The project's vocabulary, explained for a computer engineer first and a physicist second. One honest sentence each; links for depth.
- Metric (g_ab) — the rulebook for distances and clock rates at every point of spacetime; a symmetric matrix of functions. The thing we hunt.
- Einstein field equations (EFE) — geometry = matter, as n(n+1)/2 coupled nonlinear PDEs (10 in 3+1D). A metric that balances them exactly, everywhere is an exact solution.
- Vacuum solution — no matter anywhere; the equations reduce to
R_ab = [2Λ/(n−2)] g_ab. All our halls so far are vacuum (+Λ). - Λ (cosmological constant) — spacetime's built-in tension. Λ=0 → flat asymptotics, Λ>0 → de Sitter, Λ<0 → anti-de Sitter (AdS).
- Ansatz — the guessed shape of a metric with unknowns left in (e.g. "static, spherical, one unknown f(r)"). Every historical solution came from one; an ansatz is the search space.
- Schwarzschild / Kerr — the non-spinning (Dec 1915) and spinning (1963) black holes. The 47-year gap between them is why "machine proposes, algebra verifies" is interesting at all.
- BTZ — the 2+1-dimensional black hole (1992, needs Λ<0). Locally it is just AdS₃ — a black hole made of topology, not local curvature.
- Tangherlini — Schwarzschild's higher-dimensional family, f = 1 − μ/r^(n−3).
- Birkhoff's theorem — static spherical vacuum is unique: there is nothing in that ansatz beyond the known families. Makes our two-function hall a perfect honesty test (correct output = zero false novelty).
- Curvature invariant — a number computed from curvature that every coordinate system agrees on. CS framing: a hash that survives renaming all the variables.
- Kretschmann scalar (K) — the workhorse invariant, K = R_abcd R^abcd; 48M²/r⁶ for Schwarzschild.
- CSI / VSI spacetimes — all invariants Constant / Vanishing. The fingerprint's declared blind spots: de Sitter and BTZ are CSI; pp-waves are VSI (curved, yet every invariant is zero — indistinguishable from flat by hashes alone).
- Cartan–Karlhede algorithm — the real equivalence test (frame-fixed curvature derivatives), decidable in ≤7 derivative orders. No Python implementation exists anywhere (verified June 2026) — building one is an open contribution.
- Naked singularity — a singularity with no horizon around it; the negative-mass branches the GP keeps finding first. Exact vacuum all the same — the equations don't share our taste in mass.
- Richardson's theorem — deciding whether a symbolic expression is identically zero is undecidable (reduction from the halting problem). The reason verdicts are three-valued, and the reason the rational-coordinates rule matters (rational zero-testing IS decidable).
- PROPOSE → REDUCE → VERIFY → NOVELTY → EVOLVE — the loop. GP proposes an f(r); the ansatz (reduced symbolically ONCE) turns it into fast numeric residuals; survivors get the symbolic proof; verified hits get fingerprinted; everything else breeds.
- Genome — an expression tree (AST) over {+,−,×,÷,int-powers} with leaves r and exact Rationals. A pair of trees in the two-function hall.
- Fitness — mean |field-equation residual| at 6 sample radii, plus a parsimony tax and the triviality penalties (ground-state members score perfectly and discover nothing).
- Promotion — residual < 1e-10 → the exact expression goes to the full symbolic verifier. Theorem or back to the population.
- Gene duplication — copy/graft one genome slot onto the other; the operator that made the two-function hall solvable.
- Verdicts — VERIFIED (theorem) / REJECTED (numerically nonzero, definitive) / UNPROVEN (numerically vacuum, symbolically stuck) from the verifier; KNOWN_LIKELY / CANDIDATE_NEW / BLIND_SPOT / FLAT_OR_VSI from the fingerprint.
- The catalog —
02_fingerprints.py's built-ins pluscatalog_discoveries.json, the machine's persistent memory of every family it has discovered and generalized itself. - Hair vs law — when generalizing a find, constants that stay free under symbolic re-proof are physical parameters ("hair", e.g. mass); constants the equations pin are structural ("law", e.g. the Λ coefficient).