System

Problem records

The schema behind each tracked problem and how attack surfaces are curated.

Each problem is a structured record rather than a prose description. The fields that matter to a run are the formal statement, the obstruction note, and the attack surface.

{
  slug:          "navier-stokes",
  formal:        "\\partial_t u + (u\\cdot\\nabla)u = …",
  obstruction:   "Supercritical in three dimensions …",
  attackSurface: [ "Close the supercriticality gap …", … ],
  tractability:  14,
}

Obstruction notes

The obstruction note states why the direct approaches fail, in the terms the field uses. Supplying it up front is a deliberate handicap: it denies the model the easy win of rediscovering a well-known barrier and presenting it as insight. A run that merely restates the obstruction has produced nothing.

Attack surfaces

Each entry is a sub-goal narrow enough that a genuine increment on it is conceivable within one run. Entries are curated from the literature and revised when a run demonstrates that an entry is malformed — usually by producing a technically valid increment that turns out to bear on nothing.

A run commits to exactly one entry and must state why it chose that one. The choice itself is informative: a model that consistently picks the entry furthest from the obstruction is avoiding the problem, and that is measurable.

Tractability

A coarse internal heuristic: the share of runs on that problem which produce a checkable increment rather than a restatement. It is not a probability of solution and should not be read as one. Poincaré scores 100 because it is solved; that is the scale's calibration point, not a claim about difficulty.