In computer science and mathematical logic, a proof assistant or interactive theorem prover is a software tool to assist with the development of formal proofs by human–machine collaboration. This involves some sort of interactive proof editor, or other interface, with which a human can guide the search for proofs, the details of which are stored in, and some steps provided by, a computer. A recent effort within this field is making these tools use artificial intelligence to automate the formalization of ordinary mathematics. == Automated proof checking == Automated proof checking is the process of using software for checking proofs for correctness. It is one of the most developed fields in automated reasoning. Automated proof checking differs from automated theorem proving in that automated proof checking simply mechanically checks the formal workings of an existing proof, instead of trying to develop new proofs or theorems itself. Because of this, the task of automated proof verification is much simpler than that of automated theorem proving, allowing automated proof checking software to be much simpler than automated theorem proving software. Because of this small size, some automated proof checking systems can have less than a thousand lines of core code, and are thus themselves amenable to both hand-checking and automated software verification. The Mizar system, HOL Light, and Metamath are examples of automated proof checking systems. Automated proof checking can be done either as a batch operation, or interactively, as part of an interactive theorem proving system. == History == Automath, which was developed by Nicolaas Govert de Bruijn starting in 1967, is often considered the first proof checker and the first system to utilize the Curry–Howard correspondence between programs and proofs. Automath was used by L.S. van Benthem Jutting in 1977 to formalize Landau's Foundations of Analysis, which was the first formalization of the real numbers. In 1973, Robert Boyer and J Moore published Proving Theorems about LISP Functions which aimed to verify programs, not mathematics. Their theorem prover is now known as ACL2. In the 1970s, Edinburgh LCF introduced the idea of using a functional programming language as the metalanguage for a theorem prover, and led to the HOL family of proof assistants. The 1990s saw the rise of Rocq, (then known as Coq), which has been used for many large-scale formalization projects. Since the late 2010s, Lean, a proof assistant strongly influenced by Rocq, has become another popular choice, especially for formalizing mathematics. == System comparison == ACL2 – a programming language, a first-order logical theory, and a theorem prover (with both interactive and automatic modes) in the Boyer–Moore tradition. HOL theorem provers – A family of tools ultimately derived from the LCF theorem prover. In these systems, the logical core is a library of their programming language. Theorems represent new elements of the language and can only be introduced via "strategies" which guarantee logical correctness. Strategy composition gives users the ability to produce significant proofs with relatively few interactions with the system. Members of the family include: HOL4 – The "primary descendant", still under active development. Support for both Moscow ML and Poly/ML. Has a BSD-style license. HOL Light – A thriving "minimalist fork". OCaml based. ProofPower – Went proprietary, then returned to open source. Based on Standard ML. IMPS, An Interactive Mathematical Proof System. Isabelle is an interactive theorem prover where other systems can be encoded. Isabelle/HOL is its most popular instance, whose foundation is close to that of the HOL prover. Other instances include Isabelle/ZF and Isabelle/FOL. The main code-base is BSD-licensed, but the Isabelle distribution bundles many add-on tools with different licenses. Jape – Java based. Lean is both an interactive theorem prover and a functional, dependently-typed programming language. It is based on the calculus of inductive constructions with non-cumulative universes. Since version 4 (released in 2023), it is self-hosting. It can be used to formalise mathematics (and has a large, coherent library for formal mathematics), but also for software and hardware verification. LEGO Matita – A light system based on the calculus of inductive constructions. MINLOG – A proof assistant based on first-order minimal logic. Mizar – A proof assistant based on first-order logic, in a natural deduction style, and Tarski–Grothendieck set theory. PhoX – A proof assistant based on higher-order logic which is eXtensible. Prototype Verification System (PVS) – a proof language and system based on higher-order logic. Rocq (formerly named Coq) – A popular interactive theorem prover based on the calculus of inductive constructions. Theorem Proving System (TPS) and ETPS – Interactive theorem provers also based on simply typed lambda calculus, but based on an independent formulation of the logical theory and independent implementation. == User interfaces == A commonly used front-end for proof assistants was the Emacs-based Proof General, developed at the University of Edinburgh. Nowadays, many provers include their own editor. Rocq includes RocqIDE, which is based on OCaml/Gtk. Isabelle includes Isabelle/jEdit, which is based on jEdit and the Isabelle/Scala infrastructure for document-oriented proof processing. More recently, Visual Studio Code extensions have been developed for Rocq, Isabelle by Makarius Wenzel, and for Lean 4 by the leanprover developers. == Formalization extent == Freek Wiedijk has been keeping a ranking of proof assistants by the amount of formalized theorems out of a list of 100 well-known theorems. As of September 2025, only six systems have formalized proofs of more than 70% of the theorems, namely Isabelle, HOL Light, Lean, Rocq, Metamath and Mizar. == Notable formalized proofs == The following is a list of notable proofs that have been formalized within proof assistants.
