KHENOR studies whether mathematical relations between apparently different byte sequences can reduce storage. The public file lab now uses KH4.1 with exact XOR-recurrence fitting and backward decoding for KH4.0. A separate private prototype (KH6) tests sparse exceptions to affine transformations. This is engineering research, not a proven new theorem or general-purpose compression breakthrough.
Read an input file piece by piece; select a compact, exact representation or ordinary compression fallback; verify each decoded block with SHA-256.
The user-owned decoder must have enough information to recover every byte. Desktop disk streaming removes the former 4 MB demo cap where browser file APIs permit.
Detect when a later block is approximately an affine transformation of a previous block. Save the parameters and the exact positions of deviations, then verify the reconstruction.
Derived from algebraic properties; novelty and commercial advantage are not established. The experimental decoder is not distributed through this website.
The public codec now solves a GF(2) linear system over all eight bitplanes to propose short XOR-of-lags generators. A candidate is written only if every input byte matches the equation and its complete encoded frame is smaller than the alternatives. Unlike content recognition, this calculation only sees bytes.
Linear recurrence discovery is well-established mathematics. The goal here is a verifiable extension of the public experimental codec, not a claim of universal superiority. It performs poorly on arbitrary incompressible bytes.
| Dataset | Original | KH4.0 | KH4.1 | Zstd -3 |
|---|---|---|---|---|
| Synthetic XOR recurrence (512 KiB) | 524,288 B | 524,434 B | 200 B | 524,313 B |
| Real PDF | 3,516 B | 2,236 B | 2,236 B | 2,167 B |
| Real JavaScript source | 12,633 B | 5,110 B | 5,110 B | 5,168 B |
| Real PNG | 263,754 B | 252,347 B | 252,347 B | 252,931 B |
| ZIP binary | 24,141 B | 23,063 B | 23,063 B | 22,886 B |
Exact binary reconstruction verified; the synthetic XOR source was deliberately generated from an XOR recurrence, not sampled from real-world data. For ordinary files KH4.1 selected the same Deflate fallback as KH4.0. Zstd comparison uses zstd -3 directly on each uncompressed source file; KH4 file containers include filename, framing and checksums, so the formats are not identical in metadata. Decoder and runtime distribution cost is excluded. Not proof of a broadly superior codec.
| Dataset | Source bytes | KH5 | KH6 | Zstd -3 |
|---|---|---|---|---|
| Synthetic: nonlocal sparse affine | 40,960 | 41,400 | 37,328 | 40,973 |
| Synthetic: exact affine | 40,960 | 37,306 | 37,306 | 40,973 |
| Real JavaScript source | 12,633 | 5,792 | 5,792 | 5,292 |
| Real PDF | 25,983 | 25,574 | 25,574 | 24,839 |
| Real PNG | 344,167 | 333,692 | 333,692 | 326,714 |
| Random bytes | 65,536 | 66,187 | 66,187 | 65,549 |
All sizes are complete test archives and verified exact reconstructions. Synthetic sparse-affine data were deliberately chosen to exercise the new operator. KH6 is still slower in some workloads, has a 64 MiB in-memory R&D limit, and cannot be read by the public KH4.1 decoder. Zstandard was used via zstd -3 on each dataset.
Not every arbitrary file has a short lossless description. Decoder size, reference dictionaries and shared operator vocabulary must count in a fair comparison. Real-world usefulness depends on compression ratio, throughput, memory, latency and random-access performance—not a single synthetic test.
Streamed private mathematical references, faster native implementations, adversarial/fuzz testing, cross-file reuse, stable format compatibility, and customer workloads. We will benchmark against Zstd and deduplicating archives rather than claiming that any file can shrink to a sentence.
