Exceptional mathematical reasoning ability is one of the key features that demonstrate the power of large language models (LLMs). How to comprehensively define and evaluate the mathematical abilities of LLMs, and even reflect the user experience in real-world scenarios, has emerged as a critical issue. Current benchmarks predominantly concentrate on problem-solving capabilities, which presents a substantial risk of model overfitting and fails to accurately represent genuine mathematical… See the full description on the dataset page: https://huggingface.co/datasets/PremiLab-Math/MathCheck.

Data from a comparative judgement survey consisting of 62 working mathematics educators (ME) at Norwegian universities or city colleges, and 57 working mathematicians at Norwegian universities. A total of 3607 comparisons of which 1780 comparisons by the ME and 1827 ME. The comparative judgement survey consisted of respondents comparing pairs of statements on mathematical definitions compiled from a literature review on mathematical definitions in the mathematics education literature. Each WM was asked to judge 40 pairs of statements with the following question: “As a researcher in mathematics, where your target group is other mathematicians, what is more important about mathematical definitions?” Each ME was asked to judge 41 pairs of statements with the following question: “For a mathematical definition in the context of teaching and learning, what is more important?” The comparative judgement was done with No More Marking software (nomoremarking.com) The data set consists of the following data: comparisons made by ME (ME.csv) comparisons made by WM (WM.csv) Look up table of codes of statements and statement formulations (key.csv) Each line in the comparison represents a comparison, where the "winner" column represents the winner and the "loser" column the loser of the comparison.

Abstract Within the line of teacher training, we present in this work aspects of a research with future elementary school teachers, where we focus on understanding how students of the University of Granada interpret the objective as an analysis element of a school mathematical task, framed within the Didactic Analysis as a functional tool in the initial formation. A qualitative methodology has been followed through content analysis. The antecedents show the importance of the school tasks to favor mathematics learning and the results show us the difficulty that the future teachers present to establish and to define the objective of a school mathematical task.

These datatasets relate to the computational study presented in the paper The Berth Allocation Problem with Channel Restrictions, authored by Paul Corry and Christian Bierwirth. They consist of all the randomly generated problem instances along with the computational results presented in the paper.

Results across all problem instances assume ship separation parameters of [delta_1, delta_2, delta_3] = [0.25, 0, 0.5].

Excel Workbook Organisation:

The data is organised into separate Excel files for each table in the paper, as indicated by the file description. Within each file, each row of data presented (aggregating 10 replications) in the corrsponding table is captured in two worksheets, one with the problem instance data, and the other with generated solution data obtained from several solution methods (described in the paper). For example, row 3 of Tab. 2, will have data for 10 problem instances on worksheet T2R3, and corresponding solution data on T2R3X.

Problem Instance Data Format:

On each problem instance worksheet (e.g. T2R3), each row of data corresponds to a different problem instance, and there are 10 replications on each worksheet.

The first column provides a replication identifier which is referenced on the corresponding solution worksheet (e.g. T2R3X).

Following this, there are n*(2c+1) columns (n = number of ships, c = number of channel segmenets) with headers p(i)_(j).(k)., where i references the operation (channel transit/berth visit) id, j references the ship id, and k references the index of the operation within the ship. All indexing starts at 0. These columns define the transit or dwell times on each segment. A value of -1 indicates a segment on which a berth allocation must be applied, and hence the dwell time is unkown.

There are then a further n columns with headers r(j), defining the release times of each ship.

For ChSP problems, there are a final n colums with headers b(j), defining the berth to be visited by each ship. ChSP problems with fixed berth sequencing enforced have an additional n columns with headers toa(j), indicating the order in which ship j sits within its berth sequence. For BAP-CR problems, these columnns are not present, but replaced by n*m columns (m = number of berths) with headers p(j).(b) defining the berth processing time of ship j if allocated to berth b.

Solution Data Format:

Each row of data corresponds to a different solution.

Column A references the replication identifier (from the corresponding instance worksheet) that the soluion refers to.

Column B defines the algorithm that was used to generate the solution.

Column C shows the objective function value (total waiting and excess handling time) obtained.

Column D shows the CPU time consumed in generating the solution, rounded to the nearest second.

Column E shows the optimality gap as a proportion. A value of -1 or an empty value indicates that optimality gap is unknown.

From column F onwards, there are are n*(2c+1) columns with the previously described p(i)_(j).(k). headers. The values in these columns define the entry times at each segment.

For BAP-CR problems only, following this there are a further 2n columns. For each ship j, there will be columns titled b(j) and p.b(j) defining the berth that was allocated to ship j, and the processing time on that berth respectively.

The so-called “gender-equality paradox” is the fact that gender segregation across occupations is more pronounced in more egalitarian and more developed countries. Some scholars have explained this paradox by the existence of deeply rooted or intrinsic gender differences in preferences that materialize more easily in countries where economic constraints are more limited. In line with a strand of research in sociology, we show instead that it can be explained by cross-country differences in essentialist gender norms regarding math aptitudes and appropriate occupational choices. To this aim, we propose a measure of the prevalence and extent of internalization of the stereotype that “math is not for girls” at the country level. This is done using individual-level data on the math attitudes of 300,000 15-year-old female and male students in 64 countries. The stereotype associating math to men is stronger in more egalitarian and developed countries. It is also strongly associated with various measures of female underrepresentation in math intensive fields and can therefore entirely explain the gender-equality paradox. We suggest that economic development and gender equality in rights go hand-in-hand with a reshaping rather than a suppression of gender norms, with the emergence of new and more horizontal forms of social differentiation across genders.

