Plasma outruns light without breaking it
Theorem.Plasma outruns light without breaking it — from ω² = ωₚ² + c²k² alone: the phase velocity exceeds c at every propagating frequency (1.1547c at ωₚ/ω = ½) while the group velocity trails (0.866c), and v_φ·v_g = c² exactly.
Proof.from ω² = ωₚ² + c²k² alone: the phase velocity exceeds c at every propagating frequency (1.1547c at ωₚ/ω = ½) while the group velocity trails (0.866c), and v_φ·v_g = c² exactly — reciprocals about light speed; at cutoff n → 0 gives v_φ → ∞ and v_g → 0, the dispersion relation's own division by zero, which is why the ionosphere reflects shortwave. Superluminal phase carries no signal (Brillouin/Sommerfeld 1914).
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/fire/plasma/ball/index.ts#plasmaSpeedByTheorem
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
"Plasma outruns light without breaking it" 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 plasmaSpeedByTheorem.
- 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 (plasmaSpeedByTheorem @ src/fire/plasma/ball) 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 plasmaSpeedByTheorem (src/fire/plasma/ball/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.