Tootfinder

Dilogarithm identities of higher degree and cluster $a$-variable periodicity
Zachary Nash, Dylan Rupel
https://arxiv.org/abs/2507.10555 https://

Dilogarithm identities of higher degree and cluster $a$-variable periodicity
We use the periodicities of cluster groupoid mutations established by Li and the second author to prove that the dilogarithm identities of higher degree obtained by Nakanishi follow from the classical dilogarithm identities associated to a periodicity of cluster mutations when the exchange matrix is full rank.

Analytic Dilogarithm Identities
Cetin Hakimoglu
https://arxiv.org/abs/2506.10206 https://arxiv.org/pdf/2506.10206

Analytic Dilogarithm Identities
By showing that the ratio of two beta-like integrals equals an integer, new Dilogarithm identities are derived, as well as analytic proofs to conjectured identities. New, non-trivial 2-term and ladder-like Dilogarithm identities are derived about ${Q}[\sqrt{2}]$, ${Q}[\sqrt{5}]$, ${Q}[\sqrt{-7}]$, and ${Q}[\sqrt{3}]$, . This also leads also to a connection between identities ${Q}[\sqrt{13}]$ and ${Q}[\sqrt{3}]$. Single-term and two-term complex Dilogarithm identities are derived, in addition to…

ICE Lawyers Are Hiding Their Names in Immigration Court #fascism

ICE Lawyers Are Hiding Their Names in Immigration Court
ICE attorneys fighting to deport immigrants are able to obscure their identities — no masks required.

fresh_webs: Freshwater stream webs
A set of 26 networks of trophic-level species interactions in streams in New Zealand, Maine and North Carolina. Networks include the identities of aquatic insect, algae and fish species and their trophic interactions. Excel and plain text adjacency matrices available; webs can be downloaded individually or as a group.
This network has 110 nodes and 718 edges.
Tags: Biological, Food web, Unweighted, Metadata

New Polynomial Identities and Some Consequences
Kunle Adegoke
https://arxiv.org/abs/2506.06617 https://arxiv.org/pdf/2506.06617

New Polynomial Identities and Some Consequences
Using an elementary approach involving the Euler Beta function and the binomial theorem, we derive two polynomial identities; one of which is a generalization of a known polynomial identity. Two well-known combinatorial identities, namely Frisch's identity and Klamkin's identity, appear as immediate consequences of the polynomial identities. We subsequently establish several combinatorial identities, including a generalization of each of Frisch's identity and Klamkin's identity. Finally, we dev…

Critical Ising correlations on a torus
Baran Bayraktaroglu, Konstantin Izyurov
https://arxiv.org/abs/2506.11324 https://arxiv.org/pdf…

Critical Ising correlations on a torus
We prove convergence of multi-point spin correlations in the critical Ising model on a torus. Via Pfaffian identities, this also implies convergence of other correlations, including correlations of spins with fermionic and energy observables. We obtain explicit formulae for the scaling limits in terms of theta functions, verifying the predictions in the physics literature.

Soft Photon, Gluon and Graviton Theorems in (A)dS from Conformal Invariance
Jiajie Mei, Yuyu Mo
https://arxiv.org/abs/2506.11766 https://

Soft Photon, Gluon and Graviton Theorems in (A)dS from Conformal Invariance
We present new soft theorems for photon, gluon, and graviton correlators at tree level in (Anti)-de Sitter space. The results are derived by applying conformal Ward identities to constrain the structure of Witten diagrams.

Pohozaev-type identities for classes of quasilinear elliptic local and nonlocal equations and systems, with applications
Gurdev Chand Anthal, Prashanta Garain
https://arxiv.org/abs/2506.08667

Pohozaev-type identities for classes of quasilinear elliptic local and nonlocal equations and systems, with applications
In this article, we establish Pohozaev-type identities for a class of quasilinear elliptic equations and systems involving both local and nonlocal $p$-Laplace operators. Specifically, we obtain these identities in $\mathbb{R}^n$ for the purely anisotropic $p$-Laplace equations, the purely fractional $p$-Laplace equations, as well as for equations that incorporate both anisotropic and fractional $p$-Laplace features. We also extend these results to the corresponding systems. To the best of our k…

The self is not singular but a fluid network of identities | Aeon Essays https://aeon.co/essays/the-self-is-not-singular-but-a-fluid-network-of-identities

The self is not singular but a fluid network of identities | Aeon Essays
You cannot be reduced to a body, a mind or a particular social role. An emerging theory of selfhood gets this complexity

fresh_webs: Freshwater stream webs
A set of 26 networks of trophic-level species interactions in streams in New Zealand, Maine and North Carolina. Networks include the identities of aquatic insect, algae and fish species and their trophic interactions. Excel and plain text adjacency matrices available; webs can be downloaded individually or as a group.
This network has 105 nodes and 343 edges.
Tags: Biological, Food web, Unweighted, Metadata

The combinatorics of partition identities in Andrews and Bachraoui's paper
Haijun Li
https://arxiv.org/abs/2506.06640 https://arx…

The combinatorics of partition identities in Andrews and Bachraoui's paper
Recently, Andrews and Bachraoui discovered several companions for some famous $q$-series formulas, and derived some now identities involving partitions and overpartitions. In this paper, we shall refine their partial results by the number of parts of partitions and furthermore, we also give the combinatorial proofs for those identities.

Nonequilibrium fluctuation-response relations for state-current correlations
Krzysztof Ptaszynski, Timur Aslyamov, Massimiliano Esposito
https://arxiv.org/abs/2506.08877

Nonequilibrium fluctuation-response relations for state-current correlations
Recently, novel exact identities known as Fluctuation-Response Relations (FRRs) have been derived for nonequilibrium steady states of Markov jump processes. These identities link the fluctuations of state or current observables to a combination of responses of these observables to perturbations of transition rates. Here, we complement these results by deriving analogous FRRs applicable to mixed covariances of one state and one current observable. We further derive novel Inverse FRRs expressing …

A potential-theoretic approach to optimal stopping in a spectrally L\'evy Model
Masahiko Egami, Tomohiro Koike
https://arxiv.org/abs/2506.10538 https:/…