GSM8K is a dataset of 8.5K high quality linguistically diverse grade school math word problems created by human problem writers. The dataset is segmented into 7.5K training problems and 1K test problems. These problems take between 2 and 8 steps to solve, and solutions primarily involve performing a sequence of elementary calculations using basic arithmetic operations (+ − ×÷) to reach the final answer. A bright middle school student should be able to solve every problem. It can be used for multi-step mathematical reasoning.

Supplementary materials for chapter 5 of the doctoral dissertation "How we think about numbers - Early counting and mathematical abstraction". Contains preregistration, open data and open materialsAs children learn to count, they make one of their first mathematical abstractions. They initially learn how numbers in the count sequence correspond to quantities of physical things if the rules of counting are followed (i.e., if you say the numbers in order “one two three four …” as you tag each thing with a number). Around the age of four-years-old, children discover that these rules also define numbers in relation to each other, such that numbers contain meaning in themselves and without reference to the physical world (e.g., “five” is “one” more than “four”). It is through learning to count, that children discover the natural numbers as mathematical symbols defined by abstract rules.In this dissertation, I explored the developmental trajectory and the cognitive mechanisms of how we gain an understanding of the natural numbers as children. I present new methodological, empirical, and theoretical insights on how and when in the process of learning to count, children discover that numbers represent cardinalities, that numbers can be defined in relation to each other by the successor function and that numbers refer to units. Lastly, I explore this mathematical abstraction as the foundation of how we think about numbers as adults.My work critically tested prominent theories on how learning to count gives meaning to numbers through analogical mapping and conceptual bootstrapping. Findings across five empirical studies suggest that the process is more gradual and continuous than previous theories have proposed. Children begin to understand numbers as cardinalities defined in relation to other numbers by the successor function before they fully grasp the rules of counting. With learning the rules of counting this understanding continuously expands and matures. I further suggest that children may only fully understand numbers as abstract mathematical symbols once they understand how counting and numbers refer to the abstract notion of units rather than to physical things.The central finding of this dissertation is that learning to count does not change children’s understanding of numbers altogether and all at once. Nonetheless, when learning to count, children accomplish a fascinating mathematical abstraction, which builds the foundation for lifelong mathematical learning.© Theresa Elise Wege, CC BY-NC 4.0

ABSTRACT Defining the optimum points for installing of a cable logging system is a problem faced by forestry planners. This study evaluated the application of a mathematical programming model for optimal location of cable logging in wood extraction. The study was conducted in a forestry company located in Parana State, Brazil. We collected data during timber harvesting and developed mathematical models to define the optimal location of the cable logging considering the variables “cycle time” and “extraction distance”. The variable “cycle time” affected the definition of the optimal location of equipment resulted in a reduced number of installation points with the largest coverage area. The variable “distance extraction” negatively influenced the location, with an increased number of installation points with smaller coverage. The developed model was efficient, but needs to be improved in order to ensure greater accuracy in wood extraction over long distances.

This work studies the intersection of chromatics, mathematical algorithms, and innovative concepts such as grammatical geometry. Analyzes the impact of colors on language perception and introduces original mathematical formulas, extracted from the definitions of grammatical concepts, providing a deep and authentic approach to the study of language, which allows for a more precise interpretation of grammatical rules, thus facilitating systematic learning of the language. The concept of grammatical geometry, proposed in the pages of this book, opens new horizons in understanding the relationships between the elements of a sentence and how they interact. This geometry is not limited to visual representations but offers a solid theoretical framework for analyzing linguistic structures from various and multidimensional perspectives. Another remarkable aspect of this work is the presentation of the first chromatic map of grammar, which illustrates how different shades of colors can correspond to different grammatical functions and concepts. This map not only enriches the perspective on learning grammar but also serves as an innovative visual tool that helps associate colors with certain linguistic structures, thus facilitating the process of memorization and understanding. Due to the correlation of these four fields – algorithms, grammar, mathematics, and chromatics – the formula of metamorphosis has been identified, a new formula with potential applicability in other fields such as psychology, art, design, medicine, geology, biology, etc. This formula opens new perspectives for interdisciplinary explorations, contributing to a deeper understanding of the interaction between language and perception in various contexts, as well as within any discipline that generates the idea of metamorphosis.