IEEE Transactions on Visualization and Computer Graphics
IEEE Transactions on Visualization and Computer Graphics is a peer-reviewed scientific journal published by the IEEE Computer Society. It covers subjects related to computer graphics and visualization techniques, systems, software, hardware, and user interface issues. TVCG has been considered the top journal in the field of visualization. Since 2011, TVCG has allowed authors to present recently accepted papers at partner conferences. These include: IEEE Visualization (VIS), including VAST, InfoVis, and SciVis. IEEE Virtual Reality Conference (IEEE VR) IEEE International Symposium on Mixed and Augmented Reality (ISMAR) ACM Symposium on Interactive 3D Graphics and Games (I3D) IEEE Pacific Visualization Conference (IEEE PacificVis) ACM SIGGRAPH/Eurographics Symposium on Computer Animation (SCA) Eurographics Symposium on Geometry Processing (SGP) Pacific Graphics Conference (PG) Eurovis - The EG and VGTC Conference on Visualization Graphics Interfaces (GI)
Tokken
Tokken is a payment system and mobile app most known for being a legal and secure option for businesses transactions within the cannabis industry, because of its compliance with bank requirements. The startup company was created by Lamine Zarrad, a former regulator at the Office of the Comptroller of the Currency. == Operability == In order for a person to start using the app, they need to provide evidence, in the form of bioidentification data and mobile carrier records, that they can legally purchase weed. After they have been verified, customers can pay directly through the app at any dispensary that is using Tokken. Tokken turns credit card transactions into a digital token, which can be exchanged back for money that can later be deposited into a bank account. All transactions are logged publicly through a blockchain leger, making the process both anonymous and verified. === Banking services === Tokken has a "pay taxes" function which enables dispensaries to pay their taxes directly to the department.
Security.txt
security.txt is an accepted standard for website security information that allows security researchers to report security vulnerabilities easily. The standard prescribes a text file named security.txt in the well known location, similar in syntax to robots.txt but intended to be machine and human readable, for those wishing to contact a website's owner about security issues. security.txt files have been adopted by Google, GitHub, LinkedIn, and Facebook. == History == The Internet Draft was first submitted by Edwin Foudil in September 2017. At that time it covered four directives, "Contact", "Encryption", "Disclosure" and "Acknowledgement". Foudil expected to add further directives based on feedback. In addition, web security expert Scott Helme said he had seen positive feedback from the security community while use among the top 1 million websites was "as low as expected right now". In 2019, the Cybersecurity and Infrastructure Security Agency (CISA) published a draft binding operational directive that requires all US federal agencies to publish a security.txt file within 180 days. The Internet Engineering Steering Group (IESG) issued a Last Call for security.txt in December 2019 which ended on January 6, 2020. A study in 2021 found that over ten percent of top-100 websites published a security.txt file, with the percentage of sites publishing the file decreasing as more websites were considered. The study also noted a number of discrepancies between the standard and the content of the file. In April 2022 the security.txt file has been accepted by Internet Engineering Task Force (IETF) as RFC 9116. == File format == security.txt files can be served under the /.well-known/ directory (i.e. /.well-known/security.txt) or the top-level directory (i.e. /security.txt) of a website. The file must be served over HTTPS and in plaintext format.
