Compression Demo
Lossless compression using UOR ring algebra observables. Every byte is decomposed through algebraic structure to find its irreducible representation.
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:
Popcount partitions Z/256Z into 9 classes. Weights cluster in few strata.
ByteRing::sub reveals sequential correlation. Residuals cluster near 0.
Page/offset split exploits clustering in quantized weights.
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 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.
| Operation | Formula | Result | Binary |
|---|
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 Type | Best Mode | Ratio | Visual |
|---|
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.