Alethic solve

/alethic-solve — Alethic Mathematical Reasoning Agent

The user's input is: $ARGUMENTS

Domain Configuration

Key	Value
domain	math
command	solve
noun	solution
verb	solve
agent_title	Mathematical Reasoning
session_skill	alethic-solve
strategy_reset_addendum	(from "Strategy Reset Addendum" section below)
disproof_addendum	(from "Disproof Escalation Addendum" section below)
adversarial_verifier	true for thorough/extreme presets; false otherwise — enables 5-round adversarial self-correction in all verifier Task calls
adversarial_breaker	true for thorough/extreme presets; false otherwise — enables adversarial breaker probe on CORRECT verdicts

Balanced Approach Addendum

Append this to the Generator's user message (unless --no-balanced is set):

7. Explore counterexamples first (balanced approach). Before committing to a proof strategy, spend at least a few sentences considering whether the statement might be FALSE. Try small cases (n = 0, 1, 2, 3), constant/linear functions, boundary conditions, and degenerate cases (empty sets, zero vectors, identity matrices). If you find a counterexample, present it as your solution. If you cannot find one, explain why and then proceed with the proof.

Strategy Reset Addendum

Injected into the Generator prompt (replacing the standard failed_approaches block) when a stall reset is triggered. The {failed_approaches} placeholder is filled by the orchestrator.

STRATEGY RESET — Previous approaches exhausted

The methods listed below have been attempted and FAILED. You are FORBIDDEN from using them.

{failed_approaches}

For each method above: DO NOT use it. DO NOT adapt it. DO NOT build on it. If your plan uses any of these methods, you MUST change your plan. Reflect on your approach — if it resembles any of the above, choose a different one.

You MUST use a categorically different proof technique. Start from a completely different mathematical foundation. Consider approaches from a different branch of mathematics entirely.

Disproof Escalation Addendum

Appended to the reset context by the orchestrator when accumulated evidence suggests the claim may be false (error category false_premise/interpretation/counterexample, or two consecutive UNSOLVED verdicts).

DISPROOF ESCALATION — Consider that the claim may be false

Previous iterations have repeatedly failed to prove this statement. Based on accumulated evidence, there is a meaningful probability that the claim is FALSE.

In addition to exploring categorically different proof techniques, you MUST also:

1. Systematically search for counterexamples: Test small cases exhaustively (n=0,1,2,3,...). For claims about real numbers, test rationals, irrationals (sqrt(2), pi, e), negative numbers, zero, and boundary cases. Use Python/SymPy to automate the search.

2. Identify necessary conditions: What would NEED to be true for the claim to hold? Can you show one of those necessary conditions fails?

3. Check known results: Does this claim conflict with known theorems? Would it imply something known to be false?

If you find evidence the claim is false, present a clear disproof:

• State the counterexample or contradiction explicitly
• Verify it computationally using Python code
• Explain why it violates the original claim

Examples

• /alethic-solve "Prove sqrt(2) is irrational" — defaults (5 iter, 3 rev, 50 budget)
• /alethic-solve -p quick "Is 17 prime?" — quick preset (2 iter, 1 rev, threshold 0.85)
• /alethic-solve -p thorough "Prove the Cayley-Hamilton theorem" — thorough preset
• /alethic-solve -p quick -i 4 "Solve x^2=2" — quick preset with iteration override
• /alethic-solve -i 8 -r 5 "Prove the Cayley-Hamilton theorem" — extended
• /alethic-solve -t 0.95 "Prove Fermat's little theorem" — stricter threshold
• /alethic-solve -B 3 "Prove the Cayley-Hamilton theorem" — 3 candidates per iteration
• /alethic-solve --textbook "Prove sqrt(2) is irrational" — textbook-style output
• /alethic-solve -p thorough --textbook "Prove the Cayley-Hamilton theorem" — thorough + textbook
• /alethic-solve --no-balanced "Prove sqrt(2) is irrational" — skip counterexample check
• /alethic-solve --resume .alethic/session-id/ "original problem" — resume from checkpoint
• /alethic-solve --file problem.md — read problem from file
• /alethic-solve -q -p thorough "Prove the Cayley-Hamilton theorem" — quiet mode (no dashboard)
• /alethic-solve --json "Is 17 prime?" — JSON output
• /alethic-solve --model sonnet "Prove Fermat's little theorem" — use Sonnet for sub-agents

Load Orchestrator

1. Find the orchestrator:

   ORCH=$(find ~/.claude/plugins -name "orchestrator.md" -path "*/alethic-common/*" 2>/dev/null | head -1)
   echo "ORCHESTRATOR: $ORCH"
   

   If not found, check the local development path:

   ORCH=$(find /home -maxdepth 6 -name "orchestrator.md" -path "*/alethic-common/*" 2>/dev/null | head -1)
   echo "ORCHESTRATOR: $ORCH"
   

2. Derive the references directory:

   REF_DIR=$(echo "$ORCH" | sed "s|alethic-common/orchestrator.md|alethic-solve/references|")
   echo "REFERENCES: $REF_DIR"
   

3. Read the orchestrator file at the path found above.

4. Follow the orchestrator instructions exactly, using this skill's Domain Configuration, Balanced Approach Addendum, and references directory.