803b96754a
Claude Code's demo proves the conservation law with measured bytes: - k=0: total=102,252 (model=440, tape=101,812) - k=1: total=85,534 (sweet spot) - k=3: total=557,169 (model=501,392 ate the savings) - xz: total=35,492 (tiny amortized decoder) As prediction improves (k↑), tape shrinks but model explodes. The sum is conserved. The weird machine moves bits between columns, never reduces the total. One real win: frozen model + arithmetic coder = sub-xz on tape alone (amortized). But the model is on the invoice. Ship it for Hutter = lose. This permanently gates: - 'Turing-complete weird machine beats unpredictability' = FALSE - '583x GW compression' = zero-noise artifact (1.5x at realistic SNR) - '16D braid adds value over LPC' = FALSE (ties at 30dB, loses at 20dB) - 'Generation beats prediction' = FALSE (generation = prediction, sum conserved) The honest map: every approach tried loses to established coders (xz on text, LPC on signals). The polynomial stays a GCCL receipt. The pipeline's real value is formal verification + anti-smuggle framework, not compression ratio.
2.9 KiB
Weird Machine Conservation Law: Proven with Real Bytes
The Claim That Was Tested
"A Turing-complete weird machine can beat unpredictability by finding generating programs instead of predicting."
The Conservation Law (now measured)
compressed_size = program_size + residual_size ≥ entropy_floor × data_size
The weird machine moves bits between the program column and the residual column. It never reduces the sum below the entropy floor.
Measured Results (Claude Code demo, lossless round-trip PASS)
| order k | tape B | model B | TOTAL B | amortized B |
|---|---|---|---|---|
| 0 | 101,812 | 440 | 102,252 | 101,812 |
| 1 | 75,806 | 9,728 | 85,534 | 75,806 |
| 3 | 55,777 | 501,392 | 557,169 | 55,777 |
| xz -9 | 35,492 | ~60KB | 35,492 | 35,492 |
As k increases:
- Tape SHRINKS (better prediction, smaller residual)
- Model EXPLODES (every new context = bytes to ship)
- TOTAL bottoms out at k=1, then BLOWS UP at k=3
Why xz Wins
xz's decoder is ~60KB, amortized across all files by the standard. It never ships a fat per-file model. The model column is effectively zero per file. That's why total = tape = 35,492.
The One Real Win (not Hutter)
Frozen model + arithmetic coder: k=3 amortized = 55,777 bytes, sub-xz on tape alone. A real frozen LLM would drive this lower. But the model must be shared out-of-band (not scored). The instant you ship the model (Hutter Prize), the model column dominates and you lose.
What This Permanently Gates
- "Turing-complete weird machine beats unpredictability" = FALSE
- Conservation forbids it. The machine is never free; it's on the invoice.
- Generation = prediction. The generating program = the model. The residual = what can't be predicted/generated. Sum is conserved.
- The Braille/T9/hachimoji substrate is a different decomposition, not a different bound. It changes where bits go, not whether they exist.
The GW SNR Sweep (same law, different data)
| SNR | program | residual | total | ratio |
|---|---|---|---|---|
| clean | 9 coeff | 0 | tiny | 583x (zero-noise artifact) |
| 60 dB | 9 coeff | small | small | 2.3x |
| 30 dB | 9 coeff | noise | ~floor | 1.5x (ties LPC) |
| 20 dB | 9 coeff | more noise | ~floor | 1.5x (LPC wins) |
Same conservation: bits move from program to residual as noise increases. Total converges to entropy floor. Nobody beats it.
The Honest Map
| Approach | Text (enwik8) | Signals (GW) | Verdict |
|---|---|---|---|
| Order-2 PPM | 3.088 b/B | — | Honest baseline |
| Braille/T9 | 4.167 b/B | — | Dead (worse than PPM) |
| 16D braid | — | 1.5x (ties LPC) | Dead (adds nothing) |
| Polynomial | Receipt | Receipt | Receipt, not compressor |
| xz | 1.989 b/B | — | The floor |
| cmix | ~1.2 b/B | — | SOTA (461 models) |
| LPC | — | ~1.5x | The signal floor |
| Frozen LLM + AC | sub-xz (amortized) | — | Real, but model not scored |