docs: move implementation sections out of the handbook pages

Three handbook pages carried sections an operator never reads, named after
source paths and build internals. They move to pages under 4-implementation,
and each handbook page keeps a short pointer.

- forge.md: the notification poller (what it polls, how it formats,
  de-duplicates and marks notifications read) is now
  agent-tools/forge-notify.md. The forge page keeps a short Notifications
  section.
- matrix.md: the retired hive-side matrix code, the evaluation assertions and
  the fluffychat-web build fixes are now networking/matrix-homeserver.md.
- github.md: the Implementation section (how `gh` and `git push`
  authenticate, and the GitHub poller) is now agent-tools/github.md.

docs/README.md and the agent-tools README list the new pages, and AGENTS.md's
note on mixed operator and implementation docs now says to move the detail
and leave a pointer.

docs/2-handbook/external-accounts/github.md

@@ -61,93 +61,8 @@ reads it: [credentials-reference.md](../swarm/credentials-reference.md).
   scope is the real blast-radius limiter, and the container boundary is
   the enforcement. See [security.md](../agents/security.md).
 
-## Implementation
+## How it works
 
-<details>
-<summary>How the agent's `gh`/`git push` actually authenticate, and how
-the notification poller works</summary>
-
-### How the agent uses it
-
-When enabled, the container gets:
-
-- **A `gh` wrapper** on `PATH` (shadowing the raw `gh`) that exports
-  `GH_TOKEN` from the token file at invocation, then execs real `gh`. So
-  `gh pr create`, `gh api …`, etc. just work — `gh` derives the identity
-  from the token.
-- **A git credential helper** (`git-credential-hive-github`), wired via a
-  host-scoped `/etc/gitconfig` entry for `https://github.com`, so
-  `git push https://github.com/<owner>/<repo>` authenticates as
-  `x-access-token` + the PAT (GitHub ignores the username for PAT auth).
-  Host-scoped, so it never touches the forge (`localhost:3000`) or any
-  other remote.
-
-Both scripts read the token from `<state>/github-token` **at invocation
-time**, so a PAT written (or rotated) mid-session takes effect immediately
-— no container rebuild or restart. Until the file exists, `gh` / `git push`
-fail unauthenticated. The build bakes the token path into the scripts
-(rather than reading it from an env var), because claude's Bash tool runs in a
-minimal environment that wouldn't carry one.
-
-### Notifications
-
-`hive-github-notify` polls github.com for the agent, turning each unread
-notification thread into a todo. it's a **separate binary and a
-separate systemd unit** from the internal forge's poller
-(`hive-forge-notify`, see [forge.md](../swarm/forge.md#notification-poller-hive-forge-notifysrcnotifyrs)),
-installed by `nix/agent-modules/github.nix` under
-`services.hyperhive.agent.github.enable`. Both binaries ship from the one
-`hive-forge-notify` derivation, so the unit is a second `ExecStart`
-path, not a new package.
-
-Two units rather than one daemon with two loops, because it puts the
-decision in nix: a hive built without this module has **no github poller
-in its closure at all**, which is what makes GitHub access separable
-rather than merely switched off. it's also why this isn't a cargo
-feature — a feature would unify across the workspace and cost every
-crate its build cache.
-
-At runtime the poller needs the PAT above. No PAT, no polling: the unit
-logs why and exits 0, which is why it's `Restart = on-failure` and
-never `always` — a clean exit on a PAT-less agent must not become a
-restart loop. The poller waits about ten minutes for the PAT to appear
-before it gives up. A path unit (`hive-github-notify.path`) starts the poller
-again when `<state>/github-token` changes, so a PAT that lands later still
-enables polling. Once polling, it re-reads the file on every
-tick, so it picks up a rotated PAT on the next tick without a restart.
-
-Forgejo models its notifications API on GitHub's, so one tolerant
-parse serves both: `id`, `repository.full_name`,
-`subject {title,url,latest_comment_url}` and `updated_at` line up field
-for field. Lenient deserializers absorb the two real differences —
-GitHub sends the thread id as a _string_ where Forgejo
-sends a number, and says `PullRequest` where Forgejo says `Pull`.
-`hive-github-notify` prefixes todo keys `gh:<id>` so a github thread id can't collide with a
-forge one.
-
-Two host differences worth knowing before touching this code:
-
-- **Auth scheme, not just value.** Forgejo takes
-  `Authorization: token <t>`; GitHub wants `Bearer <t>` plus `Accept:
-application/vnd.github+json`, `X-GitHub-Api-Version` and a
-  `User-Agent`. Sending Forgejo's form to GitHub doesn't error — it
-  authenticates as _nobody_ and silently drops to the unauthenticated
-  rate limit. The cheap way to tell the two apart is the rate-limit
-  header: `x-ratelimit-remaining` near 5000 is an authenticated user,
-  near 60 is anonymous.
-- **GitHub sets the cadence.** It returns `X-Poll-Interval` (60s in
-  practice, slower than the poller's own tick) and rate-limits callers who
-  ignore it, so the loop re-arms to the server's interval whenever that's
-  _slower_ than the poller's. A hint faster than the poller's own tick
-  isn't a reason to poll harder.
-
-⚠️ **This needs the `notifications` scope on the PAT.** A token minted
-for `gh` + `git push` typically carries `repo` only, which is enough to
-push and open PRs but **not** to read the notification stream (nor to
-mark a thread read, which is the same scope). A PAT without it doesn't
-break anything: the poller logs the refusal and stays quiet, and the
-agent never gets GitHub wakes. If an agent's GitHub
-notifications never arrive, check the token's scopes first — the
-symptom is silence, not an error.
-
-</details>
+How the agent's `gh` and `git push` authenticate, and how its GitHub
+notification poller works, is in
+[the implementation page](../../4-implementation/agent-tools/github.md).