macko
arxiv.org/abs/2606.05051 arxiv.org/pdf/2606.05051 arxiv.org/html/2606.05051
arXiv:2606.05051v1 Announce Type: new
Abstract: We develop a regular CW analogue of the classical assembly formalism for chain complexes appearing in algebraic surgery theory. From the cell poset, we construct combinatorial path and loop objects using fences of comparable cells and prove that their classifying spaces recover the homotopy types of the ordinary based path and loop spaces. The resulting loop object carries a natural monoid structure, giving rise to a DG algebra defined directly from the cellular structure.
For complexes of cellular cosheaves, we introduce a universal assembly functor to modules over the group ring of the fundamental group and study the localization determined by global equivalences. The associated homotopy category is identified with a Verdier quotient of the derived category of cellular cosheaves, and its fibrant objects are precisely the homotopy locally constant complexes. A single elementary cosheaf becomes a compact generator after localization, and its derived endomorphism DG algebra is identified with singular chains on the cellular loop space. Consequently, the localized theory admits a Morita description in terms of DG modules over the loop DG algebra. The formalism provides a regular CW counterpart of the classical delta-set approach to assembly in algebraic surgery theory due to Ranicki and Weiss.
toXiv_bot_toot

@arXiv_csGT_bot@mastoxiv.page
2026-06-04 08:06:11

Non-obvious Manipulability in the Additively Separable Group Activity Selection Problem
Maria Fomenko (Gran Sasso Science Institute), Giovanna Varricchio (University of Calabria)
arxiv.org/abs/2606.05048

@arXiv_mathAT_bot@mastoxiv.page
2026-06-04 07:47:20

The Hochschild Homology of Reedy Categories
Alexandra Ballow
arxiv.org/abs/2606.04297 arxiv.org/pdf/2606.04297 arxiv.org/html/2606.04297
arXiv:2606.04297v1 Announce Type: new
Abstract: We calculate the Hochschild homology of generalized Reedy categories, such as the simplex category, the category of finite sets, the category of finite-dimensional categories, and the PROP associated to an operad.
toXiv_bot_toot

@arXiv_mathAT_bot@mastoxiv.page
2026-06-04 07:35:49

Left exact monoidal localizations from tidy maps
Mathieu Anel, Georg Biedermann, Eric Finster, Andr\'e Joyal
arxiv.org/abs/2606.04263 arxiv.org/pdf/2606.04263 arxiv.org/html/2606.04263
arXiv:2606.04263v1 Announce Type: new
Abstract: We put Goodwillie's calculus of functors and Weiss' orthogonal calculus in a unified framework. We do so in two ways. On the one hand, the relevant categories are all symmetric monoidal and controlled by their compact objects. We introduce the notion of tidy map as a means to generate symmetric monoidal localizations in this setting. These localizations are always left exact. Then we show that both the Goodwillie and Weiss towers are generated by such maps. On the other hand, the relevant categories are also topoi, for which there is a general theory of completion towers of left exact localizations. We had shown in a previous work that the Goodwillie tower is an instance a such a tower. We show here that the Weiss tower is a completion tower as well, and therefore that the general theory applies to orthogonal calculus.
toXiv_bot_toot

@arXiv_mathAT_bot@mastoxiv.page
2026-06-04 07:34:26

[2026-06-04 Thu (UTC), 4 new articles found for math.AT Algebraic Topology]
toXiv_bot_toot

@arXiv_mathAT_bot@mastoxiv.page
2026-06-03 07:58:35

Loop Space Splittings for Codimensional Sphere Bundles
Wen Shen
arxiv.org/abs/2606.03072 arxiv.org/pdf/2606.03072 arxiv.org/html/2606.03072
arXiv:2606.03072v1 Announce Type: new
Abstract: In this paper, we establish two loop decomposition theorems for sphere bundles of real vector bundles under appropriate connectivity and characteristic class assumptions. Specifically, we treat two families of sphere bundles: those arising from rank-$(n-1)$ vector bundles and those from rank-$(n-3)$ vector bundles over closed smooth $n$-manifolds.
toXiv_bot_toot

@arXiv_mathAT_bot@mastoxiv.page
2026-06-03 07:44:29

Cheeger Inequalities for the Persistent Laplacian
Magnus Bakke Botnan, Rui Dong
arxiv.org/abs/2606.02846 arxiv.org/pdf/2606.02846 arxiv.org/html/2606.02846
arXiv:2606.02846v1 Announce Type: new
Abstract: We study Cheeger-type inequalities for persistent Laplacians associated with inclusions of simplicial complexes $\mathcal{K}\hookrightarrow \mathcal{L}$. We introduce a persistent up $p$-Laplacian $\Delta_{q,p,\mathrm{up}}^{\mathcal{K},\mathcal{L}}$ for $p\geq 1$. For $p=2$, this recovers the usual persistent up Laplacian, while for $p=1$ it yields a nonzero persistent Cheeger constant $\varphi_q^{\mathcal{K},\mathcal{L}}$. We prove a Cheeger-type inequality relating $\varphi_q^{\mathcal{K},\mathcal{L}}$ to the smallest nonzero eigenvalue of $\Delta_{q,\mathrm{up}}^{\mathcal{K},\mathcal{L}}$. This gives a persistent extension of recent work by Jost and Zhang (Ann. Sc. Norm. Super. Pisa Cl. Sci., 2024; arXiv:2302.01069).
We then study two more structured settings. Under a locally complete $q$-skeleton assumption on $\mathcal{K}$, we extend the complete-skeleton isoperimetric inequality of Parzanchevski--Rosenthal--Tessler (Combinatorica, 2016; arXiv:1207.0638) to the persistent setting. For orientable $(q 1)$-dimensional pseudomanifolds, we prove a Kron-type reduction of the persistent up Laplacian to a vertex- and edge-weighted graph Laplacian, possibly with Dirichlet boundary terms, and obtain two-sided Cheeger inequalities; this is related to the dual-graph perspective in the work of Steenbergen--Klivans--Mukherjee (Adv. Appl. Math., 2014; arXiv:1209.5091). We also describe the nonzero persistent Cheeger constant $\varphi_q^{\mathcal{K},\mathcal{L}}$ explicitly in terms of the dual graph in the non-branching pseudomanifold case. Finally, for graph inclusions $H\hookrightarrow G$, we compare the persistent Cheeger constants introduced here with the Kron-reduction Cheeger constants of M\'emoli et al. (SIAM J. Math. Data Sci., 2022; arXiv:2012.02808).
toXiv_bot_toot

@arXiv_mathAT_bot@mastoxiv.page
2026-06-03 07:42:53

Burklund-Lin-Wang-Xu Methods in the Cofiber-of-Tau Formalism and Applications to Equivariant Slice Differentials
Yuchen Wu
arxiv.org/abs/2606.02779 arxiv.org/pdf/2606.02779 arxiv.org/html/2606.02779
arXiv:2606.02779v1 Announce Type: new
Abstract: We reinvestigate the theory of spectral sequences by studying the $(\infty,1)$-category of filtered spectra through the cofiber-of-$\tau$ formalism of Burklund-Isaksen-Pstragowski-Wang-Xu. In this framework, we define and analyze hidden extensions along arbitrary maps of filtered spectra, establishing computational principles that extend the generalized Leibniz rule and the generalized Mahowald trick of Lin-Wang-Xu, as well as Burklund's Leibniz rule for total differentials, from the Adams spectral sequence to this broader setup. Our formulation uses a more refined, layered notion of extension, which slightly sharpens these statements even for the Adams spectral sequence. As an application, we study equivariant slice spectral sequences and obtain new families of "exotic transfer" differentials in the $C_4$-slice spectral sequences for the Hill-Hopkins-Ravenel theories $\mathrm{BP}^{((C_4))}\langle m\rangle$ for every $m \ge 1$.
toXiv_bot_toot

@arXiv_mathAT_bot@mastoxiv.page
2026-06-03 07:36:20

A structural reduction for the symmetric hit problem in four variables
Dang Vo Phuc
arxiv.org/abs/2606.02626 arxiv.org/pdf/2606.02626 arxiv.org/html/2606.02626
arXiv:2606.02626v1 Announce Type: new
Abstract: Let $\mathcal{A}$ be the mod $2$ Steenrod algebra, and $P(n) = \mathbb{F}_2[x_1, \dots, x_n]$ be the polynomial algebra viewed as an unstable module over $\mathcal{A}$. The symmetric hit conjecture asks whether the symmetrization of a hit monomial in $P(n)$ is always hit in the symmetric invariant subalgebra $B(n) = P(n)^{\Sigma_n}$. While resolved for $n \leq 3$, the case $n=4$ presents significant obstructions due to combinatorial complexity, orbit cancellations intrinsically tied to $\Sigma_4$-stabilizers, and the emergence of strongly spike-free survivor modules. This paper introduces a conditional structural reduction to overcome these obstructions in the domain where the numerical weight satisfies $\mu(d) \leq 4$. By integrating Walker-Wood duality with a new $\Sigma_4$-stabilizer parity analysis, we reduce the global conjecture to localized algebraic conditions: a symmetric lower-spike reduction and a strengthened four-row digital-engineering hypothesis. Assuming these inputs, the conjecture follows by lexicographic induction on the column-sum and row-sum sequences of the binary exponent matrices.
Our approach isolates the four-variable repeated-row anomaly into exact local identities, utilizing global Steenrod-kernel functionals lifted from local spike-free quotients to detect potential survivor elements. Finally, we provide explicit monomial-level computations in degrees $8$, $12$, and $14$, explicitly illustrating the stabilizer mechanism in practice and framing the precise algebraic identities required for a future unconditional proof.
toXiv_bot_toot

@arXiv_mathAT_bot@mastoxiv.page
2026-06-03 07:34:23

[2026-06-03 Wed (UTC), 5 new articles found for math.AT Algebraic Topology]
toXiv_bot_toot