🧮 Math Exception Lab — zero-training reasoning stack
A math-specialized model from the Hub, wrapped in an inference-time stack: meta-abstraction → world state → latent/diffusion-style draft sampling → EBM scoring → sympy-backed verifier → persistent memory graph. Nothing is trained — the model is loaded from the Hub as-is; every 'layer' is orchestration around inference.
⚠️ No model — and certainly none running at ~$0/hour of inference — can solve a Millennium Prize Problem. These are open research problems with $1M bounties precisely because no one has solved them. This tab produces a research plan: formalization, state of the art, an attack strategy, and a Lean-style proof skeleton — the things a researcher on a budget actually needs to start.
Every solve is logged: problem → strategy → verified result. The graph lives in the Space's disk (/tmp/memory_graph.json) and resets when the Space restarts — use this tab to inspect it.
The stack (all inference-time — zero training)
| Layer | What it does |
|---|---|
| Meta-abstraction | Classifies the problem topic and proof-vs-compute intent before inference. |
| World layer | Injects a state summary (topic, strategy) into the model's system prompt. |
| Latent / diffusion-style thinking | Samples k parallel drafts, then a refine round 'denoises' toward consensus. |
| EBM scoring | Energy = −(sample agreement) + penalties for contradicted/unverified answers; picks the minimum. |
| Verifier (Lean-style claim check) | sympy computes ground truth where the problem shape allows it; VERIFIED / UNVERIFIED / CONTRADICTED. |
| Memory graph | networkx graph of problems → strategies → results, persisted to disk. |
Honest limits: a ≤7B model with zero training is strong on competition math and routine undergrad problems, not on research-level problems. The verifier only fires when the problem maps to a sympy-computable ground truth; otherwise answers are labeled UNVERIFIED. The Millennium tab produces research plans, not proofs.
ZeroGPU note: GPU time is borrowed per request (free accounts get a daily quota; PRO gets more). No dedicated GPU is ever paid for.