A potential-theoretic approach to optimal stopping in a spectrally Lévy Model
We present a systematic solution method for optimal stopping problem of one-dimensional spectrally negative Lévy processes. Our main tools are based on potential theory, particularly the Riesz decomposition and the maximum principle. This novel approach allows us to handle a broad class of reward functions. That is, we solve the problem in a general setup without relying on specific form of the reward function or on the fluctuation identities. We provide a step-by-step solution procedure, whic…

See @… this is the book about Olivetti visual identity and such things I mentioned during lunch: https://www.triest-verlag.ch/en/produkte/b

Olivetti Identities

fresh_webs: Freshwater stream webs
A set of 26 networks of trophic-level species interactions in streams in New Zealand, Maine and North Carolina. Networks include the identities of aquatic insect, algae and fish species and their trophic interactions. Excel and plain text adjacency matrices available; webs can be downloaded individually or as a group.
This network has 71 nodes and 155 edges.
Tags: Biological, Food web, Unweighted, Metadata

Ryan Flynn’s documentary “You’re No Indian”, about
"tribal disenrollment",
the controversial practice of removing Indigenous people from tribal roles, will debut at the "Dances With Films Festival" on June 28.
In the film, Flynn explores how tribal disenrollment has stripped over 11,000 Native American people of their tribal membership,
thereby erasing their identities, rights and connections to their communities.
Fueled by casino profits, p…

'You’re No Indian' Doc Exposes Tribal Disenrollment
You’re No Indian' Doc that Exposes the Human Rights Crisis Behind Tribal Disenrollment to Debut at Dances With Films

The Treasury’s Office of Foreign Assets Control (OFAC) sanctioned Song Kum Hyok (Song), a malicious cyber actor associated with the sanctioned Democratic People’s Republic of Korea (DPRK) Reconnaissance General Bureau (RGB) hacking group Andariel.
https://home.treasury.gov/news/press-rel…

Sanctions Imposed on DPRK IT Workers Generating Revenue for the Kim Regime
WASHINGTON — Today, the U.S. Department of the Treasury’s Office of Foreign Assets Control (OFAC) sanctioned Song Kum Hyok, (Song), a malicious cyber actor associated with the sanctioned Democratic People’s Republic of Korea (DPRK) Reconnaissance General Bureau (RGB) hacking group Andariel.Song facilitated an information technology (IT) worker scheme in which individuals, often DPRK nationals working from countries such as China and Russia, were recruited and provided with falsified ident…

I've been thinking a lot lately about how porous our identities are: how we are shaped by every experience, person, bit of information.
How this shaping means losing parts of ourselves...or at least who we would have been without external influences.
It brought to mind a piece I wrote about the drive to retrieve, catalogue & preserve a sense of self amidst this loss of #identity

Recollecting Hailey
I’m trying to capture myself. I can feel myself disintegrating. I feel my atoms dispersed. I am disappearing.

Algebraic identities to prove that a neat finite free algebra is tracically \'etale
Claude Quitt\'e, Henri Lombardi
https://arxiv.org/abs/2506.03851

Algebraic identities to prove that a neat finite free algebra is tracically étale
The central objective of this article is to provide an elementary proof of the following theorem, of which we are unaware of any trace in the existing literature. If $B$ is a net finite free algebra over a commutative ring $A$, then it is tracically étale (its trace form is nondegenerate) and a fortiori étale over A. As indicated in the title, our proof is based on algebraic identities. This confirms the implicit adage that much of the most abstract commutative algebra is concentrated in alge…

The idol, the butcher: Expanding gap in attitudes toward Stalin reflects Ukraine and Russia's diverging identities - Euromaidan Press
https://euromaidanpress.com/2025/06/21/the-idol-the-butcher-expanding-gap-in-attitudes-toward-stalin-reflects-ukraine-and-russias-diverging-identities/

The existence and uniqueness of Hashiguchi connection in KG-approach
S. G. Elgendi, A. Soleiman
https://arxiv.org/abs/2506.09739 https://

The existence and uniqueness of Hashiguchi connection in KG-approach
In this study, we treat intrinsic Finsler geometry using the Klein-Grifone approach (KG-approach). A uniqueness and existence theorem for the Hashiguchi connection on a Finsler manifold is investigated intrinsically (in coordinate-free fashion). Calculations are made for the Hashiguchi connection's torsion and curvature tensors. Some properties are examined, together with the Bianchi identities of the associated curvature and torsion tensors. An overview of the four fundamental linear connectio…

Fast Ramanujan-type Series for Logarithms. Part I
Jorge Zuniga
https://arxiv.org/abs/2506.08245 https://arxiv.org/pdf/2506.08245

Fast Ramanujan-type Series for Logarithms. Part I
This report introduces new series and variations of some hypergeometric type identities for fast computing of logarithms $\log\,p$ for small positive integers $p$. These series were found using Wilf Zeilberger (WZ) method and/or integer detection algorithms (LLL) providing highly efficient linearly convergent rational approximants for these constants. Some of the new identities are of $_4F_3$ type, but higher ones are found as well and hypergeometric series for log p, with variable p, have been…

This https://arxiv.org/abs/2412.00040 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A Short Proof of Knuth's Old Sum
We give a short proof of the well-known Knuth's old sum and provide some generalizations. Our approach utilizes the binomial theorem and integration formulas derived using the Beta function. Several new polynomial identities and combinatorial identities are derived.

Super Kawaii Vocalics: Amplifying the "Cute" Factor in Computer Voice
Yuto Mandai, Katie Seaborn, Tomoyasu Nakano, Xin Sun, Yijia Wang, Jun Kato
https://arxiv.org/abs/2507.06235

Super Kawaii Vocalics: Amplifying the "Cute" Factor in Computer Voice
"Kawaii" is the Japanese concept of cute, which carries sociocultural connotations related to social identities and emotional responses. Yet, virtually all work to date has focused on the visual side of kawaii, including in studies of computer agents and social robots. In pursuit of formalizing the new science of kawaii vocalics, we explored what elements of voice relate to kawaii and how they might be manipulated, manually and automatically. We conducted a four-phase study (grand N = 512) with…

Self-Supervised Real-Time Tracking of Military Vehicles in Low-FPS UAV Footage
Markiyan Kostiv, Anatolii Adamovskyi, Yevhen Cherniavskyi, Mykyta Varenyk, Ostap Viniavskyi, Igor Krashenyi, Oles Dobosevych
https://arxiv.org/abs/2507.05229