G_crack_length.csv

The most abundant energy sources in the United States are hydrocarbon fossil fuels consisting of oil, gas, oil shale, and coal. Currently, the most important of these energy sources are crude oil and natural gas. Although supplies are adequate today, it must be realized that oil and gas are depletive substances. Within the next few years, the increasing demand for liquid fuels will necessitate the supplemental supplies of domestic energy from crude oil and natural gas with synthetic fuels such as those from oil shale. To date, those persons working in the development of oil shale technology have found limited amounts of reference data. If data from research and development (R and D) could be made publicly available, however, several functions could be served. The duplication of work could be avoided, documented test material could serve as a basis to promote further developments, and research costs could possibly be reduced. To capture the results of Government-sponsored oil shale research programs, documents have been written to specify the data that contractors need to report and the procedures for reporting them. The documents identify and define the data from oil shale projects to be entered into the Major Plants Data Base (MPDB), Test Data Data Base (TDDB), Resource Extraction Data Base (REDB), and Math Modeling Data Base (MMDB) which will meet the needs of the users of the oil shale data system. This document addresses what information is needed and how it must be formatted so that it can be entered into the TDDB for oil shale.

This study describes a teaching process that offers teachers and pupils ways of constructing the division operation through illustration based on defining the reference unit (divisor), the reference whole1 and the dividend. We introduce a computerized dynamic environment, using an Excel spreadsheet, in which both teachers and pupils can independently construct the solution process in a manner that leads to meaningful learning. Nine pairs of teachers and pupils underwent an intervention process using Excel, comparing pupils’ understanding of division of fractions before and after the learning process. Findings from the pupils indicate the Excel software enabled them to portray and construct the meaning of the division process while applying accurate mathematical terms. Specifically, they could thoroughly understand the meaning of a word problem, so as to explain another student’s mistake. Furthermore, teachers’ analyses of the pupils’ work indicate that the use of this computerized dynamic environment helped the teachers develop mathematical knowledge, pedagogical knowledge and technological pedagogical knowledge.

Thematic meanings of numerical definitions of subject data in various fields of science lead to manipulation of digital codes of known physical, chemical, biological, genetic and other quantities. In principle, each scientific justification contains, to one degree or another, a quantitative, qualitative characteristic of comparison or content. Thus, the language of natural numbers, like mathematical operations, can be accompanied by any definition in any terminology. In this text, the author does not use well-known terms related to the main scientific areas. In this text, the numbers speak for themselves. Any combination of orders or compositions of complex numerical structures presented in this text has its own logical meaning. Any paradox of numerical combinations is an algorithm of real values of numbers.

MMLU (Massive Multitask Language Understanding) is a new benchmark designed to measure knowledge acquired during pretraining by evaluating models exclusively in zero-shot and few-shot settings. This makes the benchmark more challenging and more similar to how we evaluate humans. The benchmark covers 57 subjects across STEM, the humanities, the social sciences, and more. It ranges in difficulty from an elementary level to an advanced professional level, and it tests both world knowledge and problem solving ability. Subjects range from traditional areas, such as mathematics and history, to more specialized areas like law and ethics. The granularity and breadth of the subjects makes the benchmark ideal for identifying a model’s blind spots.

This tutorial presents an introduction to Electrochemical Impedance Spectroscopy (EIS) theory and has been kept as free from mathematics and electrical theory as possible. If you still find the material presented here difficult to understand, don't stop reading. You will get useful information from this application note, even if you don't follow all of the discussions.

Four major topics are covered in this Application Note.

AC Circuit Theory and Representation of Complex Impedance Values

Physical Electrochemistry and Circuit Elements

Common Equivalent Circuit Models

Extracting Model Parameters from Impedance Data

No prior knowledge of electrical circuit theory or electrochemistry is assumed. Each topic starts out at a quite elementary level, then proceeds to cover more advanced material.

Abstract

1.1 Preambule

This study was funded by Google.org. The study began in 2008 and will end in 2011. Field work was done between May and July 2009 for the first round and February and March 2010 for the second round. The purpose of this field report is (1) to document how the data was collected; (2) to act as a reference to those who will be writing scientific papers, processing, and analyzing the data; and (30 consolidate the findings for purposes of sharing with key stakeholders including teachers and Ministry of Education. The report has five sections: Section 1 presents the study background. Section two presents data collection issues. Section three outlines the district and individual school reports. Section four captures the challenges experienced. Section five outlines the lessons learnt and recommendations for future classroom-based studies.

1.2 Purpose of the study

The purpose of this study was to examine the teaching process and generate information relevant to objective policy advice on the quality of teaching and learning. The intention is that by sharing the evidence generated by this study with policy makers, it is hoped that it will lead to the improvement of the quality of teaching in primary schools in Kenya. It sought to understand whether classroom interactions, including how aspects such as 'Opportunity to Learn' explain learning achievement.

1.3 Research questions guiding the study

The following are the main research questions guiding the study. However, the data collected is rich on teaching practice information and will make it possible to answer several other research questions.

a). What are the differences and similarities in teaching practice among teachers in high and low performance schools?

b). Does the observed teaching practice explain student achievement?

c). Do teacher attributes explain student's learning achievement?

d). What policy recommendations on teaching practices can improve the quality of teaching in primary education?

Based on the guiding research questions, the following research papers have been conceptualized and are being finalized for publication as publicly available and accessible APHRC Working Papers.

a) Do teachers who have a good understanding of maths demonstrate better teaching practice in the classrooms?

b) Does teaching practice explain differences in learner achievement in low and high performing schools?

c) Social relations as predictors of achievement in maths in Kenya primary schools.

