Inside

Answer. The final output model: value, unit, equations used, assumptions, confidence, caveats, explanation, and a status of answered, degraded, or refused.

Assumption. A claim the answer depends on that the question did not state: an idealization ("no air resistance") or an estimated value ("a rubber duck masses about 25 g"). Always listed explicitly in the answer.

Assumptions table. data/fermi_assumptions.json: default values with low/high bounds, rationale, and source for quantities that Fermi questions need.

Caveat. A warning attached to an answer: a discarded root, a failed sanity check, an unimplemented check, an absurd consequence.

Classification. Output of stage 1: standard, fermi, or out_of_scope, with reasoning.

Confidence. A label (low, medium, high) and a 0 to 1 score, computed by code from retrieval score, dimension check, magnitude check, and assumption count (formula in PLAN.md section 7). Never self-reported by the LLM.

Constant. A physical constant with value, unit, uncertainty, and source (data/constants.json), for example standard gravity or the gas constant.

Constrained decoding. Masking tokens during generation so a Fermi model can only emit schema-valid JSON, retrieved equation ids, numbers present in its input, and valid units. Makes hallucinated equations and invented numbers impossible by construction.

Data factory. The code that generates Fermi model training data from the equation database and templates, with every standard example verified by Noether.

Degraded answer. An answer where a stage failed but the pipeline still returns something useful: what it tried, where it failed, and why.

Dimensional analysis / dimension check. Verifying that quantities have compatible physical dimensions (length, mass, time, and so on). Adding meters to seconds is a dimension error.

Equation. A database entry: a SymPy-parseable relation plus variables with units, domain, assumptions, validity conditions, tags, source, and license.

Escalation. ADR-010 routing: when solem can't produce a valid plan in 5 attempts, celeste gets one attempt before the answer degrades.

Eval leakage. Eval questions (or near-paraphrases) appearing in data, prompts, or training sets, which inflates scores without improving the system.

Fake LLM. FakeLLMClient: a deterministic stand-in returning canned, schema-valid responses, so tests and demos run without trained weights.

Fermi models. Our own from-scratch language models: fermi-tellus-1 (~3M params), fermi-solem-1 (~30M), fermi-celeste-1 (~120M), and fermi-luna-1 for tests. Not to be confused with Fermi questions or the Fermi engine. See docs/MODELS.md.

Fermi question / Fermi estimation. A question answered by decomposing it into estimable quantities, multiplying through, and reporting an order of magnitude. Named after Enrico Fermi. Covers absurd hypotheticals.

Grounding. Tying every claim in an answer to something checkable: a retrieved equation id, a constant from the table, or an explicit assumption. An ungrounded claim is a guess.

Hybrid search. Combining keyword (lexical) search with vector (semantic) search, usually by rank fusion. Planned for v0.6.

Known value. A quantity the plan treats as given: a value, a unit, and an origin (given, constant, or assumption).

Limit-case test. Checking that a formula behaves sensibly at extremes (as mass goes to 0, the force goes to 0). Planned for v0.8.

Noether. Our math engine, named for Emmy Noether, who tied symmetries to conservation laws. Built on SymPy (rearranges and solves equations) and Pint (carries and checks units); we wrote the safe parser, unit-aware solving, sanity checks, and Fermi engine around them (src/askphysics/solver/). Does all the math; the models never do. Formerly called the symbolic algebra machine.

Order of magnitude. The power of ten nearest a value. Fermi answers are graded on this (|log10(a) - log10(e)| <= 1).

Out of scope. A question we will not answer numerically: no physical meaning, unknowable data, or research-level. Gets a refusal with a reason and a redirect.

Pint. The Python units library. Every quantity carries its unit through the computation.

Plan. Output of stage 3: the target symbol, unknowns, known values with units, equation ids, assumptions, and strategy. Strict JSON, validated before compute.

Recall@k. The fraction of questions where the correct equation appears in the top k retrieval results. A v0.6 release metric.

Redirect. The "closest answerable version" offered with a refusal.

Rerank. A second scoring pass over the top retrieval candidates with a more expensive model (for example, a cross-encoder) to reorder them.

Retrieval. Stage 2: finding equations and worked examples relevant to the question. Keyword-based in v0.1.

Sanity check. Stage 5: dimension check, order-of-magnitude check against typical ranges, and (from v0.8) limit cases.

SymPy. The Python symbolic math library. Rearranges equations and evaluates solutions.

Target. The symbol the question asks for (for example v).

Task format. The fixed text layout (task token plus JSON payload) a Fermi model was trained on for classify, plan, or explain. See docs/PROMPTS.md.

Tokenizer. Our byte-level BPE that turns text into token ids. Digits are single tokens so numbers copy exactly.

Typical range. Per-variable [low, high] bounds in equation data, used by the magnitude check.

Worked example. A solved problem in data/examples.json, used as retrieval context for planning.