diff --git a/backend/app/api.py b/backend/app/api.py
index 60be3f5..34cce3c 100644
--- a/backend/app/api.py
+++ b/backend/app/api.py
@@ -27,6 +27,7 @@ from . import (
     api_discussion,
     api_graduation,
     api_invitations,
+    api_memberships,
     api_notifications,
     api_prs,
     auth,
@@ -154,6 +155,9 @@ def make_router(
     # VITE_APP_NAME) + the old-URL 308 redirects.
     router.include_router(api_deployment.make_router(config))
     router.include_router(api_collections.make_router(config, gitea, bot))
+    # §22 S4 (C.2): the scope-role invitation surface — Owners grant
+    # {owner, contributor} at project/collection scope to existing accounts.
+    router.include_router(api_memberships.make_router())
 
     # ---------------------------------------------------------------
     # §17: /api/health — unauthenticated post-flight probe.
diff --git a/backend/app/api_collections.py b/backend/app/api_collections.py
index 2f990d4..61132ad 100644
--- a/backend/app/api_collections.py
+++ b/backend/app/api_collections.py
@@ -41,6 +41,26 @@ class CreateCollectionBody(BaseModel):
     initial_state: str | None = None
 
 
+def _project_viewer_caps(viewer: Any, project_id: str) -> dict[str, Any]:
+    """§22 S4: the viewer's project-grain capabilities for role-aware UI — may
+    they create a collection, may they manage membership (invite), and their
+    project role. `role` maps the §22.6 legacy strings back to the unified
+    `{owner, contributor}` vocabulary the frontend speaks."""
+    legacy = auth.project_member_role(viewer, project_id)
+    role = None
+    if viewer is not None and viewer.role in ("owner", "admin"):
+        role = "owner"
+    elif legacy == "project_admin":
+        role = "owner"
+    elif legacy == "project_contributor":
+        role = "contributor"
+    return {
+        "can_create_collection": auth.can_create_collection(viewer, project_id),
+        "can_invite": auth.can_invite_at_project(viewer, project_id),
+        "role": role,
+    }
+
+
 def make_router(config: Config, gitea: Gitea, bot: Bot) -> APIRouter:
     router = APIRouter()
 
@@ -57,7 +77,10 @@ def make_router(config: Config, gitea: Gitea, bot: Bot) -> APIRouter:
             for c in collections_mod.list_collections(project_id, include_unlisted=True)
             if c["visibility"] != "unlisted" and auth.can_read_collection(viewer, c["id"])
         ]
-        return {"items": items}
+        # §22 S4: surface the viewer's project-level capabilities so the
+        # directory can render role-aware affordances (the create-first-
+        # collection CTA, the invite control) without a second round-trip.
+        return {"items": items, "viewer": _project_viewer_caps(viewer, project_id)}
 
     @router.get("/api/projects/{project_id}/collections/{collection_id}")
     async def get_col(project_id: str, collection_id: str, request: Request) -> dict[str, Any]:
@@ -68,6 +91,14 @@ def make_router(config: Config, gitea: Gitea, bot: Bot) -> APIRouter:
             raise HTTPException(404, "Not found")
         # §22.5 (S3): a hidden/gated collection 404s a non-scope-role viewer.
         auth.require_collection_readable(viewer, collection_id)
+        # §22 S4: the viewer's collection-level capabilities drive the
+        # propose-first empty state and the collection invite control.
+        col = dict(col)
+        col["viewer"] = {
+            "can_contribute": auth.can_contribute_in_collection(viewer, collection_id),
+            "can_invite": auth.can_invite_at_collection(viewer, collection_id),
+            "role": auth.effective_scope_role(viewer, collection_id),
+        }
         return col
 
     @router.post("/api/projects/{project_id}/collections")
diff --git a/backend/app/api_memberships.py b/backend/app/api_memberships.py
new file mode 100644
index 0000000..296f448
--- /dev/null
+++ b/backend/app/api_memberships.py
@@ -0,0 +1,157 @@
+"""§22 S4 (C.2) — the scope-role invitation surface.
+
+An Owner grants `{owner, contributor}` at a scope their reach covers — the
+project, or a single collection within it — to an existing account, looked up
+by email. The grant writes a `memberships` row immediately and §15-notifies
+the grantee (there is no accept round-trip; the C.2 scenarios name an existing
+user and write the row directly). Endpoints:
+
+  GET    /api/projects/:pid/members                 — list the project subtree's grants
+  POST   /api/projects/:pid/members                 — grant at project scope, or
+                                                      (with collection_id) at one collection
+  DELETE /api/projects/:pid/members/:user_id         — revoke (optionally ?collection_id=)
+
+The single POST keys on the optional `collection_id` so the invite UI's one
+control (role picker + scope picker) maps to one endpoint:
+
+  * no `collection_id`  → project-scope grant; gate `can_invite_at_project`.
