feat(t27f): petal_menu.t27 is Icarus-lowerable and simulates 10/10 (M4 of #10782)

specs/t27f/frontend.t27

@@ -9,7 +9,10 @@
 ; What this spec does not restate:
 ; - The rules of each surface. They stay in the spec that decides it (spec_graph*.t27, reel.t27,
 ;   deck.t27, token_floor*.t27, lesson_reel.t27, hot.t27, claw/t27f_gate.t27, claw/preview.t27,
-;   particle_field.t27, ui_plan.t27, t27mcp/dashboard.t27). This spec names the surface only.
+;   particle_field.t27, ui_plan.t27, t27mcp/dashboard.t27, petal_menu.t27). This spec names the
+;   surface only.
+; - The T27 OS home (SF_PETAL_MENU, 2026-10-19): the 27-petal triangle, its hit test and its
+;   open/close rule live in petal_menu.t27; its hosts are the trios app today and an FPGA later.
 ; - Tool names. A surface drawn by an MCP tool points at its row of specs/t27mcp/tool_schema.t27.
 ; - Which tool belongs to TRI CLAW. specs/t27mcp/service.t27 decides that by prefix (t27_ and t27f_
 ;   are the t27 module's, mounted into TRI CLAW's /mcp). This spec checks that every T27F tool is
@@ -51,10 +54,11 @@ pub const SF_MAP_VIDEO : u32 = 9;      // honeycomb reel as video and live playe
 pub const SF_PARTICLE_LIVE : u32 = 10; // T27F Live, particle_field.t27 + particle_engine.t27
 pub const SF_UI_PLAN : u32 = 11;       // trusted-widget UI plan, ui_plan.t27
 pub const SF_DASHBOARD : u32 = 12;     // corpus and session health, t27mcp/dashboard.t27, tool t27_dashboard
-pub const SF_COUNT : u32 = 13;
+pub const SF_PETAL_MENU : u32 = 13;    // T27 OS home: the 27-petal triangle menu, petal_menu.t27
+pub const SF_COUNT : u32 = 14;
 pub const SF_NONE : u32 = 255;
 
-pub const SURFACE_NAMES : str = "graph,outline,map_still,graph_page,hot,check,preview,particle_reel,still,map_video,particle_live,ui_plan,dashboard";
+pub const SURFACE_NAMES : str = "graph,outline,map_still,graph_page,hot,check,preview,particle_reel,still,map_video,particle_live,ui_plan,dashboard,petal_menu";
 
 /// What draws a surface today.
 pub const ST_LIVE : u8 = 0;
@@ -63,7 +67,7 @@ pub const ST_PARTIAL : u8 = 2;
 pub const ST_BLOCKED : u8 = 3;
 pub const ST_SPEC : u8 = 4;
 
-pub const SURFACE_STATUS : [13]u8 = [0, 0, 0, 0, 2, 3, 4, 1, 1, 4, 4, 4, 0];
+pub const SURFACE_STATUS : [14]u8 = [0, 0, 0, 0, 2, 3, 4, 1, 1, 4, 4, 4, 0, 4];
 
 /// Where a surface is made: an MCP tool, a t27.ai page, the Railway lab, the TRI CLAW App, nowhere.
 pub const MK_MCP : u8 = 0;
@@ -72,7 +76,7 @@ pub const MK_LAB : u8 = 2;
 pub const MK_APP : u8 = 3;
 pub const MK_NONE : u8 = 4;
 
-pub const SURFACE_MAKER : [13]u8 = [0, 0, 0, 1, 0, 3, 3, 2, 2, 4, 4, 4, 0];
+pub const SURFACE_MAKER : [14]u8 = [0, 0, 0, 1, 0, 3, 3, 2, 2, 4, 4, 4, 0, 4];
 
 /// What a caller wants shown.
 pub const I_SPEC_SHAPE : u32 = 0;  // the structure of one spec
@@ -85,7 +89,8 @@ pub const I_EDITING : u32 = 6;     // a spec redrawn while it is edited
 pub const I_HEALTH : u32 = 7;      // the state of the corpus and the session
 pub const I_LIVE_AGENT : u32 = 8;  // an agent's work as a live particle field
 pub const I_APP : u32 = 9;         // an application screen built from trusted widgets
-pub const I_COUNT : u32 = 10;
+pub const I_OS_HOME : u32 = 10;    // the T27 OS home screen: 27 petals, a petal opens its menu
+pub const I_COUNT : u32 = 11;
 
 /// The drawing tools TRI CLAW's chat agent carries. service.t27 gives its coder persona CODER_TOOLS
 /// for writing a spec; these are for showing one.
@@ -171,6 +176,9 @@ pub fn route(intent: u32, host: u8) -> u32 {
     if (intent == I_APP) {
         return SF_UI_PLAN;
     }
+    if (intent == I_OS_HOME) {
+        return SF_PETAL_MENU;
+    }
     return SF_NONE;
 }
 
@@ -244,6 +252,13 @@ test a_report_is_a_particle_still_and_a_lesson_a_particle_reel {
     assert SURFACE_MAKER[SF_PARTICLE_REEL] == MK_LAB;
 }
 
+test the_os_home_is_the_petal_menu_and_nothing_draws_it_yet {
+    assert route(I_OS_HOME, HOST_CLAUDE_CODE_DESKTOP) == SF_PETAL_MENU;
+    assert route(I_OS_HOME, HOST_SITE) == SF_PETAL_MENU;
+    assert pick(I_OS_HOME, HOST_CLAUDE_CODE_DESKTOP) == SF_NONE;
+    assert claim_ok(SF_PETAL_MENU, true) == false;
+}
+
 test what_cannot_be_made_has_a_stand_in_or_none {
     assert pick(I_TOPIC_MAP, HOST_CLAUDE_CODE_DESKTOP) == SF_MAP_STILL;
     assert pick(I_PR, HOST_CLAUDE_CODE_DESKTOP) == SF_GRAPH;