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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.
21 results for "topological phases" — page 1 of 2
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_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
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
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
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
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
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
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
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
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
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
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
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
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
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),
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
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