docs: Matrix (Synapse) — member chat, Space auto-invite via portal sync

infrastructure.md

@@ -32,6 +32,7 @@ single sign-on, and per-app isolation.
 | **Admin Panel** | Admin-only member overview, spend, balance management | panel.inference.coop | [code/admin-panel](https://git.inference.coop/code/admin-panel) |
 | **SearXNG** | Self-hosted web search (feeds the chat's search) | search.inference.coop | — |
 | **Loomio** | Member governance | forum.inference.coop | — |
+| **Matrix (Synapse)** | Member chat server (federated; SSO login via Cloudron) | matrix.inference.coop | — |
 | **Gitea** | Git hosting (code + docs) | git.inference.coop | — |
 | **Surfer** | Static hosting (landing page, thanks page) | inference.coop | [co-op/website](https://git.inference.coop/co-op/website) |
 | **Listmonk** | Member newsletter (auto-synced from membership) | newsletter.inference.coop | — |
@@ -41,6 +42,21 @@ single sign-on, and per-app isolation.
 Open Collective (billing and fiscal sponsorship) is the one external service in
 the flow — see [opencollective.com/inference-cooperative](https://opencollective.com/inference-cooperative).
 
+## Matrix
+
+Members get a federated Matrix account on our self-hosted Synapse
+(matrix.inference.coop, user IDs `@username:inference.coop`) using their
+Cloudron SSO login. The portal invites every active member — and Nathan's
+federated account — to the private **Inference Cooperative** Space (with a
+**General** room) on every membership sync, so new members land in the space
+automatically. Invites honor rate limits; external/federated members can be
+added via the portal's `MATRIX_EXTRA_MXIDS` env.
+
+Federation is enabled (delegated via `.well-known/matrix/server` on the bare
+domain, port 443), so members can also join from any homeserver they already
+use. The `@inference-bot:inference.coop` admin account (used by the portal
+for invites) has no password — token lives in the portal env.
+
 ## How membership is wired
 
 Membership flows through the member portal, which is the single source of truth