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.

335 results for "Lie group" — page 11 of 17

V_3_11 Verified Mathematics & Information

V_3_11 — Mathematical Optimization: Linear Programming, Convex Methods, and Gradient Descent

Mathematical optimization — finding the best solution from a set of feasible alternatives — is one of the most practically impactful branches of mathematics, with applications spanning logistics, finance, engineering, ma

mathematical optimization linear programming simplex method convex optimization gradient descent stochastic gradient descent
V_2_15 Verified Mathematics & Information

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

Galois theory field extension polynomial roots solvability by radicals quintic equation group theory
M_5_03 Verified Forbidden Archaeology

M_5_03 — Piri Reis Map and Cartographic Anomalies

The Piri Reis map is a fragment of a world map drawn on gazelle parchment by the Ottoman admiral and cartographer Piri Reis (Ahmed Muhiddin Piri) in 1513 CE, rediscovered in the Topkapi Palace library, Istanbul, in 1929.

Piri Reis portolan chart Ottoman 1513 Antarctica coastline
M_1_18 Verified Forbidden Archaeology

M_1_18 — Ancient Metallurgy Anomalies

Ancient metallurgical achievements frequently surpass what conventional archaeological narratives would predict for their time periods, leading to enduring debates about the sophistication of pre-industrial materials sci

ancient metallurgy Damascus steel wootz Delhi iron pillar Antikythera mechanism Roman concrete
A_4_12 Verified Foundations

A_4_12 — Pali Canon (Tipitaka) — Earliest Buddhist Scriptures

The Pali Canon (Tipiṭaka, "Three Baskets") is the oldest complete collection of Buddhist scriptures, preserved in the Pali language by the Theravada tradition of Sri Lanka and Southeast Asia. Transmitted orally for appro

Pali Canon Tipitaka Tripitaka Sutta Pitaka Vinaya Pitaka Abhidhamma
ZH_5_05 Verified Archaeoastronomy

ZH_5_05 — Cross-Cultural Constellation Patterns: Connecting Star Groupings Worldwide

Every documented human culture groups stars into constellations or asterisms — named patterns that organize the sky into a readable, memorizable, and culturally meaningful map. Yet surprisingly few star groupings are uni

constellations cross-cultural asterism star patterns IAU Greek
ZG_2_00 Linguistics & Communication

ZG_2_00 — Language Families History: Subfolder Summary

ZG_4_00 Linguistics & Communication

ZG_4_00 — Applied Sociolinguistics: Subfolder Summary

Q_1_22 Credible Cosmology & Physics

Q_1_22 — Dark Flow and Cosmic Dipole Anomalies

Dark flow refers to a claimed coherent bulk motion of galaxy clusters toward a specific region of the sky at velocities inconsistent with the predictions of standard ΛCDM cosmology, first reported by NASA Goddard astroph

dark flow bulk flow cosmic dipole CMB anisotropy Kashlinsky
Q_1_07 Verified Cosmology & Physics

Q_1_07 — CMB Anomalies and the Axis of Evil

The Cosmic Microwave Background (CMB) — the afterglow of the Big Bang, emitted ~380,000 years after the universe began — is the most precisely measured radiation in the history of science. It matches the theoretical pred

CMB cosmic microwave background WMAP Planck anisotropy anomaly
Credible

INTERDOC_22 — Near-Death Experience, Afterlife Belief, and Cross-Cultural Evidence

[KEY FINDING] The AWARE (AWAreness during REsuscitation) study — a four-year prospective study across 15 hospitals in the UK, US, and Austria, led by Sam Parnia (published 2014, Resuscitation) — found that 39% of 140 car

near-death experience NDE afterlife out-of-body experience cardiac arrest AWARE study
ZB_5_00 Ecology & Biology

ZB_5_00 — Systems Applied Ecology: Subfolder Summary

ZC_5_00 Social Science

ZC_5_00 — Modern Applied Social Science: Subfolder Summary

G_3_08 Verified Modern Frameworks

G_3_08 — Water Anomalies — Structured Water, Memory Claims, and EZ Water

Water (H₂O) is simultaneously the most familiar and most anomalous substance on Earth. Its seemingly simple molecular structure belies a staggering array of anomalous properties — at least 72 documented anomalies compare

water structured water exclusion zone water EZ water Pollack water memory
G_3_06 Verified Modern Frameworks

G_3_06 — Systems Collapse and Complexity Theory Applied to Civilizations

This document examines Systems Collapse and Complexity Theory Applied to Civilizations, a topic within the Modern Frameworks research area. Key areas of investigation include Tainter's Foundational Thesis, The Western Ro

systems collapse complexity theory Joseph Tainter diminishing returns Peter Turchin cliodynamics
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
O_2_22 Credible Earth Anomalies

O_2_22 — Carolina Bay Anomalies

The Carolina bays are a collection of approximately 500,000 shallow, elliptical depressions concentrated along the Atlantic Coastal Plain of the southeastern United States, from New Jersey to northern Florida, with the h

Carolina bays oriented depressions elliptical lakes Younger Dryas impact Clovis sand rims
T_4_13 Credible Psychology & Social

T_4_13 — Political Psychology: Ideology, Moral Foundations, and the Psychology of Political Belief

Political psychology — the scientific study of the psychological bases of political behavior, beliefs, and ideologies — investigates why people hold the political views they do, how they process political information, an

political psychology ideology conservatism liberalism moral foundations theory Haidt
T_4_00 Psychology & Social

T_4_00 — Social Group: Subfolder Summary

T_5_00 Psychology & Social

T_5_00 — Applied Specialized: Subfolder Summary