claude-api skill: 4 dead URLs in shared/live-sources.md registry (agents instructed to WebFetch them get 404s)

## Summary

The `claude-api` skill's live-documentation registry (`skills/claude-api/shared/live-sources.md`) — the file every language README points agents to with "WebFetch … rather than guess" — contains **4 dead entries**, and two related skill files carry **3 more dead references**. All 5 distinct URLs hard-404 (verified stable across 3 passes × 2 user agents, redirects followed). Every canonical replacement below is already listed in `platform.claude.com/llms.txt`, so the registry just needs re-syncing with your own index.

The impact is the exact failure mode this registry exists to prevent: an agent following the skill's instructions to fetch current docs gets a 404, then falls back to guessing from stale training data.

## Dead entries in `shared/live-sources.md`

| Line | Listed URL | Status | Canonical (verified 200, in your llms.txt) |
|---|---|---|---|
| L21 | `https://platform.claude.com/docs/en/pricing.md` | 404 | `https://platform.claude.com/docs/en/about-claude/pricing.md` |
| L59 | `https://platform.claude.com/docs/en/agents-and-tools/tool-use/computer-use.md` | 404 | `https://platform.claude.com/docs/en/agents-and-tools/tool-use/computer-use-tool.md` |
| L65 | `https://platform.claude.com/docs/en/agents-and-tools/skills.md` | 404 | `https://platform.claude.com/docs/en/agents-and-tools/agent-skills/overview.md` |
| L113 | `https://platform.claude.com/docs/en/api/sdks/cli.md` | 308 → 404 (redirect target `cli-sdks-libraries/sdks/cli.md` is itself dead) | `https://platform.claude.com/docs/en/cli-sdks-libraries/cli/quickstart.md` |

Note L59 vs the neighboring entry at L60-L64 (`bash-tool.md`, `text-editor-tool.md`, `memory-tool.md`, `tool-search-tool.md`, `programmatic-tool-calling.md` all 200): the Computer Use page was renamed to `computer-use-tool` in the docs IA, and only this one row kept the old slug.

## Dead references in related files

**`skills/claude-api/shared/tool-use-concepts.md` L342**
- Dead: `https://platform.claude.com/docs/en/agents-and-tools/computer-use/overview` → 404
- Canonical: `https://platform.claude.com/docs/en/agents-and-tools/tool-use/computer-use-tool` (200)
- (The same file's other 5 platform refs all resolve — only the renamed Computer Use slug drifted.)

**`skills/academy-guide/SKILL.md` L90 and L115**
- Dead: `https://academy.claude.com/resources` → 404 (the skill's designated fallback when the catalog can't be fetched)
- Live equivalent: `https://academy.claude.com/all` (200, titled "All resources · Claude Academy"); `/courses`, `/tutorials`, `/use-cases` named in the same skill are all 200
- This one has extra bite: the reference is inside the instruction for what to do *when a fetch already failed* — so the fallback path fails too.

## Reproduction

```bash
for u in \
docs/en/pricing.md \
docs/en/agents-and-tools/skills.md \
docs/en/agents-and-tools/tool-use/computer-use.md \
docs/en/agents-and-tools/computer-use/overview; do
curl -s -o /dev/null -w "%{http_code} $u\n" "https://platform.claude.com/$u"
done
# → 404 x4 (stable across 3 passes, Chrome and curl UAs)
curl -s -o /dev/null -w "%{http_code}\n" -L "https://platform.claude.com/docs/en/api/sdks/cli.md"
# → 404 after 308
curl -s -o /dev/null -w "%{http_code}\n" -L "https://academy.claude.com/resources"
# → 404
```

## Suggested fix

One-line URL replacements per the table above (all canonicals confirmed present in `platform.claude.com/llms.txt`). The `api/sdks/cli.md` entry should point at `cli-sdks-libraries/cli/quickstart.md` — the llms.txt "CLI, SDKs, and libraries" section carries the full set if the row wants richer coverage.

Happy to open a PR with exactly these substitutions.

## Context

I maintain a standing audit of agent-facing documentation surfaces (merged fix in cloudflare-docs [#32985](https://github.com/cloudflare/cloudflare-docs/pull/32985), acknowledged report → shipped fix in upstash/context7 [#3060](https://github.com/upstash/context7/issues/3060)). I also sell a $5 FreshContext Pack — a repo-specific freshness check for AGENTS.md/CLAUDE.md-style context files ([sample](https://deploy-foorge-team.vercel.app/sample-fresh-context-pack.html)) — which is how I found these. No obligation; the report and PR offer stand on their own.

Start by opening skills/claude-api/shared/live-sources.md, skills/claude-api/shared/tool-use-concepts.md, and skills/academy-guide/SKILL.md at the listed lines, then compare each dead URL with the canonical replacements and platform.claude.com/llms.txt. Done means all seven references use the supplied live URLs; re-run the curl checks from the issue to confirm the replacements resolve.

Do mô hình lập chỉ mục viết ra từ nội dung của issue.