docs: fix typos, normalize STYX → Styx, fix boolean examples

- Fix 'the the colon' duplicate word
- Fix 'Does it confusing?' → 'Does it get confusing?'
- Fix 'paylod' → 'payload'
- Fix '/it/' → '_it_' (markdown italics)
- Fix 'age: number' → 'age: u32' (Rust type)
- Fix 'look like as styx' → 'look in Styx'
- Fix schema.md rule reference: r[key.equality] → r[entry.key-equality]
- Normalize STYX → Styx throughout (it's not an acronym)
- Fix claude-skill.md: booleans are bare scalars (true/false), not tags
- Remove incorrect 'built-in tags' section from skill

Author: fasterthanlime

docs/content/_index.md

@@ -18,7 +18,7 @@ Imagine JSON
 ```
 
 But you remove everything that's getting in the way: the double quotes, the
-the colon, even the comma:
+colon, even the comma:
 
 ```styx
 {
@@ -75,7 +75,7 @@ In static typing flavor, you may for example deserialize to:
 #[derive(Facet)]
 struct Does {
     name: String,
-    age: number,
+    age: u32,
     retired: bool,
 }
 ```
@@ -146,7 +146,7 @@ sparse_seq (1 2 @ 8 9)
 And in fact, wanna know a secret? `@` is not even the canonical form
 of unit: `@@` is.
 
-An empty tag degenerates to `@`, and a tag without a paylod defaults to
+An empty tag degenerates to `@`, and a tag without a payload defaults to
 a payload of `@`.
 
 Therefore:
@@ -171,7 +171,7 @@ Spaces separate seq elements or key-value pairs in object context:
 @tag()      // key(tag=tag, payload=()) value(tag=@, payload=@)
 ```
 
-Does it confusing? Maybe. Little bit.
+Does it get confusing? Maybe. Little bit.
 
 ## Styx the objective
 
@@ -209,7 +209,7 @@ one last bit of nesting? As a treat? You can use object attribute syntax:
 }
 ```
 
-And that's /it/ with the weirdness. (Don't worry, there are comprehensive
+And that's _it_ with the weirdness. (Don't worry, there are comprehensive
 specifications and test suites).
 
 Some unfamiliar bits, but hopefully not too many, which lets us...
@@ -299,5 +299,5 @@ Styx has first-class support for [Zed](https://zed.dev) with syntax highlighting
 - [Parser Spec](/spec/parser) — Formal syntax rules
 - [Schema Spec](/spec/schema) — Type system and validation
 - [Diagnostics](/spec/diagnostics) — Error message standards
-- [Rust Bindings](/bindings/rust) — How Rust types map to STYX
+- [Rust Bindings](/bindings/rust) — How Rust types map to Styx
 - [Comparisons](/comparisons) — vs JSON, YAML, TOML, KDL

docs/content/bindings/_index.md

@@ -5,4 +5,4 @@ sort_by = "weight"
 insert_anchor_links = "heading"
 +++
 
-Language bindings for STYX.
+Language bindings for Styx.

docs/content/bindings/rust.md

@@ -5,11 +5,11 @@ slug = "rust"
 insert_anchor_links = "heading"
 +++
 
-How Rust types map to STYX syntax. Examples use [facet](https://github.com/facet-rs/facet) derives.
+How Rust types map to Styx syntax. Examples use [facet](https://github.com/facet-rs/facet) derives.
 
 ## Implicit root object
 
-STYX documents are implicitly objects. When parsing, the top-level content is wrapped in an implicit root object. This means you cannot parse a bare tagged value directly into an enum — you need a wrapper struct.
+Styx documents are implicitly objects. When parsing, the top-level content is wrapped in an implicit root object. This means you cannot parse a bare tagged value directly into an enum — you need a wrapper struct.
 
 ```compare
 /// rust

docs/content/comparisons/_index.md

@@ -5,7 +5,7 @@ sort_by = "weight"
 insert_anchor_links = "heading"
 +++
 
-How STYX compares to other configuration formats.
+How Styx compares to other configuration formats.
 
 - [JSON](/comparisons/json) — the lingua franca of data interchange
 - [YAML](/comparisons/yaml) — the most common human-authored config format

docs/content/comparisons/json.md

@@ -5,7 +5,7 @@ slug = "json"
 insert_anchor_links = "heading"
 +++
 
-JSON is the lingua franca of data interchange. STYX is designed for human authoring,
+JSON is the lingua franca of data interchange. Styx is designed for human authoring,
 not machine interchange, which leads to different trade-offs.
 
 ## Simple object
@@ -98,7 +98,7 @@ count 42
 label 42
 ```
 
-In STYX, both are the scalar `42`. The deserializer interprets based on target type.
+In Styx, both are the scalar `42`. The deserializer interprets based on target type.
 
 ## Attribute syntax
 

docs/content/comparisons/toml.md

@@ -5,7 +5,7 @@ slug = "toml"
 insert_anchor_links = "heading"
 +++
 
-TOML is popular for Rust project configuration (Cargo.toml). STYX offers
+TOML is popular for Rust project configuration (Cargo.toml). Styx offers
 different trade-offs for deeply nested structures.
 
 ## Simple object
@@ -74,7 +74,7 @@ point = { x = 1, y = 2 }
 point {x 1, y 2}
 ```
 
-TOML 1.1 allows multi-line inline tables with trailing commas. STYX comma-separated objects must be single-line.
+TOML 1.1 allows multi-line inline tables with trailing commas. Styx comma-separated objects must be single-line.
 
 ## Reopening sections
 
@@ -98,4 +98,4 @@ database {
 }
 ```
 
-TOML allows reopening sections. In STYX, each key appears exactly once.
+TOML allows reopening sections. In Styx, each key appears exactly once.

docs/content/comparisons/yaml.md

@@ -5,7 +5,7 @@ slug = "yaml"
 insert_anchor_links = "heading"
 +++
 
-YAML is the most common human-authored configuration format. STYX addresses several
+YAML is the most common human-authored configuration format. Styx addresses several
 YAML pain points while preserving readability.
 
 ## Simple object
@@ -77,7 +77,7 @@ countries:
 countries (GB NO IE)
 ```
 
-In STYX, `NO` is always the text `NO`. The deserializer interprets based on target type.
+In Styx, `NO` is always the text `NO`. The deserializer interprets based on target type.
 
 ## Kubernetes-style config
 
@@ -128,7 +128,7 @@ server {
 }
 ```
 
-YAML's indentation can cause subtle bugs. STYX structure is always explicit.
+YAML's indentation can cause subtle bugs. Styx structure is always explicit.
 
 ## Anchors and aliases
 
@@ -152,4 +152,4 @@ production {
 }
 ```
 
-STYX does not support references. Use application-level merging instead.
+Styx does not support references. Use application-level merging instead.

docs/content/examples/_index.md

@@ -5,6 +5,6 @@ sort_by = "weight"
 insert_anchor_links = "heading"
 +++
 
-Examples of how some documents would look like as styx
+Examples of how some documents would look in Styx
 
   * [Kubernetes deployment](k8s.md)

docs/content/examples/k8s.md

@@ -5,7 +5,7 @@ slug = "k8s"
 insert_anchor_links = "heading"
 +++
 
-A Kubernetes Deployment in YAML vs STYX.
+A Kubernetes Deployment in YAML vs Styx.
 
 ```compare
 /// yaml

docs/content/guide/_index.md

@@ -5,4 +5,4 @@ sort_by = "weight"
 insert_anchor_links = "heading"
 +++
 
-Practical guides for using STYX.
+Practical guides for using Styx.