RESEARCH BASE

Search 3,721 documents across 34 fields — every claim tier-rated by evidence

3,721 Documents 34 Sections 43,625 Citations 34,852 Keywords Indexed 4 Evidence Tiers

3,633 are the core, quality-scored corpus (34 lettered sections — see How We Work); the remaining 88 are cross-corpus synthesis documents (68 InterDocs, 12 Connections, 8 Theories) also indexed here.

486 results for "set theory" — page 2 of 25

G_2_05 Verified Modern Frameworks

G_2_05 — Graph Theory and Knowledge Network Analysis

Graph theory — the mathematical study of networks of nodes (vertices) connected by edges (links) — provides a rigorous framework for analyzing the structure of connections in systems ranging from ancient social hierarchi

graph theory network analysis knowledge graphs small world scale-free Euler
G_2_14 Credible Modern Frameworks

G_2_14 — Information Theory Applied to Ancient Scripts and Codes

Information theory — founded by Claude Shannon (1948) — provides a mathematical framework for quantifying the information content, redundancy, and statistical structure of communication systems. When applied to ancient s

information theory entropy Shannon script decipherment undeciphered
T_4_15 Credible Psychology & Social

T_4_15 — The Psychology of Cooperation and Trust: Game Theory, Reciprocity, and Institutions

Cooperation — acting in ways that benefit others at a cost to oneself — is both theoretically puzzling (why would natural selection favor organisms that sacrifice fitness for others?) and practically essential (every hum

cooperation trust game theory prisoner's dilemma reciprocity altruism
T_1_18 Verified Psychology & Social

T_1_18 — Attachment Theory

Attachment theory — one of the most influential frameworks in developmental and clinical psychology — proposes that early bonds between infants and caregivers shape social, emotional, and cognitive development across the

attachment-theory john-bowlby mary-ainsworth strange-situation secure-attachment avoidant
T_1_14 Verified Psychology & Social

T_1_14 — Self-Determination Theory: Autonomy, Competence, Relatedness, and Intrinsic Motivation

Self-Determination Theory (SDT) — developed by Edward Deci and Richard Ryan (University of Rochester, 1985–present) — is one of the most influential and empirically supported theories of human motivation, proposing that

self-determination theory SDT Deci Ryan intrinsic motivation extrinsic motivation
T_1_15 Credible Psychology & Social

T_1_15 — Schema Theory: Cognitive Frameworks, Scripts, and Knowledge Organization

Schema theory — the idea that the mind organizes knowledge into structured mental frameworks (schemas) that guide perception, memory, and reasoning — is one of the foundational concepts in cognitive psychology, linking w

schema schema theory Bartlett Piaget assimilation accommodation
T_3_05 Verified Psychology & Social

T_3_05 — Psychology of Motivation and Drive

Motivation — the processes that initiate, direct, and sustain goal-directed behavior — is one of psychology's most extensively studied domains, with applications spanning education, workplace productivity, health behavio

motivation psychology drive theory intrinsic motivation extrinsic motivation self-determination theory Deci
T_5_10 Credible Psychology & Social

T_5_10 — The Psychology of Money: Behavioral Economics, Financial Decision-Making, and Wealth Psychology

The psychology of money explores how cognitive biases, emotional responses, social pressures, and personality traits systematically distort financial decision-making — departing dramatically from the "rational economic a

psychology of money behavioral economics Kahneman Tversky prospect theory loss aversion
ZD_1_17 Credible Information & Computation

ZD_1_17 — Integrated Information Theory

Integrated Information Theory (IIT) is a mathematical theory of consciousness developed by Giulio Tononi (University of Wisconsin-Madison, 2004; IIT 3.0, 2014; IIT 4.0, 2022) that attempts to explain what consciousness i

integrated-information-theory iit consciousness phi giulio-tononi qualia
P_5_06 Verified Philosophy & Meaning

P_5_06 — Philosophy of Mathematics

The philosophy of mathematics investigates the nature of mathematical objects, the status of mathematical truth, and the relationship between mathematics and the physical world. The fundamental question is: Are mathemati

philosophy of mathematics mathematical realism Platonism mathematics nominalism formalism logicism
R_5_19 Verified Biology & Evolution

