Update Hanoi formula with agent-actionable instructions (gt-brd1b.3)

Add comprehensive execution protocol to formula description:
- EXECUTION LOOP: find ready step, close it, repeat
- ON RESUME: same as fresh start, molecule IS the state
- DO/DO NOT guidelines for autonomous execution
- MONITORING guidance for mega-molecules

This enables agents to execute Hanoi autonomously through restarts,
proving nondeterministic idempotence at scale.

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

.beads/formulas/towers-of-hanoi.formula.toml

@@ -1,4 +1,39 @@
-description = "Solve Towers of Hanoi for {disks} disks. Generates 2^{disks} - 1 steps, each a trivial move operation. Demonstrates mechanical structure generation for arbitrarily long workflows."
+description = """
+AGENT EXECUTION PROTOCOL - Towers of Hanoi ({disks} disks, {total_moves} steps)
+
+PURPOSE: This is a durability proof, not computation. Steps are pre-computed.
+Your job is to execute them mechanically, proving crash-recovery at scale.
+
+EXECUTION LOOP:
+1. Find current state: bd mol current <mol-id>
+2. Find the next ready (unblocked) step
+3. Close it: bd close <step-id>
+4. Repeat until no ready steps remain
+
+ON RESUME (after crash/restart/handoff):
+- Same as fresh start. The molecule IS the state.
+- Query `bd mol current <mol-id>`, continue from there.
+- No memory of previous session needed.
+
+DO:
+- Close steps as fast as possible (they're trivial mechanical moves)
+- Use `gt handoff` when context fills (proactive cycling)
+- Trust the pre-computed solution - every move is already correct
+
+DO NOT:
+- Try to solve Hanoi yourself - moves are already computed
+- Mark steps in_progress - just close them directly
+- Ask for permission - this is GUPP territory, just execute
+- Stop for human input - run autonomously until complete
+
+MONITORING:
+- Progress: Count closed children of the molecule
+- For mega-molecules: Use convoy dashboard when available
+- Completion: All steps closed = molecule complete
+
+This proves Gas Town can execute arbitrarily long workflows with
+nondeterministic idempotence - different sessions, same outcome.
+"""
 formula = "towers-of-hanoi"
 version = 1
 

.beads/formulas/towers-of-hanoi.formula.yaml

@@ -18,10 +18,41 @@
 # This formula uses for-each to generate all moves at cook time.
 
 formula: towers-of-hanoi
-description: >
-  Solve Towers of Hanoi for {disks} disks. Generates 2^{disks} - 1 steps,
-  each a trivial move operation. Demonstrates mechanical structure generation
-  for arbitrarily long workflows.
+description: |
+  AGENT EXECUTION PROTOCOL - Towers of Hanoi ({disks} disks, {total_moves} steps)
+
+  PURPOSE: This is a durability proof, not computation. Steps are pre-computed.
+  Your job is to execute them mechanically, proving crash-recovery at scale.
+
+  EXECUTION LOOP:
+  1. Find current state: bd mol current <mol-id>
+  2. Find the next ready (unblocked) step
+  3. Close it: bd close <step-id>
+  4. Repeat until no ready steps remain
+
+  ON RESUME (after crash/restart/handoff):
+  - Same as fresh start. The molecule IS the state.
+  - Query `bd mol current <mol-id>`, continue from there.
+  - No memory of previous session needed.
+
+  DO:
+  - Close steps as fast as possible (they're trivial mechanical moves)
+  - Use `gt handoff` when context fills (proactive cycling)
+  - Trust the pre-computed solution - every move is already correct
+
+  DO NOT:
+  - Try to solve Hanoi yourself - moves are already computed
+  - Mark steps in_progress - just close them directly
+  - Ask for permission - this is GUPP territory, just execute
+  - Stop for human input - run autonomously until complete
+
+  MONITORING:
+  - Progress: Count closed children of the molecule
+  - For mega-molecules: Use convoy dashboard when available
+  - Completion: All steps closed = molecule complete
+
+  This proves Gas Town can execute arbitrarily long workflows with
+  nondeterministic idempotence - different sessions, same outcome.
 version: 1
 
 vars: