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.
50 results for "topological phase" — page 1 of 3
ZA_4_10 — Topological Phases of Matter
The discovery of topological phases of matter — states of matter that cannot be described by Landau's conventional symmetry-breaking paradigm but are instead characterized by topological invariants (mathematical quantiti
ZA_4_20 — Topological Insulators: Quantum Materials with Protected Surface States
Topological insulators (TIs) are a revolutionary class of quantum materials that behave as electrical insulators in their bulk but possess conducting surface or edge states that are protected by the fundamental symmetrie
Q_1_13 — Cosmic Strings and Topological Defects
Cosmic strings are one-dimensional topological defects that may have formed during symmetry-breaking phase transitions in the early universe, analogous to cracks in ice or vortex lines in superfluids. Predicted by Kibble
Z_1_12 — Genome Architecture and 3D Organization
The human genome — approximately 6.4 billion base pairs of DNA — is packed into a nucleus only ~6 μm in diameter. If stretched end-to-end, the DNA of a single human cell would extend about 2 meters, yet it is packaged an
ZA_4_15 — Condensed Matter Physics: Emergent Phenomena in Many-Body Systems
Condensed matter physics — the largest subfield of physics by number of active researchers — studies the collective behavior of vast numbers of interacting particles (electrons, atoms, ions, spins) in solid, liquid, and
Z_4_16 — Phase Separation in Cell Biology: Membraneless Organelles and Biomolecular Condensates
Liquid-liquid phase separation (LLPS) is the biophysical process by which proteins and nucleic acids demix from the surrounding cytoplasm or nucleoplasm to form concentrated, membrane-free droplets called biomolecular co
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
ZA_4_23 — Topological Insulators and Quantum Materials
Topological insulators (TIs) are a revolutionary class of quantum materials that behave as electrical insulators in their bulk but conduct electricity on their surfaces through topologically protected metallic states. Di
Q_4_25 — Time Crystals: Wilczek and Experimental Realization
A time crystal is a phase of matter that spontaneously breaks time-translation symmetry, exhibiting periodic motion in its ground state or steady state without energy input — the temporal analogue of how ordinary crystal
ZA_4_13 — Quantum Spin Liquids
A quantum spin liquid (QSL) is an exotic magnetic state of matter in which quantum fluctuations prevent the localized magnetic moments (spins) in a material from ordering into any conventional pattern — no ferromagnetism
ZA_4_11 — Time Crystals and Discrete Time Symmetry Breaking
A time crystal is a phase of matter that spontaneously breaks time-translation symmetry — the fundamental physical principle that the laws of physics are the same at all times (which, via Noether's theorem, is linked to
V_2_21 — Topology Applications in Science
Topology — the branch of mathematics concerned with properties preserved under continuous deformation (stretching, bending, twisting, but not tearing or gluing) — has transformed from an abstract mathematical discipline
W_2_03 — Daoism and Chinese Alchemy
Daoism is one of the world's oldest continuous philosophical-religious traditions, originating in China by at least the 4th century BCE and likely much earlier. Its alchemical tradition encompasses both waidan (external
ZH_4_08 — Lunar Calendars: Tracking the Moon Across Cultures
Lunar calendars — systems of timekeeping governed by the synodic month (the ~29.53-day cycle from new moon to new moon) — represent humanity's oldest systematic method of measuring time. Evidence from the Lascaux cave pa
ZH_4_16 — Lunar Mythology: Moon as Deity, Calendar, and Symbol Worldwide
The Moon — the most visible and rhythmically changing celestial body — has been a central object of mythology, worship, and symbolic elaboration in virtually every human culture. The 29.5-day synodic cycle (new moon to n
ZH_1_13 — Bronze Age Astronomy: Alignments, Calendars, and Knowledge 2000–1000 BCE
The Bronze Age (broadly ~3300–1200 BCE, with regional variation) witnessed a decisive transformation in astronomical knowledge — from the horizon-based, monument-encoded astronomy of the Neolithic to the beginning of sys
C_1_19 — The Triple Goddess Pattern: Maiden, Mother, Crone
The Triple Goddess — typically expressed as Maiden, Mother, and Crone corresponding to the waxing, full, and waning moon — represents one of the most influential archetypes in comparative mythology and modern Paganism, t
C_2_06 — Chinese Dragon Mythology & Ancient Scriptures (Research Dossier)
This document examines Chinese Dragon Mythology & Ancient Scriptures (Research Dossier), a topic within the Global Traditions research area. Key areas of investigation include Dragon as water/weather regulator, Dragon as
Z_3_06 — Genetics of Circadian Rhythms
Circadian rhythms — endogenous ~24-hour oscillations in physiology and behavior — are generated by an intracellular transcription-translation feedback loop (TTFL) encoded by a set of core clock genes conserved across ani
Z_4_11 — The Cell Cycle: Division, Checkpoints, and Cancer
The cell cycle — the ordered series of events by which a cell grows, replicates its DNA, and divides into two daughter cells — is one of the most fundamental processes in biology and one of the most intensively studied i
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