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.
34 results for "normal subgroup" — page 2 of 2
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
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
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
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
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
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, $
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),
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
Y_5_00 — Extreme Physical Paranormal: Subfolder Summary
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
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
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
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).
I_5_00 — Cultural Psychological Phenomena: Subfolder Summary
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