Archive HACHIMOJI_DNA_ENCODING.md

archive/2026-07-02/docs/HACHIMOJI_DNA_ENCODING.md

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+# Hachimoji DNA Encoding Specification
+
+**Version:** 0.1
+**Status:** Draft
+**Purpose:** Computational substrate, not compression format.
+
+## 1. Alphabet
+
+Eight bases, ASCII-ordered for monotone lexicographic sorting:
+
+| Index | Base | Phase | Bits |
+|-------|------|-------|------|
+| 0 | A | 0° | 000 |
+| 1 | B | 45° | 001 |
+| 2 | C | 90° | 010 |
+| 3 | G | 135° | 011 |
+| 4 | P | 180° | 100 |
+| 5 | S | 225° | 101 |
+| 6 | T | 270° | 110 |
+| 7 | Z | 315° | 111 |
+
+**Key property:** ASCII sort order = index order = lexicographic rank.
+This means `sorted(sequences)` produces the same order as `sorted(sequences, key=dna_to_int)`.
+
+## 2. Symbol Encoding
+
+Each symbol (byte, word, or chunk) maps to a fixed-length DNA sequence.
+
+- **1-byte chunks:** 256 symbols → 3 bases/symbol (8³ = 512 ≥ 256)
+- **2-byte chunks:** 65,536 symbols → 6 bases/symbol (8⁶ = 262,144 ≥ 65,536)
+- **n unique symbols:** `ceil(log₈(n))` bases/symbol
+
+The LUT assigns sequences by rank:
+- Rank 0 → "AAA...A" (lowest)
+- Rank 1 → "AAA...B"
+- Rank n → highest sequence
+
+## 3. Monotone Property
+
+If symbols are ranked by frequency (most frequent = rank 0), then:
+- Most frequent symbol → shortest/lowest DNA sequence
+- Lexicographic sort of DNA = frequency sort of symbols
+- This is NOT compression — it's structured representation
+
+## 4. LUT Format
+
+```json
+{
+  "format": "hachimoji_lut_v1",
+  "bases": "ABCGPSTZ",
+  "chunk_size": 1,
+  "bases_per_symbol": 3,
+  "entries": {
+    "AAA": "20",
+    "AAB": "65",
+    "AAC": "74"
+  }
+}
+```
+
+- Keys: DNA sequences (base-8 encoded ranks)
+- Values: hex-encoded byte chunks
+- Portable: JSON, human-readable, self-describing
+
+## 5. File Format
+
+```
+.dna file:  raw DNA sequence (text, A-Z only)
+.lut file:  JSON LUT (see above)
+.meta file: encoding metadata (optional JSON)
+```
+
+## 6. Roundtrip Guarantee
+
+```
+decode(encode(data)) == data
+```
+
+Verified at encode time. No lossy steps. No approximation.
+
+## 7. Computational Properties
+
+The DNA sequence is not just encoded data — it's a computational address:
+
+- **Sequence index** (base-8 integer) = symbolic rank
+- **Lexicographic order** = rank order (monotone)
+- **LUT lookup** = O(1) per symbol
+- **Sortable** by standard string sort (= rank sort)
+- **Portable** across systems (plain text + JSON)
+
+## 8. Integration with SilverSight
+
+- `HachimojiCodec.lean` — formal encode/decode specification
+- `HachimojiLUT.lean` — LUT hierarchy (k=2, k=6, k=50)
+- `PhaseCircle` — ℤ/360ℤ address space
+- `dna_lut.py` — Python LUT implementation
+- `dna_encode_file.py` — file encoder/decoder
+
+## 9. Not This
+
+- ❌ Not a compression format (bits/byte not the goal)
+- ❌ Not a DNA storage format (no synthesis/sequencing constraints)
+- ❌ Not a cryptographic scheme (no security claims)
+- ✅ A computational substrate for manifold/QUBO/eigenvalue work