Self-Supervised Real-Time Tracking of Military Vehicles in Low-FPS UAV Footage
Multi-object tracking (MOT) aims to maintain consistent identities of objects across video frames. Associating objects in low-frame-rate videos captured by moving unmanned aerial vehicles (UAVs) in actual combat scenarios is complex due to rapid changes in object appearance and position within the frame. The task becomes even more challenging due to image degradation caused by cloud video streaming and compression algorithms. We present how instance association learning from single-frame annota…

Earlier this semester I joined "Remnants of Resistance," a podcast by colleagues in CSUN's library and Queer Studies faculty, to talk genetics and queer identity
#LGBTQ #genetics #evolution

This https://arxiv.org/abs/2404.19431 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csIT_…

Toward Practical and Theoretical Integration of Sensing and Communication in URA Systems
This work addresses the problem of integrated sensing and communications (ISAC) involving a massive number of unsourced and uncoordinated users. In the proposed model, known as the unsourced ISAC system (UNISAC), all active communication and sensing users simultaneously share a short frame to transmit their signals without requiring scheduling by the base station or the need to announce their identities. Consequently, the received signal from each user is heavily affected by interference from n…

#supervillainabookorplay
#HashtagGames
"Much Ado About Ultron"
Witty banter, mistaken identities, and one AI bent on human extinction.
Shakespeare would love it.

Campaigning through the lens of Google: A large-scale algorithm audit of Google searches in the run-up to the Swiss Federal Elections 2023
Tobias Rohrbach, Mykola Makhortykh, Maryna Sydorova
https://arxiv.org/abs/2507.06018

Campaigning through the lens of Google: A large-scale algorithm audit of Google searches in the run-up to the Swiss Federal Elections 2023
Search engines like Google have become major sources of information for voters during election campaigns. To assess potential biases across candidates' gender and partisan identities in the algorithmic curation of candidate information, we conducted a large-scale algorithm audit analyzing Google's selection and ranking of information about candidates for the 2023 Swiss Federal Elections, three and one week before the election day. Results indicate that text searches prioritize media sources in …

Denmark plans to clamp down on AI-generated deepfakes by changing copyright law to give its citizens rights to their own body, facial features, and voice (Miranda Bryant/The Guardian)
https://www.theguardian.com/technology/202

Ami·es journalistes : saviez-vous que vous pouvez trahir vos sources par l'utilisation d'une messagerie chiffrée protégeant mal votre graph social (c'est-Š-dire "qui parle Š qui") ?
Avec la complicité des États-Unis (pour Signal et Matrix) ou de la France (pour Olvid), c'est pourtant le cas.
Pour en savoir plus, je donne une conférence sur la protection des métadonnées par les messageries chiffrées Š @…

What Really Drives Thermopower: Specific Heat or Entropy as the Unifying Principle Across Magnetic, Superconducting, and Nanoscale Systems
Morteza Jazandari, Jahanfar Abouie, Daryoosh Vashaee
https://arxiv.org/abs/2506.06745

What Really Drives Thermopower: Specific Heat or Entropy as the Unifying Principle Across Magnetic, Superconducting, and Nanoscale Systems
Thermopower, a key parameter in thermoelectric performance, is often linked to either specific heat or entropy, yet the fundamental quantity that governs it has remained elusive. In this work, we present a unified theoretical framework that identifies entropy per carrier, not specific heat, as the universal driver of thermopower across both closed and open systems. Using thermodynamic identities and the Onsager-Kelvin relation, we show that thermopower is universally proportional to entropy per…

Called my state rep & senator & now calling US Rep & Senators. Telling them:
1) no law enforcement should conceal identities & affiliation; uniforms, names & faces must be known (no ice disguises).
2) no 287(g) deals between local law enforcement & ice; federal law enforcement should not be done by local leos.
3) US should not wage war on iran, the War Powers Act must stop potus' military adventurism.
4) big bad bill must not pass for re…

:heart_trans: #TransRightsAreHumanRights :heart_trans:

Trigonometric Ratios Can Prove the Pythagorean Theorem
Shoya Kise, Takesa Uehara, Takashi Shinzato
https://arxiv.org/abs/2506.06304 https://

Trigonometric Ratios Can Prove the Pythagorean Theorem
Recent interest in noncircular trigonometric proofs has underscored the need for alternative methodologies. Jackson and Johnson's 2024 study addresses a longstanding gap in the foundations of trigonometric proofs. Inspired by the work of Jackson and Johnson [JJ24], we present three noncircular proofs of the Pythagorean theorem based on trigonometric identities. First, we establish the Pythagorean theorem via an isosceles triangle construction and the tangent double-angle formula. Second, we pre…

Wild wall-crossing and symmetric quivers in 4d and 3d $\mathcal{N}=2$ field theories
Daniel Bryan, Piotr Su{\l}kowski
https://arxiv.org/abs/2506.09972 http…

Wild wall-crossing and symmetric quivers in 4d and 3d $\mathcal{N}=2$ field theories
We reformulate Kontsevich-Soibelman wall-crossing formulae for 4d $\mathcal{N}=2$ class $\mathcal{S}$ theories and corresponding BPS quivers, including those of wild type, as identities for generating series of symmetric quivers that represent dualities of 3d $\mathcal{N}=2$ boundary theories. We identify such symmetric quivers for both sides of the wall-crossing formulae. In the finite chamber such a quiver is captured by the symmetrized BPS quiver, whereas on the other side of the wall we fin…

This https://arxiv.org/abs/2405.02430 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csSC_…

How to generate all possible rational Wilf-Zeilberger forms?
Wilf-Zeilberger pairs are fundamental in the algorithmic theory of Wilf and Zeilberger for computer-generated proofs of combinatorial identities. Wilf-Zeilberger forms are their high-dimensional generalizations, which can be used for proving and discovering convergence acceleration formulas. This paper presents a structural description of all possible rational such forms, which can be viewed as an additive analog of the classical Ore-Sato theorem. Based on this analog, we show a structural deco…

Fast Ramanujan--type Series for Logarithms. Part II
Jorge Zuniga
https://arxiv.org/abs/2506.10321 https://arxiv.org/pdf/2506.10321

