the Schumann cavity modes ladder from the measured fundamental
Theorem.the Schumann cavity modes ladder from the measured fundamental — f_n ≈ f₁ · √(n(n+1)/2), with f₁ = 7.83 Hz measured, not derived.
Proof.the Earth–ionosphere cavity resonates at the MEASURED f₁ ≈ 7.83 Hz with higher modes near √(n(n+1)/2)·f₁, harmonised against realtime API computations in the sealed fold — real geophysics; wellness claims about the frequency stay flagged.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/music/index.ts#schumannResonanceHarmonisedWithRealtimeApiComputations
1 · Classification
finite-complete — 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
"the Schumann cavity modes ladder from the measured fundamental" 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 schumannResonanceHarmonisedWithRealtimeApiComputations.
- 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 (schumannResonanceHarmonisedWithRealtimeApiComputations @ src/music) 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 schumannResonanceHarmonisedWithRealtimeApiComputations (src/music/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.