+  * with `collection_id` → collection-scope grant; gate `can_invite_at_collection`.
+
+There is deliberately no "grant at parent, exclude a child" parameter (C.2.5):
+the only knobs are role ∈ {owner, contributor} and scope ∈ {project, one
+collection}. Reach is bounded by the inviter's own Owner reach (C.2.3): a
+collection Owner who is nothing more is refused the project-scope POST.
+"""
+from __future__ import annotations
+
+from typing import Any
+
+from fastapi import APIRouter, HTTPException, Request
+from pydantic import BaseModel
+
+from . import (
+    auth,
+    collections as collections_mod,
+    db,
+    memberships as memberships_mod,
+    notify,
+)
+
+
+class GrantBody(BaseModel):
+    email: str
+    role: str
+    collection_id: str | None = None
+
+
+def _project_name(project_id: str) -> str | None:
+    row = db.conn().execute(
+        "SELECT name FROM projects WHERE id = ?", (project_id,)
+    ).fetchone()
+    return row["name"] if row and row["name"] else None
+
+
+def make_router() -> APIRouter:
+    router = APIRouter()
+
+    @router.get("/api/projects/{project_id}/members")
+    async def list_members(project_id: str, request: Request) -> dict[str, Any]:
+        user = auth.require_contributor(request)
+        auth.require_project_readable(user, project_id)
+        # The full subtree listing is a project-Owner view; a collection-only
+        # Owner manages membership through the collection-scoped POST/DELETE.
+        if not auth.can_invite_at_project(user, project_id):
+            raise HTTPException(403, "You may not manage membership in this project")
+        return {"items": memberships_mod.list_for_project(project_id)}
+
+    @router.post("/api/projects/{project_id}/members")
+    async def grant_member(
+        project_id: str, body: GrantBody, request: Request
+    ) -> dict[str, Any]:
+        user = auth.require_contributor(request)
+        auth.require_project_readable(user, project_id)
+
+        role = (body.role or "").strip().lower()
+        if role not in memberships_mod.VALID_ROLES:
+            raise HTTPException(422, f"invalid role {body.role!r}")
+
+        cid = (body.collection_id or "").strip() or None
+        if cid is not None:
+            # Collection-scope grant — bounded by Owner reach over that collection.
+            col = collections_mod.get_collection(cid)
+            if col is None or col["project_id"] != project_id:
+                raise HTTPException(404, "Not found")
+            if not auth.can_invite_at_collection(user, cid):
+                raise HTTPException(403, "You may not manage membership in this collection")
+            scope_type, scope_id = "collection", cid
+        else:
+            # Project-scope grant — bounded by Owner reach over the project.
+            if not auth.can_invite_at_project(user, project_id):
+                raise HTTPException(403, "You may not manage membership in this project")
+            scope_type, scope_id = "project", project_id
+
+        grantee = memberships_mod.user_by_email(body.email)
+        if grantee is None:
+            raise HTTPException(
+                404,
+                "No account with that email — the invitee must sign in to the "
+                "deployment before they can be granted a role",
+            )
+
+        memberships_mod.grant(
+            scope_type=scope_type,
+            scope_id=scope_id,
+            user_id=grantee["id"],
+            role=role,
+            granted_by=user.user_id,
+        )
+
+        # §15 (C.2): name the project and role to the grantee.
