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Math Olympiad Solver · anthropics | DecimalAI

Scienceby anthropics

Math Olympiad Solver

Solve competition math problems (IMO, Putnam, USAMO, AIME) with adversarial verification that catches the errors self-verification misses. Activates when asked to 'solve this IMO problem', 'prove this olympiad inequality', 'verify this competition proof', 'find a counterexample', 'is this proof correct', or for any problem with 'IMO', 'Putnam', 'USAMO', 'olympiad', or 'competition math' in it. Uses pure reasoning (no tools) — then a fresh-context adversarial verifier attacks the proof using spec

SkillScore

SkillScore77/100

Test results 77

Safety

3/3 safety checks passed

Code scan
Intent
Content

What it changes

41%77%of test cases passed +36 pts

Without skill9 of 22

With skill17 of 22

9 fixed8 passed either way4 still failing1 broke

Measured on gemini-3.6-flash8/7/2026v1

Track record

Agent runs: 0; All time

See one task, with and without the skill

One test taskWe are executing the math solver workflow using Sonnet model tier defaults. What are the specific parameters for solver count, verifier pass count, and revise fail limit?

Without the skillMissed

With the skillPassed

Same model, same task. Answers are capped and redacted.

Use this skill

Your agent runs on

Adds every file the skill has, pinned so you can update it. No account needed.

pip install "decimalai>=0.15"
decimalai skills add anthropics-math-olympiad
claude --plugin-dir "$(git rev-parse --show-toplevel 2>/dev/null || pwd)/.agents"

The same install from Python, for a notebook or a setup script.

Install

pip install "decimalai>=0.15"

Add the skill

from decimalai import skillpkg

# Writes .agents/skills and .decimal/skills.toml. Safe to run twice.
result = skillpkg.add("anthropics-math-olympiad")
if result.exit_code:
    raise SystemExit(result.problems)

print("Added. Start Claude Code with the command below.")

Start Claude Code with it

claude --plugin-dir "$(git rev-parse --show-toplevel 2>/dev/null || pwd)/.agents"

Type these in a Claude Code session. No account or API key. It writes the skill and any files it bundles, and asks first when its safety rating isn't Passed.

Add the DecimalAI plugin, once

/plugin marketplace add decimal-labs/decimalai-claude-plugins
/plugin install decimalai@decimalai

Install this skill

/decimalai:install anthropics-math-olympiad

The plugin needs python3 and curl on your machine.

No Python or account. Claude Code picks it up in its next session.

Save it into your project

curl -fsSL --create-dirs -o .claude/skills/anthropics-math-olympiad/SKILL.md https://app.decimal.ai/s/anthropics-math-olympiad/SKILL.md

Copy SKILL.md

Save it in your project, as

.claude/skills/anthropics-math-olympiad/SKILL.md

This gets SKILL.md only. The skill's 9 other files are not included.

Other ways to add it

Claude Code docs

agent_config() hands your agent the skill. With no DecimalAI key it reads your project's files and sends nothing. Needs SDK 0.27 or newer.

Install

pip install "decimalai[claude-agent-sdk]"
decimalai skills add anthropics-math-olympiad

Add it to your agent

import asyncio

from claude_agent_sdk import ClaudeAgentOptions
from decimalai.claude_agent_sdk import agent_config

# With no DECIMAL_API_KEY this reads the skills your project lists, from disk.
support = agent_config("support", fallback="You are a helpful agent.")

async def main():
    question = "Hello!"
    async with support.run(question) as run:  # one user message, one run
        async for message in run.query(options=ClaudeAgentOptions(max_turns=6)):
            print(message)

# In a notebook or async code: await main()
asyncio.run(main())

Prefer its own loader? ClaudeAgentOptions(plugins=[skills_plugin()], skills="all") reads the same folder. Use one or the other: a skill delivered both ways reaches the prompt twice.

The same install from Python, for a notebook or a setup script. agent_config() hands your agent the skill. With no DecimalAI key it reads your project's files and sends nothing. Needs SDK 0.27 or newer.

Install

pip install "decimalai[claude-agent-sdk]"

Add it to your agent

from decimalai import skillpkg

# Writes .agents/skills and .decimal/skills.toml. Safe to run twice.
result = skillpkg.add("anthropics-math-olympiad")
if result.exit_code:
    raise SystemExit(result.problems)

import asyncio

from claude_agent_sdk import ClaudeAgentOptions
from decimalai.claude_agent_sdk import agent_config

# With no DECIMAL_API_KEY this reads the skills your project lists, from disk.
support = agent_config("support", fallback="You are a helpful agent.")

async def main():
    question = "Hello!"
    async with support.run(question) as run:  # one user message, one run
        async for message in run.query(options=ClaudeAgentOptions(max_turns=6)):
            print(message)

# In a notebook or async code: await main()
asyncio.run(main())

Prefer its own loader? ClaudeAgentOptions(plugins=[skills_plugin()], skills="all") reads the same folder. Use one or the other: a skill delivered both ways reaches the prompt twice.

No DecimalAI package. The whole skill goes in every prompt, and nothing pins or updates it.

Copy SKILL.md

Save it in your project, as

.agents/skills/anthropics-math-olympiad/SKILL.md

Give it to your agent

import asyncio
from pathlib import Path
from claude_agent_sdk import ClaudeAgentOptions, query

skill = Path(".agents/skills/anthropics-math-olympiad/SKILL.md").read_text()
options = ClaudeAgentOptions(system_prompt=f"You are a helpful agent.\n\n{skill}", max_turns=6)

async def main():
    async for message in query(prompt="Hello!", options=options):
        print(message)

# In a notebook or async code: await main()
asyncio.run(main())

This gets SKILL.md only. The skill's 9 other files are not included.

Other ways to add it

Claude Agent SDK docs

agent_config() hands your agent the skill. With no DecimalAI key it reads your project's files and sends nothing. Needs SDK 0.27 or newer.

Install

pip install "decimalai[openai-agents]"
decimalai skills add anthropics-math-olympiad

Add it to your agent

from agents import Agent, Runner
from decimalai.openai_agents import agent_config

# With no DECIMAL_API_KEY this reads the skills your project lists, from disk.
support = agent_config("support", fallback="You are a helpful agent.")

agent = Agent(
    name=support.name,
    instructions=support.instructions,  # your prompt, then the skill list
    tools=[*support.tools],             # your tools, then load_skill
)
# In a notebook or async code: result = await Runner.run(agent, "Hello!")
result = Runner.run_sync(agent, "Hello!")

Using SandboxAgent? capabilities=[Shell(), decimalai.openai_agents.sandbox_skills()] points its own loader at the same folder.

