Atlas	The revision-pinned Fieldbook index of open and recently solved mathematics, containing source placements and a smaller set of reviewed dossiers.
Source placement	One row extracted from a particular location in the pinned source snapshot; multiple placements can refer to the same mathematical problem.
Canonical problem	A single normalized identity for a mathematical problem across repeated mentions, names, and sources.
Revision-pinned record	A record tied to an exact revision of its source so the version used can be inspected.
Source snapshot	A frozen version of source material captured at a particular revision and retrieval date.
Reviewed dossier	A richer editorial record with a clear statement, status, field, depth, source trail, and learning guidance.
Editorial dossier	The full reviewed-problem view whose Overview, Context, and Formal levels present increasing mathematical precision.
Primary source	The principal outbound source attached to a Fieldbook record; it is a starting point for verification.
Source trail	The chain of links and citations from a Fieldbook summary to the material supporting it.
Provenance	Information about where content came from, which revision was used, what changed, and which parts are editorial additions.
Open placement	A source placement classified as unresolved in the pinned index, subject to later correction or reclassification.
Solved since 1995	A source placement associated with a problem reported solved from 1995 onward; the cited result should still be verified.
Depth	Fieldbook guidance about the background and abstraction a reader is likely to need, not a measure of importance.
Gateway	A Fieldbook depth label for a problem whose statement can be approached with relatively little specialized background.
Deep	A Fieldbook depth label for a problem that normally requires substantial university-level background in its field.
Very deep	A Fieldbook depth label for a problem whose statement or literature depends on advanced specialized theory.
Reading path	An optional route through prerequisites, reading steps, sources, and notes for one problem.
Reading sequence	A checklist of suggested steps for approaching a problem; completion records progress but does not certify mastery.
Suggested prerequisite	A topic recommended before a reading step; it is editorial guidance rather than a source-supplied requirement.
Field note	A private note linked to a problem, source, experiment, or reading step.
Local revision history	The sequence of note revisions stored in the current browser profile, not a cloud backup.
Installed lab	A bundled and reviewed interactive experiment that runs in the browser and is linked to a mathematical problem.
Input boundary	The exact range, dataset, or assumptions accepted by a lab.
Interpretation boundary	A statement of what a lab result does and does not establish.
Static dataset	A fixed table bundled with the product rather than fetched or recomputed from a live external service.
Demonstration data	Clearly labeled sample content used to show a feature; it is not a real public post or scholarly review.
Conjecture	A precisely stated mathematical claim believed or suspected to be true but not yet proved in its full stated form.
Open problem	A mathematical question for which no generally accepted solution is known under the stated formulation.
Theorem	A mathematical statement whose truth has been established by a proof.
Proof	A logically valid argument deriving a conclusion from stated assumptions, definitions, axioms, and established results.
Counterexample	An example satisfying a universal claim's assumptions but not its conclusion; one valid counterexample disproves that claim.
Disproof	An argument, often a counterexample, that establishes that a claim is false as stated.
Partial result	A proved result resolving only part of a problem, such as a restricted range, special class, or one direction.
Special case	A narrower version of a general problem obtained by adding assumptions or restricting the objects studied.
Equivalent formulation	A statement proved true exactly when another statement is true; proving either one proves the other.
Peer review	Evaluation of scholarly work by qualified researchers; it is quality control, not an infallible guarantee.
Educational evidence	A computation or visualization supporting a displayed finite case without establishing a general conjecture.
Algebra	The study of operations, equations, and abstract structures such as groups, rings, fields, and vector spaces.
Analysis	The study of limits, continuity, change, approximation, and infinite processes.
Functional analysis	The study of vector spaces of functions and the operators acting on them, especially Banach and Hilbert spaces.
Combinatorics	The study of finite or discrete structures, including counting, arrangements, and extremal questions.
Geometry	The study of shape, size, position, distance, curvature, and structures preserving those properties.
Graph theory	The study of graphs, which are collections of vertices joined by edges.
Number theory	The study of integers and related arithmetic structures, including primes, divisibility, and Diophantine equations.
