Inside

Every question goes through six stages. Language models handle three of them, and none of those three produces a number.

question -> 1 classify -> 2 retrieve -> 3 plan -> 4 compute -> 5 sanity check -> 6 explain
            (tellus)      (database)    (solem)   (Noether)    (Noether)          (solem)

1. Classify. Is this a standard problem, a Fermi estimate ("how many piano tuners are in Chicago?"), or not physics at all? Out-of-scope questions stop here with a reason and, when possible, a physics question to ask instead.
2. Retrieve. Search the equation database for equations whose tags match the question's words.
3. Plan. A Fermi model writes a plan: which equation, which variable to solve for, and which value goes where. It can only pick equations that retrieval found and numbers that appear in the question or the constants, and every value's units must fit its variable. The decoder makes anything else impossible to write, not just unlikely.
4. Compute. Noether rearranges the equation symbolically, plugs in the values with their units, and converts the result to the right unit.
5. Sanity check. Do the dimensions work out? Is the result negative where it can't be, or zero only because the plan assumed a zero? Is it within a believable range? Did the plan use every value the question gave? Does the question fit a look-alike equation just as well? These checks set the confidence.
6. Explain. The model writes a short explanation. Any digit it writes must be a number from the plan or the result.

When a plan doesn't work

The router (ADR-010) tries again instead of showing a bad answer:

• A plan that fails validation, can't be computed, or gives an impossible result is thrown away, and solem tries again with the equations listed in a new order, up to 5 times. Then celeste, the biggest model, gets one try.
• A plan that works but leaves one of the question's values unused is kept as a fallback while the router looks for one that uses everything. If none does, the fallback is shown, flagged.
• If nothing works, the answer is PARTIAL: it says which stage stopped and why. An impossible number is never shown.

Why this design

A small model can't be trusted with arithmetic, and a big one can't either, not every time. So the models only read and write; every number comes from symbolic algebra, every unit is tracked by Pint, and every equation comes from a reviewed database with a source and a license. The full design is in ARCHITECTURE.md and the decisions behind it in DECISIONS.md.