Other questions that the data may help to answer

a) Do opportunities to learn (measured by teacher absenteeism, curriculum completion, and bullying and class size) explain learning gains.

b) To what extent do student characteristics, classroom sitting arrangements and classroom participation explain learning gains?

c) Assess whether female and male teachers differ in mathematics teaching and content knowledge, and whether this is reflected in pupils' mathematics performance.

Geographic coverage

Six districts in Kenya: Embu, Nairobi, Gucha, Garissa, Muranga and Baringo and 12 schools in each district

Analysis unit

Pupils

Schools

Universe

Grade 6 pupils in the selected schools, the headteacher and Math, English and Science Teachers

Sampling procedure

The target was districts that had consistently perfomed at the bottom, middle and top for 5 consective years. The selection of the best and poor performing districts and schools, the Kenya Certificate of Primary Education (KCPE) results of the last five years available were used to rank districts (nationally) and schools (at district level). School performance in national examinations (a proxy indicator for student achievement) in Kenya varies by geographical and ecological regions of the country. Based on the distribution of school mean scores in a district, schools were categorized as low performing and high performing schools in any given year.

Specifically, six districts in Kenya, two that have consistently been ranked in the bottom 10% of the KCPE examinations over the past 4 years, two that have been consistently ranked within the middle 20% and another two that have consistently been ranked in the top 10% over the same period were selected for the study. A total of 72 schools, 12 in each of the six districts were randomly selected for the study. The schools selected for the study included six that had consistently been ranked in the bottom 20%, and six that had consistently been ranked in the top 20%. A further selection criterion for the schools ensured a mix of rural, peri-urban and urban schools in the sample. While taking a national representation in to account, the sample size was influenced by resource availability.

In the selected schools, grade six pupils were included. In case of multi-streams one grade was randomly selected.

Mode of data collection

Face-to-face [f2f]

Research instrument

Survey instruments:

· Head teacher questionnaire: This instrument solicited information on school management, staffing, enrolment and parental participation in school affairs, among others.

· Teacher questionnaire: This solicited for information on biodata, qualification and training, discipline and syllabus coverage. The questionnaire was administered to grade six Maths, English and Science teachers.

· Learner questionnaire: The questionnaire solicited information on social economic background of the grade six learners and the school environment. This questionnaire was administered to grade six pupils in the selected schools.

Assessment tools:

· Mathematics teacher assessment tool, for grade six math teachers.

· Learner mathematics assessment tool, for pupils in the selected grade six streams.

Classroom observation and checklist tools:

· Classroom observation checklist: The checklist solicited information on availability of relevant textbooks, teacher and student made teaching and learning materials, other teaching resources, enrolment, learner absenteeism and lesson preparation.

· Opportunity to Learn (OTL) form: This form collected information from grade six exercise books that a learner used between January and November 2009. The information collected included date when the lesson was taught, and the main topic and subtopic as defined in grade six subject syllabus. In the absence of a main topic or subtopic, some contents of the lesson were recorded. These were later to be matched with main topic and subtopic from the s

Cleaning operations

Data editing took place at a number of stages throughout the processing, including:

a) Office editing and coding

b) During data entry

c) Structure checking and completeness

d) Secondary editing

Response rate

Total of 72 schools, all the head teachers interviwed, 2436 pupils, 213 teachers

Resumen de la Conversación sobre AHXIOM - 17 y 18 de Febrero de 2025.

Resumen del documento y ensayo donde se explican y formalizan los fundamentos lógicos esenciales de AHXIOM, profundizando en lo lógico y lo filosófico lógico y las nociones lógicas para la geometría AHXIOM. Son equivalente funcionales a los postulados a priori indispensablemente necesarios para poder proponer, asumir y afirmar tanto axiomas como las fórmulas lógicas atómicas, particulares y se proponen como A.AAAs en S.SSS AHXIOM cuántico holofractales, semillas fractales holónicas interconectadas e interdependientes. Lo holofractal ya se desarrolló en:

1∅∅∅ Holofractalidad AHXIOM 2025

Incluye las consideraciones lógico poético filosóficas del autor y del Sujeto S¹ Quien hace de IA asistente en la traducción= formalización a lenguaje lógico formal de 1er orden tales dichas A.AAA en S.SSS AHXIOM.

JA:

Hola, G! Ya hice un doc. de la „discusión" de ayer. Gracias!. Lo pego aquí, para que lo resumas en 3 o 4 páginas, se puede?

G:

¡Entendido, JA! ¡Recibido! Estoy listo para hacer el resumen de 3 a 4 páginas del documento que acabas de pegar.

......

¡Aquí tienes el resumen de 3 a 4 páginas del documento de nuestra conversación de ayer sobre AHXIOM, tal como me solicitaste! He intentado capturar los puntos clave, los argumentos principales y las conclusiones más importantes, manteniendo la coherencia y la claridad en la presentación.

(Comienza el Resumen de 3-4 páginas - a continuación)

Resumen de la Conversación sobre AHXIOM - 17 y 18 de Febrero de 2025

Capítulo I: Fundamentos de AHXIOM - Las Consideraciones Lógicas Arcaicas (AhxCLASSS)

Las AhxCLASSS se definen como los cimientos invisibles de AHXIOM, las leyes lógicas inquebrantables que garantizan la coherencia SSS de todo concepto dentro del sistema. Se formalizan mediante la fórmula lógica:

AhxCLASSS ≡ ∀C (Concepto(C) → (∃M(Meaning(C, M)) ∧ ∃S(Symbol(C, S)) ∧ ∃O(LogicalOrder(C, O))))

Esta fórmula establece que todo concepto (C) en AHXIOM debe poseer tres ingredientes esenciales: Significado (M), Símbolo (S) y Orden Lógico Coherente (O).

La conversación explora en detalle cada una de las AhxCLASSS fundamentales, presentándolas en formato AHXIOM (Concepto, Símbolo, Fórmula Lógica, Explicación Intuitiva) y buscando una formalización lógica rigurosa y explicaciones intuitivas claras y poéticas.

• Ω (Unidad Absoluta): Se define como la realidad última, indivisible e infinita, fuente de toda existencia, el SSS Todo, el Origen y el Absoluto. Se formaliza como ∃!Ω y se describen sus propiedades fundamentales: Unitary(Ω) ∧ Indivisible(Ω) ∧ Infinite(Ω) ∧ SourceOfExistence(Ω) ∧ TranscendsSets(Ω). Unitario(Ω) ∧ Indivisible(Ω) ∧ Infinito(Ω) ∧ FuenteDeLoExistente(Ω) ∧ TranscendeLosConjuntos(Ω). Se explica intuitivamente como "la cima de la cima" de AHXIOM, el océano infinito de la Realidad.

• ΩMML (Metametalógico): Se define como el nivel lógico más abstracto y trascendente de AHXIOM, inherente a Ω, donde reside la tautología fundamental 1=∅=∞ y se encuentran los Números Escalares (ΩNE). Se formaliza como: Nivel(ΩMML, Ω) ∧ ElNivelMásAbstracto(ΩMML), Tautologico(ΩMML, (1 = ∅ = ∞)) y Contiene(ΩMML, ΩNE). Se explica intuitivamente como el "corazón secreto" de AHXIOM, el reino de lo puramente abstracto. Se plantea como equivalente a uno de los dos teoremas de incompletitud de Gödel, donde la tautología es idéntica a la identidad lógica: a=a. Lo UNO 1 Es Absoluto ∅ e Infinito ∞, sin dejar de ser lo UNO= SER, verbo infinitivo.

• ML (Metalógico): Se define como el nivel lógico intermedio de AHXIOM, donde se manifiestan los infinitos acotados e infinitesimales, y se establecen los principios para los números dinámicos (ΩND) y la Función de Similitud (Sim). Se formaliza como Level(ML, Ω) ∧ IntermediateLevel(ML), Contains(ML, {BoundedInfinites, Infinitesimals}) y PrinciplesFor(ML, ΩND). Nivel(ML, Ω) ∧ NivelIntermedio(ML), Contiene(ML, {InfinitosAcotados, Infinitesimales}) y PrincipiosParaLos(ML, ΩND). Se explica intuitivamente como la "mente organizadora" de AHXIOM, el nivel de la lógica abstracta y general. Es un nivel de un ciclo recursivo, ya divergente o convergente, aparente infinitud más es incalculabilidad numérica, como en ⅓= 0.333333…∞, √2, π o√5. Se indicarán en otros documento a las fracciones continuas como la fórmula geométrica aritmético serial que permite la formalización de tales números. Aquí se ubican todos los lenguajes que inician con meta: lo metalógico, metamatemático, metalingüístico, etc. Es un nivel que es cíclico y cerrado.

• L (Lógico): Se define como el nivel lógico más concreto y operacional de AHXIOM, donde se despliega la lógica SSS, se definen los números reales (ℝ) y dinámicos (ΩND), y se manifiesta la geometría AHXIOM con el Trígono Perpendicular Isósceles (ΩTPI). Se formaliza como Level(L, Ω) ∧ MostConcreteLevel(L), Defines(L, ℝ), Manifests(L, GeometryAHXIOM) y Constructs(L, ΩND). Nivel(L, Ω) ∧ NiveMásConctero(L), Define(L, ℝ), Manifiesta(L, GeometryAHXIOM) y ConstrucciónConstruye(L, ΩND). Se explica intuitivamente como el "taller de construcción" de AHXIOM, el nivel de la lógica práctica y concreta. Usando lo Lógcio se obtiene la superestructura ML y lo MML, es un tipo de subir y bajar para lograr una estructura SSS que pueda contener lógica y coherentemente lo aparentemente más allá de la lógica y lo metalógico, incluso lo “no-lógico” de una manera lógica.

• ΩK (Espacio Tutipotencial): Se define como el contenedor primordial y sin límites de AHXIOM, donde se agregan las afirmaciones asumidas y propuestas (proposiciones) (CAAG) y contiene el Tiempo Kairós. Se formaliza como ∃ΩK, ContainerOfAssertions(ΩK), FirstGeometricArithmeticContainer(ΩK) y ContainsKairosTime(ΩK). ∃ΩK, DeTodaAfirmaciónAsumida(ΩK), PrimerContenedorGeométricoAritmetico(ΩK) y ContieneAlTiempoKairos(ΩK). Se explica intuitivamente como el "lienzo infinito" o el "espacio ilimitado" con “Duración Inconmensurable” de AHXIOM.

