AzeMark 2 · AzeForge 0.6.3

Notation codex.

AzeForge is a library for both humans and AI agents. People read this page to author valid AzeMark; agents treat it as the human companion to grammar.json and the AI-authoring contract. Every spelling below is verified against the pinned 0.6.3 compiler Sources and generated grammar. Copy the AzeMark column verbatim; do not invent near-miss keys.

Closed grammar. Unknown words of three or more letters are diagnostics, not new functions. Use only the registered names on this page.

Symbols and Greek names

Rendered	AzeMark	Kind	Example	Reads as
α	`alpha`	Lower Greek	`alpha`	Significance level
β	`beta`	Lower Greek	`beta`	Regression coefficient
γ	`gamma`	Lower Greek	`gamma`	Decay constant
δ	`delta`	Lower Greek	`delta`	Small change
ε	`epsilon`	Lower Greek	`forall e in R of body`	Arbitrary tolerance
ζ	`zeta`	Lower Greek	`zeta`	Damping ratio
η	`eta`	Lower Greek	`eta`	Efficiency
θ	`theta`	Lower Greek	`cos theta`	Rotation angle
κ	`kappa`	Lower Greek	`kappa`	Curvature
λ	`lambda`	Lower Greek	`lambda`	Wavelength
μ	`mu`	Lower Greek	`(x_i - mu)^2`	Population mean
ν	`nu`	Lower Greek	`G_(mu, nu)`	Tensor index
ξ	`xi`	Lower Greek	`xi`	Random variable
ο	`omicron`	Lower Greek	`omicron`	Small omicron
π	`pi`	Lower Greek	`pi`	Circle constant
ρ	`rho`	Lower Greek	`rho`	Density
σ	`sigma`	Lower Greek	`sigma^2`	Standard deviation
τ	`tau`	Lower Greek	`tau`	Time constant
υ	`upsilon`	Lower Greek	`upsilon`	Frequency ratio
φ	`phi`	Lower Greek	`phi`	Phase angle
χ	`chi`	Lower Greek	`chi`	Susceptibility
ψ	`psi`	Lower Greek	`psi`	Stream function
ω	`omega`	Lower Greek	`omega`	Angular frequency
Α	`Alpha`	Upper Greek	`Alpha`	Uppercase alpha
Β	`Beta`	Upper Greek	`Beta`	Uppercase beta
Γ	`Gamma`	Upper Greek	`Gamma`	Uppercase gamma
Δ	`Delta`	Upper Greek	`Delta`	Finite difference
Ε	`Epsilon`	Upper Greek	`Epsilon`	Uppercase epsilon
Ζ	`Zeta`	Upper Greek	`Zeta`	Uppercase zeta
Η	`Eta`	Upper Greek	`Eta`	Uppercase eta
Θ	`Theta`	Upper Greek	`Theta`	Uppercase theta
Ι	`Iota`	Upper Greek	`Iota`	Uppercase iota
Κ	`Kappa`	Upper Greek	`Kappa`	Uppercase kappa
Λ	`Lambda`	Upper Greek	`Lambda`	Uppercase lambda
Μ	`Mu`	Upper Greek	`Mu`	Uppercase mu
Ν	`Nu`	Upper Greek	`Nu`	Uppercase nu
Ξ	`Xi`	Upper Greek	`Xi`	Uppercase xi
Ο	`Omicron`	Upper Greek	`Omicron`	Uppercase omicron
Π	`Pi`	Upper Greek	`Pi`	Uppercase pi
Ρ	`Rho`	Upper Greek	`Rho`	Uppercase rho
Σ	`Sigma`	Upper Greek	`sum i=1..n of i^2`	Summation operator
Τ	`Tau`	Upper Greek	`Tau`	Uppercase tau
Υ	`Upsilon`	Upper Greek	`Upsilon`	Uppercase upsilon
Φ	`Phi`	Upper Greek	`Phi`	Uppercase phi
Χ	`Chi`	Upper Greek	`Chi`	Uppercase chi
Ψ	`Psi`	Upper Greek	`Psi(x, t)`	Wave function
Ω	`Omega`	Upper Greek	`Omega`	Ohms and solid angle
ℏ	`hbar`	Physics name	`i hbar frac(partial, partial t) Psi(x, t)`	Reduced Planck constant
∂	`partial`	Physics name	`frac(partial, partial t)`	Partial derivative
∇	`nabla`	Physics name	`nabla^2`	Laplacian operator
∞	`infinity`	Physics name	`integral x=0..infinity of exp(-x^2) dx`	Unbounded limit
∅	`emptyset`	Physics name	`emptyset`	Empty set