WIPO GREEN
WIPO GREEN is a World Intellectual Property Organization program established in 2013 that supports global efforts to address climate change and food security through sharing of sustainable technology innovations. == WIPO GREEN database == The WIPO GREEN database is the foundation of the platform. The database is a free, solutions-oriented, global innovation catalog that connects needs for solving environmental or climate change problems with sustainable solutions from prototypes to marketable products available for sale, license, collaborations, knowledge transfer, joint ventures, or collaborations. Green technology innovators can promote their products, businesses, organizations, and governments looking for green technologies can explain their needs and seek collaboration with providers. As of July 2022, WIPO GREEN has over 120,000 technologies, needs and experts, more than 2000 users in 110 countries, and has recorded over 1000 connections made between technology providers and seekers. The database utilizes AI-assisted auto-matching, user uploads tracing and alerts, full-text search for solutions based on long need descriptions, and the Patent2Solution search function for finding commercial applications of a patent, which are some of the unique features of the database. Free registration is required for detailed record view and uploading. All technologies uploaded to the WIPO GREEN database remain the property of the rights holder. It is up to the rights holder and the collaborating parties to structure agreements in the manner they feel is most appropriate and effective. WIPO GREEN does not require that technologies or innovations uploaded to the database be patented or in the process of being patented. Therefore, technology providers can upload their technology while related patent applications are pending. Technology providers are encouraged to upload technology solutions on the WIPO GREEN database and connect with other users to explore partnerships, technology transfers, including funding and licensing opportunities. == Acceleration projects == Acceleration projects work with WIPO GREEN partners and local organizations to explore local challenges and green opportunities for particular environmental needs. These projects are organized annually in different countries or regions around and connect providers and seekers of green technologies. For example, the Latin America Acceleration Project explores innovative new technologies in the region and facilitates green technology exchange between providers and seekers in green opportunities in intensified crop rotation, soil re-carbonization, and forest management in Argentina; zero-till or conservation agriculture in Brazil; and wine production in Chile. In October 2021, a project in Indonesia on palm oil mill effluent (POME), a by-product of palm oil production that emits greenhouse gases and reportedly harms flora and fauna in local rivers, identified viable green solutions to turn the high organic content of POME wastewater into biogas and other environmentally friendly uses. Former projects took place in Cambodia, Indonesia, and the Philippines around wastewater treatment, agriculture, and water technologies. == The Green Technology Book == In November 2022 at UNFCCC COP27, WIPO introduced its new Flagship publication the Green Technology Book. This digital-first publication aims to put innovation, technology and intellectual property at the forefront in the fight against climate change. The inaugural edition of this annual publication focused on available solutions for climate-change adaptation to reduce vulnerability as well as to increase resilience to the impacts of climate change. The book was created in cooperation with the Climate Technology Center and Network (CTCN) and the Egyptian Academy of Scientific Research and Technology (ASTR). It features 200 adaptation technologies, which are also available in the WIPO GREEN database of innovative technologies and needs. == Partners Network == WIPO GREEN partners are public or private institutions that wish to collaborate to advance WIPO GREEN’s mission. The network is aimed at helping the implementation and diffusion of green technology innovations around the world. Partners include government institutions, intergovernmental organizations, academia, and businesses – from small and medium-sized enterprises to Fortune 500 companies. As of 2022, WIPO GREEN has a network of over 146 partner organizations involved in green technology.
