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

CHANGELOG.md

@@ -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.

schemas/math.schema.json

@@ -5,7 +5,7 @@
   "description": "One line of derived/math.jsonl: a formula of the package read in the form scienting-math/1 by a pinned tool, its tree, symbol keys and issues; never authoritative; spec/09-figures-tables-equations.md §9.4, spec/12-package.md §12.7.",
   "$defs": {
     "kind": {
-      "description": "What a tree node is. The kinds of scienting-math/1 are num, sym, text, const, oper, dots, empty, add, neg, pm, mp, mul, times, div, op, frac, binom, sqrt, root, pow, sub, prime, fact, apply, lim, sum, prod, coprod, int, iint, iiint, oint, bigcup, bigcap, abs, norm, angle, floor, ceil, braces, interval, rel, list, lines, cases, matrix and opaque (spec/09 §9.4). The schema takes any lowercase name, so that a later minor version of the form may add a kind; a consumer that meets a kind it does not know treats that node as it treats opaque.",
+      "description": "What a tree node is. The kinds of scienting-math/1 are num, sym, text, const, oper, dots, empty, add, neg, pm, mp, mul, times, div, op, frac, binom, sqrt, root, pow, sub, prime, fact, prescript, mark, apply, lim, sum, prod, coprod, int, iint, iiint, oint, bigcup, bigcap, abs, norm, angle, floor, ceil, braces, interval, rel, list, lines, cases, matrix and opaque (spec/09 §9.4). The schema takes any lowercase name, so that a later minor version of the form may add a kind; a consumer that meets a kind it does not know treats that node as it treats opaque.",
       "type": "string",
       "pattern": "^[a-z][a-z0-9-]*$",
       "examples": [

spec/09-figures-tables-equations.md

@@ -74,6 +74,8 @@ Brackets group and leave no node.
 | `times`, `div`, `op` | Two operands, after the operator's command for `op` | `\times`; `/` or `\div`; any other binary operator. |
 | `frac`, `binom`, `sqrt`, `root` | Numerator and denominator; the radicand, after the index for `root` | Fractions, binomials and roots. |
 | `pow`, `sub`, `prime`, `fact` | The base, and the script for `pow` and `sub` | Scripts, primes and factorials on what is not a symbol. |
+| `prescript` | The lower script, the upper script, the base | Scripts before their base, as in the isotope `^{31}\text{P}`. |
+| `mark` | The sign or operator | A sign or operator with no operand: a charge (`x^{+}`), the radical dot of `\cdot\text{OH}`, a formula cut by its converter. |
 | `apply` | The function's command, its argument, and its subscript if any | A named function: `\cos(x)`, `\log_{2} n`, `\max_{i} x_{i}`. |
 | `lim` | The command, what is under it, the body | `\lim`, `\liminf` and `\limsup`. |
 | `sum`, `prod`, `coprod`, `int`, `iint`, `iiint`, `oint`, `bigcup`, `bigcap` | The lower limit, the upper limit, the body | A big operator, whose body runs to the next sign outside brackets. |