balance · φ⁻3 · hue 2 · 5

AM-GM inequality

discoveredTheoremsWaveThirtyNine · src/9/1 · bounded-witness

9/1 bounded-witness self-contained anim/balance

Theorem.AM-GM inequality — the arithmetic mean is ≥ the geometric mean for positive reals, equality iff all equal.

Proof.the arithmetic mean is ≥ the geometric mean for positive reals, equality iff all equal — verified over many tuples on n ≤ 6 plus the equality case.

Checked by exact arithmetic over the stated finite range — a verified witness, evidence toward the claim, not a ∀-proof.

src/9/1/index.ts#discoveredTheoremsWaveThirtyNine

1 · Classification

bounded-witness — self-contained computation, no external lean

2 · Provenance

Documented theorem re-derived by exhaustive computation (humanityNovel=false); first-in-this-registry is the only sense of discovered.

Acknowledgment

"AM-GM inequality" is a re-derivation, acknowledged to documented mathematics — the original proof is the prior art this re-derivation acknowledges; not new to humanity — the contribution is the reproducible computation discoveredTheoremsWaveThirtyNine.

Prior art: documented mathematics — the original proof is the prior art this re-derivation acknowledges
Novelty: not new to humanity — a re-derivation (humanityNovel = false)
Contribution: a reproducible computation (discoveredTheoremsWaveThirtyNine @ src/9/1) that re-derives the result at zero tokens — the contribution is the verifiable recomputation, NOT the theorem

3 · Reproducibility

Recompute from source: npm run theorems:verify recomputes discoveredTheoremsWaveThirtyNine (src/9/1/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.