Color science
Color science is the scientific study of color including lighting and optics; measurement of light and color; the physiology, psychophysics, and modeling of color vision; and color reproduction. It is the modern extension of traditional color theory. == Organizations == International Commission on Illumination (CIE) Illuminating Engineering Society (IES) Inter-Society Color Council (ISCC) Society for Imaging Science and Technology (IS&T) International Colour Association (AIC) Optica, formerly the Optical Society of America (OSA) The Colour Group Society of Dyers and Colourists (SDC) American Association of Textile Chemists and Colorists (AATCC) Association for Research in Vision and Ophthalmology (ARVO) ACM SIGGRAPH Vision Sciences Society (VSS) Council for Optical Radiation Measurements (CORM) == Journals == The preeminent scholarly journal publishing research papers in color science is Color Research and Application, started in 1975 by founding editor-in-chief Fred Billmeyer, along with Gunter Wyszecki, Michael Pointer and Rolf Kuehni, as a successor to the Journal of Colour (1964–1974). Previously most color science work had been split between journals with broader or partially overlapping focus such as the Journal of the Optical Society of America (JOSA), Photographic Science and Engineering (1957–1984), and the Journal of the Society of Dyers and Colourists (renamed Coloration Technology in 2001). Other journals where color science papers are published include the Journal of Imaging Science & Technology, the Journal of Perceptual Imaging, the Journal of the International Colour Association (JAIC), the Journal of the Color Science Association of Japan, Applied Optics, and the Journal of Vision. == Conferences == Congress of the International Color Association IS&T Color and Imaging Conference (CIC) SIGGRAPH International Symposium for Color Science and Art == Selected books == Berns, Roy S. (2019). Billmeyer and Saltzman's Principles of Color Technology (4th ed.). Wiley. doi:10.1002/9781119367314. 3rd ed. (2000). Daw, Nigel (2012). How Vision Works: The Physiological Mechanisms Behind What We See. Oxford. doi:10.1093/acprof:oso/9780199751617.001.0001. Elliot, Andrew J.; Fairchild, Mark D.; Franklin, Anna, eds. (2015). Handbook of Color Psychology. Cambridge. doi:10.1017/CBO9781107337930. Fairchild, Mark D. (2013). Color Appearance Models (3rd ed.). Wiley. doi:10.1002/9781118653128. Author's website. 2nd ed. (2005). Hunt, Robert W. G. (2004). The Reproduction of Colour (6th ed.). Wiley. doi:10.1002/0470024275. Kuehni, Rolf G. (2012). Color: An Introduction to Practice and Principles (3rd ed.). Wiley. doi:10.1002/9781118533567. 1st ed. (1997). Luo, Ming R., ed. (2016). Encyclopedia of Color Science and Technology. Springer. doi:10.1007/978-1-4419-8071-7. MacAdam, David L., ed. (1970). Sources of Color Science. MIT Press. Reinhard, Erik; Khan, Erum Arif; Akyuz, Ahmet Oguz; Johnson, Garrett (2008). Color Imaging: Fundamentals and Applications. CRC Press. doi:10.1201/b10637. Schanda, János, ed. (2007). Colorimetry: Understanding the CIE System. Wiley. doi:10.1002/9780470175637. Shamey, Renzo; Kuehni, Rolf G. (2020). Pioneers of Color Science. Springer. doi:10.1007/978-3-319-30811-1. Wyszecki, Günter; Stiles, Walter S. (1982). Color Science: Concepts and Methods, Quantitative Data and Formulae (2nd ed.). Wiley.
Central Equipment Identity Register
A Central Equipment Identity Register (CEIR) is a database of mobile equipment identifiers (IMEI – for networks of GSM standard, MEID – for networks of CDMA standard). Such an identifier is assigned to each SIM slot of the mobile device. Different kinds of IMEIs could be, White, for devices that are allowed to register in the cellular network; Black, for devices that are prohibited to register in the cellular network; and Grey, for devices in intermediate status (when it is not yet defined in which of the lists - black or white - the device should be placed). Depending on the rules of mobile equipment registration in a country the CEIR database may contain other lists or fields beside IMEI. For example, the subscriber number (MSISDN), which is bound to the IMEI, the ID of the individual (passport data, National ID, etc.) who registered IMEI in the database, details of the importer who brought the device into the country, etc. == History == Originally abbreviation CEIR stood for IMEI Database, created and provided by GSM Association. It was proposed to blacklist the IMEIs of stolen or lost phones. It was assumed that any MNO would be able to receive this list to block the registration of such devices on their network. Thus, it turns out that a stolen phone, once blacklisted by the GSMA CEIR, cannot be used on a large number of cellular networks, which means that the theft of mobile devices will become meaningless. However, it soon became clear that the MNOs on their initiative were not going to do this because if many phones stopped working in their networks, but works in another, it puts them at a disadvantage and can lead to an outflow of subscribers. It became clear that the blocking of stolen devices should be introduced simultaneously