docs: scienting-math/1 tree kinds prescript and mark

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_017R7sgDNvUGWY2zFPCq2JH6
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@@ -72,7 +72,7 @@ The last two make some files that were valid invalid, which [spec/00](spec/00-in
Because a complex formula's key compares sources, a producer aligning a reading in a form with another reading respells the other's math first.
`hashes.jsonl` gains a case, `math-form`, whose values `paperspec check` also computes without `form`; the rule `doc.math.form` is registered for validators that implement the form, which the reference validator does not.
- `derived/math.jsonl` ([spec/12 §12.7](spec/12-package.md#127-derived-files), [spec/09 §9.4](spec/09-figures-tables-equations.md#94-the-math-form), `math.schema.json`): one line per formula, `{node, run, tool, form, tree, symbols, complete, issues, label?}`, papermath's reading without the canonical TeX, which is the source; `run` is null for an equation, as in `derived/mathml.jsonl`, and `label` is omitted when the source has no `\tag`.
A tree node is an array whose first item is its kind; the schema takes any lowercase kind and issue code, so the form can add some in a minor version, and lists the 47 kinds and six codes of version 1.
A tree node is an array whose first item is its kind; the schema takes any lowercase kind and issue code, so the form can add some in a minor version, and lists the 49 kinds and six codes of version 1.
The validator now checks derived files: each line against its schema, that it names a formula of the package (`doc.derived.node`), that a math line's formula is TeX and its `complete` and `symbols` agree with its tree (`doc.derived.math`), and that a checks-only package carries none (`doc.policy.withheld`), since a tree or MathML reads the withheld text.
The main example gains `derived/math.jsonl`, papermath 0.1.0's reading of its equation and of two math runs, copied by hand because the oracle does not implement the form; `paperspec check` validates fourteen variants of it, and no fixture's hashes change.
There are now 43 schemas, which the 0.1.0 entry above, held to the repository by `paperspec check`, states too.