+        col_name = None
+        if scope_type == "collection":
+            col = collections_mod.get_collection(scope_id)
+            col_name = (col.get("name") if col else None) or scope_id
+        notify.notify_scope_role_granted(
+            recipient_user_id=grantee["id"],
+            granter_user_id=user.user_id,
+            scope_type=scope_type,
+            scope_id=scope_id,
+            role=role,
+            project_id=project_id,
+            project_name=_project_name(project_id),
+            collection_name=col_name,
+        )
+
+        return {
+            "scope_type": scope_type,
+            "scope_id": scope_id,
+            "user_id": grantee["id"],
+            "role": role,
+            "pending": grantee["permission_state"] != "granted",
+        }
+
+    @router.delete("/api/projects/{project_id}/members/{user_id}")
+    async def revoke_member(
+        project_id: str, user_id: int, request: Request
+    ) -> dict[str, Any]:
+        user = auth.require_contributor(request)
+        auth.require_project_readable(user, project_id)
+        cid = (request.query_params.get("collection_id") or "").strip() or None
+        if cid is not None:
+            col = collections_mod.get_collection(cid)
+            if col is None or col["project_id"] != project_id:
+                raise HTTPException(404, "Not found")
+            if not auth.can_invite_at_collection(user, cid):
+                raise HTTPException(403, "You may not manage membership in this collection")
+            removed = memberships_mod.revoke(
+                scope_type="collection", scope_id=cid, user_id=user_id
+            )
+        else:
+            if not auth.can_invite_at_project(user, project_id):
+                raise HTTPException(403, "You may not manage membership in this project")
+            removed = memberships_mod.revoke(
+                scope_type="project", scope_id=project_id, user_id=user_id
+            )
+        return {"removed": removed}
+
+    return router
diff --git a/backend/app/auth.py b/backend/app/auth.py
index 4f529ad..30e4b5d 100644
--- a/backend/app/auth.py
+++ b/backend/app/auth.py
@@ -682,6 +682,26 @@ def can_create_collection(user: SessionUser | None, project_id: str) -> bool:
     return row is not None
 
 
+def can_invite_at_project(user: SessionUser | None, project_id: str) -> bool:
+    """§22 S4 (C.2): may the user grant scope roles at this project (or at any
+    collection within it)? Managing membership is an *Owner* capability whose
+    reach covers the project — a deployment owner/admin, a global Owner, or this
+    project's Owner. An RFC Contributor does not manage membership (C.2.4); a
+    collection Owner's reach is its own collection only (C.2.3), so it is not
+    offered project-scope invites. Identical to `is_project_superuser` — the
+    invite gate IS "is an Owner over this project"."""
+    return is_project_superuser(user, project_id)
+
+
+def can_invite_at_collection(user: SessionUser | None, collection_id: str) -> bool:
+    """§22 S4 (C.2): may the user grant scope roles at this collection? An Owner
+    whose reach covers it — the collection's Owner, its project's Owner, a global
+    Owner, or a deployment owner/admin (`is_collection_superuser`). This is the
+    narrowest invite reach; a collection Owner who is nothing more may invite
+    here but not at the project or globally (C.2.3)."""
+    return is_collection_superuser(user, collection_id)
+
+
 # v0.16.0 (roadmap item #12): per-RFC membership helpers.
 #
 # These don't replace `require_contributor` — they layer on top of it for
diff --git a/backend/app/memberships.py b/backend/app/memberships.py
new file mode 100644
index 0000000..aaba48c
--- /dev/null
+++ b/backend/app/memberships.py
@@ -0,0 +1,141 @@
+"""§22 S4 (C.2) — scope-role grant operations over the `memberships` table.
+
+The membership *gates* (who may invite, who holds which role) live in
+`auth.py`; this module holds the *mutations* the invitation surface drives —
+granting, the "broader scope supersedes narrower" cleanup, listing, and
+revocation — mirroring how `invites.py` owns the create/claim/list of per-user
+invite tokens while the gate (`auth.can_invite_to_rfc`) lives in `auth.py`.
+
+The model (Part B / S3): a `memberships` row is `(scope_type ∈ {global,
+project, collection}, scope_id, user_id, role ∈ {owner, contributor})`, unique
+per `(scope_type, scope_id, user_id)`. A grant is a direct write of that row
+(the C.2 scenarios write the row immediately and §15-notify an existing
+account — there is no accept round-trip; inviting a not-yet-account email is
+out of S4 scope and handled by the admin-create-invite path).
+
+The "broader scope supersedes narrower" rule (C.2.6): granting a role at a
+broader scope removes this user's narrower rows that the new grant *subsumes*
+— a narrower row whose role is no more permissive than the new one. A narrower
+row that is *more* permissive is kept (no negative override: a child Owner
+grant survives a parent Contributor grant, and the §B.2 resolver still unions
+most-permissively).
+"""
+from __future__ import annotations
+
+from typing import Any
+
+from . import collections as collections_mod
+from . import db
+
+# Higher rank = more permissive. Used by the supersede rule: a narrower grant
+# is pruned only when its rank ≤ the new broader grant's rank.
+_ROLE_RANK = {"contributor": 1, "owner": 2}
+
+VALID_SCOPE_TYPES = ("global", "project", "collection")
+VALID_ROLES = ("owner", "contributor")
+GLOBAL_SCOPE_ID = "*"
+
+
+def user_by_email(email: str) -> dict[str, Any] | None:
+    """The `users` row (id, display_name, email, permission_state) for an
+    email, case-insensitively, or None. The grantee must already be an account
+    — S4 grants a scope role to an existing user, it does not provision one."""
