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.

34 results for "normal subgroup" — page 2 of 2

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
ZA_4_06 Verified Physics & Quantum

ZA_4_06 — Phase Transitions and Symmetry Breaking in Physics

Phase transitions — transformations between distinct states of matter or vacuum configurations — are among the most fundamental phenomena in physics, uniting condensed matter, particle physics, and cosmology under a comm

phase transitions symmetry breaking spontaneous symmetry breaking Higgs mechanism Landau theory order parameter
I_2_02 Verified UAP Disclosure

I_2_02 — Government Investigation of Anomalous Phenomena

For nearly eight decades, the United States government — along with allies and adversaries — has maintained a sprawling, often covert apparatus for investigating anomalous phenomena spanning unidentified aerial/aerospace

government investigation anomalous phenomena Project Blue Book Project Sign Project Grudge AATIP
I_1_09 Speculative UAP Disclosure

I_1_09 — Cryptid-UAP Connection Analysis

The cryptid-UAP connection hypothesis proposes that anomalous creature sightings (cryptids) and unidentified aerial phenomena (UAP) are not separate categories of unexplained experience but are related manifestations of

cryptid UAP Mothman Skinwalker Ranch window areas high strangeness
I_5_17 Credible UAP Disclosure

I_5_17 — UAP and Consciousness: The Intersection

A persistent, under-discussed feature of serious UAP research is that the most intense witness reports — close-encounter cases, repeated-percipient cases, and the "contact phenomenon" — show high correlation with altered

UAP UFO consciousness observer dependent contact phenomenon Vallée
V_1_14 Verified Mathematics & Information

V_1_14 — Mathematical Constants: e, φ, √2, and Beyond

Mathematical constants are fixed numerical values that arise naturally from mathematical structures — appearing independently across diverse areas from geometry and analysis to probability and physics. The most famous, $

mathematical constants pi Euler number golden ratio phi square root two
V_3_01 Verified Mathematics & Information

V_3_01 — Statistics & Probability: Pascal to Bayes

Probability and statistics — the mathematics of uncertainty — emerged as formal disciplines from the Pascal-Fermat correspondence (1654) on the "problem of points" (how to divide stakes in an interrupted game of chance),

statistics probability Pascal Fermat Bayes Bernoulli
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
Y_5_00 Altered States

Y_5_00 — Extreme Physical Paranormal: Subfolder Summary

Y_5_21 Credible Altered States

Y_5_21 — Sound Healing and Acoustic Therapy: Vibration, Resonance, and Therapeutic Sound

Sound healing encompasses a spectrum from evidence-based clinical music therapy to ancient and modern practices using specific frequencies, instruments, and resonance for therapeutic purposes. Clinical music therapy — pr

sound healing acoustic therapy cymatics binaural beats 432 hz 528 hz
Y_5_19 Verified Altered States

Y_5_19 — Congenital Insensitivity to Pain: SCN9A, Nociception, and the Neuroscience of Painlessness

Congenital insensitivity to pain (CIP) encompasses a group of rare inherited conditions in which individuals are born with absent or severely diminished pain perception while retaining other sensory modalities (touch, pr

congenital insensitivity to pain CIP CIPA SCN9A Nav1.7 nociception
Y_5_22 Credible Altered States

Y_5_22 — Brainwave Entrainment: Neural Oscillation, Binaural Beats, and Auditory Driving

Brainwave entrainment refers to the capacity of external rhythmic stimuli — auditory, visual, or electromagnetic — to synchronize endogenous neural oscillation patterns toward the frequency of the stimulus, a phenomenon

brainwave entrainment binaural beats auditory driving neural oscillation EEG alpha waves
Y_2_14 Credible Altered States

Y_2_14 — Dying Process Phenomenology: Shared Death Experiences and After-Death Communication

The phenomenology of death and the experiences reported by those who witness the dying process include several distinct categories of altered-state phenomena that extend beyond the well-known near-death experience (NDE).

shared death experience after-death communication deathbed visions grief hallucinations terminal lucidity Moody
I_5_00 UAP Disclosure

I_5_00 — Cultural Psychological Phenomena: Subfolder Summary