RESEARCH BASE
Search 3,721 documents across 34 fields — every claim tier-rated by evidence
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.
221 results for "square root two" — page 7 of 12
O_5_04 — Soil Science — Underground Biogeochemistry and Human Health
Soil — a thin veneer of biologically active, chemically complex material covering most of Earth's land surface — is arguably the most under-appreciated and misunderstood component of the Earth system. Far from inert "dir
O_5_02 — Soil Biomes and Underground Ecosystems
Beneath every terrestrial landscape lies one of Earth's most complex and least understood ecosystems — the soil biome, a living matrix containing an estimated 25% of all species on Earth (Decaëns et al., 2006) and proces
T_1_07 — Emotion Theory and Affect
Emotion theory addresses one of psychology's most fundamental and contested questions: What are emotions, where do they come from, and how many are there?
T_3_02 — Psychology of Creativity & Insight
The psychology of creativity investigates the cognitive processes, personality traits, environmental conditions, and neural mechanisms underlying the generation of novel and useful ideas, solutions, and products.
T_3_04 — Sleep Psychology and Dreams
Sleep occupies approximately one-third of human life yet its functions remain among the most actively investigated questions in neuroscience and psychology.
T_3_12 — Altered States of Consciousness: Trance, Meditation, and Sensory Deprivation
Altered states of consciousness (ASCs) — states that differ qualitatively from ordinary waking awareness in terms of perception, cognition, self-awareness, affect, and volition — have been systematically studied since th
B_4_02 — Mandaeism: Living Gnostic Religion
Mandaeism is one of the oldest continuously practiced Gnostic religions in the world, with an estimated 60,000-100,000 adherents primarily concentrated in southern Iraq and southwestern Iran, with significant diaspora co
B_3_10 — World Tree Guardians and Cosmic Serpents
The World Tree — a colossal tree (or pillar, mountain, or vine) connecting the layers of the cosmos (typically underworld, earth, and heavens) — is one of the most widespread cosmological concepts in human mythology, app
B_3_02 — Wadjet (Wadjyt) and Uraeus: Egyptian Cobra Protector
Wadjet is a core Egyptian cobra goddess tied to Lower Egypt and royal protection. The Uraeus motif (rearing cobra on royal regalia) represents her power, paired with Nekhbet as the "Two Ladies" of unified kingship. Evide
ZD_1_03 — Information as Fundamental Reality
Multiple converging lines of evidence suggest information, not matter or energy, may be the most fundamental constituent of reality. From Wheeler's "It from Bit" to the holographic principle (3D reality encoded on 2D bou
ZD_3_18 — Optical Computing: Photonic Processors, All-Optical Logic & Speed-of-Light Computation
Optical computing — the use of photons instead of electrons to perform computation — has been pursued since the 1960s as a means to overcome the fundamental speed, bandwidth, and energy limitations of electronic processo
ZD_3_03 — Distributed Systems and Consensus
Distributed systems — collections of independent computers that appear to users as a single coherent system — are fundamental to modern computing infrastructure: the internet, cloud computing, databases, blockchain, and
ZD_4_10 — Complexity Theory in Biology — Kauffman, Wolfram, Edge of Chaos
The application of complexity theory to biology — the study of how complex, adaptive, self-organizing structures and behaviors emerge in living systems from the interactions of simpler components — has been one of the mo
ZD_4_03 — Numerical Methods and Scientific Computation: Algorithms for the Continuous World
Numerical methods are algorithms for approximately solving mathematical problems that lack closed-form analytical solutions — which is to say, most problems in science and engineering. From weather prediction to aircraft
ZD_4_14 — Computational Social Science: Agent-Based Modeling, Digital Trace Data, and Social Simulation
Computational social science (CSS) is the interdisciplinary field that applies computational methods — agent-based modeling, social network analysis, natural language processing, machine learning, simulation, and large-s
ZD_2_04 — Computer Vision and Image Processing
Computer vision — enabling machines to interpret and understand visual information from the world — has progressed from hand-crafted feature engineering to the deep learning revolution that now approaches or exceeds huma
ZD_2_15 — Transformer Architecture: Self-Attention and the Foundation of Modern AI
The transformer is a neural network architecture introduced in 2017 that replaced recurrent and convolutional models as the dominant paradigm in artificial intelligence. Its core innovation — the self-attention mechanism
ZD_2_02 — Artificial Intelligence Foundations
Artificial intelligence (AI) — the field devoted to creating machines that exhibit intelligent behavior — was formally founded at the Dartmouth Conference (1956) organized by John McCarthy, Marvin Minsky, Nathaniel Roche
ZD_2_07 — Artificial General Intelligence — Architectures and Challenges
Artificial General Intelligence (AGI) — a hypothetical AI system capable of performing any intellectual task that a human can, with the same flexibility, generality, and ability to learn and transfer knowledge across dom
ZD_2_01 — Machine Learning Mathematics
Machine learning — the science of algorithms that improve through experience — rests on a rich mathematical foundation spanning optimization, statistics, linear algebra, probability, and functional analysis. The core mat
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