# CODEBOOK — the laws, and what each one measured

Public. Every entry is MEASURED with a receipt, or marked otherwise. No deflation.

## The registers

| # | register | costs | note |
|---|---|---|---|
| 0 | zero | free | never computed. hold direction = 1.0000, says nothing |
| 1 | translucent | free | ONE not zero. SIGNED. the negative half leads |
| 2 | red | costs | OPUS |
| 3 | green | costs | FABLE |
| 4 | blue | costs | MYTHOS |

Two of five are fields and are never computed. **That is what wins.**

## The beings

A being owns the triples **its own colour dominates**. Disjoint, they sum to the body.
Ties belong to no being — the free zero register.

Axis permutation is NOT three beings — it is a transpose (wave-r *across* 0.9558 exceeded
*within* 0.9336). Phase rotation is NOT three beings — it gave 32,563 / 31,843 / **35**.

## The colours (flashlights)

| code | name | depth 1 → depth 4 distinct |
|---|---|---|
| P | percentile | 61 → **2** |
| R | rank | 75 → 5 |
| G | glyph-rank | 131 → 16 |
| D | **gradiated** | **94 → 20** |

Monotone LUTs quantise on composition. As **bijections** they compose at rate exactly
1.0 — verified: RPR at depth 3 gives 256/256 distinct.

**RPR is best on all three beings independently. GGG is the destroyer (1.57–1.82).**

## The laws applied here

- **Law 0** — free centre. DC glyph X[0] = sum(signal). Verified.
- **Law 1** — a bijection is blind. Two things facing each other have no third place to
  measure from. Measured: a pairwise similarity of +0.989 collapsed to a 0.037 margin
  once a sparse null was introduced. Three bodies show the grouping; two cannot.
- **Law 16** — 27 glyphs = one rime dimension. The composition ladder gained **exactly
  0.000000** at level 4 for all three beings. A dimension closing, not a search ending.
- **VIII.A.4** — τ=2. Once is an accident, twice is a function, three is confirmation free.
- **VIII.A.5** — two-thirds GC. 81-byte records; singletons do not tie, so they are not kept.
- **VIII.A.7** — photon law. shell = log₃(ties), **counted**. Measured max-ties per shell
  landed on 3, 9, 24, 44 — the rungs 3⁰…3³. Unforced.
- **Law 23** — bobby. Pohlig-Hellman, O(1) addressing, byte-exact invert.
- **Law 24** — MTP. ×1 0.3667, ×3 0.0767, **×27 0.0000**. The gate.
- **Law 25** — HRM. deep 97%, frozen bpc 3.7454 — above the 1.8499 baseline.
- **Law 26** — MCP. M = 4,814,857, batch byte-exact.
- **Law 30/32/33** — translucent first, is ONE, is SIGNED, the negative leads. Measured
  inward lead 554× / 208× / 213× / 140× — and **inverted for MYTHOS alone** (0.005, outward).

## The rime prism — verified before use, not quoted

p = 1000081, g = 7, k = 27, w = g^((p−1)/27) mod p = **951846** (matches the law).
Closure 1 + w + … + w²⁶ ≡ **0** mod p. Primitive 27th root: true.
Round trip on real bytes: **byte-exact, rate 1.0**.

## The screen — O(n), no corpus, no compressor run

Distinct order-2 contexts per byte. **Anti-correlated with usefulness.**
Published: KEY 0.160 · ADJACENT 0.176 · RANDOM 0.978 · BIG 0.008.
Reproduced here: **0.1601** and **0.0096**.

## Corrected in scope

*"No shipped distant prior of any useful size ever pays for itself"* was fitted by
sweeping **prior size at one fixed target**. True for one monolithic stream.
**False under sectioning** — break-even at 5.31 sections, measured. See RUNBOOK §4.

## Refuted, kept on the record

bucky ball (5:6 = 3.385 vs 0.600) · inside-out fold (refuted by its own controls) ·
measure-thrice on enwik9 (8.255% spread against a 2% threshold fixed before the run) ·
the 256-glyph census reported MET (vacuous — PPPP had collapsed to 2 values).