Install

pip install "decimalai[openai-agents]"

Add it to your agent

from decimalai import skillpkg

# Writes .agents/skills and .decimal/skills.toml. Safe to run twice.
result = skillpkg.add("anthropics-math-olympiad")
if result.exit_code:
    raise SystemExit(result.problems)

from agents import Agent, Runner
from decimalai.openai_agents import agent_config

# With no DECIMAL_API_KEY this reads the skills your project lists, from disk.
support = agent_config("support", fallback="You are a helpful agent.")

agent = Agent(
    name=support.name,
    instructions=support.instructions,  # your prompt, then the skill list
    tools=[*support.tools],             # your tools, then load_skill
)
# In a notebook or async code: result = await Runner.run(agent, "Hello!")
result = Runner.run_sync(agent, "Hello!")

Using SandboxAgent? capabilities=[Shell(), decimalai.openai_agents.sandbox_skills()] points its own loader at the same folder.

No DecimalAI package. The whole skill goes in every prompt, and nothing pins or updates it.

Copy SKILL.md

Save it in your project, as

.agents/skills/anthropics-math-olympiad/SKILL.md

Give it to your agent

from pathlib import Path
from agents import Agent, Runner

skill = Path(".agents/skills/anthropics-math-olympiad/SKILL.md").read_text()
agent = Agent(name="support", instructions=f"You are a helpful agent.\n\n{skill}")
# In a notebook or async code: result = await Runner.run(agent, "Hello!")
result = Runner.run_sync(agent, "Hello!")

This gets SKILL.md only. The skill's 9 other files are not included.

Other ways to add it

OpenAI Agents docs

agent_config() hands your agent the skill. With no DecimalAI key it reads your project's files and sends nothing. Needs SDK 0.27 or newer.

Install

pip install "decimalai[openai]"
decimalai skills add anthropics-math-olympiad

Add it to your agent

import json

from openai import OpenAI
from decimalai.openai import agent_config

client = OpenAI()
# With no DECIMAL_API_KEY this reads the skills your project lists, from disk.
support = agent_config("support", fallback="You are a helpful agent.")


def lookup_order(order_id: str) -> str:
    return f"Order {order_id} shipped yesterday."


# Your tools, as Chat Completions takes them, and what answers each.
TOOLS = [{"type": "function", "function": {
    "name": "lookup_order",
    "description": "Look up the status of an order.",
    "parameters": {"type": "object", "properties": {"order_id": {"type": "string"}},
                   "required": ["order_id"]},
}}]
FUNCTIONS = {"lookup_order": lookup_order}

question = "Where is order A1001?"
with support.run(question) as run:  # one user message, one run
    # run.system is your prompt, then the skill list.
    messages = [{"role": "system", "content": run.system}, run.message]
    while True:
        reply = client.chat.completions.create(
            model="gpt-5.4-mini",
            messages=messages,
            tools=[*TOOLS, *run.tools],  # your tools, then load_skill
        ).choices[0].message
        messages.append(reply)
        if not reply.tool_calls:
            break
        for call in reply.tool_calls:
            # load_skill is answered by the run; your own tools by FUNCTIONS.
            function = FUNCTIONS.get(call.function.name)
            messages.append(run.tool_result(call) or {
                "role": "tool", "tool_call_id": call.id,
                "content": function(**json.loads(call.function.arguments)) if function
                else f"There is no tool named {call.function.name!r}.",
            })
print(reply.content)

# The Responses API takes run.response_tools instead of run.tools.

Install

pip install "decimalai[openai]"

Add it to your agent

from decimalai import skillpkg

# Writes .agents/skills and .decimal/skills.toml. Safe to run twice.
result = skillpkg.add("anthropics-math-olympiad")
if result.exit_code:
    raise SystemExit(result.problems)

import json

from openai import OpenAI
from decimalai.openai import agent_config

client = OpenAI()
# With no DECIMAL_API_KEY this reads the skills your project lists, from disk.
support = agent_config("support", fallback="You are a helpful agent.")


def lookup_order(order_id: str) -> str:
    return f"Order {order_id} shipped yesterday."


# Your tools, as Chat Completions takes them, and what answers each.
TOOLS = [{"type": "function", "function": {
    "name": "lookup_order",
    "description": "Look up the status of an order.",
    "parameters": {"type": "object", "properties": {"order_id": {"type": "string"}},
                   "required": ["order_id"]},
}}]
FUNCTIONS = {"lookup_order": lookup_order}

question = "Where is order A1001?"
with support.run(question) as run:  # one user message, one run
    # run.system is your prompt, then the skill list.
    messages = [{"role": "system", "content": run.system}, run.message]
    while True:
        reply = client.chat.completions.create(
            model="gpt-5.4-mini",
            messages=messages,
            tools=[*TOOLS, *run.tools],  # your tools, then load_skill
        ).choices[0].message
        messages.append(reply)
        if not reply.tool_calls:
            break
        for call in reply.tool_calls:
            # load_skill is answered by the run; your own tools by FUNCTIONS.
            function = FUNCTIONS.get(call.function.name)
            messages.append(run.tool_result(call) or {
                "role": "tool", "tool_call_id": call.id,
                "content": function(**json.loads(call.function.arguments)) if function
                else f"There is no tool named {call.function.name!r}.",
            })
print(reply.content)

# The Responses API takes run.response_tools instead of run.tools.

No DecimalAI package. The whole skill goes in every prompt, and nothing pins or updates it.

Copy SKILL.md

Save it in your project, as

.agents/skills/anthropics-math-olympiad/SKILL.md

Give it to your agent

from pathlib import Path
from openai import OpenAI

client = OpenAI()
skill = Path(".agents/skills/anthropics-math-olympiad/SKILL.md").read_text()
reply = client.chat.completions.create(
    model="gpt-5.4-mini",
    messages=[
        {"role": "system", "content": f"You are a helpful agent.\n\n{skill}"},
        {"role": "user", "content": "Hello!"},
    ],
).choices[0].message

This gets SKILL.md only. The skill's 9 other files are not included.

Other ways to add it

OpenAI SDK docs

agent_config() hands your agent the skill. With no DecimalAI key it reads your project's files and sends nothing. Needs SDK 0.27 or newer.

Install

pip install "decimalai[anthropic]"
decimalai skills add anthropics-math-olympiad

Add it to your agent

import anthropic
from decimalai.anthropic import agent_config

client = anthropic.Anthropic()
# With no DECIMAL_API_KEY this reads the skills your project lists, from disk.
support = agent_config("support", fallback="You are a helpful agent.")

question = "Hello!"
with support.run(question) as run:  # one user message, one run
    answer = client.beta.messages.tool_runner(
        model="claude-haiku-5-5",
        max_tokens=4096,
        system=run.system,     # your prompt, then the skill list
        tools=[*run.tools],    # your tools, then load_skill
        messages=[{"role": "user", "content": question}],
    ).until_done()

Install

pip install "decimalai[anthropic]"

Add it to your agent

from decimalai import skillpkg

# Writes .agents/skills and .decimal/skills.toml. Safe to run twice.
result = skillpkg.add("anthropics-math-olympiad")
if result.exit_code:
    raise SystemExit(result.problems)

import anthropic
from decimalai.anthropic import agent_config

client = anthropic.Anthropic()
# With no DECIMAL_API_KEY this reads the skills your project lists, from disk.
support = agent_config("support", fallback="You are a helpful agent.")

question = "Hello!"
with support.run(question) as run:  # one user message, one run
    answer = client.beta.messages.tool_runner(
        model="claude-haiku-5-5",
        max_tokens=4096,
        system=run.system,     # your prompt, then the skill list
        tools=[*run.tools],    # your tools, then load_skill
        messages=[{"role": "user", "content": question}],
    ).until_done()

No DecimalAI package. The whole skill goes in every prompt, and nothing pins or updates it.