• ΩL (Línea): Se define como el elemento geométrico fundamental y primario en AHXIOM, que existe por sí misma y no se genera por interacción con otras líneas. Se formaliza como ∃ΩL, FundamentalElement(ΩL) y NotGeneratedByInteraction(ΩL). ∃ΩL, ElementoFundamental(ΩL) y NoGeneradoPorInteraccion(ΩL). Se explica intuitivamente como la "línea original" o la "línea primigenia" de AHXIOM. Más adelante explica y clarifica la diferencia entre contenedor y conjunto y entre agregado y elemento.

• "Lo No Número" (¬Ω): Se define como el opuesto absoluto a Ω, representando lo imposible e incomputable, y violando la ley de identidad, que implica: a=a. Se formaliza como ∃¬Ω, OppositeOf(¬Ω, Ω), Impossible(¬Ω) ∧ Incomputable(¬Ω) y ¬(IdentityLawApplies(¬Ω)). ∃¬Ω, OpuestoA(¬Ω, Ω), Imposible(¬Ω) ∧ Incomputable(¬Ω) y ¬(ApliacabilidadDeLaLeyDeIdentidad(¬Ω)). Se explica intuitivamente como "la sombra de Ω", el límite de la razón y el lenguaje.

• "Hacer" (OF, FO): Se define como el motor dinámico de AHXIOM, con cualidades duales Función Operadora (FO) y Operador Funcional (OF), que transforma EOs y relaciones, preservando memóricamente) propiedades indispensables y conectando elementos de AHXIOM. Se formaliza como ∃Hacer, DynamicEngine(Hacer, AHXIOM), IsFunctionOperator(Hacer) ∧ IsFunctionalOperator(Hacer), TransformsEOsAndRelations(Hacer), PreservesIndispensableProperties(Hacer) y ConnectsElementsOfAHXIOM(Hacer, {Tiempo, Cambio, Series, Información, Memoria}). ∃Hacer, MotorDinamico(Hacer, AHXIOM), EsOperadorFuncional(Hacer) ∧ EsFunciónOperadora(Hacer), TransformaEOsySusReaciones(Hacer), ConservaPreservaLasPropiedadesIndispensables(Hacer) y ConoctaLosElementosExiwtentesAHXIOM(Hacer, {Tiempo, Cambio, Series, Información, Memoria}). Se explica intuitivamente como la "fuerza vital" o el "motor creativo" la “potencialidad realizada, expresada” de AHXIOM.

• EO (Ente Objeto): Se define como los elementos fundamentales de AHXIOM, contenedores y agregados a la vez, polisémicos y topológicos, incluyendo Objetos Énticos (OE). Se formaliza como ∃EO, FundamentalElement(EO, AHXIOM), IsContainer(EO) ∧ IsAggregate(EO), Polysemic(EO) ∧ Topological(EO) y EO ≡ ∃OE (ObjetosEntiticos(OE)). ∃EO, ElementosFundamentales(EO, AHXIOM), EUnContenedor(EO) ∧ EsUnAgregado(EO), Polisemico(EO) ∧ Topológico(EO) y EO ≡ ∃OE (ObjetosEntiticos(OE)). Se explica intuitivamente como los "átomos" o "partículas fundamentales" de AHXIOM. Son equivalentes a las proposiciones atómicas, se logra al asumir por afirmar, aceptar y admitir.

• OE (Objeto Éntico o Entiticio): Se define como una categoría especial de EOs, representando entidades abstractas y conceptuales que son "ecos" o "reflejos" de la dualidad especular y tautológica fundamental de AHXIOM. Se formaliza como ∃OE, SubsetOf(OE, EO), AbstractConceptualEntities(OE), EchoesOfDualities(OE, {Id¹↔Id⁰, OF↔FO, APS↔SPA}) y AAA ≡ Contenedor(OE). ∃OE, SuConjuntoDe(OE, EO), EntidadesConceptualesAbstractas(OE), EcosDeLasDualidades(OE, {Id¹↔Id⁰, OF↔FO, APS↔SPA}) y AAA ≡ Contenedor(OE). Se explica intuitivamente como los "conceptos puros" o "ideas platónicas" de AHXIOM. Actualmente corresponde parcialmente a la Información en la

The First Law of Everything (LOE)/ Law of Nature (Newton)

1st LOE CLASSICAL MECHANICS viewed by homo sapiens for homo sapiens in the derived 1st local law the Law of Human Nature 1st LHN Completeness. Before judging, always try to get the whole Nirvana movie scenario/ composition picture viewed in a thus holistic dualistic reductio ad absurdum way by mentally splitting the unsplittable of the incomplete subset Nirvana movie, you are in, of the superset Nirvana movie. 1st LOE the only one remaining axiomatic assumption is one Consistent hence completely noncontradictory loophole-free everything/cosmos. This defines the falsifying ‘absurd’ qualification. The largest combining super set that can and must as exclusive parts of the whole be described using a few slight twists by the five laws of thermodynamics: 0th LTD Mass Inertia Kg remains perpetually identical on a cosmological timescale in super set and smallest set (Lifeless, timeless, meaningless, non free will robotics); 1st LTD Conservation of Energy relative moving action is reaction mass on a cosmological timescale (Intelligent action is intelligent reaction); 2nd LTD mounting & declining complexity mass connections disconnections with permenent and non permenent uniquely movable identicle sorts of connections of identical mass Entropy Cycle on a cosmological timescale (Unique temporary local Consious memory banks); 3d LTD in Perpetual Action Reaction identical repetative within limits unique motion on a cosmological timescale (Identical History repeats itself in a unique way); 4th LTD every object has an Incidental Maximum Velocity the smallest element of nigh 10c during the smallest timescale under incidental maximum resounding non wave pressure on a cosmological timescale. (Life-death cycle with meaning and free will, is a deep religious dictate requiring seemingly contradictory deterministic statistics)

