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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.

21 results for "topological phases" — page 1 of 2

ZA_4_10 Verified Physics & Quantum

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

topological insulator topological phase quantum Hall effect integer quantum Hall fractional quantum Hall topological order
ZA_4_15 Verified Physics & Quantum

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

condensed matter band theory phase transitions topological phases superconductivity strongly correlated
ZA_4_20 Verified Physics & Quantum

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

topological insulators topological materials quantum spin Hall effect surface states band topology Charles Kane
Q_1_13 Credible Cosmology & Physics

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

cosmic strings topological defects phase transition domain walls magnetic monopoles textures
ZA_4_23 Verified Physics & Quantum

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

topological insulator topological order quantum spin Hall Dirac cone surface states Kane-Mele
ZA_4_13 Verified Physics & Quantum

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

quantum spin liquid QSL frustrated magnetism resonating valence bond RVB Anderson
V_2_21 Verified Mathematics & Information

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

topology topological invariants Euler characteristic knot theory persistent homology topological data analysis
W_2_03 Verified World Civilizations

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

Daoism Taoism internal alchemy neidan waidan external alchemy
ZH_4_08 Verified Archaeoastronomy

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

lunar calendar synodic month lunisolar Islamic calendar Hebrew calendar Chinese calendar
ZH_4_16 Verified Archaeoastronomy

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

moon mythology lunar deity moon worship lunar calendar moon symbolism Selene
C_1_19 Credible Global Traditions

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

triple-goddess maiden-mother-crone hecate brigid morrígan norns
Z_1_12 Verified Molecular Biology

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

genome architecture 3D genome chromatin organization topologically associating domains TADs chromosome territories
Q_2_13 Verified Cosmology & Physics

Q_2_13 — Interstellar Medium, Dust, and Nebulae

The space between stars is far from empty — the interstellar medium (ISM) is a complex, dynamic ecosystem of gas, dust, magnetic fields, and cosmic rays that pervades galaxies and plays a central role in stellar birth, d

interstellar medium ISM interstellar dust nebula emission nebula planetary nebula
ZD_5_17 Verified Information & Computation

ZD_5_17 — Quantum Computing: Qubits, Gates & Quantum Information Processing

Quantum computing harnesses quantum mechanical phenomena — superposition, entanglement, and interference — to perform computations fundamentally impossible for classical machines. First proposed by Richard Feynman in 198

quantum computing qubit quantum gate superposition entanglement quantum supremacy
ZD_4_12 Verified Information & Computation

ZD_4_12 — Quantum Computing — Architecture, Algorithms, and Implications

Quantum computing — computation that exploits the principles of quantum mechanics (superposition, entanglement, and interference) to process information in ways fundamentally different from classical computers — represen

quantum computing qubit superposition entanglement quantum gate Shor algorithm
P_4_13 Verified Philosophy & Meaning

P_4_13 — Chinese Philosophy — Dao, Confucius, and Beyond

Chinese philosophy encompasses one of the world's richest and longest-continuous intellectual traditions, spanning from the Zhou dynasty (~1046–256 BCE) to the present. The foundational period — the Hundred Schools of Th

Chinese philosophy Daoism Taoism Confucius Confucianism Laozi
S_1_04 Verified Future Technology

S_1_04 — Quantum Computing and Information Processing Frontiers

Quantum computing exploits the principles of quantum mechanics — superposition (a qubit existing in multiple states simultaneously), entanglement (correlated states across distance), and interference (constructive/destru

quantum computing qubit superposition entanglement quantum gate quantum circuit
ZA_2_07 Credible Physics & Quantum

ZA_2_07 — Magnetic Monopoles: The Missing Magnets

Magnetic monopoles — hypothetical particles carrying isolated north or south magnetic charge — remain one of the most sought-after objects in physics. Maxwell's equations exhibit a tantalizing asymmetry: while electric c

magnetic monopole Dirac monopole 't Hooft-Polyakov monopole charge quantization Dirac string grand unified theory
ZA_5_02 Verified Physics & Quantum

ZA_5_02 — Quantum Computing and Qubit Technologies

Quantum computing exploits the principles of quantum mechanics — superposition (a qubit can exist in a combination of 0 and 1 simultaneously), entanglement (qubits can share correlations impossible in classical systems),

quantum computing qubit superposition entanglement quantum gate quantum circuit
ZA_5_13 Verified Physics & Quantum

ZA_5_13 — Anyons and Fractional Quantum Hall Effect

Anyons are quasiparticles that exist exclusively in two-dimensional systems and obey quantum statistics intermediate between bosons and fermions — when two identical anyons are exchanged, the wave function acquires a pha

anyons fractional quantum Hall effect topological order non-Abelian anyons braiding Laughlin wave function