Fast Ramanujan--type Series for Logarithms. Part II
This work extends the results of the preprint Ramanujan type Series for Logarithms, Part I, arXiv:2506.08245, which introduced single hypergeometric type identities for the efficient computing of $\log(p)$, where $p\in\mathbb{Z}_{>1}$. We present novel formulas for arctangents and methods for a very fast multiseries evaluation of logarithms. Building upon a $\mathcal{O}((p-1)^{6})$ Ramanujan type series asymptotic approximation for $\log(p)$ as $p\rightarrow1$, formulas for computing $n$ simult…

Replaced article(s) found for physics.bio-ph. https://arxiv.org/list/physics.bio-ph/new
[1/1]:
- Nonlinear Response Identities and Bounds for Nonequilibrium Steady States
Ruicheng Bao, Shiling Liang

The U.S. military B-2 Spirit bomber pilots and crew involved with the coordinated strikes on Iran's nuclear facilities last month have been invited to attend a July 4 celebration at the White House
-- but it's not clear what measures have been taken to protect their identities.
The White House confirmed to Military.com that those involved in the mission, dubbed Operation Midnight Hammer, were invited to the White House's July 4 celebration.
It follows comments mad…

Pilots Who Conducted Iran Strikes Invited to White House on July 4, Raising Security Concerns
The B-2 Spirit bomber pilots and crew involved with the strikes on Iran's nuclear facilities last month have been invited to attend a July 4 celebration at the White House, but it's not clear what measures have been taken to protect their identities.

Denmark plans to clamp down on AI-generated deepfakes by changing copyright law to give its citizens rights to their own body, facial features, and voice (Miranda Bryant/The Guardian)
https://www.theguardian.com/technology/202

This https://arxiv.org/abs/2405.15049 has been replaced.
initial toot: https://mastoxiv.page/@arXi…

Breaking Barriers: Investigating Gender Dynamics in Introductory Physics Lab Classes
The persistent underrepresentation of women and other gender minorities in physical science fields has been an ongoing concern. This study investigates gender dynamics in introductory physics laboratory courses, focusing on whether students of different gender identities exhibit equal inclination and confidence in conducting lab experiments, and whether they face barriers that impact their participation. Conducted across three institutions and involving non-physics STEM students enrolled in alg…

TL;DR Amazon's SES in sandbox mode only sends to validated addresses and identities defined in the configuration.
https://winkelwagen.de/2025/05/29/aws-ses-message-rejected-email-address-is-not-verified/

AWS SES Message rejected: Email address is not verified.
I configured one of our Magento 2 stage instances today to use Amazon SES to send emails instead of dumping them into mailhog. But I got the following error: Message rejected: Email address is not …

MoDA: Multi-modal Diffusion Architecture for Talking Head Generation
Xinyang Li, Gen Li, Zhihui Lin, Yichen Qian, GongXin Yao, Weinan Jia, Weihua Chen, Fan Wang
https://arxiv.org/abs/2507.03256

MoDA: Multi-modal Diffusion Architecture for Talking Head Generation
Talking head generation with arbitrary identities and speech audio remains a crucial problem in the realm of digital humans and the virtual metaverse. Recently, diffusion models have become a popular generative technique in this field with their strong generation and generalization capabilities. However, several challenges remain for diffusion-based methods: 1) inefficient inference and visual artifacts, which arise from the implicit latent space of Variational Auto-Encoders (VAE), complicating…

#CFP: AAR-Southeast Conference Theme: Shifting Identities and Fractured Communities
https://ift.tt/ovKT4YF
The Call for Papers for the 2026 Meeting is live! Submissions due October 1, 2025
via Input 4 RELCFP …

#CFP: AAR-Southeast Conference Theme: Shifting Identities and Fractured Communities
The Call for Papers for the 2026 Meeting is live! Submissions due October 1, 2025

Some $q$-transformation formulas and Rogers-Ramanujan type identities
Chang Xu, Dunkun Yang
https://arxiv.org/abs/2506.16711 https://…

Some $q$-transformation formulas and Rogers-Ramanujan type identities
In this paper, we explore the role that Liu's transformation formula can play in discovering Rogers-Ramanujan type identities. Specifically, we combine Liu's transformation formula with other $q$-series summations to derive a series of parameterized identities. Thereafter, through careful selection of these parameters, we obtain $75$ Rogers-Ramanujan type identities from Slater's list, and uncover several new Rogers-Ramanujan type identities.

"Denmark to tackle deepfakes by giving people copyright to their own features"
https://www.theguardian.com/technology/2025/jun/27/deepfakes-denmark-copyright-law-artificial-intelligence

Cauchy identities for genus 2 Schur polynomials
S. Arthamonov, Sh. Shakirov, W. Yan
https://arxiv.org/abs/2506.18338 https://arxiv.or…

Cauchy identities for genus 2 Schur polynomials
Genus 2 Macdonald polynomials $Ψ^{(q,t)}_{j_1,j_2,j_3}$ generalize ordinary Macdonald polynomials in several aspects. First, they provide common eigenfunctions for commuting difference operators that generalize the Macdonald difference operators of type $A_1$. Second, the algebra generated by these difference operators together with multiplication operators admits an action of genus 2 mapping class group (MCG) that generalizes the well-known action of $SL(2,{\mathbb Z})$ for ordinary Macdonald…

An energy-stable parametric finite element method for the Willmore flow in three dimensions
Weizhu Bao, Yifei Li, Dongmin Wang
https://arxiv.org/abs/2506.21025

An energy-stable parametric finite element method for the Willmore flow in three dimensions
This work develops novel energy-stable parametric finite element methods (ES-PFEM) for the Willmore flow and curvature-dependent geometric gradient flows of surfaces in three dimensions. The key to achieving the energy stability lies in the use of two novel geometric identities: (i) a reformulated variational form of the normal velocity field, and (ii) incorporation of the temporal evolution of the mean curvature into the governing equations. These identities enable the derivation of a new vari…

Transaction Proximity: A Graph-Based Approach to Blockchain Fraud Prevention
Gordon Y. Liao, Ziming Zeng, Mira Belenkiy, Jacob Hirshman
https://arxiv.org/abs/2505.24284

Transaction Proximity: A Graph-Based Approach to Blockchain Fraud Prevention
This paper introduces a fraud-deterrent access validation system for public blockchains, leveraging two complementary concepts: "Transaction Proximity", which measures the distance between wallets in the transaction graph, and "Easily Attainable Identities (EAIs)", wallets with direct transaction connections to centralized exchanges. Recognizing the limitations of traditional approaches like blocklisting (reactive, slow) and strict allow listing (privacy-invasive, adoption barriers), we propose…

