数学发现引擎

Requirements

• Python 3
• Two pip packages

pip install anthropic networkx

Or from the requirements file:

pip install -r discovery_engine/requirements.txt

Setup

Basic Examples

```bash

Example Output

``` Loading knowledge graph from knowledge_graph.json... Loaded in 0.8s — {'nodes': 9466, 'edges': 13504, 'techniques': 360} Mode: LIVE (API) Orchestrator model: claude-sonnet-4-20250514 Worker model: claude-haiku-4-5-20251001 Prompt caching: ON

Problem: Prove the Erdős primitive set conjecture Start nodes: ['s_divisibility_definition', 's_antichain_in_boolean_lattice'] Goal: f(A) = sum 1/(a log a) is maximized when A is the set of primes

--- Iteration 1 | Expanding sn_0001 (depth 0) | Frontier: 0 --- State: Erdős primitive set conjecture Candidates: ['t_axiomatize_from_instances', 't_compose_with_identity', 't_complex_analysis_to_integers', 't_probabilistic_existence'] ○ t_axiomatize -> sn_0002 (conf=95%) Primitive set = antichain in (Z>1, |) ○ t_compose -> sn_0003 (conf=80%) FTA + multiplicative structure ○ t_complex -> sn_0004 (conf=65%) Von Mangoldt weights ○ t_probabilistic -> sn_0005 (conf=50%) Erdős-Kac connection

--- Iteration 2 | Expanding sn_0004 (depth 1) | Frontier: 3 --- ...

★ GOAL REACHED at sn_0042!

=== DISCOVERED PATH === Layer 0: [START] -> Erdős primitive set conjecture (conf=100%) Layer 1: [t_axiomatize_from_instances] -> antichain formalized (conf=95%) Layer 2: [t_compose_with_identity] -> FTA + multiplicative structure (conf=80%) Layer 3: [t_complex_analysis_to_integers] -> von Mangoldt weights (conf=65%) Layer 4: [t_reduce_to_canonical_form] -> Markov chain model (conf=55%) Layer 5: [t_probabilistic_existence] -> stationary distribution bound (conf=60%) Layer 6: [t_exhaustion_squeeze] -> f(A) ≤ f(primes). QED. (conf=75%) === END ===

Quick start

python3 -m http.server 8765
open http://localhost:8765/graph_viewer_3d.html    # 3D viewer (recommended)
open http://localhost:8765/graph_viewer.html        # 2D viewer (lighter)

Opening HTML files directly (file://) won't work — fetch() of knowledge_graph.json is blocked by the browser's same-origin policy. Use a local server.

Configuring Worker APIs

Workers are the LLMs that attempt each technique application. Three modes are available:

Configuring the Orchestrator (Master AI)

The orchestrator is the "brain" that parses problems, selects techniques, and evaluates results. It runs separately from the workers.

Mode 1: Dry Run (free, no API)

Uses mock workers that return synthetic results based on graph structure. Good for testing the search logic.

python3 -m discovery_engine.discover --dry-run \
    "Prove that for any primitive set A, f(A) <= f(primes)"

Mode 2: CLI Workers (uses Claude Code subscription)

Spawns claude -p subprocesses. No API key needed — uses your existing Claude Code subscription billing.

python3 -m discovery_engine.discover --use-cli \
    --start s_divisibility_definition,s_antichain_in_boolean_lattice \
    --goal "f(A) = sum 1/(a log a) is maximized when A is the set of primes" \
    "Erdős primitive set conjecture"

Default: 2 parallel workers. Override with --workers N.

Mode 3: API Workers (Anthropic API key)

Direct API calls with prompt caching. The cheapest per-call option for large searches.

export ANTHROPIC_API_KEY=sk-ant-...
python3 -m discovery_engine.discover \
    "Prove the Erdős primitive set conjecture"

Default worker model: claude-haiku-4-5-20251001 (~20x cheaper than Sonnet). Override with --worker-model.

Default: 5 parallel workers. Override with --workers N.

Token Optimizations

Three optimizations reduce API cost by ~90-95%:

1. Haiku workers — workers apply a single technique to a single state, a focused task that Haiku handles well
2. Prompt caching — the static worker system prompt is marked with cache_control: {"type": "ephemeral"}, so after the first call all subsequent calls within 5 minutes pay only ~10% for that block
3. Trimmed prompts — user prompts are ~200-400 tokens (3 example inputs/outputs, 8 context nodes, no verbose instructions)

---

CLI workers — uses your Claude Code subscription

python3 -m discovery_engine.discover --use-cli \ --start s_divisibility_definition,s_antichain_in_boolean_lattice \ --goal "f(A) = sum 1/(a log a) is maximized when A is the set of primes" \ "Erdős primitive set conjecture"

Full API mode with LLM orchestration

export ANTHROPIC_API_KEY=sk-ant-... python3 -m discovery_engine.discover --llm-orchestrate \ --model claude-sonnet-4-20250514 \ --worker-model claude-haiku-4-5-20251001 \ --workers 5 --max-depth 7 --max-iterations 200 --candidates 4 \ "Prove the Erdős primitive set conjecture" ```

All CLI Flags

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