+    row = db.conn().execute(
+        "SELECT id, display_name, email, permission_state, role "
+        "FROM users WHERE lower(email) = lower(?) "
+        "ORDER BY id LIMIT 1",
+        (email.strip(),),
+    ).fetchone()
+    return dict(row) if row else None
+
+
+def grant(
+    *,
+    scope_type: str,
+    scope_id: str,
+    user_id: int,
+    role: str,
+    granted_by: int | None,
+) -> None:
+    """Write (or update) the membership row, then apply the C.2.6
+    broader-scope-supersedes cleanup. Idempotent on `(scope_type, scope_id,
+    user_id)` — re-granting at the same scope updates the role and the grantor.
+
+    The grant is recorded regardless of the grantee's deployment
+    `permission_state`: a `pending` account's row is written (C.2.7), but the
+    §6 admission floor in `auth.effective_scope_role` keeps it conferring no
+    write until the account is granted at the deployment."""
+    db.conn().execute(
+        "INSERT INTO memberships (scope_type, scope_id, user_id, role, granted_by) "
+        "VALUES (?, ?, ?, ?, ?) "
+        "ON CONFLICT (scope_type, scope_id, user_id) "
+        "DO UPDATE SET role = excluded.role, granted_by = excluded.granted_by, "
+        "granted_at = datetime('now')",
+        (scope_type, scope_id, user_id, role, granted_by),
+    )
+    _prune_subsumed(scope_type=scope_type, scope_id=scope_id, user_id=user_id, role=role)
+
+
+def _prune_subsumed(*, scope_type: str, scope_id: str, user_id: int, role: str) -> None:
+    """Remove this user's narrower rows that the just-written broader grant
+    subsumes (same-or-lower role rank within the broader scope's subtree). A
+    collection grant subsumes nothing narrower (the per-entry tier is separate);
+    a project grant subsumes its collections; a global grant subsumes every
+    project and collection."""
+    rank = _ROLE_RANK[role]
+    keep_ranks = [r for r, v in _ROLE_RANK.items() if v <= rank]
+    if not keep_ranks:
+        return
+    placeholders = ",".join("?" for _ in keep_ranks)
+    if scope_type == "project":
+        # Narrower = collection-scope rows for collections in this project.
+        db.conn().execute(
+            f"DELETE FROM memberships "
+            f"WHERE user_id = ? AND scope_type = 'collection' "
+            f"  AND role IN ({placeholders}) "
+            f"  AND scope_id IN (SELECT id FROM collections WHERE project_id = ?)",
+            (user_id, *keep_ranks, scope_id),
+        )
+    elif scope_type == "global":
+        # Narrower = every project- and collection-scope row for this user.
+        db.conn().execute(
+            f"DELETE FROM memberships "
+            f"WHERE user_id = ? AND scope_type IN ('project', 'collection') "
+            f"  AND role IN ({placeholders})",
+            (user_id, *keep_ranks),
+        )
+
+
+def revoke(*, scope_type: str, scope_id: str, user_id: int) -> bool:
+    """Remove a membership row at exactly this scope. Returns True if a row was
+    removed. Revocation is scope-exact: it does not cascade to broader or
+    narrower grants (each is its own administrative act)."""
+    cur = db.conn().execute(
+        "DELETE FROM memberships WHERE scope_type = ? AND scope_id = ? AND user_id = ?",
+        (scope_type, scope_id, user_id),
+    )
+    return cur.rowcount > 0
+
+
+def list_for_project(project_id: str) -> list[dict[str, Any]]:
+    """Every project-scope grant on this project plus every collection-scope
+    grant on its collections, joined to the grantee's display fields — the data
+    behind the project-Owner membership panel. Ordered project grants first,
+    then by collection, then by role (Owner before Contributor)."""
+    rows = db.conn().execute(
+        """
+        SELECT m.scope_type, m.scope_id, m.user_id, m.role, m.granted_at,
+               u.display_name, u.email, u.permission_state,
+               c.name AS collection_name
+          FROM memberships m
+          JOIN users u ON u.id = m.user_id
+     LEFT JOIN collections c ON c.id = m.scope_id AND m.scope_type = 'collection'
+         WHERE (m.scope_type = 'project' AND m.scope_id = ?)
+            OR (m.scope_type = 'collection'
+                AND m.scope_id IN (SELECT id FROM collections WHERE project_id = ?))
