web/docs: align api descriptions to edut id

docs/api/governance-installer.openapi.yaml

@@ -27,7 +27,7 @@ paths:
               schema:
                 $ref: '#/components/schemas/InstallTokenResponse'
         '403':
-          description: Membership inactive, identity assurance insufficient, or governance entitlement inactive.
+          description: EDUT ID inactive, identity assurance insufficient, or governance entitlement inactive.
           content:
             application/json:
               schema:
@@ -95,7 +95,7 @@ paths:
               schema:
                 $ref: '#/components/schemas/LeaseHeartbeatResponse'
         '403':
-          description: Membership/assurance/boundary/entitlement invalid.
+          description: EDUT ID/assurance/boundary/entitlement invalid.
           content:
             application/json:
               schema:
@@ -118,7 +118,7 @@ paths:
               schema:
                 $ref: '#/components/schemas/OfflineRenewResponse'
         '403':
-          description: Membership/assurance/boundary/entitlement invalid.
+          description: EDUT ID/assurance/boundary/entitlement invalid.
           content:
             application/json:
               schema:

docs/api/marketplace.openapi.yaml

@@ -2,7 +2,7 @@ openapi: 3.0.3
 info:
   title: EDUT Marketplace API
   version: v1
-  description: Membership-gated offer and entitlement commerce endpoints.
+  description: EDUT ID-gated offer and entitlement commerce endpoints.
 servers:
   - url: https://api.edut.ai
 security:
@@ -57,7 +57,7 @@ paths:
           description: Not found
   /marketplace/checkout/quote:
     post:
-      summary: Create checkout quote (membership required)
+      summary: Create checkout quote (EDUT ID required)
       requestBody:
         required: true
         content:
@@ -72,7 +72,7 @@ paths:
               schema:
                 $ref: '#/components/schemas/CheckoutQuoteResponse'
         '403':
-          description: Membership not active
+          description: EDUT ID not active
   /marketplace/checkout/confirm:
     post:
       summary: Confirm checkout transaction and mint entitlement

docs/api/member-channel.openapi.yaml

@@ -4,7 +4,7 @@ info:
   version: 1.0.0
   description: |
     Deterministic member communication channel contract.
-    App notifications are derived from wallet-authenticated membership and entitlement state.
+    App notifications are derived from wallet-authenticated EDUT ID and entitlement state.
 servers:
   - url: https://api.edut.ai
 security:
@@ -28,7 +28,7 @@ paths:
               schema:
                 $ref: '#/components/schemas/DeviceRegisterResponse'
         '403':
-          description: Membership is not active for this wallet.
+          description: EDUT ID is not active for this wallet.
           content:
             application/json:
               schema:
@@ -99,7 +99,7 @@ paths:
               schema:
                 $ref: '#/components/schemas/EventListResponse'
         '403':
-          description: Membership inactive or suspended.
+          description: EDUT ID inactive or suspended.
           content:
             application/json:
               schema:

docs/api/secret-system.openapi.yaml

@@ -2,7 +2,7 @@ openapi: 3.0.3
 info:
   title: EDUT Secret System API
   version: v1
-  description: Wallet-first designation and membership activation endpoints.
+  description: Wallet-first designation and EDUT ID activation endpoints.
 servers:
   - url: https://api.edut.ai
 paths:
@@ -100,7 +100,7 @@ paths:
           description: Session missing, invalid, revoked, or expired
   /secret/membership/quote:
     post:
-      summary: Get current membership mint quote
+      summary: Get current EDUT ID activation quote
       description: Canonical technical route. Public EDUT ID alias is `/secret/id/quote`.
       requestBody:
         required: true
@@ -117,7 +117,7 @@ paths:
                 $ref: '#/components/schemas/MembershipQuoteResponse'
   /secret/membership/confirm:
     post:
-      summary: Confirm membership mint transaction
+      summary: Confirm EDUT ID activation transaction
       description: Canonical technical route. Public EDUT ID alias is `/secret/id/confirm`.
       requestBody:
         required: true
@@ -127,14 +127,14 @@ paths:
               $ref: '#/components/schemas/MembershipConfirmRequest'
       responses:
         '200':
-          description: Membership active
+          description: EDUT ID active
           content:
             application/json:
               schema:
                 $ref: '#/components/schemas/MembershipConfirmResponse'
   /secret/membership/status:
     get:
-      summary: Resolve membership status by wallet or designation code
+      summary: Resolve EDUT ID status by wallet or designation code
       description: Canonical technical route. Public EDUT ID alias is `/secret/id/status`.
       parameters:
         - in: query
@@ -150,7 +150,7 @@ paths:
             type: string
       responses:
         '200':
-          description: Membership status resolved
+          description: EDUT ID status resolved
           content:
             application/json:
               schema: