universal lossless compression impossible (information)
Theorem.universal lossless compression impossible (information) — for every n ≤ 12 there are 2ⁿ inputs but only 2ⁿ − 1 strictly shorter codes, shortfall EXACTLY one.
Proof.for every n ≤ 12 there are 2ⁿ inputs but only 2ⁿ − 1 strictly shorter codes, shortfall EXACTLY one — no injective compressor shrinks all inputs (pigeonhole; Shannon/Kolmogorov floor cited).
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/9/1/index.ts#discoveredTheoremsWaveNineteen
1 · Classification
finite-complete — computed witness within a cited frame (the unbounded form leans on the cited literature)
2 · Provenance
Documented theorem re-derived by exhaustive computation (humanityNovel=false); first-in-this-registry is the only sense of discovered.
Acknowledgment
"universal lossless compression impossible (information)" 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 discoveredTheoremsWaveNineteen.
- 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 (discoveredTheoremsWaveNineteen @ 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 discoveredTheoremsWaveNineteen (src/9/1/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.