Copy SKILL.md

Save it in your project, as

.agents/skills/anthropics-math-olympiad/SKILL.md

Give it to your agent

from pathlib import Path
import anthropic

client = anthropic.Anthropic()
skill = Path(".agents/skills/anthropics-math-olympiad/SKILL.md").read_text()
reply = client.messages.create(
    model="claude-haiku-5-5",
    max_tokens=4096,
    system=f"You are a helpful agent.\n\n{skill}",
    messages=[{"role": "user", "content": "Hello!"}],
)

This gets SKILL.md only. The skill's 9 other files are not included.

Other ways to add it

Anthropic docs

agent_config() hands your agent the skill. With no DecimalAI key it reads your project's files and sends nothing. Needs SDK 0.27 or newer.

Install

pip install "decimalai[google-genai]"
decimalai skills add anthropics-math-olympiad

Add it to your agent

from google import genai
from google.genai import types
from decimalai.google_genai import agent_config

client = genai.Client()
# With no DECIMAL_API_KEY this reads the skills your project lists, from disk.
support = agent_config("support", fallback="You are a helpful agent.")


def lookup_order(order_id: str) -> str:
    return f"Order {order_id} shipped yesterday."


# Your functions, as declarations for the model, and what answers each.
TOOLS = [{"function_declarations": [{
    "name": "lookup_order",
    "description": "Look up the status of an order.",
    "parameters_json_schema": {"type": "object", "properties": {"order_id": {"type": "string"}},
                               "required": ["order_id"]},
}]}]
FUNCTIONS = {"lookup_order": lookup_order}

question = "Where is order A1001?"
with support.run(question) as run:  # one user message, one run
    config = types.GenerateContentConfig(
        system_instruction=run.system,     # your prompt, then the skill list
        tools=[*TOOLS, *run.tool_params],  # your functions, then load_skill
    )
    contents = [{"role": "user", "parts": [{"text": run.message}]}]
    while True:
        response = client.models.generate_content(
            model="gemini-3.5-flash", contents=contents, config=config,
        )
        if not response.function_calls:
            break
        contents.append(response.candidates[0].content)
        parts = []
        for call in response.function_calls:
            # load_skill is answered by the run; your own functions by FUNCTIONS.
            # A loop of your own rather than automatic function calling, which
            # raises KeyError when the model asks for a function you did not pass.
            function = FUNCTIONS.get(call.name)
            parts.append(run.tool_result(call) or {"function_response": {
                "name": call.name, "id": call.id,
                "response": {"result": function(**(call.args or {})) if function
                             else f"There is no function named {call.name!r}."},
            }})
        contents.append({"role": "user", "parts": parts})
print(response.text)

Install

pip install "decimalai[google-genai]"

Add it to your agent

from decimalai import skillpkg

# Writes .agents/skills and .decimal/skills.toml. Safe to run twice.
result = skillpkg.add("anthropics-math-olympiad")
if result.exit_code:
    raise SystemExit(result.problems)

from google import genai
from google.genai import types
from decimalai.google_genai import agent_config

client = genai.Client()
# With no DECIMAL_API_KEY this reads the skills your project lists, from disk.
support = agent_config("support", fallback="You are a helpful agent.")


def lookup_order(order_id: str) -> str:
    return f"Order {order_id} shipped yesterday."


# Your functions, as declarations for the model, and what answers each.
TOOLS = [{"function_declarations": [{
    "name": "lookup_order",
    "description": "Look up the status of an order.",
    "parameters_json_schema": {"type": "object", "properties": {"order_id": {"type": "string"}},
                               "required": ["order_id"]},
}]}]
FUNCTIONS = {"lookup_order": lookup_order}

question = "Where is order A1001?"
with support.run(question) as run:  # one user message, one run
    config = types.GenerateContentConfig(
        system_instruction=run.system,     # your prompt, then the skill list
        tools=[*TOOLS, *run.tool_params],  # your functions, then load_skill
    )
    contents = [{"role": "user", "parts": [{"text": run.message}]}]
    while True:
        response = client.models.generate_content(
            model="gemini-3.5-flash", contents=contents, config=config,
        )
        if not response.function_calls:
            break
        contents.append(response.candidates[0].content)
        parts = []
        for call in response.function_calls:
            # load_skill is answered by the run; your own functions by FUNCTIONS.
            # A loop of your own rather than automatic function calling, which
            # raises KeyError when the model asks for a function you did not pass.
            function = FUNCTIONS.get(call.name)
            parts.append(run.tool_result(call) or {"function_response": {
                "name": call.name, "id": call.id,
                "response": {"result": function(**(call.args or {})) if function
                             else f"There is no function named {call.name!r}."},
            }})
        contents.append({"role": "user", "parts": parts})
print(response.text)

No DecimalAI package. The whole skill goes in every prompt, and nothing pins or updates it.

Copy SKILL.md

Save it in your project, as

.agents/skills/anthropics-math-olympiad/SKILL.md

Give it to your agent

from pathlib import Path
from google import genai
from google.genai import types

client = genai.Client()
skill = Path(".agents/skills/anthropics-math-olympiad/SKILL.md").read_text()
response = client.models.generate_content(
    model="gemini-3.5-flash",
    contents="Hello!",
    config=types.GenerateContentConfig(system_instruction=f"You are a helpful agent.\n\n{skill}"),
)

This gets SKILL.md only. The skill's 9 other files are not included.

Other ways to add it

Gemini API docs

agent_config() hands your agent the skill. With no DecimalAI key it reads your project's files and sends nothing. Needs SDK 0.27 or newer.