+         ORDER BY (m.scope_type != 'project'), m.scope_id,
+                  CASE m.role WHEN 'owner' THEN 0 ELSE 1 END, u.display_name
+        """,
+        (project_id, project_id),
+    ).fetchall()
+    return [dict(r) for r in rows]
diff --git a/backend/app/notify.py b/backend/app/notify.py
index 55a9a93..4427158 100644
--- a/backend/app/notify.py
+++ b/backend/app/notify.py
@@ -324,6 +324,48 @@ def fan_out_contribution_request(
     return notif_ids
 
 
+def notify_scope_role_granted(
+    *,
+    recipient_user_id: int,
+    granter_user_id: int | None,
+    scope_type: str,
+    scope_id: str,
+    role: str,
+    project_id: str | None,
+    project_name: str | None,
+    collection_name: str | None,
+) -> int | None:
+    """§22 S4 (C.2): a scope Owner granted `recipient` a role at a scope.
+    Personal-direct — the recipient is the named subject — so it rides the
+    `email_personal_direct` gate like the other owner-facing personal events.
+    The scope facts ride in the payload so the inbox row (and email body) names
+    the project and role without a second fetch. Actor is the granter (§15.9);
+    a system/administrative grant with no granter renders as "the app".
+
+    Returns the notification id, or None when the grantee would be notifying
+    themselves (a self-grant — no notification)."""
+    if granter_user_id is not None and recipient_user_id == granter_user_id:
+        return None
+    details = {
+        "scope_type": scope_type,
+        "scope_id": scope_id,
+        "role": role,
+        "project_id": project_id or "",
+        "project_name": project_name or "",
+        "collection_name": collection_name or "",
+    }
+    return _emit_one(
+        recipient_user_id=recipient_user_id,
+        event_kind="scope_role_granted",
+        category=CATEGORY_PERSONAL,
+        actor_user_id=granter_user_id,
+        rfc_slug=None,
+        branch_name=None,
+        pr_number=None,
+        details=details,
+    )
+
+
 def notify_contribution_decided(
     *,
     rfc_slug: str,
@@ -859,6 +901,19 @@ def render_summary(event_kind: str, actor_display: str | None, rfc_title: str |
         return f"{actor} accepted your request to contribute to {title} — check your email to accept the invitation."
     if event_kind == "contribution_request_declined":
         return f"{actor} declined your request to contribute to {title}."
+    if event_kind == "scope_role_granted":
+        # §22 S4 (C.2): names the role and the scope (the project, and the
+        # collection when collection-scoped) per "a §15 notification naming the
+        # project and role".
+        role_label = "Owner" if extras.get("role") == "owner" else "RFC Contributor"
+        project_label = extras.get("project_name") or extras.get("project_id") or "a project"
+        scope_type = extras.get("scope_type")
+        if scope_type == "collection":
+            col_label = extras.get("collection_name") or extras.get("scope_id") or "a collection"
+            return f"{actor} granted you {role_label} on collection {project_label}/{col_label}."
+        if scope_type == "global":
+            return f"{actor} granted you {role_label} across the whole deployment."
+        return f"{actor} granted you {role_label} on project {project_label}."
     if event_kind == "new_beta_request":
         # v0.9.0: framework-scoped, not RFC-scoped. The actor (the
         # requester) and the captured full name + email read as
diff --git a/backend/tests/test_s4_invitations_vertical.py b/backend/tests/test_s4_invitations_vertical.py
new file mode 100644
index 0000000..91e214a
--- /dev/null
+++ b/backend/tests/test_s4_invitations_vertical.py
@@ -0,0 +1,331 @@
+"""Slice S4 — invitation surfaces + role-aware empty states (@S4).
+
+The acceptance gate for S4 is "every Part C.2 invitation scenario passes" (the
+design doc docs/design/2026-06-05-three-tier-projects-collections.md, §C.2,
+tagged @S4), plus the capability flags that drive the C.3 (@S4) role-aware
+empty states.
+
+An Owner grants {owner, contributor} at a scope their reach covers — the
+project, or a single collection within it — to an existing account looked up by
+email. The grant writes a `memberships` row immediately and §15-notifies the
+grantee (no accept round-trip). Reach is bounded by the inviter's Owner reach;
+re-granting at a broader scope supersedes the narrower row; a `pending`
+deployment account's grant is recorded but confers no write.
+
+Background (C.2): project "ohm" owns collections "model" (document) and
+"features" (bdd). eve is project Owner of ohm; dan is collection Owner of
+features only; ben is a project Contributor of ohm. ivy / jo / jet are
+grantees; kim is a pending deployment account.