Additive number theory	The part of number theory studying representations as sums and the effect of addition on sets of numbers.
Topology	The study of properties preserved by continuous deformation, such as connectedness, compactness, and holes.
Model theory	The study of mathematical structures through the formal languages and logical theories used to describe them.
Formal language	A set of finite strings formed from a specified alphabet according to stated rules.
Dynamical system	A rule describing how a state changes over time, either in discrete steps or continuously.
Diophantine equation	An algebraic equation for which solutions are sought in integers or, more broadly, rational or algebraic numbers.
Prime number	A positive integer greater than 1 with exactly two positive divisors: 1 and itself.
Prime gap	The difference between consecutive prime numbers.
Twin primes	A pair of prime numbers differing by 2, such as 11 and 13.
Hadamard matrix	A square matrix with entries +1 and -1 whose rows are mutually orthogonal.
Perfect cuboid	A rectangular box whose edges, face diagonals, and space diagonal are all positive integers; no example is known.
Bounded linear operator	A linear operator whose output norm is at most a fixed constant times the input norm.
Hilbert space	A complete inner-product space supporting geometric ideas such as angles, orthogonality, and projection.
Banach space	A complete normed vector space in which every Cauchy sequence converges within the space.
Invariant subspace	A subspace M preserved by an operator T, meaning T(M) is contained in M.
Compact operator	An operator mapping bounded sets into sets whose closures are compact.
Self-adjoint operator	An operator equal to its adjoint on the appropriate domain.
Eigenvalue	A scalar lambda for which a nonzero vector v satisfies T(v) = lambda v.
Spectrum	The scalar values for which an operator fails to have a suitably bounded inverse; in finite dimensions these are the eigenvalues.
Riemann zeta function	A complex function initially defined for Re(s) > 1 by the sum of n^(-s), then analytically continued to nearly the whole complex plane.
Critical strip	The region 0 < Re(s) < 1 where the non-trivial zeros of the Riemann zeta function lie.
Critical line	The vertical line Re(s) = 1/2 inside the critical strip.
Riemann hypothesis	The conjecture that every non-trivial zero of the Riemann zeta function has real part 1/2.
Collatz trajectory	The sequence made by repeatedly dividing an even positive integer by 2 or replacing an odd one by 3n + 1.
Goldbach decomposition	A representation of an even integer as the sum of two prime numbers.
Computational complexity	The study of resources such as time or memory required to solve computational problems as input size grows.
P versus NP	The open question of whether every problem whose proposed solution can be checked efficiently can also be solved efficiently.
Graph minor	A graph obtained from another by deleting vertices, deleting edges, and contracting edges.
No-three-in-line problem	The problem of placing as many points as possible on an n by n grid with no three selected points on one straight line.
Four-manifold	A manifold that locally resembles four-dimensional Euclidean space.
Homeomorphism	A continuous bijection with a continuous inverse; homeomorphic spaces are topologically equivalent.
Diffeomorphism	A smooth bijection with a smooth inverse; diffeomorphic manifolds have the same smooth structure.
Jacobian determinant	The determinant of the matrix of first partial derivatives, describing local change in oriented volume.
Polynomial inverse	An inverse map whose coordinate functions are also polynomials.
IndexedDB	A browser database API for structured data stored on the user's device.
Data eviction	Removal of browser-stored site data because it was cleared, private browsing ended, storage pressure occurred, or browser policy applied.
Saved on this device	The data is stored in the current browser profile; it may be lost and is not automatically backed up.
Offline ready	Core installed assets and local data can be used without a network connection after required files are cached.
Cloud synchronization	Automatic copying and reconciliation of data through a remote service across devices or profiles.
JSON	A text format for structured data used by Fieldbook for portable local-data exports.
LaTeX	A document-preparation system built on TeX and widely used to structure technical text and typeset mathematics.
Encrypted vault export	A Fieldbook export option intended to protect file contents with encryption.
Voice recognition	Conversion of speech to text by the browser's speech service; depending on the browser, audio may be sent to its vendor after consent.
Analytics consent	The user's explicit choice to allow privacy-limited product analytics; without consent the Fieldbook analytics script does not load.