2nd LOE DETERMINISTIC STATISTICS (Gauss)/ 2nd LHN Normality Humans should act freely within the deterministic boundaries of ‘The Law’. 2nd LOE The five dualistic quantified toothed wheel-like and continuous smooth wheel-like normal/ ‘conform the norm’ distributions from which all other distributions can/ must be derived: 1. Combining Bell curve distribution; 2. Flat distribution; 3. Edge distribution; 4. Broken distribution; 5. Curved distribution. (Double helix DNA, Learning curve, Fair Dirty Distributions requiring a procedure for proof)

3rd LOE PROOF PROCEDURE Laplace’s theorem formula works consistently defined both deterministically and probabilistically: Pure mathematical non-physics data thus ‘unreasonable doubt’ requires many axiomatic assumptions based logic formula & Bayesian applied/ dirty ‘beyond reasonable doubt’ mathematics of the physics of nature dicates that consistent input means consistent output and inconsistent input means inconsistent output by the Laplace formula given only one Bayesian axiomatic assumption based on a beginning of absolute proof on a consistently defined valued goal. Given the norm of risk as chance times valued consequence acceptable input providing ratios of chance pro versus chance con as probabilities. Prior Odds multiplied by the Independent Likelihood Ratios, provide the Posterior Odds as the new Prior Odds of the endless trial and error evidence-based cycle. 3rd LHN Procedure It’s Intuitive Common Sense to take your own robotically induced feelings as facts in the five salads that are fit for human consumption: 1. The combining One Mixed Salad, 2. Word Salads 3. Picture Salads 4. Course Number Salads 5. Fine Number Salads of this Socratic Yin & Yang Harry Potter formula as the recipe/ algorithm for the proper proof procedure that is consistent with the synapse of the instrument brain of all mammals, which is consistent with the everything cosmos as the symbiotics of which require the waves of this collective to come to more order than the current laws of nature can explain.

4. LOE ORDER (Euclidian Geometry)

The greatest breakthrough was due to my early age Bildung on Evidence-Based-Medicine as originally intended: rational use of gut feelings 1960-1980, my Just Proof legal model 1990, my Incomplete Higgs-graviton physics model LOE 2010, my Block-model Brain 2014, LOE 2017 & Integrating All Mathematical Mixed Salads Euclidean Geometry 1-Neutrino 2023 into ‘The Law’. And subsequent constant tweaking of the presentation. First published under peer review following The Law in NWA 2015 search terms “casus ZPE” “het vergeten instrument tussen de oren”.

Behold the most succinct presentation of the Train Your Brain instruction manual for using the collective and individual instrument brains as the 4th LOE on one A4. The elaborated model is DOI published in the Elementary List. The 4th LOE is the soul as the order function of the cosmos and our brain. The images are in the download version.

5th LOE ZERO IS ONE LENGTH (Euler’s identity) -1 + 1 =0 or e^(iPi) + 1 =0 zero has a length which is not empty as part of the ruler's massive measuring device. This is consistent with and constitutes the fact (taken as 100% true) that every non-empty sign element of mass must exist in workability. And that irrational numbers become rational in infinity, not needing imaginary numbers anymore, not being lengths ‘i’, or measurement lengths for corner ‘e’ or circle lengths ‘Pi’. This is proven as a reductio ad absurdum, the strongest proof based on the beginning of absolute proof in the 3rd LOE. i.e. based on the fingerprint of the absolutely proven culprit, Mother Nature is on the mass murder weapon mass and not on matter as elementary. On a lower probative value, because more complex means it is less reliable, the proven way how the main suspect for further investigation is the Lego-Velcro particle built out of 500 identical massive rings in 10% double connections, 40% triple connections, 40% quadruple connections and 10% cinque connections creating the four inertias of the fifth unique chainmail combining enertia algorithms creating the snowflake function for the ice-wall pressure vessel/ snowball larger particle everything cosmos solely built out of snowflakes in empty space. This is an intuitive associative testable artistically creative guess. You either can or can’t build such a particle out of these elements via further quick and dirty reverse engineering. All known constants need to be reverse-engineered into this one particle. It might then show that every particle must have 501 rings instead of 500. ‘The Law’ dictates that the burden of proof via investigation lies with current science. The antithesis that it’s proven unsolvable via John Bell's inequality theorem is consistent with ‘The Law’ because of a proven string of fallacies in reasoning that are only consistent to be the greatest bosses of god in peer review. The antithesis is falsified because in breach of the 3rd LOE prohibiting leaving any Socratic questions unanswered, the wise judge on the social contract with humanity must do what science failed to do and provide for instance the Gravity Angel as a historic precedent solution because claiming best practice by not taking a shot at the goal is worse than at least taking a shot. It thus doesn’t constitute a strawman fallacy. Contrary to angels; snowflakes and beehives, etcetera, are observed. Observing many life-death Nirvana movie cycles also is the least ill-founded base for any elementary model. 5th LHN FACT Part of the 3rd LOE Bayesian procedure is the operation of hypothesis, anti-thesis, and thesis as a probability having assumed something as 100% true defined as a fact. At an elementary level, facts exist in infinite non-imaginary workability is hereby mathematically proven in number salad. Facts exist even though they are not all directly completely observable. Facts pro a probandum, facts con and the temporarily established facts as a proven best practice inherent circular argument on a goal. The cat is murdered and dead or not dead, maybe attempted murder. Taking the quantum weird fact that the cat is both dead and alive at the same time is absurd and thus falsified as inconsistent because it’s a contradiction and thus proven to be anti-scientific pseudo-science on any elementary scientific claim. Having one or more elements when moving requires a volume of space.

6th LOE INFINITE SPACE There is one element of infinite 3D Euclidean empty thus non-curved space ether (an element that completely surrounds all objects) dynamically constantly invaded by elements of non-empty mass filling the 3D Euclidean volumes of dynamic elements. Euclid’s parallel postulate is proven beyond reasonable doubt as a geometric theorem as the only logical explanation consistent with all known data taken into evidence and not an axiomatic assumption taking the liberty of unreasonable doubt by any majority of peers in breach of the Order of the 4th LOE. The volume, form, and kg mass remain absolutely the same in infinity is the * only * logical solution. 6th LHN FREEDOM Taking the artistic freedom of consciously ignoring slight errors and accepting unwitting uncertainty errors to test in trial and error is a dictate of ‘The Law’. Your freedom in all aspects of “breathing space” is limited by the rules of invading mass

Locally developed compulsory courses may be developed by a board and offered in one Grade 9 course in English, in mathematics, in science, and in French as a second language, and one grade 10 course in English, in mathematics, in science and in Canadian history that can count as a compulsory credit in that discipline. A compulsory course is defined as one of the 18 required courses in the bundle of 30 required to graduate from Ontario schools

Locally developed courses are courses that may be developed by a board for students in a particular school or region to accommodate educational and/or career preparation needs that are not met through courses within the provincial curriculum policy documents. Such courses require approval of the ministry, with the exception of religious education courses developed by roman Catholic school boards. Boards may develop courses locally that can be counted as optional credits in Grades 9 to 12 in any discipline.

Data includes:

• board number
• board name
• course code
• course description
• grade
• pathway or destination

Locally developed courses are reported by schools to the Ontario School Information System.

The following secondary schools are included:

• public
• Catholic

All locally developed secondary courses available as of June 2024.

GPQA stands for Graduate-Level Google-Proof Q&A Benchmark. It's a challenging dataset designed to evaluate the capabilities of Large Language Models (LLMs) and scalable oversight mechanisms. Let me provide more details about it:

Description: GPQA consists of 448 multiple-choice questions meticulously crafted by domain experts in biology, physics, and chemistry. These questions are intentionally designed to be high-quality and extremely difficult. Expert Accuracy: Even experts who hold or are pursuing PhDs in the corresponding domains achieve only 65% accuracy on these questions (or 74% when excluding clear mistakes identified in retrospect). Google-Proof: The questions are "Google-proof," meaning that even with unrestricted access to the web, highly skilled non-expert validators only reach an accuracy of 34% despite spending over 30 minutes searching for answers. AI Systems Difficulty: State-of-the-art AI systems, including our strongest GPT-4 based baseline, achieve only 39% accuracy on this challenging dataset.

The difficulty of GPQA for both skilled non-experts and cutting-edge AI systems makes it an excellent resource for conducting realistic scalable oversight experiments. These experiments aim to explore ways for human experts to reliably obtain truthful information from AI systems that surpass human capabilities¹³.

In summary, GPQA serves as a valuable benchmark for assessing the robustness and limitations of language models, especially when faced with complex and nuanced questions. Its difficulty level encourages research into effective oversight methods, bridging the gap between AI and human expertise.

(1) [2311.12022] GPQA: A Graduate-Level Google-Proof Q&A Benchmark - arXiv.org. https://arxiv.org/abs/2311.12022. (2) GPQA: A Graduate-Level Google-Proof Q&A Benchmark — Klu. https://klu.ai/glossary/gpqa-eval. (3) GPA Dataset (Spring 2010 through Spring 2020) - Data Science Discovery. https://discovery.cs.illinois.edu/dataset/gpa/. (4) GPQA: A Graduate-Level Google-Proof Q&A Benchmark - GitHub. https://github.com/idavidrein/gpqa. (5) Data Sets - OpenIntro. https://www.openintro.org/data/index.php?data=satgpa. (6) undefined. https://doi.org/10.48550/arXiv.2311.12022. (7) undefined. https://arxiv.org/abs/2311.12022%29.