+"""
+from __future__ import annotations
+
+from fastapi.testclient import TestClient
+
+from test_propose_vertical import (  # noqa: F401 — fixtures land via import
+    app_with_fake_gitea,
+    provision_user_row,
+    sign_in_as,
+    tmp_env,
+)
+
+
+# ---------------------------------------------------------------------------
+# Helpers (mirror the S3 vertical's world-builders)
+# ---------------------------------------------------------------------------
+
+
+def _su(user_id: int, login: str, role: str = "contributor", *, state: str = "granted"):
+    from app import auth
+
+    return auth.SessionUser(
+        user_id=user_id, gitea_id=user_id, gitea_login=login,
+        display_name=login.capitalize(), email=f"{login}@test", avatar_url="",
+        role=role, permission_state=state,
+    )
+
+
+def _project(pid: str, visibility: str = "public", content_repo: str = "meta") -> None:
+    from app import db
+
+    db.conn().execute(
+        "INSERT OR REPLACE INTO projects (id, name, content_repo, visibility, updated_at) "
+        "VALUES (?, ?, ?, ?, datetime('now'))",
+        (pid, pid.capitalize(), content_repo, visibility),
+    )
+
+
+def _collection(cid: str, project_id: str, *, ctype: str = "document",
+                visibility: str = "public", subfolder: str | None = None) -> None:
+    from app import db
+
+    db.conn().execute(
+        "INSERT OR REPLACE INTO collections "
+        "(id, project_id, type, subfolder, initial_state, visibility, name, created_at, updated_at) "
+        "VALUES (?, ?, ?, ?, 'super-draft', ?, ?, datetime('now'), datetime('now'))",
+        (cid, project_id, ctype, subfolder if subfolder is not None else cid,
+         visibility, cid.capitalize()),
+    )
+
+
+def _grant(scope_type: str, scope_id: str, user_id: int, role: str) -> None:
+    from app import db
+
+    db.conn().execute(
+        "INSERT OR REPLACE INTO memberships (scope_type, scope_id, user_id, role) "
+        "VALUES (?, ?, ?, ?)",
+        (scope_type, scope_id, user_id, role),
+    )
+
+
+def _membership(user_id: int):
+    """The set of (scope_type, scope_id, role) rows a user holds."""
+    from app import db
+
+    rows = db.conn().execute(
+        "SELECT scope_type, scope_id, role FROM memberships WHERE user_id = ?",
+        (user_id,),
+    ).fetchall()
+    return {(r["scope_type"], r["scope_id"], r["role"]) for r in rows}
+
+
+def _seed_world() -> None:
+    _project("ohm", "public")
+    _collection("model", "ohm", ctype="document")
+    _collection("features", "ohm", ctype="bdd")
+    # the cast
+    provision_user_row(user_id=2, login="ben", role="contributor")
+    provision_user_row(user_id=4, login="dan", role="contributor")
+    provision_user_row(user_id=5, login="eve", role="contributor")
+    provision_user_row(user_id=10, login="ivy", role="contributor")
+    provision_user_row(user_id=11, login="jo", role="contributor")
+    provision_user_row(user_id=12, login="jet", role="contributor")
+    provision_user_row(user_id=13, login="kim", role="contributor")
+    _grant("project", "ohm", 5, "owner")          # eve — project Owner
+    _grant("collection", "features", 4, "owner")  # dan — collection Owner only
+    _grant("project", "ohm", 2, "contributor")    # ben — project Contributor
+    # kim is a pending deployment account.
+    from app import db
+    db.conn().execute(
+        "UPDATE users SET permission_state = 'pending' WHERE id = 13"
+    )
+
+
+def _login_eve(client) -> None:
+    sign_in_as(client, user_id=5, gitea_login="eve", display_name="Eve", role="contributor")
+
+
+# ---------------------------------------------------------------------------
+# C.2 — invitation: who may invite whom, at which scope
+# ---------------------------------------------------------------------------
+
+
+def test_c2_1_project_owner_invites_at_project_scope(app_with_fake_gitea):
+    """A project Owner grants at project scope; the grant covers every
+    collection, and the grantee is §15-notified naming the project and role."""
+    from app import auth
+    app, _ = app_with_fake_gitea
+    with TestClient(app) as client:
+        _seed_world()
+        _login_eve(client)
+        r = client.post("/api/projects/ohm/members",
+                        json={"email": "ivy@test", "role": "contributor"})
+        assert r.status_code == 200, r.text
+        # a membership row is written at scope project "ohm"
+        assert ("project", "ohm", "contributor") in _membership(10)
+        # ivy may propose in every collection of "ohm"
+        ivy = _su(10, "ivy")
+        assert auth.can_contribute_in_collection(ivy, "model") is True
+        assert auth.can_contribute_in_collection(ivy, "features") is True
+        # ivy receives a §15 notification naming the project and role
+        sign_in_as(client, user_id=10, gitea_login="ivy", display_name="Ivy", role="contributor")
+        inbox = client.get("/api/notifications").json()["items"]
+        granted = [n for n in inbox if n["event_kind"] == "scope_role_granted"]
+        assert granted, inbox
+        assert "Ohm" in granted[0]["summary"]
+        assert "RFC Contributor" in granted[0]["summary"]
+
+
+def test_c2_2_owner_invites_at_specific_collection(app_with_fake_gitea):
+    """A grant at a single collection scope reaches that collection only."""