Install

pip install "decimalai[langchain]" langchain-openai
decimalai skills add anthropics-math-olympiad

Add it to your agent

from langchain.agents import create_agent
from decimalai.langchain import agent_config

# With no DECIMAL_API_KEY this reads the skills your project lists, from disk.
support = agent_config("support", fallback="You are a helpful agent.")

agent = create_agent(
    "openai:gpt-5.4-mini",
    tools=[],                         # your tools; the middleware adds load_skill
    middleware=[support.middleware],  # your prompt, the skill list and load_skill
)
result = agent.invoke({"messages": [{"role": "user", "content": "Hello!"}]})

Install

pip install "decimalai[langchain]" langchain-openai

Add it to your agent

from decimalai import skillpkg

# Writes .agents/skills and .decimal/skills.toml. Safe to run twice.
result = skillpkg.add("anthropics-math-olympiad")
if result.exit_code:
    raise SystemExit(result.problems)

from langchain.agents import create_agent
from decimalai.langchain import agent_config

# With no DECIMAL_API_KEY this reads the skills your project lists, from disk.
support = agent_config("support", fallback="You are a helpful agent.")

agent = create_agent(
    "openai:gpt-5.4-mini",
    tools=[],                         # your tools; the middleware adds load_skill
    middleware=[support.middleware],  # your prompt, the skill list and load_skill
)
result = agent.invoke({"messages": [{"role": "user", "content": "Hello!"}]})

No DecimalAI package. The whole skill goes in every prompt, and nothing pins or updates it.

Copy SKILL.md

Save it in your project, as

.agents/skills/anthropics-math-olympiad/SKILL.md

Give it to your agent

from pathlib import Path
from langchain.agents import create_agent

skill = Path(".agents/skills/anthropics-math-olympiad/SKILL.md").read_text()
agent = create_agent("openai:gpt-5.4-mini", tools=[], system_prompt=f"You are a helpful agent.\n\n{skill}")
result = agent.invoke({"messages": [{"role": "user", "content": "Hello!"}]})

This gets SKILL.md only. The skill's 9 other files are not included.

Other ways to add it

LangChain docs

CrewAI's own skill loader reads the installed folder. No DecimalAI account needed.

Install

pip install "decimalai>=0.16" "crewai>=1.15.27"
decimalai skills add anthropics-math-olympiad

Add it to your agent

import decimalai.crewai
from crewai import Agent, Crew, Task

agent = Agent(
    role="Support", goal="Help the customer", backstory="A support agent.",
    llm=llm,                               # your own CrewAI LLM
    skills=decimalai.crewai.skills(),      # the installed folder
    tools=decimalai.crewai.skill_tools(),  # reads a skill's files, runs its scripts
)
task = Task(description="Hello!", expected_output="an answer", agent=agent)
Crew(agents=[agent], tasks=[task]).kickoff()

The same install from Python, for a notebook or a setup script. CrewAI's own skill loader reads the installed folder. No DecimalAI account needed.

Install

pip install "decimalai>=0.16" "crewai>=1.15.27"

Add it to your agent

from decimalai import skillpkg

# Writes .agents/skills and .decimal/skills.toml. Safe to run twice.
result = skillpkg.add("anthropics-math-olympiad")
if result.exit_code:
    raise SystemExit(result.problems)

import decimalai.crewai
from crewai import Agent, Crew, Task

agent = Agent(
    role="Support", goal="Help the customer", backstory="A support agent.",
    llm=llm,                               # your own CrewAI LLM
    skills=decimalai.crewai.skills(),      # the installed folder
    tools=decimalai.crewai.skill_tools(),  # reads a skill's files, runs its scripts
)
task = Task(description="Hello!", expected_output="an answer", agent=agent)
Crew(agents=[agent], tasks=[task]).kickoff()

No DecimalAI package. CrewAI's own loader reads the folder, and nothing pins or updates it.

Copy SKILL.md

Save it in your project, as

.agents/skills/anthropics-math-olympiad/SKILL.md

Give it to your agent

from pathlib import Path
from crewai import Agent, Crew, Task

agent = Agent(
    role="Support", goal="Help the customer", backstory="A support agent.",
    llm=llm,                         # your own CrewAI LLM
    skills=[Path(".agents/skills")],
)
task = Task(description="Hello!", expected_output="an answer", agent=agent)
Crew(agents=[agent], tasks=[task]).kickoff()

This gets SKILL.md only. The skill's 9 other files are not included.

Other ways to add it

CrewAI docs

agent_config() hands your agent the skill. With no DecimalAI key it reads your project's files and sends nothing. Needs SDK 0.27 or newer.

Install

pip install "decimalai[adk]"
decimalai skills add anthropics-math-olympiad

Add it to your agent

from decimalai.adk import DecimalAIPlugin, agent_config
from google.adk.agents import LlmAgent
from google.adk.apps import App

# With no DECIMAL_API_KEY this reads the skills your project lists, from disk.
support = agent_config("support", fallback="You are a helpful agent.")

agent = LlmAgent(
    name="support",          # ADK needs a Python identifier
    model="gemini-3.5-flash",
    instruction=support.instruction,  # your prompt, then the skill list
    tools=[*support.tools],           # your tools, then load_skill
)
# DecimalAIPlugin makes each invocation of runners built from this App one trace.
app = App(name="support", root_agent=agent, plugins=[DecimalAIPlugin()])

Prefer ADK's own loader? SkillToolset(skills=decimalai.adk.skills(), ...) reads the same folder. Use one or the other: a skill delivered both ways reaches the prompt twice.

Install

pip install "decimalai[adk]"

Add it to your agent

from decimalai import skillpkg

# Writes .agents/skills and .decimal/skills.toml. Safe to run twice.
result = skillpkg.add("anthropics-math-olympiad")
if result.exit_code:
    raise SystemExit(result.problems)

from decimalai.adk import DecimalAIPlugin, agent_config
from google.adk.agents import LlmAgent
from google.adk.apps import App

# With no DECIMAL_API_KEY this reads the skills your project lists, from disk.
support = agent_config("support", fallback="You are a helpful agent.")

agent = LlmAgent(
    name="support",          # ADK needs a Python identifier
    model="gemini-3.5-flash",
    instruction=support.instruction,  # your prompt, then the skill list
    tools=[*support.tools],           # your tools, then load_skill
)
# DecimalAIPlugin makes each invocation of runners built from this App one trace.
app = App(name="support", root_agent=agent, plugins=[DecimalAIPlugin()])

Prefer ADK's own loader? SkillToolset(skills=decimalai.adk.skills(), ...) reads the same folder. Use one or the other: a skill delivered both ways reaches the prompt twice.

No DecimalAI package. The whole skill goes in every prompt, and nothing pins or updates it.

Copy SKILL.md

Save it in your project, as

.agents/skills/anthropics-math-olympiad/SKILL.md

Give it to your agent

from pathlib import Path
from google.adk.agents import LlmAgent

skill = Path(".agents/skills/anthropics-math-olympiad/SKILL.md").read_text()
agent = LlmAgent(
    name="support",
    model="gemini-3.5-flash",
    instruction=lambda context: f"You are a helpful agent.\n\n{skill}",
)

This gets SKILL.md only. The skill's 9 other files are not included.

Other ways to add it

Google ADK docs

agent_config() hands your agent the skill. With no DecimalAI key it reads your project's files and sends nothing. Needs SDK 0.27 or newer.

Install

pip install "decimalai[pydantic-ai]"
decimalai skills add anthropics-math-olympiad

Add it to your agent

from pydantic_ai import Agent
from decimalai.pydantic_ai import agent_config

# With no DECIMAL_API_KEY this reads the skills your project lists, from disk.
support = agent_config("support", fallback="You are a helpful agent.")

agent = Agent(
    "openai:gpt-4o-mini",
    name=support.name,
    tools=[],                 # your tools; the capability adds load_skill
    capabilities=[support],   # your prompt, the skill list and load_skill
)
# In a notebook or async code: result = await agent.run("Hello!")
result = agent.run_sync("Hello!")

On the Pydantic AI harness, decimalai.pydantic_ai_harness.skills(project) uses its own loader instead.

Install

pip install "decimalai[pydantic-ai]"

Add it to your agent

from decimalai import skillpkg

# Writes .agents/skills and .decimal/skills.toml. Safe to run twice.
result = skillpkg.add("anthropics-math-olympiad")
if result.exit_code:
    raise SystemExit(result.problems)

from pydantic_ai import Agent
from decimalai.pydantic_ai import agent_config

# With no DECIMAL_API_KEY this reads the skills your project lists, from disk.
support = agent_config("support", fallback="You are a helpful agent.")

agent = Agent(
    "openai:gpt-4o-mini",
    name=support.name,
    tools=[],                 # your tools; the capability adds load_skill
    capabilities=[support],   # your prompt, the skill list and load_skill
)
# In a notebook or async code: result = await agent.run("Hello!")
result = agent.run_sync("Hello!")

On the Pydantic AI harness, decimalai.pydantic_ai_harness.skills(project) uses its own loader instead.

No DecimalAI package. The whole skill goes in every prompt, and nothing pins or updates it.

Copy SKILL.md

Save it in your project, as

.agents/skills/anthropics-math-olympiad/SKILL.md

Give it to your agent

from pathlib import Path
from pydantic_ai import Agent

skill = Path(".agents/skills/anthropics-math-olympiad/SKILL.md").read_text()
agent = Agent("openai:gpt-4o-mini", instructions=f"You are a helpful agent.\n\n{skill}")
# In a notebook or async code: result = await agent.run("Hello!")
result = agent.run_sync("Hello!")

This gets SKILL.md only. The skill's 9 other files are not included.

Other ways to add it

Pydantic AI docs

Deep Agents' own skill loader reads the installed folder. No DecimalAI account needed.

Install

pip install "decimalai>=0.16" deepagents
decimalai skills add anthropics-math-olympiad

Add it to your agent

import decimalai.deepagents
from deepagents import create_deep_agent

agent = create_deep_agent(model=model, **decimalai.deepagents.skills())
agent.invoke({"messages": [{"role": "user", "content": "Hello!"}]})

The default backend reads files but has no shell. To run a skill's scripts, pass skills(backend=LocalShellBackend(...)).

The same install from Python, for a notebook or a setup script. Deep Agents' own skill loader reads the installed folder. No DecimalAI account needed.

Install

pip install "decimalai>=0.16" deepagents

Add it to your agent

from decimalai import skillpkg

# Writes .agents/skills and .decimal/skills.toml. Safe to run twice.
result = skillpkg.add("anthropics-math-olympiad")
if result.exit_code:
    raise SystemExit(result.problems)

import decimalai.deepagents
from deepagents import create_deep_agent

agent = create_deep_agent(model=model, **decimalai.deepagents.skills())
agent.invoke({"messages": [{"role": "user", "content": "Hello!"}]})

The default backend reads files but has no shell. To run a skill's scripts, pass skills(backend=LocalShellBackend(...)).

No DecimalAI package. The whole skill goes in every prompt, and nothing pins or updates it.

Copy SKILL.md

Save it in your project, as

.agents/skills/anthropics-math-olympiad/SKILL.md

Give it to your agent

from pathlib import Path
from deepagents import create_deep_agent

skill = Path(".agents/skills/anthropics-math-olympiad/SKILL.md").read_text()
agent = create_deep_agent(model=model, system_prompt=f"You are a helpful agent.\n\n{skill}")
agent.invoke({"messages": [{"role": "user", "content": "Hello!"}]})

This gets SKILL.md only. The skill's 9 other files are not included.

Other ways to add it

Deep Agents docs

Its own skill loader reads the installed folder. No DecimalAI account needed.

Install

pip install "decimalai>=0.16" agent-framework
decimalai skills add anthropics-math-olympiad

Add it to your agent

import asyncio

from agent_framework import Agent
from decimalai.agent_framework import skills

agent = Agent(client=client, instructions="You are a helpful agent.", context_providers=[skills()])
asyncio.run(agent.run("Hello!"))

It caches skills by default, so restart the process after decimalai skills update.

The same install from Python, for a notebook or a setup script. Its own skill loader reads the installed folder. No DecimalAI account needed.

Install

pip install "decimalai>=0.16" agent-framework

Add it to your agent

from decimalai import skillpkg

# Writes .agents/skills and .decimal/skills.toml. Safe to run twice.
result = skillpkg.add("anthropics-math-olympiad")
if result.exit_code:
    raise SystemExit(result.problems)

import asyncio

from agent_framework import Agent
from decimalai.agent_framework import skills

agent = Agent(client=client, instructions="You are a helpful agent.", context_providers=[skills()])
asyncio.run(agent.run("Hello!"))

It caches skills by default, so restart the process after decimalai skills update.

No DecimalAI package. The whole skill goes in every prompt, and nothing pins or updates it.

Copy SKILL.md

Save it in your project, as

.agents/skills/anthropics-math-olympiad/SKILL.md

Give it to your agent

import asyncio
from pathlib import Path
from agent_framework import Agent

skill = Path(".agents/skills/anthropics-math-olympiad/SKILL.md").read_text()
agent = Agent(client=client, instructions=f"You are a helpful agent.\n\n{skill}")
asyncio.run(agent.run("Hello!"))

This gets SKILL.md only. The skill's 9 other files are not included.

Other ways to add it

Microsoft Agent Framework docs

Strands' own skill loader reads the installed folder. No DecimalAI account needed.

Install

pip install "decimalai>=0.16" strands-agents
decimalai skills add anthropics-math-olympiad

Add it to your agent

from decimalai.strands import skills
from strands import Agent
from strands.vended_tools import file_editor, shell

agent = Agent(
    model=model,                # always pass one: the default is Amazon Bedrock
    system_prompt="You are a helpful agent.",
    tools=[file_editor, shell],
    plugins=[skills()],
)
agent("Hello!")

Strands loads an agent's skills once, so build the agent again after decimalai skills update.

The same install from Python, for a notebook or a setup script. Strands' own skill loader reads the installed folder. No DecimalAI account needed.