in all mobile networks of the country by legislative measures at the initiative of the communications regulator. In this case, as a rule, a national IMEI database is created, which contains general lists of blocked IMEIs. Since the registration in the cellular operator's network is directly blocked by a network node called EIR (Equipment Identity Register), the system that contains the national IMEI base became known as Central EIR (CEIR). To avoid confusion the database of GSM Association was renamed to IMEI Database - IMEI DB (it was in 2003-2008, see “Document History” at IMEI Database File Format Specification). Also sometimes a common IMEI database for several EIRs is called SEIR (Shared EIR). In each country, the CEIR can interact with IMEI DB differently. National CEIR may not communicate with IMEI DB at all. Firstly, it is separately decided whether CEIR will send information about its blacklist to IMEI DB (which IMEIs are placed in it or removed from there). Secondly, upon receipt of the blacklist from IMEI DB, the regulator decides from which countries it will receive it (IMEI DB stores the information exactly who blacklisted the IMEI). For example, you can get a list from neighboring countries, from countries in your region, from around the world. In addition to the blacklist, the GSMA is developing a list of IMEIs allocated to manufacturers for use in their devices. The manufacturer for each new device model gets at least one TAC (Type Allocation Code) allocated by GSMA, consisting of 8 digits, to which he can add a 6-digit serial number to obtain the IMEI. Thus, with one TAC, a manufacturer can release up to 1 million devices with a unique IMEI. Usually, CEIR receives a list of allocated TACs from the GSMA, since if the first 8 digits of the IMEI of a device are not in this list, this is a sign that it is counterfeit. If the central database of identifiers does not work with GSM networks, but with CDMA, then for the same purposes it is necessary to interact with another worldwide database that contains MEIDs – MEID Database. A system that directly blocks the registration of a mobile device on a cellular network – EIR. Each MNO must have at least one EIR, to which IMEI check requests (CheckIMEI) are sent when registering a device on the network. A typical EIR and CERI interaction scheme: The CEIR accumulates black, white, and grey lists using various data sources and verification methods. These lists are periodically transmitted to all EIRs. EIR uses them when processing every CheckIMEI request to determine whether to allow the device on the network or not. EIR can transmit some data to the CEIR database too. Usually, changes in a grey list – new IMEIs on the network that are not in any list – are transmitted from EIR to CEIR. In addition to synchronizing lists across multiple networks, the main function of CEIR is to implement the scenarios of changes at these lists. This usually requires interaction with various IT systems (databases) of other organizations and/or with subscribers. Еxamples of such scenarios: Whitelisting the IMEI of devices imported by the legal entity Whitelisting the IMEI of devices manufactured domestically Whitelisting the IMEI of devices imported by individual Blacklisting the IMEI of stolen/lost devices Binding IMEI to the subscriber's number and, vice versa, unbinding IMEI from the subscriber == System implementation results == The goals and results of CEIR implementation in a country are usually: Reducing mobile phone theft Reducing the import of devices stolen in other countries Reducing the presence of counterfeit devices on the market (null IMEI, incorrect IMEI, changed IMEI) Reducing illegal imports of mobile devices (increase in the collection of customs duties) Additionally, CEIR most often contributes to the solution of such problems: Combating various mobile fraud schemes Obtaining more accurate statistics on the state of the mobile communications market for the regulator Fight against terrorism (the ability to block the device at once in all mobile networks of the country). Known results achieved in some countries: Great Britain – reducing mobile phone theft. Turkey – reducing mobile phone theft, decreasing the current account deficit of Turkey and maximizing tax revenues. Uzbekistan – preventing black import of mobile devices by 98%, increase in revenues from the import of mobile devices by 700%. Kenya – disposing the market of counterfeit mobile equipment. Azerbaijan – disposing the market of counterfeit mobile equipment. Ukraine – increasing of legally imported mobile devices by 95%, increase in revenues from the import of mobile devices. == CEIR and EIR manufacturers == Some countries have used local developers to implement CEIR for their country (Great Britain, Turkey, India, and Azerbaijan). EIR is a system that is standardized in a 2G-5G networks. Such system may be established at mobile network even it doesn’t use black list and there are no CEIR in a country. Some developers of MNO’s signal core include EIR in a complex solution. However, its standard capabilities are usually lacking for specific requirements when implementing CEIR.