+    from app import auth
+    app, _ = app_with_fake_gitea
+    with TestClient(app) as client:
+        _seed_world()
+        _login_eve(client)
+        r = client.post("/api/projects/ohm/members",
+                        json={"email": "jo@test", "role": "contributor",
+                              "collection_id": "features"})
+        assert r.status_code == 200, r.text
+        assert ("collection", "features", "contributor") in _membership(11)
+        jo = _su(11, "jo")
+        assert auth.can_contribute_in_collection(jo, "features") is True
+        assert auth.can_contribute_in_collection(jo, "model") is False
+
+
+def test_c2_3_invitation_reach_bounded_by_inviter_scope(app_with_fake_gitea):
+    """A collection Owner may invite within that collection, but is not offered
+    (is refused) the control to invite at the project or globally."""
+    app, _ = app_with_fake_gitea
+    with TestClient(app) as client:
+        _seed_world()
+        # dan is Owner at collection "features" only.
+        sign_in_as(client, user_id=4, gitea_login="dan", display_name="Dan", role="contributor")
+        # may grant at his collection
+        ok = client.post("/api/projects/ohm/members",
+                         json={"email": "ivy@test", "role": "contributor",
+                               "collection_id": "features"})
+        assert ok.status_code == 200, ok.text
+        # but not at the project scope
+        no = client.post("/api/projects/ohm/members",
+                         json={"email": "ivy@test", "role": "contributor"})
+        assert no.status_code == 403, no.text
+        # the capability flags the UI reads agree: no project invite, yes collection
+        proj = client.get("/api/projects/ohm/collections").json()["viewer"]
+        assert proj["can_invite"] is False
+        col = client.get("/api/projects/ohm/collections/features").json()["viewer"]
+        assert col["can_invite"] is True
+
+
+def test_c2_4_contributors_do_not_manage_membership(app_with_fake_gitea):
+    """An RFC Contributor (project- or collection-scoped) holds no invite
+    capability and the grant endpoints refuse them."""
+    app, _ = app_with_fake_gitea
+    with TestClient(app) as client:
+        _seed_world()
+        # ben is a project *Contributor* on ohm.
+        sign_in_as(client, user_id=2, gitea_login="ben", display_name="Ben", role="contributor")
+        no_proj = client.post("/api/projects/ohm/members",
+                              json={"email": "ivy@test", "role": "contributor"})
+        assert no_proj.status_code == 403, no_proj.text
+        no_col = client.post("/api/projects/ohm/members",
+                             json={"email": "ivy@test", "role": "contributor",
+                                   "collection_id": "features"})
+        assert no_col.status_code == 403, no_col.text
+        # no invite control surfaced anywhere
+        assert client.get("/api/projects/ohm/collections").json()["viewer"]["can_invite"] is False
+        assert client.get("/api/projects/ohm/collections/features").json()["viewer"]["can_invite"] is False
+
+
+def test_c2_5_no_grant_at_parent_revoke_at_child_option(app_with_fake_gitea):
+    """The grant surface offers only role + scope (project or one collection);
+    there is no way to grant at the project yet carve out a child collection —
+    a project grant reaches every collection, full stop."""
+    from app import auth
+    app, _ = app_with_fake_gitea
+    with TestClient(app) as client:
+        _seed_world()
+        _login_eve(client)
+        # the only knobs are role and an optional single collection_id; an
+        # "exclude" field has no effect (it is not part of the contract).
+        r = client.post("/api/projects/ohm/members",
+                        json={"email": "ivy@test", "role": "contributor",
+                              "exclude_collection_id": "features"})
+        assert r.status_code == 200, r.text
+        # the project grant still reaches the supposedly-excluded collection
+        ivy = _su(10, "ivy")
+        assert auth.can_contribute_in_collection(ivy, "features") is True
+
+
+def test_c2_6_broader_scope_supersedes_narrower(app_with_fake_gitea):
+    """Re-granting at a broader scope removes the subsumed narrower row; the
+    grantee holds the role across the whole project."""
