fix: Sync embedded formulas with .beads/formulas

🤖 Generated with [Claude Code](https://claude.com/claude-code) Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>
2026-01-04 23:13:44 -08:00
parent 32cc3e42bc
commit 7507cd85c4
5 changed files with 10222 additions and 1 deletions
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+description = """
+AGENT EXECUTION PROTOCOL - Towers of Hanoi
+
+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 = 2
+
+[vars]
+[vars.source_peg]
+default = "A"
+description = "Starting peg"
+[vars.target_peg]
+default = "C"
+description = "Target peg"
+[vars.auxiliary_peg]
+default = "B"
+description = "Helper peg"
+
+# 3-disk solution: 7 moves (2^3 - 1)
+# Each step is a simple acknowledgment - the agent just closes it.
+
+[[steps]]
+id = "setup"
+title = "Verify initial state"
+description = "All 3 disks stacked on peg A. Largest on bottom."
+
+[[steps]]
+id = "move-1"
+title = "Move disk 1: A → C"
+description = "Move the smallest disk from peg A to peg C."
+needs = ["setup"]
+
+[[steps]]
+id = "move-2"
+title = "Move disk 2: A → B"
+description = "Move disk 2 from peg A to peg B."
+needs = ["move-1"]
+
+[[steps]]
+id = "move-3"
+title = "Move disk 1: C → B"
+description = "Move disk 1 from peg C to peg B."
+needs = ["move-2"]
+
+[[steps]]
+id = "move-4"
+title = "Move disk 3: A → C"
+description = "Move the largest disk from peg A to peg C."
+needs = ["move-3"]
+
+[[steps]]
+id = "move-5"
+title = "Move disk 1: B → A"
+description = "Move disk 1 from peg B to peg A."
+needs = ["move-4"]
+
+[[steps]]
+id = "move-6"
+title = "Move disk 2: B → C"
+description = "Move disk 2 from peg B to peg C."
+needs = ["move-5"]
+
+[[steps]]
+id = "move-7"
+title = "Move disk 1: A → C"
+description = "Move disk 1 from peg A to peg C."
+needs = ["move-6"]
+
+[[steps]]
+id = "verify"
+title = "Verify final state"
+description = "All 3 disks now on peg C. Tower intact, all moves were legal."
+needs = ["move-7"]