R_5_19 — Evolutionary Game Theory: Cooperation, Altruism, and Strategy in Nature

Evolutionary game theory applies mathematical game theory to biological evolution, explaining how natural selection favors strategies for survival and reproduction in competitive and cooperative interactions. The field's

evolutionary game theory prisoner's dilemma tit for tat altruism kin selection reciprocity
R_1_06 Verified Biology & Evolution

R_1_06 — Symbiogenesis — Lynn Margulis and Cooperative Evolution

Symbiogenesis — the evolutionary origin of new organisms, organelles, or metabolic capabilities through the permanent merger of previously independent life forms — is one of the most consequential biological discoveries

symbiogenesis Lynn Margulis endosymbiosis mitochondria chloroplasts serial endosymbiotic theory
S_4_17 Verified Future Technology

S_4_17 — Space Habitats & In-Situ Resource Utilization (ISRU): Off-World Settlement Engineering

Space habitats and In-Situ Resource Utilization (ISRU) — the extraction and processing of local materials (regolith, water ice, atmospheric gases) to support human presence beyond Earth — constitute the engineering found

space habitat ISRU O'Neill cylinder Mars settlement lunar base radiation shielding
ZA_2_13 Verified Physics & Quantum

ZA_2_13 — Quantum Gravity Approaches

Quantum gravity is the unfinished quest to unify general relativity (GR) — which describes gravity as spacetime curvature at macroscopic scales — with quantum mechanics (QM), which governs microscopic physics. The challe

quantum gravity loop quantum gravity string theory causal dynamical triangulations spin foam asymptotic safety
ZA_1_10 Verified Physics & Quantum

ZA_1_10 — Feynman Diagrams: The Visual Language of Quantum Field Theory

Feynman diagrams — the pictorial representations of mathematical expressions describing the behavior of subatomic particles — are among the most powerful and iconic tools in theoretical physics, invented by Richard Feynm

Feynman diagram quantum field theory perturbation theory propagator vertex scattering amplitude
V_1_02 Verified Mathematics & Information

V_1_02 — Infinity, Paradoxes, and Mathematical Philosophy

Infinity has been a source of wonder, terror, and paradox since the ancient Greeks first grappled with Zeno's paradoxes of motion. Georg Cantor's revolutionary set theory (1870s-1890s) proved that infinities come in diff

infinity Cantor set theory Zeno paradoxes Russell paradox continuum hypothesis
V_4_03 Verified Mathematics & Information

V_4_03 — Geometric Probability and Buffon's Needle

Geometric probability assigns probabilities to random geometric events — needle drops, random points in regions, random lines intersecting figures — formalizing questions that blend chance with spatial structure. Buffon'

geometric probability Buffon needle Bertrand paradox integral geometry stochastic geometry random convex sets
V_4_18 Verified Mathematics & Information

V_4_18 — Information Theory Cross-Discipline Bridge

Information theory, founded by Claude Shannon in 1948, provides a universal mathematical framework for quantifying uncertainty, communication capacity, and data compression. Its core concepts — entropy, mutual informatio

information theory Shannon entropy Kolmogorov complexity thermodynamic entropy holographic principle genetic code
V_4_01 Verified Mathematics & Information

V_4_01 — Discrete Mathematics and Logic

Discrete mathematics — the study of mathematical structures that are countable, separated, or distinct (as opposed to continuous) — provides the theoretical bedrock for computer science, digital communication, and rigoro

discrete mathematics mathematical logic propositional logic predicate logic set theory Gödel incompleteness
V_4_07 Credible Mathematics & Information

V_4_07 — Chaos Theory Applications: Sensitivity, Strange Attractors, and Prediction

Chaos theory — the study of deterministic systems that exhibit sensitive dependence on initial conditions — is one of the most consequential mathematical discoveries of the 20th century, fundamentally altering our unders

chaos theory butterfly effect Lorenz strange attractor sensitivity nonlinear dynamics