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Compression Demo

Lossless compression using UOR ring algebra observables. Every byte is decomposed through algebraic structure to find its irreducible representation.

raw bytes permute ring-diff SPEC / torus rANS compressed

From Landauer to Minimal Representation

The Landauer limit establishes that erasing one bit of information costs a minimum of kT·ln(2) energy. This defines the irreducible information content of any data — the bits that cannot be removed without thermodynamic cost.

Hologram compression uses UOR algebraic observables to find this minimal representation:

Stratum

Popcount partitions Z/256Z into 9 classes. Weights cluster in few strata.

Ring Differential

ByteRing::sub reveals sequential correlation. Residuals cluster near 0.

Torus Position

Page/offset split exploits clustering in quantized weights.

Float Structure

Byte-plane transpose. Exponent bytes carry far less entropy than mantissa.

Each observable reveals a different kind of redundancy invisible in the raw encoding. Shannon entropy is the floor; UOR algebra is the lens for reaching it.

Four compression modes, each targeting a different data profile:

Mode 0: Generic Mode 1: Stratum Mode 2: Float Mode 3: Quantized

Mode selection is automatic: analyze the first 1024 bytes, compute stratum histogram + torus page concentration + exponent entropy, pick the best mode.

Ring Algebra Explorer

Interactive Z/256Z ring operations. These are the primitives that power ring-differential coding.

00101010
10001001
OperationFormulaResultBinary

Stratum Analysis

Stratum = popcount. Bytes partition into 9 equivalence classes by number of set bits. Data that clusters in few strata compresses well with SPEC.

Stratum sizes: C(8,k) = [1, 8, 28, 56, 70, 56, 28, 8, 1]

Compression Ratios

Compression ratio = original / compressed. Higher is better. All compression is bit-perfect lossless.

Data TypeBest ModeRatioVisual

Float Byte-Plane Visualization

f32 values split into 4 byte planes. The MSB (sign+exponent) has extremely low entropy; the LSB (mantissa_lo) is near-random.

Stratum histogram per plane shows why plane 3 compresses so well with SPEC.