The geometric bookkeeping guide to Feynman integral reduction and $\varepsilon$-factorised differential equations
Iris Bree, Federico Gasparotto, Antonela Matija\v{s}i\'c, Pouria Mazloumi, Dmytro Melnichenko, Sebastian P\"ogel, Toni Teschke, Xing Wang, Stefan Weinzierl, Konglong Wu, Xiaofeng Xu
https://arxiv.org/abs/250…

The geometric bookkeeping guide to Feynman integral reduction and $\varepsilon$-factorised differential equations
We report on three improvements in the context of Feynman integral reduction and $\varepsilon$-factorised differential equations: Firstly, we show that with a specific choice of prefactors, we trivialise the $\varepsilon$-dependence of the integration-by-parts identities. Secondly, we observe that with a specific choice of order relation in the Laporta algorithm, we directly obtain a basis of master integrals, whose differential equation on the maximal cut is in Laurent polynomial form with res…

Indefinite theta functions arising from affine Lie superalgebras and sums of triangular numbers
Toshiki Matsusaka, Miyu Suzuki
https://arxiv.org/abs/2506.04722

Indefinite theta functions arising from affine Lie superalgebras and sums of triangular numbers
We extend the recently developed theory of Roehrig and Zwegers on indefinite theta functions to prove certain power series are modular forms. As a consequence, we obtain several power series identities for powers of the generating function of triangular numbers. We also show that these identities arise as specializations of denominator identities of affine Lie superalgebras.

Orthogonality of polar Legendre polynomials and approximation
Abdelhamid Rehouma
https://arxiv.org/abs/2506.04918 https://arxiv.org/p…

Orthogonality of polar Legendre polynomials and approximation
Let $\{Q_{n}(x)\}$ be a system of integral Legendre polynomials of degree exactly n,and let $\{P_{n}(x)\}$ be polar polynomials primitives of integral Legendre polynomials. We derive some identities and relations and extremal problems and minimization involving of polar integral Legendre polynomials.

CALICO: Computing Annihilators from Linear Identities Constraining (differential) Operators
Giuseppe Bertolini, Gaia Fontana, Tiziano Peraro
https://arxiv.org/abs/2506.13653

CALICO: Computing Annihilators from Linear Identities Constraining (differential) Operators
We elaborate on the method of parametric annihilators for deriving integral relations. Parametric annihilators are differential operators that annihilate multivalued integration kernels appearing in suitable integral representations of special functions. We illustrate this approach in a way that applies to a broad variety of integral representations. We describe a method for computing parametric annihilators based on efficient linear solvers and use them to derive relations between a wide class…

The class of congruence meet semidistributive varieties is not strong Maltsev
Andrew Moorhead
https://arxiv.org/abs/2506.07881 https://

The class of congruence meet semidistributive varieties is not strong Maltsev
We present a proof that there is no single finite package of identities which characterizes the class of congruence meet semidistributive varieties.

Congresswoman Nydia Velšzquez on Saturday held a rally outside a U.S. Immigration and Customs Enforcement field office in New York City to promote her recently introduced "No Masks for ICE Act".
“We would never accept it if the NYPD operated in masks without names or badges
— and we shouldn’t accept it from ICE either,”
Velšzquez (D-N.Y.) said in a statement, referring to the New York Police Department.
“When agents hide their faces and identities they creat…

Velázquez Leads 'No Masks for ICE Act' Rally at NYC Field Office | Common Dreams
"When agents hide their faces and identities they create chaos, fear, and open the door to abuse. Immigrant communities are left wondering if they're being arrested or kidnapped."

The Danish government will clamp down on the creation and dissemination of AI-generated deepfakes by changing copyright law to ensure that everybody has the right to their own body, facial features and voice.
https://www.theguardian.com/technology/202

"America Is Becoming the World’s Largest Tax Haven"
By Joseph E. Stiglitz
https://rooseveltinstitute.org/blog/largest-tax-haven/

NourID : A Digital Energy Identity Framework for Efficient Subsidy Allocation in Morocco
Fatima Zahra Iguenfer, Younes Lamhamedi Cherradi, Nada Belkhayat, Hiba Jebbar
https://arxiv.org/abs/2507.04424

NourID+: A Digital Energy Identity Framework for Efficient Subsidy Allocation in Morocco
We introduce NourID+, a digital energy identity framework that addresses Morocco's need for trusted energy subsidy allocation through authenticated digital identity integration. NourID+ creates a strong foundation for future subsidy programs by unifying three government-issued and digitalized credentials: Moroccan national identity cards (CIN), cadastral plans, and property ownership certificates are transformed into unique digital energy IDs (DE-IDs) that map authenticated identities with spec…

Ramanujan's partition generating functions modulo $\ell$
Kathrin Bringmann, William Craig, Ken Ono
https://arxiv.org/abs/2506.06101 https://

Ramanujan's partition generating functions modulo $\ell$
For the partition function $p(n)$, Ramanujan proved the striking identities $$ P_5(q):=\sum_{n\geq 0} p(5n+4)q^n =5\prod_{n\geq 1} \frac{\left(q^5;q^5\right)_{\infty}^5}{(q;q)_{\infty}^6}, $$ $$ P_7(q):=\sum_{n\geq 0} p(7n+5)q^n =7\prod_{n\geq 1}\frac{\left(q^7;q^7\right)_{\infty}^3}{(q;q)_{\infty}^4}+49q \prod_{n\geq 1}\frac{\left(q^7;q^7\right)_{\infty}^7}{(q;q)_{\infty}^8}, $$ where $(q;q)_{\infty}:=\prod_{n\geq 1}(1-q^n).$ As these identities imply his celebrated congruences modulo 5 …

Replaced article(s) found for cs.DM. https://arxiv.org/list/cs.DM/new
[1/1]:
- Distribution of codewords on the faces of a hypercube and new combinatorial identities
Jamolidin K. Abdurakhmanov

Being autistic, I have to keep telling myself, "Yes, being gender-fluid is valid, and Norway lets me be who I am," just to really accept myself. 🏳️‍⚧️🇳🇴
https://en.wikipedia.org/wiki/Gender_fluidity

An Addendum to Plouffe's Ramanujan Identities
Segun Olofin Akerele
https://arxiv.org/abs/2507.00040 https://arxiv.org/pdf/2507.00…

An Addendum to Plouffe's Ramanujan Identities
We introduce a new class of polylogarithm sums closely related to a family studied by L. Vepštas in 2010. These generalized sums depend on two free parameters and yield closed-form expressions involving the Dirichlet eta function. Additionally, we present an alternative proof for a hyperbolic sum originally discussed by Ramanujan.