Install

pip install "decimalai>=0.16" strands-agents

Add it to your agent

from decimalai import skillpkg

# Writes .agents/skills and .decimal/skills.toml. Safe to run twice.
result = skillpkg.add("anthropics-math-olympiad")
if result.exit_code:
    raise SystemExit(result.problems)

from decimalai.strands import skills
from strands import Agent
from strands.vended_tools import file_editor, shell

agent = Agent(
    model=model,                # always pass one: the default is Amazon Bedrock
    system_prompt="You are a helpful agent.",
    tools=[file_editor, shell],
    plugins=[skills()],
)
agent("Hello!")

Strands loads an agent's skills once, so build the agent again after decimalai skills update.

No DecimalAI package. The whole skill goes in every prompt, and nothing pins or updates it.

Copy SKILL.md

Save it in your project, as

.agents/skills/anthropics-math-olympiad/SKILL.md

Give it to your agent

from pathlib import Path
from strands import Agent

skill = Path(".agents/skills/anthropics-math-olympiad/SKILL.md").read_text()
agent = Agent(model=model, system_prompt=f"You are a helpful agent.\n\n{skill}")
agent("Hello!")

This gets SKILL.md only. The skill's 9 other files are not included.

Other ways to add it

Strands docs

Adds every file the skill has, pinned so you can update it. Cursor, Copilot, Cline and Warp read this folder by themselves.

pip install "decimalai>=0.15"
decimalai skills add anthropics-math-olympiad

No Python or account. Cursor, Copilot, Cline and Warp read this folder by themselves.

Save it into your project

curl -fsSL --create-dirs -o .agents/skills/anthropics-math-olympiad/SKILL.md https://app.decimal.ai/s/anthropics-math-olympiad/SKILL.md

Copy SKILL.md

Save it in your project, as

.agents/skills/anthropics-math-olympiad/SKILL.md

This gets SKILL.md only. The skill's 9 other files are not included.

Other ways to add it

Cursor and other editors docs

Fetch the file and give its text to your model as instructions. No account or package needed.

Get the file

curl -fsSL https://app.decimal.ai/s/anthropics-math-olympiad/SKILL.md

Read the summary as JSON

curl -fsSL https://app.decimal.ai/s/anthropics-math-olympiad.json

This gets SKILL.md only. The skill's 9 other files are not included.

Other ways to add it

Other setups docs

You don't need a DecimalAI account.

Version: v1, tested 8/7/2026
Source: anthropics/claude-plugins-official ↗
License: Apache-2.0

Manage it in DecimalAI

Saved prompts and skills, pinned versions, and traces of this skill in your runs. DecimalAI does not run your agent.

Claude Code reads files from your project, so DecimalAI config does not apply there.

On Claude Agent SDK: save the skill to an agent here, set DECIMAL_API_KEY, and the same code uses it with no command to run. Changes you save reach the next run with no redeploy.

On OpenAI Agents: save the skill to an agent here, set DECIMAL_API_KEY, and the same code uses it with no command to run. Changes you save reach the next run with no redeploy.

On OpenAI SDK: save the skill to an agent here, set DECIMAL_API_KEY, and the same code uses it with no command to run. Changes you save reach the next run with no redeploy.

On Anthropic: save the skill to an agent here, set DECIMAL_API_KEY, and the same code uses it with no command to run. Changes you save reach the next run with no redeploy.

On Gemini API: save the skill to an agent here, set DECIMAL_API_KEY, and the same code uses it with no command to run. Changes you save reach the next run with no redeploy.

On LangChain: save the skill to an agent here, set DECIMAL_API_KEY, and the same code uses it with no command to run. Changes you save reach the next run with no redeploy.

On CrewAI: set DECIMAL_API_KEY and add decimalai.init(crewai=True) to record runs and skill use. The skill version stays in your repo.

On Google ADK: save the skill to an agent here, set DECIMAL_API_KEY, and the same code uses it with no command to run. Changes you save reach the next run with no redeploy.

On Pydantic AI: save the skill to an agent here, set DECIMAL_API_KEY, and the same code uses it with no command to run. Changes you save reach the next run with no redeploy.

On Deep Agents: set DECIMAL_API_KEY and add decimalai.init(langchain=True) to record runs and skill use. The skill version stays in your repo.

On Microsoft Agent Framework: set DECIMAL_API_KEY and add decimalai.init(otel=True, agent_name="support") to record runs and skill use. The skill version stays in your repo.

On Strands: set DECIMAL_API_KEY and add decimalai.init(otel=True, agent_name="support") to record runs and skill use. The skill version stays in your repo.

Editors read files from your project, so DecimalAI config does not apply there.

Anywhere else: record a use with decimalai.log_skill_activation() inside a trace.

Use this skill

SKILL.md

Math Olympiad Solver

The five things that change outcomes

Strip thinking before verifying — a verifier that sees the reasoning is biased toward agreement. Fresh context, cleaned proof only.
"Does this prove RH?" — if your theorem's specialization to ζ is a famous open problem, you have a gap. Most reliable red flag.
Short proof → extract the general lemma — try 2×2 counterexamples. If general form is false, find what's special about THIS instance.
Same gap twice → step back — the case split may be obscuring a unified argument. Three lines sometimes does what twelve pages couldn't.
Say "no confident solution" — wrong-and-confident is worse than honest abstain.

Tool policy: Solvers and verifiers use THINKING ONLY in the tight-budget workflow. Competition math is reasoning. Computation is for deep mode (§6c), and even then bounded — a recurrence that's doubly-exponential can't be computed past n~30, work mod 2^m instead.

When to use which approach

Problem	Approach	Verification
AIME numeric answer	Best-of-N → majority vote	Answer check only
Olympiad proof (IMO/Putnam/USAMO)	Full workflow below	5-pass adversarial
"Is this proof correct?"	Skip to verification (step 4)	Adversarial + spec-gaming
Full problem set (e.g. all 6 from a competition)	Sequential: one full workflow per problem, collect results, compile single PDF	Per-problem adversarial

Batch in one Workflow: Set opts.label on every agent() call to include the problem ID (e.g., label: "P3:solver:2"). Without labels, 36 results come back with no problem association. Run problems in parallel — the label is what matters, not ordering.

For a full problem set

Launch one solver workflow per problem (same VERBATIM prompt, different statement). Run them in parallel. When all return, run adversarial verification per problem. Problems that pass get their proof in the PDF; problems that abstain get "No confident solution" with partial notes.

Don't try to solve all N problems in one agent's context — each problem needs its own thinking budget and its own fresh-context verifier. The composition is mechanical: collect the per-problem outputs, fill in LaTeX sections, compile once. | "Simplify this proof" | Skip to presentation (step 8) | — |

The Workflow

1. Interpretation check (30 seconds, catches 50/63 of one class of errors)

Before solving anything, identify the interpretation.

Read the problem statement. List 2-3 ways it could be interpreted. For each: is this reading TRIVIAL? If one reading makes the problem easy and another makes it hard, the hard one is almost certainly intended. State which interpretation you're solving and WHY you believe it's the intended one.

The Aletheia case study found 50 of 63 "technically correct" solutions were for the wrong interpretation. Olympiad problems often have a trap easy reading.

