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.
1,346 results for "foundations of mathematics" — page 16 of 68
V_4_13 — Mathematics of Voting: Arrow's Theorem, Fairness, and Electoral Systems
The mathematics of voting — a branch of social choice theory — applies rigorous mathematical analysis to the problem of aggregating individual preferences into collective decisions, revealing deep impossibility results t
V_3_09 — Fourier Analysis: Signal Processing and the Mathematics of Frequency
Fourier analysis — the decomposition of functions into constituent sinusoidal waves — is one of the most transformative mathematical ideas in science and engineering. Joseph Fourier's 1822 insight that any periodic funct
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
V_2_19 — Category Theory: Abstract Structure, Functors & Topos Theory
Category theory — often called the "mathematics of mathematics" — provides a universal language for describing mathematical structures and the relationships between them, emphasizing morphisms (arrows, maps, transformati
M_1_11 — Baigong Pipes: Natural Formation or Anomalous Technology?
The Baigong pipes (also called the "Baigong alien ruins") are a collection of pipe-like iron-rich structures found in and around three caves on Mount Baigong (also transliterated Bai Gong Shan), near Delingha in the remo
A_1_15 — Mesopotamian Wisdom Literature
Mesopotamian wisdom literature — spanning over 2,000 years from Sumerian proverb collections (c. 2500 BCE) to late Babylonian philosophical dialogues (c. 500 BCE) — represents humanity's earliest sustained written engage
A_1_04 — Enki, Enlil, and the Sumerian Divine-Political Hierarchy
Enki and Enlil are the two most consequential deities in Sumerian religion, representing fundamentally opposed principles: Enki embodies wisdom, craft, water, and compassion toward humanity; Enlil embodies authority, cos
A_1_16 — Behistun Inscription and Old Persian Royal Texts
The Behistun Inscription (also spelled Bisotun, located on a cliff face in western Iran) is the most important Old Persian royal text and one of the most significant epigraphic monuments in the history of scholarship — i
A_1_07 — Enuma Elish — The Babylonian Creation Epic
The Enuma Elish ("When on high…") is the Babylonian creation epic — a cosmogonic poem of approximately 1,100 lines inscribed on seven clay tablets, composed ca. 1100 BCE (though likely drawing on older traditions back to
A_1_06 — Ugaritic Literature and the Baal Cycle
This document examines Ugaritic Literature and the Baal Cycle, a topic within the Foundations research area. Key areas of investigation include Ras Shamra — Accidental Discovery, The City of Ugarit, The Library and Archi
A_2_01 — Bible Serpent References
The Bible contains extensive references to serpents, dragons, and reptilian-type beings whose original meanings differ sharply from later theological reinterpretation. The Hebrew word "nachash" carries meanings of serpen
A_2_06 — Zohar, Merkabah Literature, and Hekhalot Texts
The Zohar, Merkabah literature, and Hekhalot texts constitute the foundational corpus of Jewish mysticism spanning roughly 1,500 years of development. Merkabah ("chariot") mysticism — rooted in Ezekiel 1 and 10 — represe
A_2_04 — Dead Sea Scrolls Expanded
The Dead Sea Scrolls (DSS), discovered between 1947–1956 in 11 caves near Qumran on the northwest shore of the Dead Sea, comprise over 900 manuscripts dating from the 3rd century BCE to the 1st century CE. Beyond their w
A_2_02 — Nag Hammadi & Gnostic Texts
The Nag Hammadi Library is a collection of 13 leather-bound papyrus codices containing 52 texts, discovered in 1945 near Nag Hammadi, Upper Egypt. Written in Coptic and dated to the 3rd–4th centuries CE (with originals p
A_2_07 — 2 Enoch (Slavonic) and 3 Enoch (Hebrew Apocalypse)
2 Enoch (the "Slavonic Apocalypse of Enoch" or "Book of the Secrets of Enoch") and 3 Enoch (the "Hebrew Apocalypse of Enoch" or "Sefer Hekhalot") are two distinct pseudepigraphical texts that extend the Enochic tradition
A_2_05 — The Hermetic Tradition: Thoth, Hermes Trismegistus, and the Emerald Tablet
This document examines The Hermetic Tradition: Thoth, Hermes Trismegistus, and the Emerald Tablet, a topic within the Foundations research area. Notable findings include: Ancient Egyptian tradition describes a Book of Th
A_4_06 — Quranic Cosmology, Jinn, and Islamic Angelology
The Quran — Islam's primary sacred text (610–632 CE) — presents a rich cosmological framework that includes seven heavens and seven earths, a Throne of God (al-Arsh) upon the cosmic waters, a fully populated invisible re
A_4_08 — Bhagavata Purana — Naga and Avatar Sections
The Bhagavata Purana (also called Srimad Bhagavatam) is one of the eighteen Mahapuranas ("Great Ancient Histories") of Hindu literature, composed in Sanskrit between approximately the 6th and 10th centuries CE. Its twelv
A_4_18 — Confucian Analects: Foundations of East Asian Thought
The Analects (Lúnyǔ 論語, "Collected Sayings") is the foundational text of Confucianism, comprising 20 books of aphorisms, dialogues, and biographical fragments attributed to Confucius (Kǒngzǐ 孔子, 551–479 BCE) and compiled
A_4_27 — Korean Samguk Yusa: Myths, Miracles, and the Foundations of Korean Identity
The Samguk Yusa (삼국유사, "Memorabilia of the Three Kingdoms") is a collection of legends, folktales, Buddhist miracle stories, and historical accounts relating to the Three Kingdoms of Korea (Goguryeo, Baekje, and Silla) a
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