Wavelet based solutions to the Poisson and the Helmholtz equations on the $n$-dimensional unit sphere
Ilona Iglewska-Nowak, Piotr Stefaniak
https://arxiv.org/abs/2507.03451

Wavelet based solutions to the Poisson and the Helmholtz equations on the $n$-dimensional unit sphere
We present a method of solving partial differential equations on the $n$-dimensional unit sphere using methods based on the continuous wavelet transform derived from approximate identities. We give an explicit analytical solution to the Poisson equation and to the Helmholtz equations. For the first one and for some special values of the parameter in the latter one, we derive a closed formula for the generalized Green function.

#ai

Dissecting Circles to Prove a Square: A Novel Geometric Proof of the Pythagorean Theorem Using Circular Segments and Area Decomposition
Luca Nathanael Chang
https://arxiv.org/abs/2507.02896

Dissecting Circles to Prove a Square: A Novel Geometric Proof of the Pythagorean Theorem Using Circular Segments and Area Decomposition
The Pythagorean Theorem has been proved in hundreds of ways, yet it inspires fresh insights through geometry and trigonometry. In this paper, we offer a new proof based on three circles that circumscribe the sides of a right triangle. Rather than invoke coordinate geometry, the argument relies purely on classical Euclidean constructions, trigonometric identities independent of the theorem itself, and a careful analysis of the areas of circular segments. The key idea is to evaluate the area of…

This https://arxiv.org/abs/2505.09918 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_nli…

Classical integrable spin chains of Landau-Lifshitz type from R-matrix identities
We describe a family of 1+1 classical integrable space-discrete models of the Landau-Lifshitz type through the usage of ansatz for $U$-$V$ (Lax) pair with spectral parameter satisfying the semi-discrete Zakharov-Shabat equation. The ansatz for $U$-$V$ pair is based on $R$-matrices satisfying the associative Yang-Baxter equation and certain additional properties. Equations of motion are obtained using a set of $R$-matrix identities. In the continuous limit we reproduce the previously known famil…

psi: Plant Photosystem I excitation energy transfer network (2020)
Weighted directed network of the light-harvesting Photosystem Ι (PSI) of the plant Pisum sativum. The nodes represent chromophores with different identities (i.e. chlorophyll a, chlorophyll b, β-carotene and derivates, lutein, violaxanthin), while edges represent FRET transfer between chromophores. The link directionality connecting nodes in the PSI network depends on the energy levels of the connected chromophores. The…

Two $2/5$-level mock theta conjecture-like identities
Stepan Konenkov, Eric T. Mortenson
https://arxiv.org/abs/2506.01886 https://arx…

Two $2/5$-level mock theta conjecture-like identities
Determining the explicit forms and modularity for string functions and branching coefficients for Kac--Moody algebras after Kac, Peterson, and Wakimoto is an important problem. In a pair of papers, Borozenets and Mortenson determined the explicit forms for fractional-level string functions for the Kac--Moody algebra $A_{1}^{(1)}$. For positive fractional-level string functions they obtained mock theta conjecture-like identities, and for negative fractional-level string functions, they obtained …

Some wear balaclavas. Some wearneck gators, sunglasses and hats. Some wear masks and casual clothes.
Across the country, armed federal immigration officers have increasingly hidden their identities while carrying out immigration raids, arresting protesters and roughing upprominent Democratic critics.
It’s a trend that has sparked alarm among civil rights and law enforcement experts alike.
Mike German, a former FBIagent, said officers’ widespread use of masks was unprecedent…

This https://arxiv.org/abs/2503.22664 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Identities of relatively free algebras of Lie nilpotent associative algebras
In this paper, we consider the relatively free algebra of rank $n$, $F_n(\mathfrak{N}_p)$, in the variety of Lie nilpotent associative algebras of index $p$, denoted by $\mathfrak{N}_p$, over a field of characteristic zero. We describe an explicit minimal basis for the polynomial identities of $F_n(\mathfrak{N}_p)$ when $p=3$ and $p=4$, for all $n$, except for $F_3(\mathfrak{N}_4)$. In the general case, we exhibit a lower and an upper bound for the minimal $k$ such that $[x_1,x_2]\cdots[x_{2k-1…

This https://arxiv.org/abs/2409.16330 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On certain $q$-multiple sums
We present outlines of a general method to reach certain kinds of $q$-multiple sum identities. Throughout our exposition, we shall give generalizations to the results given by Dilcher, Prodinger, Fu and Lascoux, Zeng, and Guo and Zhang concerning $q$-series identities related to divisor functions. Our exposition shall also provide a generalization of the duality relation for finite multiple harmonic $q$-series given by Bradley. Utilizing these generalizations, we will also arrive at some new in…

Argyres-Douglas Theories, Macdonald Indices and Arc Space of Zhu Algebra
George Andrews, Anindya Banerjee, Chinmaya Bhargava, Ranveer Kumar Singh, Runkai Tao
https://arxiv.org/abs/2507.06294

Argyres-Douglas Theories, Macdonald Indices and Arc Space of Zhu Algebra
In this paper, we relate the MacDonald index of a 4d $\mathcal{N}=2$ SCFT with the Hilbert series of the arc space of the Zhu algebra of the corresponding Schur VOA. Using this, we conjecture a simple formula for the MacDonald index of $(A_1,D_{2n+1})$ Argyres-Douglas theory. We perform checks of the formula against the known Schur limits and RG flows. To match the Schur limit, we prove new $q$-series identities.