Subscripts, superscripts, and expression forms

Form	AzeMark	Rule	Reads as
Subscript	`x_i`	One base, one index	Indexed variable
Superscript	`x^2`	One base, one power	Square and exponent
Combined power	`(x')^2`	Parenthesize before combining	Primed base raised to a power
Prime marks	`x'` or `x''`	Up to two primes per base	Derived forms
Multi-index	`G_(mu, nu)`	One subscript group	Tensor indices
Fraction	`frac(1, n)`	Numerator, denominator	Rational expression
Root	`sqrt(x)`	Radicand	Square root
Nth root	`root(n, x)`	Index, radicand	Cube and higher roots
Absolute	`abs(x)`	Single argument	Absolute value
Bounded sum	`sum i=1..n of i^2`	Bound `i=1..n`, then `of`, then body	Finite series with Σ
Bounded product	`product k=1..m of k`	Bound `k=1..m`, then `of`, then body	Finite product with Π
Integral	`integral x=0..L of f(x) dx`	Bound `x=0..L`, then `of`, then body; differential matches the bound name	Definite integral with ∫
Unbounded integral	`integral x=0..infinity of exp(-x^2) dx`	`infinity` as the upper bound	Improper integral
Limit	`limit n->infinity of V_0`	Variable, arrow, target, then `of`	Approach a value
Universal quantifier	`forall e in R of body`	Name, set, then `of`	For every element, with ∀
Existential quantifier	`exists M in R of body`	Name, set, then `of`	There exists, with ∃
Membership	`x in R`	Element, then set	Set membership with ∈
Non-membership	`x notin S`	Element, then set	Exclusion with ∉
Subset	`A subset B`	Two sets	Strict inclusion with ⊂
Subset or equal	`A subseteq B`	Two sets	Inclusion with ⊆
Superset	`A supset B`	Two sets	Strict containment with ⊃
Union	`A union B`	Two sets	Combined sets with ∪
Intersection	`A intersect B`	Two sets	Shared elements with ∩
Equivalence	`A equiv B`	Two expressions	Logical equivalence with ≡
Vector	`vector [x, y]`	Bracket list; one item is an arrow vector	Bold tuple or arrow vector
Matrix	`matrix [[a, b], [c, d]]`	Rows are bracket groups	Plain matrix
Parenthesized matrix	`pmatrix [[cos theta, -sin theta], [sin theta, cos theta]]`	Rows are bracket groups	Rotation matrix
Determinant matrix	`vmatrix [[a, b], [c, d]]`	Rows are bracket groups	Determinant bars
Cases	`cases(w_k x^k when k < m; 0 otherwise)`	Branches separated by `;`, conditions with `when`	Piecewise definition
Sine	`sin theta`	Angle argument	Trigonometric function
Cosine	`cos theta`	Angle argument	Trigonometric function
Exponential	`exp(-x^2)`	Exponent argument	Natural exponential

