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