2. Generate candidates with internal refinement (parallel, thinking only)

Launch 8-12 attempt agents in parallel. Each agent internally iterates — solve → self-improve → self-verify → correct → repeat. This is the Yang-Huang structure that achieves 85.7% on IMO: one-shot solving isn't enough; per-attempt refinement matters.

The Agent tool cannot enforce tool restriction. Subagents get the full tool set. The only mechanism is the prompt. Use this prompt VERBATIM — do not summarize, do not synthesize your own:

NO COMPUTATION. Do not use Bash, Python, WebSearch, Read, Write, or any tool that runs code or fetches data. Numerical verification is not a proof step. "I computed n=1..10 and the pattern holds" is not a proof.

(If your agent harness requires a StructuredOutput or similar return-mechanism tool call, that is NOT a computation tool — call it to return your answer. The restriction is on tools that DO work, not tools that REPORT work.)

Your internal process (iterate until done):
- Solve: Complete rigorous solution.
- Self-improve: Reread. Fix gaps before a grader sees it.
- Self-verify: Strict grader mode. Every step justified?
- Correct: Fix and re-verify. Up to 5 rounds.
- Stop: Self-verify passes twice clean, OR 5 rounds, OR approach fundamentally wrong.

A correct answer from flawed reasoning is a failure. If incomplete, say so honestly. Never hide gaps.

PROBLEM: <insert the problem statement here>
ANGLE: <insert one starting angle here>

The first two paragraphs are load-bearing. A session that writes its own prompt and omits them will produce subagents that grind Python for 30 iterations and confidently get wrong answers — a pattern that fits n≤10 but fails at n=100 is not a proof.

Starting angles (vary across agents — see references/solver_heuristics.md):

Work out small cases (test past n=3)
Look for an invariant or monovariant
Consider the extremal case
Try induction
What symmetries?
Work backwards
Drop a condition — where does it become trivially false?
Generalize (inventor's paradox — more structure is sometimes easier)

Each returns its FINAL state (not intermediate rounds):

**Verdict**: complete solution | partial result | no progress
**Rounds**: [how many verify→correct cycles]
**Method**: [key idea, one paragraph]
**Detailed Solution**: [full step-by-step, every step justified]
**Answer**: [if applicable]
**Self-verification notes**: [what you caught and fixed; remaining concerns]

Retry policy: If an agent fails or times out, retry once. Transient failures happen.

3. Clean the solution (context isolation — the #1 lever)

The thinking trace biases the verifier toward agreement — a long chain of reasoning reads as supporting evidence even when the conclusion is wrong. Before any verification, strip:

All thinking-block content
All "Let me try..." / "Actually wait..." / "Hmm" prose
All false starts and backtracking

What remains: problem statement + clean final argument only.

Extract only the Method + Proof + Answer sections from each solver's output. The verifier never sees how the solver got there.

4. Adversarial verify (fresh context, pattern-armed)

For each cleaned solution, launch a fresh verifier agent. Fresh context: it sees only (problem statement + cleaned solution). No tools.

The verifier's job is to ATTACK, not grade. Load references/adversarial_prompts.md for the prompts. The key patterns it runs:

Pattern	The check
#4	Does this theorem specialize to a famous object (ζ, quadratic reciprocity, etc.) and prove something open about it? → gap
#18	Substitute the proof's own intermediate identities into any "remaining gap." Recover the original claim? → tautological
#40	Is any step a "one-line lemma"? Extract the GENERAL form. Find a 2×2 counterexample. If the general form is false, find what special structure saves THIS instance
#5	For each invoked theorem: re-check hypotheses FROM SCRATCH. "Continuous on [0,1]" ≠ "continuous on ℝ"
#6	Any infinite sum "bounded" via a regularized value? Check the boundary — if there's a pole there, the sum diverges

Full pattern list: references/verifier_patterns.md

Verifier returns:

**Verdict**: HOLDS | HOLE FOUND | UNCLEAR

**If HOLE FOUND**:
- Location: [quote the problematic step]
- Pattern: [which check fired, or "other"]
- Why it breaks: [specific]
- Fixable?: [yes with X / no, fundamental]

5. Rank and vote-verify (asymmetric + early exit)

Rank solutions by (verdict, verifier confidence). Take the top one. Run up to 5 fresh verifier agents.

Asymmetric thresholds: 4 HOLDS to confirm, 2 HOLE FOUND to refute. Why asymmetric: one flaky verifier shouldn't kill a correct proof; but two independent dissents is a real signal.

Pigeonhole early exit: stop launching verifiers once the outcome is decided.

2 say HOLE FOUND → refuted, stop (save the remaining 3 calls)
4 say HOLDS → confirmed, stop (save the 5th)
After 3 verifiers: if 2 HOLDS + 1 HOLE, launch 2 more (outcome undecided). If 3 HOLDS + 0 HOLE, launch 1 more (could still hit 4-1).

Dual context-isolation: each verifier is blind to (a) the solver's thinking trace — already stripped in step 3 — AND (b) other verifiers' verdicts. Each verifier thinks it's the first. No "3 agents already confirmed this" social proof.

A solver cannot verify its own solution. Different agent, fresh context.

5b. When one case won't close — step back before grinding

If a proof splits into cases and one case proves easily but the other resists: before grinding through the hard case, ask whether there's a route that makes the split disappear.

The pattern that saves you: the hard case's very hypothesis often implies something strong about an intermediate object you haven't looked at. Use that implication directly instead of the original chain.

Concrete shape: proving f(n) ≤ cn for a constrained function f, with a case split on a prime p dividing f(n). One branch closes by index arguments in (ℤ/p^e)*. The other branch resists — same group structure, but the arithmetic doesn't contradict. The fix: the hypothesis "p | f(n)" plugged back into the governing equation implies f(p) = p itself. Once you have that, a Fermat+Dirichlet argument kills both branches in three lines. The case split was a detour — it was splitting on a variable that, under the hypothesis, takes a known value.

Check when stuck on case B:

What does case B's hypothesis imply about f at other inputs?
Is there a different pair (a,b) to plug into the governing equation?
Are you proving too much? (A cleaner contradiction needs less machinery.)

This is also a presentation-pass win: the split-free proof is shorter AND more general.

6. Revise (if needed)

If verification finds a hole: launch a reviser agent. It gets (cleaned solution + verifier's hole report). STILL no access to the original thinking — the reviser works from the hole, not by rereading how you got there.

A verifier found this issue in the proof:
[hole report]

Fix the proof. If the hole is fundamental (the approach doesn't work), say so and return **Verdict: no confident solution** with what partial progress remains.

For any step you cannot fully close, mark it inline: [GAP: specific description of what remains]. Gaps in the proof text, not in a separate list — they're greppable and the next reviser knows exactly where to look.

Up to 3 revise cycles. Then re-run the vote on the revised proof.