Stability and rigidity results of space-like hypersurface in the Minkowski space
Jianhua Chen, Haiyun Deng, Haiqin Xie, Jiabin Yin
https://arxiv.org/abs/2506.01012

Stability and rigidity results of space-like hypersurface in the Minkowski space
In this paper, we establish some rigidity theorems for space-like hypersurfaces in Minkowski space by using a Weinberger-type approach with P-functions and integral identities. Firstly, for space-like hypersurfaces $M$ represented as graphs $x_{n+1}=u(x)$ over domain $Ω\subset\mathbb R^n$, if higher-order mean curvature ratio $\frac{H_{k}}{H_l}(l

This https://arxiv.org/abs/2505.19301 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCR_…

A Novel Zero-Trust Identity Framework for Agentic AI: Decentralized Authentication and Fine-Grained Access Control
Traditional Identity and Access Management (IAM) systems, primarily designed for human users or static machine identities via protocols such as OAuth, OpenID Connect (OIDC), and SAML, prove fundamentally inadequate for the dynamic, interdependent, and often ephemeral nature of AI agents operating at scale within Multi Agent Systems (MAS), a computational system composed of multiple interacting intelligent agents that work collectively. This paper posits the imperative for a novel Agentic AI I…

The gender-fluid flag reminds me that it’s okay to dress however the hell I want at different times, and that gender doesn’t have to fit into strict boxes.
I can be any gender at any time, or whenever my body feels like being something else, I love me.
Here’s what the gender-fluid flag colors stand for, from top to bottom:
- Pink represents femininity
- White stands for the absence of gender or agender identities
- Purple is for a mix or blending of masculinit…

Characteristic polynomials of semimatroids and their connections to matroids, hyperplane arrangements and graph colorings
Fu Houshan
https://arxiv.org/abs/2506.07071

Characteristic polynomials of semimatroids and their connections to matroids, hyperplane arrangements and graph colorings
We primarily investigate the properties of characteristic polynomials of semimatroids. In particular, we provide a combinatorial interpretation of their coefficients, generalizing the Whitney's Broken Circuit Theorem. We also prove that the unsigned coefficients of the characteristic polynomial form a unimodal and log-concave sequence, extending the Rota-Heron-Welsh Conjecture to semimatroids. Furthermore, we present convolution identities for the multiplicative characteristic and Tutte polynom…

psi: Plant Photosystem I excitation energy transfer network (2020)
Weighted directed network of the light-harvesting Photosystem Ι (PSI) of the plant Pisum sativum. The nodes represent chromophores with different identities (i.e. chlorophyll a, chlorophyll b, β-carotene and derivates, lutein, violaxanthin), while edges represent FRET transfer between chromophores. The link directionality connecting nodes in the PSI network depends on the energy levels of the connected chromophores. The…

Phases in WLZZ Matrix Models
A. Mironov, A. Oreshina, A. Popolitov
https://arxiv.org/abs/2507.05406 https://arxiv.org/pdf/2507.05406

Phases in WLZZ Matrix Models
We discuss the space of solutions to the Ward identities associated with the WLZZ models. We mostly concentrate on the case of these models described by a two-matrix model with the cubic potential in one of the matrices. We study how this space of solutions can be described by the freedom in choosing integration contours in the matrix integral.

Point Jacobi-type preconditioning and parameter tuning for Calderon-preconditioned Burton-Miller method in transmission problems
Keigo Tomoyasu, Hiroshi Isakari
https://arxiv.org/abs/2506.01440

Point Jacobi-type preconditioning and parameter tuning for Calderon-preconditioned Burton-Miller method in transmission problems
It was recently demonstrated that the boundary element method based on the Burton-Miller formulation (BM-BEM), widely used for solving exterior problems, can be adapted to solve transmission problems efficiently. This approach utilises Calderon's identities to improve the spectral properties of the underlying integral operator. Consequently, most eigenvalues of the squared BEM coefficient matrix, i.e. the collocation-discretised version of the operator, cluster at a few points in the complex pl…

Morabo Morojele’s creative career was remarkable.
What wove his three identities together – musician, development worker and writer – was his conscious, committed pan-Africanism
and his master craftsman’s skill with sound:
the sound of his drums and the sound of his words as they rose off the page.
Through his books, and his (far too few) recordings, that beauty lives with us still.
Robala ka khotso (Sleep in peace)

Morabo Morojele: The social and political drum beats of the Lesotho jazz musician
The jazz drummer, novelist and development scholar died on May 20.

This https://arxiv.org/abs/2505.21739 has been replaced.
initial toot: https://mastoxiv.page/@arXi…

Reflections of Cultural Wealth: Exploring Identity in Physics through Photo Elicitation
This paper presents a photo elicitation project that invites students to explore their identities in STEM and surface the cultural wealth they bring into the physics classroom. Grounded in critical race theory, educational theory, and affective neuroscience, the project asks students to take original photographs representing aspects of their lived experience-such as motivation, belonging, and support systems-and to write short reflections connecting these images to their journey in science. The…

psi: Plant Photosystem I excitation energy transfer network (2020)
Weighted directed network of the light-harvesting Photosystem Ι (PSI) of the plant Pisum sativum. The nodes represent chromophores with different identities (i.e. chlorophyll a, chlorophyll b, β-carotene and derivates, lutein, violaxanthin), while edges represent FRET transfer between chromophores. The link directionality connecting nodes in the PSI network depends on the energy levels of the connected chromophores. The…

Binomial Convolution of Sequences
Kunle Adegoke
https://arxiv.org/abs/2507.04179 https://arxiv.org/pdf/2507.04179

Binomial Convolution of Sequences
Given any two sequences of complex numbers, we establish simple relations between their binomial convolution and the binomial convolution of their individual binomial transforms. We employ these relations to derive new identities involving Fibonacci numbers, Bernoulli numbers, harmonic numbers, odd harmonic numbers and binomial coefficients.

Cities and Identities: An Overview of the Global South
https://ift.tt/BUL1dzV
updated: Thursday, June 26, 2025 - 9:37amfull name / name of organization: Dr. Cyrine Kortas, a…
via Input 4 RELCFP

Cauchy identities for Grothendieck polynomials and a dual RSK correspondence through pipe dreams
Hugh Dennin
https://arxiv.org/abs/2506.21052 https://

Cauchy identities for Grothendieck polynomials and a dual RSK correspondence through pipe dreams
The Cauchy identity gives a recipe for decomposing a double Grothendieck polynomial $\mathfrak{G}^{(β)}_w(x;y)$ as a sum of products $\mathfrak{G}^{(β)}_v(x)\mathfrak{G}^{(β)}_u(y)$ of single Grothendieck polynomials. Combinatorially, this identity suggests the existence of a weight-preserving bijection between certain families of diagrams called pipe dreams. In this paper, we provide such a bijection using an algorithm called pipe dream rectification. In turn, rectification is built from a …

