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Claude Code tested semantic mass number as compressor: - M1 base-256: 1.00x (IS the data, bijection) - M2 mixed-radix: 1.10x (drops unused symbols, not compression) - M3 freq-weighted: 1.47x (= arithmetic coding in costume, needs model) - xz: 3.14x (crushes all) Base conversion is a bijection — moves information, never destroys it. Cannot compress below its radix. The doctrine already knew: mass number = 'admissibility / recoverability RECEIPT', not compressor. Entire compression arc now sealed end to end: | char-poly | receipt → GCCL integrity receipt | | Braille/T9 | 4.167 b/B → dead | | 16D/583x | zero-noise artifact → LPC in costume | | weird-machine | conservation law → bits relocate, never shrink | | mass number | base conversion → recoverability receipt | One rule: move bits between columns, never beat K(data). Everything that compresses = base conversion (no gain) or arithmetic coding (needs model, ship cost = conservation wall).
4.8 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 |
Semantic Mass Number: Base Conversion Proof (Final Branch)
The Test
"Encode data as a semantic mass number A(H)" = represent the message as one big number (the nuclide address / 10-adic residue reading).
Measured Results (lossless round-trip PASS)
| Method | bits/char | bytes | ratio | lossless |
|---|---|---|---|---|
| M1 base-256 mass number | 8.000 | 100,000 | 1.00 | PASS |
| M2 mixed-radix (155 symbols) | 7.276 | 91,107 | 1.10 | PASS |
| M3 freq-weighted (=arithmetic) | 5.401 | 67,823 | 1.47 | needs model |
| xz -9 (order-N + matching) | 2.551 | 31,892 | 3.14 | PASS |
Why It Fails
Base conversion is a bijection. A bijection moves information around, never destroys it — so it cannot compress below its radix. M1 IS the data (1.00x). M2 only beats 1.00 because the data uses 155 of 256 byte values (dropping unused-symbol slack, not compression). M3 = arithmetic coding wearing a nuclide costume — and the model must ship = conservation wall.
The Doctrine Already Knew
The de-anthropocentric revision explicitly flags "English-facing semantic compression" as the OLD ERROR and redefines: "MassNumber is the admissibility / recoverability RECEIPT projected from SemanticMass."
The measurement just put numbers behind the flag.
Final Sealed Map
| Idea | As compressor | Honest home |
|---|---|---|
| char-poly | receipt, adds overhead | GCCL integrity receipt |
| Braille/T9 | 4.167 b/B, lose to xz | dead |
| 16D / 583x GW | zero-noise artifact, LPC win | LPC in costume |
| weird-machine | conservation, k=3 worst total | bits relocate, never shrink |
| semantic mass number | base conversion, 1.00–1.10x | recoverability receipt |
One rule: you can move bits between columns, never beat K(data). Everything that "compresses" is either base conversion (bijection, no gain) or arithmetic coding (needs model, ship cost). The clever geometry buys nothing over boring xz/LPC.