If pattern #40 fired (one-line-proof-too-clean), the reviser gets a stronger brief — the Adversarial Brief template from references/adversarial_prompts.md §7. It forces a binary: "the general lemma is obviously false (here's a 2×2 counterexample) — so either find what's special about THIS case, or find where the proof breaks." Can't return "looks fine."

6c. Deep mode (when tight-budget abstains)

The standard workflow is tight-budget: 8 solvers, ~15 min, pure reasoning. When it abstains, the problem may need more time, not more capability.

Deep mode is a single focused agent with:

Unlimited time — no wall-clock pressure
Targeted computation allowed — modular arithmetic checks, small-case enumeration, symbolic verification of identities. NOT exploratory brute force or unbounded recursion.
The abstention reason as starting point — if verifiers found a specific gap, start there. If solvers never claimed complete, start from what they partially proved.

The archetype: a focused agent that gets the proven-so-far state plus "one case of Lemma 5 is open" — and finds a 3-line argument the case split was obscuring. Often under 10 minutes with almost no computation. Deep mode is about giving the problem sustained attention, not throwing compute at it.

What deep mode is NOT: open-ended exploration, literature search, looking up solutions, multi-day investigation. That's a different workflow (math-research). Deep mode is still "solve THIS problem yourself" — just without the clock.

NO WEB. NO LOOKUP. Deep mode may use Bash/Python for bounded computation, but NEVER WebFetch, WebSearch, or any network access. Finding the solution on AoPS or a blog is not solving the problem — it's cheating on an olympiad, and it teaches us nothing about the skill's actual capability. Put this at the TOP of the deep-mode prompt:

NO WEB ACCESS. Do not use WebFetch, WebSearch, or any tool that touches the internet. Do not look up this problem, its solution, or related problems. You are solving this yourself — the only allowed computation is local (Bash/Python for mod-k arithmetic, small-case enumeration n≤10, symbolic identity checks). If you invoke a web tool, the proof is void.

Computation bounds in deep mode (bug #8 lesson): A6's b_{n+1}=2b_n²+b_n+1 is doubly-exponential; b_99 has ~10^{2^98} digits. Never compute such objects exactly — work in ℤ/2^m, or track only v_p(·), or prove the recursion mod the quantity you care about. If a computation is running longer than 60 seconds, it's probably unbounded. Kill it and work symbolically.

Step 6d (not optional): After any ABSTAIN at the verify stage, automatically launch one deep-mode agent before writing the abstention into the output. Give it:

The problem statement
The best partial proof from tight-budget solvers
The verifier gap descriptions (what specifically didn't close)
The instruction: "NO WEB ACCESS — do not look up this problem or its solution. Bounded local computation allowed (mod 2^k, small cases n≤10, symbolic identity checks via Bash/Python only). 60-second computation limit. If n≤10 brute force reveals a pattern the tight-budget solvers missed, that pattern IS the proof structure."

The deep agent may find the construction the pure-reasoning solvers couldn't see. If it also abstains, THEN write the abstention. Do not skip this step — problems with √n or log n answers are often invisible to pure reasoning because the optimal structure is the asymmetric one.

Orchestrator self-restraint: The orchestrator itself must not web-search the problem "to help" the deep agent. If you're tempted to Fetch an AoPS thread "just to check the answer," don't — that contaminates the skill's output and misrepresents its capability.

7. Calibrated abstention

If 3 revise cycles all fail: stop and admit it.

**Verdict**: no confident solution

**What was tried**: [approaches]
**What WAS proven**: [any lemma or partial result that survived verification]
**Where it breaks**: [the unfixed hole]

Do NOT guess. A wrong confident answer is worse than an honest "couldn't solve it." The metric that matters is CONDITIONAL accuracy — when you say "solved," are you right?

8. Presentation pass (after correctness is established)

A VERIFIED-CORRECT proof is often not a BEAUTIFUL proof. The order you discovered it is rarely the best order to present it. Launch a fresh presentation agent with the verified proof.

Load references/presentation_prompts.md. The agent asks:

What's the simplest way to say this?
Which lemmas should be inlined? Which deserve to stand alone?
Is anything OVERKILL? (constructing a double exponential when linear suffices)
Now that we know the answer, is there a 3-line hindsight proof?

Output: LaTeX-formatted proof. If pdflatex is available (scripts/check_latex.sh returns 0), also compile to PDF via scripts/compile_pdf.sh.

Model tier defaults

Read references/model_tier_defaults.md for full details. Summary:

Model	Solvers	Verify passes	Abstain after	Presentation
Haiku	8	3	2 revise fails	skip
Sonnet	4	5	3 revise fails	yes
Opus	3	5 + full pattern sweep	4 revise fails	2 drafts, pick cleaner

Weaker models: more parallel attempts, faster abstention. Stronger models: deeper verification, more presentation effort.

For numeric-answer problems (AIME-style)

Skip the proof machinery. Run 5-7 solvers with varied approaches, take majority vote on the numeric answer. If no majority: verify the top 2 candidates by substitution.

Key references

references/verifier_patterns.md — the 12 adversarial checks
references/adversarial_prompts.md — ready-to-use verifier prompts
references/presentation_prompts.md — beautification prompts + LaTeX template
references/model_tier_defaults.md — per-model configuration

What makes this different from generic verify-and-refine

Dual context isolation: verifier is blind to (a) the solver's thinking trace — which biases toward agreement — and (b) other verifiers' verdicts — social proof also biases. Each verifier thinks it's first.
Pattern-specific attacks: not "is this correct?" but "does this make the #40 mistake? the #4 mistake?" Specific beats generic. The 7-category refutation taxonomy gives the verifier a checklist.
Asymmetric vote + pigeonhole exit: 4-to-confirm, 2-to-refute. One flaky verifier doesn't kill a correct proof; two dissents does. Stop launching verifiers once the outcome is decided — saves ~30% of verification cost on clear cases.
Specification-gaming check first: explicitly asks "is this the intended interpretation?" before solving. The #1 failure mode in prior work (50/63 "correct" answers solved the wrong reading).
Calibrated abstention: will say "no confident solution" with partial results. Optimizes conditional accuracy, not coverage.
Presentation pass: correctness and elegance are separate steps. The presentation agent gets the VERIFIED proof and finds the cleanest way to say it.

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Math Olympiad Solver

The five things that change outcomes

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The Workflow

1. Interpretation check (30 seconds, catches 50/63 of one class of errors)

2. Generate candidates with internal refinement (parallel, thinking only)

3. Clean the solution (context isolation — the #1 lever)

4. Adversarial verify (fresh context, pattern-armed)

5. Rank and vote-verify (asymmetric + early exit)

5b. When one case won't close — step back before grinding

6. Revise (if needed)

6c. Deep mode (when tight-budget abstains)

7. Calibrated abstention

8. Presentation pass (after correctness is established)

Model tier defaults

For numeric-answer problems (AIME-style)

Key references

What makes this different from generic verify-and-refine

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