docs: record weird machine conservation law (proven with real bytes)

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.

docs/weird_machine_conservation_law.md

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+# 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 |