Directive bodies and their AzeMark shape

Directive	Body shape	Minimal AzeMark	Reads as
equation	Scalar `expression` line	`V = I * R`	One readable expression
derivation	Ordered `- expression:` steps	`- expression: A_n = P_0 (1 + r)^n`	Aligned chain with prose notes
formula	One expression line	`H2O`	Digits resolve to subscripts and charge
reaction	One reaction equation	`Ag+(aq) + Cl-(aq) -> AgCl(s)`	Arrow with conditions and balance check
structure	Record list of atoms and bonds	`- kind: atom`	Molecular declaration
plot	Record list of series	`- kind: function`	Function, line, and point series
chart	Record list of bars or histogram	`- kind: bars`	Categorical bars or binned values
geometry	Ordered `- kind:` declarations	`- kind: point`	Coordinates, constructions, marks
circuit	Ordered component declarations	`- kind: resistor`	Named nodes with bound terminals
timing	Ordered signal declarations	`- kind: signal`	Wave run strings on a shared scale
control	Ordered block declarations	`- kind: block`	Signal-flow blocks, sums, and edges
free-body	Ordered body declarations	`- kind: force`	Bodies with anchored vectors
sequence	Participants plus timeline	`participants:`	Message timelines
state	Record list of states	`- kind: transition`	State machines
entity	Record list of entities	`- kind: entity`	Entities and relationships
class	Record list of classifiers	`- kind: class`	Classes and interfaces
diagram	Record list of nodes and edges	`- kind: node`	Flowchart, graph, tree, architecture
table	Keyed columns and rows	`columns:`	Typed tables with groups
algorithm	Procedure with steps	`procedure:`	Nested statements
statement	Kind plus text and proof	`kind: theorem`	Theorem-family blocks
example	Problem plus steps	`problem:`	Worked examples
figure	Required nested children	`:: equation`	Numbered wrapper
bibliography	Record list of entries	`- kind: entry`	Keyed references
callout	Keyed Markdown sections	`variant: note`	Admonition block
mermaid	Scalar source lines	`source`	Diagram escape hatch
tex	Scalar figure body	`profile: tikz`	Deployment-dependent profile

Geometry declarations

Declaration	AzeMark shape	Reads as
`point`	Authored `x`/`y`	Vertices and labels
`segment`	`from` and `to`	Arms and edges
`line`	Two references	Construction line
`ray`	Origin plus direction	Beams and half-lines
`circle`	Center plus radius or beacon	Sweep circles
`arc`	Center, radius, sweep	Directed arcs
`polygon`	Ordered `vertices`	Closed figures
`midpoint`	Two references	Bisection point
`intersection`	Two references	Crossing point
`tangent-line`	Point plus circle	Derived tangent
`perpendicular-line`	Point plus line	Derived perpendicular
`perpendicular-foot`	Point plus line	Foot of perpendicular
`angle-mark`	Three references	Annotated angle
`right-angle-mark`	Two references	Right-angle mark
`length-mark`	One reference	Measured segment
`equal-marks`	Segment list	Congruence marks

Circuit declarations

Declaration	AzeMark shape	Reads as
`node`	`ref`, optional `role: reference`	Named net; reference marks ground
`resistor`	`ref`, `value`	Two-terminal passive element
`capacitor`	`ref`, `value`	Filtering element
`voltage-source`	`ref`, `value`, `mode: dc`	Supply rail
`current-label`	Edge reference	Branch current
`voltage-label`	Node pair	Node voltage
`op-amp`	`ref`	Amplifier with bound pins
`dependent-source`	`ref`	Controlled source
`digital-input`	`ref`	Logic stimulus
`and` / `or`	`ref`	Logic gates
`d-flip-flop`	`ref`	Sequential element
`mux`	`ref`	Multiplexer
`digital-output`	`ref`	Observation point
`led`	`ref`	Indicator
`connect`	`terminal` plus `node`	Binds every pin; unbound pins error

Authoring workflow

Find the rendered form on this page.
Copy the AzeMark spelling into a four-colon outer fence or a record-list Block.
Run azeforge validate before rendering.
Read the generated directive reference for the complete field contract.