General monotone formula for homogeneous $k$-Hessian equation in the exterior domain and its applications
Jiabin Yin, Xingjian Zhou
https://arxiv.org/abs/2506.01434

General monotone formula for homogeneous $k$-Hessian equation in the exterior domain and its applications
In this paper, we deal with an overdetermined problem for the $k$-Hessian equation ($1\leq k<\frac n2$) in the exterior domain and prove the corresponding ball characterizations. Since that Weinberger type approach seems to fail to solve the problem, we give a new perspective to solve exterior overdetermined problem by combining two integral identities and geometric inequalities. In particular, when $k=1$, we give an alternative proof for Brandolini-Nitsch-Salani's results \cite{BNS}. Meanwhile…

Hecke $L$-series for Sinha modules
Erik Davis, Matthew Papanikolas
https://arxiv.org/abs/2507.04113 https://arxiv.org/pdf/2507.04113

Hecke $L$-series for Sinha modules
We investigate Goss $L$-functions associated to Anderson $t$-modules defined by Sinha having complex multiplication by Carlitz cyclotomic fields. We show that these $t$-modules are defined over the cyclotomic field and that their $L$-functions are products of Hecke $L$-series for Anderson's Hecke character defined via Coleman functions. Applying identities of Fang and Taelman, we prove that special values of these $L$-functions are expressible in terms of products of values of Thakur's geometri…

Ex-FBI agent on ICE masking:
“Masking has always been associated with police states.
I think the masking symbolizes the drift of law enforcement away from democratic controls.”
https://www.theguardian.com/us-news/2025/j

Antiquantum $q$-series and mock theta functions
Amanda Folsom, David Metacarpa
https://arxiv.org/abs/2507.03824 https://arxiv.org/pdf…

Antiquantum $q$-series and mock theta functions
Ramanujan's original definition of mock theta functions from 1920 involves their asymptotic behaviors at roots of unity on the boundary of the disk of convergence $|q|<1$. More recently this topic has been related by several authors, including the first author with Ono and Rhoades in 2013, to quantum modular forms, first defined in 2010 by Zagier. In 2021, Lovejoy defined and studied related quantum $q$-series identities, which do not hold as equalities between power series inside the…

4-type subvarieties of the variety of associative algebras
B. Sartayev
https://arxiv.org/abs/2506.02471 https://arxiv.org/pdf/2506.02…

4-type subvarieties of the variety of associative algebras
In this paper, we consider four subvarieties of the variety of associative algebras. We study these subvarieties from the point of view of operads and show connections with well-known algebras such as dendriform algebras and noncommutative Novikov algebras. Finally, we define operations, commutator and anti-commutator on these algebras and obtain some identities under these operations.

fresh_webs: Freshwater stream webs
A set of 26 networks of trophic-level species interactions in streams in New Zealand, Maine and North Carolina. Networks include the identities of aquatic insect, algae and fish species and their trophic interactions. Excel and plain text adjacency matrices available; webs can be downloaded individually or as a group.
This network has 71 nodes and 148 edges.
Tags: Biological, Food web, Unweighted, Metadata

#TransRights #Trans #GenderFluid #NonBinary

Method of Weighted Words on Cylindric Partitions
Burcu Barsak\c{c}{\i}
https://arxiv.org/abs/2507.02435 https://arxiv.org/pdf/2507.02…

Method of Weighted Words on Cylindric Partitions
We study the generating functions of cylindric partitions having profile $c=(c_1, c_2, \ldots, c_r)$ with rank $2$ and levels $2, 3$ and $4$. As a result, we give expressions alternative to Borodin's formula for these generating functions. We use the method of weighted words which was first introduced by Alladi and Gordon, later was applied by Dousse in a new version to prove some partition identities and to get infinite products. We adopt the method to our subject with a more combinatorial app…

Some series connecting Fibonacci numbers to $\pi$
Zhi-Wei Sun, Yajun Zhou
https://arxiv.org/abs/2506.01865 https://arxiv.org/pdf/2506…

Some series connecting Fibonacci numbers to $π$
In this paper, we mainly deduce several series identities connecting the Fibonacci numbers to $π$. For example, we prove that \[\sum_{k=1}^{\infty}\frac{(135 k-56) F_{8 k}-2 (105 k-44) F_{8 k-1}}{k^{3}\binom{2k}{k}^3}=\frac{7π^{2}}{3}\]and\[\sum_{k=0}^\infty\frac{\binom{2k}{k}^3}{2^{12k}}\big[ 2 (90 k+13) F_{8 k}-2 (30 k-1) F_{8 k-1}\big]=\frac{64}π.\]

MacMahon's Double Vision: Partition Diamonds Revisited
Matthias Beck, Kobe Wijesekera
https://arxiv.org/abs/2506.23354 https://ar…

MacMahon's Double Vision: Partition Diamonds Revisited
Plane partition diamonds were introduced by Andrews, Paule, and Riese (2001) as part of their study of MacMahon's $Ω$-operator in search for integer partition identities. More recently, Dockery, Jameson, Sellers, and Wilson (2024) extended this concept to $d$-fold partition diamonds and found their generating function in a recursive form. We approach $d$-fold partition diamonds via Stanley's (1972) theory of $P$-partitions and give a closed formula for a bivariate generalization of the Dockery…

Ninth degree analogue of Ramanujan's septic theta function identity
Sun Kim, \"Ors Reb\'ak
https://arxiv.org/abs/2506.01181 https://

Ninth degree analogue of Ramanujan's septic theta function identity
On page 206 in his lost notebook, Ramanujan recorded a seventh degree identity for his theta function $φ(q)$. We give an analogous ninth degree identity. We also provide an application of an entry from his second notebook on a cubic equation and an interpretation with theta functions for some of his trigonometric identities. Lastly, we calculate five examples for $φ(e^{-π\sqrt{n}})$.

Applications of Fa\`{a} di Bruno's formula to partition traces
Toshiki Matsusaka
https://arxiv.org/abs/2507.00404 https://arxiv.o…

Applications of Faà di Bruno's formula to partition traces
We revisit several partition-theoretic generating functions, including the theta quotients from Ramanujan's lost notebook, MacMahon's partition functions, and reciprocal sums of parts in partitions, through the lens of the classical Faà di Bruno formula. This approach offers a unified and natural reinterpretation of known results and provides a systematic framework for deriving new identities of a similar type.