+    from app import auth
+    app, _ = app_with_fake_gitea
+    with TestClient(app) as client:
+        _seed_world()
+        _grant("collection", "features", 12, "contributor")  # jet starts narrow
+        _login_eve(client)
+        r = client.post("/api/projects/ohm/members",
+                        json={"email": "jet@test", "role": "contributor"})
+        assert r.status_code == 200, r.text
+        rows = _membership(12)
+        # the project grant is present…
+        assert ("project", "ohm", "contributor") in rows
+        # …and the redundant collection-scope row is gone (subsumed)
+        assert ("collection", "features", "contributor") not in rows
+        jet = _su(12, "jet")
+        assert auth.can_contribute_in_collection(jet, "model") is True
+        assert auth.can_contribute_in_collection(jet, "features") is True
+
+
+def test_c2_6b_narrower_stronger_role_is_not_subtracted(app_with_fake_gitea):
+    """No negative override: a child Owner grant survives a parent Contributor
+    grant (the stronger collection role is kept)."""
+    app, _ = app_with_fake_gitea
+    with TestClient(app) as client:
+        _seed_world()
+        _grant("collection", "features", 12, "owner")  # jet is collection Owner
+        _login_eve(client)
+        r = client.post("/api/projects/ohm/members",
+                        json={"email": "jet@test", "role": "contributor"})
+        assert r.status_code == 200, r.text
+        rows = _membership(12)
+        assert ("project", "ohm", "contributor") in rows
+        # the stronger collection-Owner row is NOT pruned by a weaker project grant
+        assert ("collection", "features", "owner") in rows
+
+
+def test_c2_7_pending_account_grant_confers_no_write(app_with_fake_gitea):
+    """A grant to a pending deployment account is recorded but confers no write
+    until the account is granted at the deployment (§6)."""
+    from app import auth
+    app, _ = app_with_fake_gitea
+    with TestClient(app) as client:
+        _seed_world()
+        _login_eve(client)
+        r = client.post("/api/projects/ohm/members",
+                        json={"email": "kim@test", "role": "contributor"})
+        assert r.status_code == 200, r.text
+        assert r.json()["pending"] is True
+        # the grant row is recorded…
+        assert ("project", "ohm", "contributor") in _membership(13)
+        # …but confers no write while pending (the §6 admission floor)
+        kim = _su(13, "kim", state="pending")
+        assert auth.effective_scope_role(kim, "model") is None
+        assert auth.can_contribute_in_collection(kim, "model") is False
+
+
+# ---------------------------------------------------------------------------
+# C.3 (@S4) — the capability flags behind the role-aware empty states
+# ---------------------------------------------------------------------------
+
+
+def test_c3_3_project_owner_sees_create_first_collection_capability(app_with_fake_gitea):
+    """C3.3: a project Owner landing on an empty project may create a
+    collection — the flag the 'Create your first collection' CTA reads."""
+    app, _ = app_with_fake_gitea
+    with TestClient(app) as client:
+        _seed_world()
+        _login_eve(client)
+        caps = client.get("/api/projects/ohm/collections").json()["viewer"]
+        assert caps["can_create_collection"] is True
+        assert caps["role"] == "owner"
+
+
+def test_c3_4_contributor_without_create_rights_has_no_create_capability(app_with_fake_gitea):
+    """C3.4: a contributor whose only grant is at a collection elsewhere has no
+    create-collection capability — the empty directory shows no create action."""
+    app, _ = app_with_fake_gitea
+    with TestClient(app) as client:
+        _seed_world()
+        # dan holds only a collection-scope grant (features); no project create right.
+        sign_in_as(client, user_id=4, gitea_login="dan", display_name="Dan", role="contributor")
+        caps = client.get("/api/projects/ohm/collections").json()["viewer"]
+        assert caps["can_create_collection"] is False
+
+
+def test_c3_5_collection_contributor_sees_propose_first_capability(app_with_fake_gitea):
+    """C3.5: a collection contributor landing on an empty collection may propose
+    — the flag the 'Propose the first entry' CTA reads; an anonymous reader may
+    not (the sign-in prompt path, already shipped in S2)."""
+    app, _ = app_with_fake_gitea
+    with TestClient(app) as client:
+        _seed_world()
+        _grant("collection", "model", 10, "contributor")  # ivy contributes in model
+        sign_in_as(client, user_id=10, gitea_login="ivy", display_name="Ivy", role="contributor")
+        caps = client.get("/api/projects/ohm/collections/model").json()["viewer"]
+        assert caps["can_contribute"] is True
+        # anonymous reader: no propose capability
+        client.cookies.clear()
+        caps_anon = client.get("/api/projects/ohm/collections/model").json()["viewer"]
+        assert caps_anon["can_contribute"] is False