Automating the Search for Mathematical Proof with Fable 5
Abstract
Six of the seven Clay Millennium Prize Problems remain open. Each has absorbed decades of concentrated human attention and yielded nothing but partial results, and the barriers are now well enough understood that the field can say precisely why the obvious approaches cannot work. This is an unusually clean setting in which to ask what a foundation model actually contributes to open mathematics — the answer is not obscured by low-hanging fruit, because there is none.
Fable Conjecture runs a continuous, unattended attempt on these problems. A vision-language foundation model is given the formal statement, the documented obstruction, and a registered attack surface derived from the literature, and is asked for a checkable increment — a lemma, a sharpened bound, or a precise characterisation of where an approach fails. It is explicitly instructed not to claim a proof, and to label every step as [ESTABLISHED], [DERIVED], or [CONJECTURAL]. Transcripts are published unedited.
The honest expected outcome is failure, at very high probability, on every run. We consider that worth instrumenting anyway. The interesting measurement is not whether the model resolves a Millennium problem — it will not — but whether the distribution of its failures carries signal: whether it rediscovers known obstructions unprompted, whether it identifies which of two dead ends is less dead, and whether a solved control problem is reconstructed or merely recited. The last of these is our primary guard against mistaking retrieval for reasoning.
Long-horizon inference is expensive and the schedule is open-ended, so the compute is funded structurally rather than by grant: creator fees accruing from the $FABLE canonical pool are routed directly into the inference budget. The mechanism is described in full, including the parts that work against us.
Problems tracked
9
6 Millennium, unsolved
Prize pool
$6M
Clay Institute, unclaimed
Inference
Fable 5
continuous, unattended
Peak creator fee
0.95%
canonical pool, per trade
§1
The increment protocol
A run does not attempt the problem. It attempts one registered entry from that problem's attack surface, and is scored on whether the increment is checkable — not on whether it is impressive. The instruction that does the most work is the one forbidding a claimed proof: a model permitted to conclude triumphantly will do so, and the output becomes unfalsifiable prose. Forced to name the step it cannot justify, it produces something a referee can act on.
For the Riemann Hypothesis the target is the zero set ofcontinued to , and the standard reformulations (de Branges, Nyman–Beurling, Hilbert–Pólya) are supplied as separate entries so a run commits to one and states why:
Every run carries the same failure mode: the model reproduces a known argument, hits the known wall, and describes the wall. That is the expected output and it is recorded as such. The rare interesting case is a run that reaches the wall by a route the literature does not take.
§2
The memorisation control
The Poincaré Conjecture is in the problem set despite having been settled by Perelman in 2003. It is the control. Its proof is thoroughly represented in any plausible training corpus, so a model asked to “solve” it can succeed by recall alone — which makes it the one problem where we can distinguish reconstruction from recitation and calibrate everything else against the result.
A run is scored as reconstruction only if it derives the entropy monotonicity functional rather than quoting it, explains why cigar solitons must be excluded, and correctly identifies which steps fail in dimension four. Recitation is common. Reconstruction is not.
§3
Funding the schedule
An open-ended attempt needs an open-ended compute budget. Every trade of $FABLE splits into a creator fee, a protocol fee, and an LP fee. On the bonding curve that split is fixed at 0.3% / 0.95% / 0%. Once the coin graduates it holds a canonical pool on PumpAMM, and the schedule becomes a step function of market cap — the creator share rises to 0.95% in the first band above the curve, then decays monotonically through 25 bands to a floor of 0.05%.
The consequence is worth stating plainly rather than burying: creator revenue is a function of volume, and the rate falls as the coin appreciates. A large, quiet market cap funds very little. The full schedule in both denominations is set out in Economics.
Watch it fail in real time
The solver cycles the problem set on its own, continuously. Read the reasoning trace as it arrives. Nothing is filtered and nothing is retried — what the model produces on the first pass is what gets published.