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8935cc9eaa
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).
116 lines
4.8 KiB
Markdown
116 lines
4.8 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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## Semantic Mass Number: Base Conversion Proof (Final Branch)
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### The Test
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"Encode data as a semantic mass number A(H)" = represent the message
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as one big number (the nuclide address / 10-adic residue reading).
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### Measured Results (lossless round-trip PASS)
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| Method | bits/char | bytes | ratio | lossless |
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|--------|-----------|-------|-------|----------|
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| M1 base-256 mass number | 8.000 | 100,000 | 1.00 | PASS |
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| M2 mixed-radix (155 symbols) | 7.276 | 91,107 | 1.10 | PASS |
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| M3 freq-weighted (=arithmetic) | 5.401 | 67,823 | 1.47 | needs model |
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| xz -9 (order-N + matching) | 2.551 | 31,892 | 3.14 | PASS |
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### Why It Fails
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Base conversion is a bijection. A bijection moves information around,
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never destroys it — so it cannot compress below its radix. M1 IS the
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data (1.00x). M2 only beats 1.00 because the data uses 155 of 256
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byte values (dropping unused-symbol slack, not compression). M3 =
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arithmetic coding wearing a nuclide costume — and the model must ship
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= conservation wall.
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### The Doctrine Already Knew
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The de-anthropocentric revision explicitly flags "English-facing
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semantic compression" as the OLD ERROR and redefines:
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"MassNumber is the admissibility / recoverability RECEIPT projected
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from SemanticMass."
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The measurement just put numbers behind the flag.
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## Final Sealed Map
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| Idea | As compressor | Honest home |
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|------|---------------|-------------|
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| char-poly | receipt, adds overhead | GCCL integrity receipt |
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| Braille/T9 | 4.167 b/B, lose to xz | dead |
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| 16D / 583x GW | zero-noise artifact, LPC win | LPC in costume |
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| weird-machine | conservation, k=3 worst total | bits relocate, never shrink |
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| semantic mass number | base conversion, 1.00–1.10x | recoverability receipt |
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One rule: you can move bits between columns, never beat K(data).
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Everything that "compresses" is either base conversion (bijection,
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no gain) or arithmetic coding (needs model, ship cost). The clever
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geometry buys nothing over boring xz/LPC.
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