docs(tools): widen the 182 reachability shape and finish the note's two language-binding facts

"Reachable only through a raw register() whose parameters is
array-rooted" was too narrow. A root oneOf reaches the same 182: the
union arm propagates listDepth unchanged because `A | B` opens no
bracket, so an array branch starts its chain at 0 exactly as an array
root does. Say "root opens an array chain -- rooted at the array, or at
an array branch of a root oneOf", in the JSDoc and the test comment,
and assert the union shape alongside the array-rooted one.

The note's Decision paragraph said the flavor guard is reached under
"a language that has a renderer but no flavor entry, and a test covers
it". The test uses ruby, absent from both tables, and the mechanism is
that schemas() reaches run_code's getters without passing
requireCodeRuntime -- so any language absent from the flavor table hits
it. State that instead.

The Consequences paragraph recorded the language-binding obligation as
two reads, assembly and execution. Within one projection there are more:
run_code's description and parameters getters each call
resolveFlavor(peekRuntime()) and schemaOf destructures both, so a reload
between them yields one schema whose halves name different languages.

.agents/notes/implemented/feature/2026-07-31-code-mode-language-dispatch.md

@@ -17,7 +17,7 @@ Language selection is a lookup on `ctx.codeRuntime.language`, resolved lazily at
 - `SDK_RENDERERS` (index.ts) maps a language to its `tools:sdk` renderer — `typescript → renderToolsSdk`, `python → renderToolsSdkPy`. The `tools:sdk` section reads the loaded runtime's language and picks the renderer; `requireCodeRuntime` rejects a `mode: code`/`both` runtime whose language is absent from the table, naming the known languages.
 - `RUN_CODE_FLAVORS` (code-mode.ts) maps a language to its two model-facing `run_code` strings (tool `description` and the `code` parameter description), so a language's SDK section and its transport schema always agree.
 
-Both tables are read with `Object.hasOwn` before use so a language named `toString`/`constructor` cannot resolve an inherited `Object.prototype` member as a renderer. The two guards differ in reachability: `SDK_RENDERERS`' in-callback guard is unreachable because `requireCodeRuntime` validated the same `const` table earlier in the same callback (it carries a `/* v8 ignore */`), while `RUN_CODE_FLAVORS`' guard is the primary, publicly reachable rejection — reading `ctx.tools.schemas()` under a runtime whose language has a renderer but no flavor entry hits it, and a test covers it. Schema emission reads the runtime through `peekRuntime()` rather than `requireRuntime()`: `undefined` (no runtime mounted, the doc-catalog schema harvest that never reaches a model) degrades to the TypeScript flavor, whereas a mounted unknown language fails loud — this is NOT the silent fallback rejected below, which concerns emitting a wrong-language SDK for a real runtime. Adding a backend language is two table entries plus its renderer — no `agent-loop` or registry-structure change.
+Both tables are read with `Object.hasOwn` before use so a language named `toString`/`constructor` cannot resolve an inherited `Object.prototype` member as a renderer. The two guards differ in reachability: `SDK_RENDERERS`' in-callback guard is unreachable because `requireCodeRuntime` validated the same `const` table earlier in the same callback (it carries a `/* v8 ignore */`), while `RUN_CODE_FLAVORS`' guard is the primary, publicly reachable rejection — any language absent from the flavor table hits it through `run_code`'s language-aware getters, which `schemas()` reaches without passing `requireCodeRuntime` first, and a test covers it. Schema emission reads the runtime through `peekRuntime()` rather than `requireRuntime()`: `undefined` (no runtime mounted, the doc-catalog schema harvest that never reaches a model) degrades to the TypeScript flavor, whereas a mounted unknown language fails loud — this is NOT the silent fallback rejected below, which concerns emitting a wrong-language SDK for a real runtime. Adding a backend language is two table entries plus its renderer — no `agent-loop` or registry-structure change.
 
 `code-mode.ts` depends only on the runtime seam (`@deepseek-ai/dsh-code-runtime`), never on a concrete backend; dispatch is by `runtime.language` at run time. The tool layer therefore lands independently of the protocol and backend PRs — it needs only the seam's `language` field, which is already on master.
 
@@ -41,4 +41,4 @@ Adding a backend language is two table entries — an `SDK_RENDERERS` entry and
 
 The cost is that the Python branch of both tables is unreachable on this base: `CodeRuntime.language` is set by the loaded backend, the only published backend is `dsh-code-runtime-worker` (`'typescript'`), and the registry reads the loaded runtime rather than a config field, so no assembled application can select `renderToolsSdkPy` or `PYTHON_FLAVOR`. The model-visible surface is therefore unchanged by this note's work until a backend reporting `'python'` is published, and this PR's coverage is unit-level — the renderer output plus the dispatch and rejection paths. The keyless snapshot for the Python model interface belongs to the PR that publishes that backend, because only there does a real `cordis.yml` over published plugins produce a Python assembly; a snapshot example that mounted a fixture runtime here would assert against a test double, which [docs/testing.md](../../../../docs/testing.md) rejects as a substitute for the assembled application transcript.
 
-Two runtime contracts the Python SDK text asserts are owed by that same backend PR. First, the instructions tell the model that exactly `tools` and `ToolCallError` are bound and that the declared `TypedDict` classes are not, so the backend must inject those two names — with `ToolCallError.toolName` populated per the seam's `errorClass` contract — and must NOT bind the declared class names into the program's globals; injecting them "helpfully" would make the SDK text false. Second, the language has to be bound to the request: `requireCodeRuntime` resolves `ctx.codeRuntime` separately at assembly and at `run_code` execution, so a reload that swapped the runtime between those two points would hand a program written against one flavor to the other. Neither is reachable here — one published backend means both reads return the same flavor and no program ever runs against this renderer's output — and the cross-language rejection is not testable until a second language exists.
+Two runtime contracts the Python SDK text asserts are owed by that same backend PR. First, the instructions tell the model that exactly `tools` and `ToolCallError` are bound and that the declared `TypedDict` classes are not, so the backend must inject those two names — with `ToolCallError.toolName` populated per the seam's `errorClass` contract — and must NOT bind the declared class names into the program's globals; injecting them "helpfully" would make the SDK text false. Second, the language has to be bound to the request: `requireCodeRuntime` resolves `ctx.codeRuntime` separately at assembly and at `run_code` execution, so a reload that swapped the runtime between those two points would hand a program written against one flavor to the other. The split is finer than those two points — `run_code`'s `description` and `parameters` getters each call `resolveFlavor(peekRuntime())`, and `schemaOf` destructures both per definition, so one projection reads the runtime twice per tool; a reload between those two reads yields a single schema whose two halves name different languages. Neither is reachable here — one published backend means both reads return the same flavor and no program ever runs against this renderer's output — and the cross-language rejection is not testable until a second language exists.