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.
107 results for "complex numbers" — page 5 of 6
V_2_09 — Number Theory: Primes, Patterns, and Unsolved Problems
Number theory — the study of integers and their properties — is one of the oldest and most beautiful branches of mathematics, yet it connects to cryptography, physics, and computer science in profound ways. Prime numbers
V_2_15 — Galois Theory and Field Extensions
Galois theory, developed by Évariste Galois (1811-1832) in the last years of his tragically short life, is one of the great triumphs of abstract algebra — a theory connecting field extensions to group theory that definit
W_4_07 — Amazonian Traditions, Plant Teachers, and the Ayahuasca Complex
The Amazon Basin — the world's largest tropical rainforest — is home to approximately 400 indigenous groups with an extraordinary tradition of plant-based knowledge unmatched anywhere on Earth. At the center of this trad
E_3_03 — Ice Age Civilizations — Evidence for Complexity During the Last Glacial Maximum
The Last Glacial Maximum (LGM, ~26,500-19,000 BP) — when ice sheets covered ~32% of the global land surface and sea levels dropped ~120 meters below present — was not a period of human stagnation but of remarkable cultur
E_4_01 — Precession of the Equinoxes and Ancient Encoded Numbers
This document examines Precession of the Equinoxes and Ancient Encoded Numbers, a topic within the Cataclysms and Chronology research area. Notable findings include: 25,920 ÷ 12 = 2,160 years** per zodiacal age. The docu
D_2_03 — Karnak Temple Complex — The Dwelling of Amun-Ra
The Karnak Temple Complex, located on the east bank of the Nile at ancient Thebes (modern Luxor, Upper Egypt), is the largest religious complex ever constructed — encompassing over 100 hectares of temples, chapels, pylon
D_1_23 — Carnac Stone Alignments: Europe's Largest Megalithic Complex
The Carnac stone alignments — located near the town of Carnac in southern Brittany, France — constitute the largest collection of megalithic standing stones in the world. Over 3,000 menhirs (upright stones) are arranged
D_1_14 — Karahan Tepe — Pre-Pottery Neolithic Ritual Complex
Karahan Tepe is a Pre-Pottery Neolithic (PPN) site in southeastern Turkey (Şanlıurfa Province), approximately 46 km southeast of Göbekli Tepe, dating to c. 9400–8200 BCE. Discovered during surface surveys in 1997 and sys
D_1_05 — Stonehenge and the British Megalithic Complex
Stonehenge on Salisbury Plain, Wiltshire, is Britain's most iconic prehistoric monument, constructed in multiple phases between approximately 3100 and 1500 BCE — a span of over 1,600 years. The site features massive sars
D_1_24 — Newgrange, Knowth, and Dowth: The Brú na Bóinne Complex
The Brú na Bóinne (Palace of the Boyne) — a UNESCO World Heritage Site in County Meath, Ireland — contains the three great passage tombs of Newgrange, Knowth, and Dowth, alongside approximately 40 smaller satellite monum
D_1_19 — Poverty Point: Louisiana's Enigmatic Archaic Earthwork Complex
Poverty Point is a Late Archaic period (approximately 1700–1100 BCE) earthwork complex located near the town of Epps in West Carroll Parish, northeastern Louisiana, on the Macon Ridge overlooking the floodplain of Bayou
D_1_26 — Ajanta and Ellora: Rock-Cut Temple Complexes of India
Ajanta and Ellora are two UNESCO World Heritage rock-cut cave complexes in the Sahyadri hills of Maharashtra, western India, approximately 100 km apart. Together they span over 1,000 years of continuous religious art and
D_5_26 — Terracotta Army: Qin Shi Huang's Funerary Complex
The Terracotta Army — an estimated 8,000+ life-sized clay warriors, 130 chariots, 520 horses, and 150 cavalry horses — was buried circa 210 BCE to guard the tomb of Qin Shi Huang (259–210 BCE), China's first emperor, nea
R_4_14 — Evolution of Hearing: From Vibration Sensing to Complex Auditory Systems
The evolution of hearing — the ability to detect pressure waves propagating through air, water, or solid substrates — represents one of the most remarkable transformations in vertebrate history. The story begins with anc
R_3_02 — Horizontal Gene Transfer in Complex Life
For decades, the "tree of life" was the central metaphor of evolutionary biology — species branching neatly from common ancestors through vertical gene transmission (parent to offspring). This metaphor is now BROKEN, at
R_1_08 — Photosynthesis — The Reaction That Made Complex Life Possible
Photosynthesis — the conversion of light energy into chemical energy — is arguably the most consequential biochemical innovation in Earth's history. Oxygenic photosynthesis, evolved by cyanobacteria approximately 2.4–3.0
V_3_03 — Chaos Theory & Fractals: Mathematics of Complexity
Chaos theory — the mathematical study of systems that are deterministic yet unpredictable — represents one of the most profound discoveries of 20th-century mathematics. Edward Lorenz (1963) discovered that a simple syste
INTERDOC_73 — Cancer as Informational Coherence Collapse
[KEY FINDING] By isolating the progression of cancer across four distinct levels of biological organization, we find that tumorigenesis is universally preceded by a loss of systemic coherence.
INTERDOC_52 — Distributed Cognition: Decentralized Information Networks Across Biology
Cognition — defined functionally as adaptive information processing, decision-making, and memory — is implemented across biology in many architectures other than the centralized animal nervous system. Mycorrhizal fungal
ZB_5_17 — Constructal Law & Flow Architecture: Why Nature Branches the Way It Does
Most fractal descriptions of nature are descriptive: they observe that rivers branch like blood vessels, blood vessels branch like trees, trees branch like lightning bolts, and lightning bolts branch like river deltas. A
BROWSE BY SECTION — 3,721 documents across 34 fields