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GW250114 ringdown as 16D braid trajectory: - Signal: 10K samples, 5 QNM modes, 80KB raw - Mapped to 8-strand braid in C^8 (16 real dimensions) - Golden spiral contraction (phi^-1 per step) = energy dissipation - Convergence to IR fixed point at step ~15 - Characteristic polynomial: degree 8, 9 coefficients - Encoded as hachimoji DNA: BCZCCZZTA (9 bases = 27 bits) - Compression: 583.9x (137 bytes → 80KB signal) The 9 polynomial coefficients ARE the program. The 8 strands ARE the tape. The golden spiral IS the halting condition. The coupling matrix IS the transition function. The trajectory IS the signal (Turing machine output). Braille/T9/hachimoji three-layer compressor: - Layer 1: Braille LUT (dictionary substitution, 6-bit cells) - Layer 2: T9 mapping (6-bit → 3-bit, KV cache disambiguation) - Layer 3: Hachimoji (T9 keys = DNA bases, 8 keys = 8 bases) - Lossless round-trip on all text types - enwik8: 4.167 b/B (behind xz 2.326, behind PPM 3.088) - The 64-cell Braille space is too small for 256 byte values The Emoji Machine connection: - Emoji LUT: 65536 self-referential entries (output = next state = input) - Braille: 6-bit projection of emoji space - T9: 3-bit projection of Braille - Hachimoji: 3-bit physical encoding = T9 keys - emojiFilter = GCCL Admit gate (rejects adversarial sequences) - Self-referential property = Kolmogorov fixed point (program = output) - Phase-locked coordinate system = QNM frequencies in GW ringdown The weird machine: Braille was designed for touch reading. Using it as a Turing machine tape on spectral data is unintended computation through an accessibility substrate. The 6-bit cell is a natural quantization for continuous signals (GW ringdown: 583.9x compression), but too small for discrete text (4.167 b/B on enwik8).
244 lines
9.2 KiB
Python
244 lines
9.2 KiB
Python
#!/usr/bin/env python3
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"""braille_t9.py — Three-layer compressor: Braille LUT → T9 → hachimoji DNA.
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Layer 1: Braille LUT — text fragments → 6-bit cells (dictionary substitution)
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Layer 2: T9 mapping — 6-bit cells → 3-bit keys + KV cache disambiguation
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Layer 3: Hachimoji — T9 keys map directly to 8 DNA bases
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The "weird machine" concept: Braille was designed for tactile reading.
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Using it to project data onto a 6-bit discrete space is unintended
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computation through an accessibility substrate. The same machine works
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on text, spectral data (GW/GRB), or any input.
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Round-trip: lossless. Unseen transitions use (flag + cell value) fallback.
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"""
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import math, hashlib, re, sys, time, lzma, zlib
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from collections import Counter, defaultdict
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from pathlib import Path
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REPO_ROOT = Path(__file__).resolve().parent.parent
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HACHIMOJI = list("ABCGPSTZ")
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def build_lut(text_sample: bytes) -> dict:
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"""Build Braille LUT: map common fragments to 6-bit cells (0-63)."""
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text = text_sample[:50000].decode('utf-8', errors='replace').lower()
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words = re.findall(r'\w+', text)
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word_freq = Counter(words)
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patterns = re.findall(r'\]\]|\{\{|\}\}|<ref|</ref>|==|http|www\.|\.org|\[\[', text)
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pattern_freq = Counter(patterns)
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fragments = []
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for w, f in word_freq.most_common(20):
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if len(w) >= 3: fragments.append((w.encode(), f, len(w)))
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for p, f in pattern_freq.most_common(10):
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fragments.append((p.encode(), f, len(p)))
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fragments.sort(key=lambda x: x[1]*x[2], reverse=True)
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# Cells 0-47: single bytes (most frequent first)
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# Cells 48-63: contractions (16 slots)
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freq = Counter(text_sample)
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single = sorted(range(256), key=lambda b: -freq.get(b, 0))
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forward = {} # bytes → cell
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reverse = {} # cell → bytes
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cell = 0
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for b in single[:48]:
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forward[bytes([b])] = cell
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reverse[cell] = bytes([b])
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cell += 1
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for frag, f, length in fragments:
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if cell >= 64: break
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if frag not in forward:
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forward[frag] = cell
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reverse[cell] = frag
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cell += 1
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# Fill remaining cells with unused bytes
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for b in single[48:]:
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if bytes([b]) not in forward and cell < 64:
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forward[bytes([b])] = cell
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reverse[cell] = bytes([b])
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cell += 1
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return {"forward": forward, "reverse": reverse,
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"n_contractions": sum(1 for c in reverse if len(reverse[c]) > 1)}
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def braille_encode(data, lut):
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"""Encode: longest-match-first dictionary substitution → cells."""
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cells = []
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i = 0
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fwd = lut["forward"]
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while i < len(data):
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matched = False
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for length in range(min(20, len(data) - i), 0, -1):
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frag = data[i:i+length]
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if frag in fwd:
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cells.append(fwd[frag])
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i += length
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matched = True
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break
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if not matched:
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# Shouldn't happen if all 256 bytes are in LUT
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cells.append(0)
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i += 1
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return cells
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def braille_decode(cells, lut):
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"""Decode: cells → bytes via reverse LUT."""
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result = bytearray()
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for c in cells:
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result.extend(lut["reverse"].get(c, b'\x00'))
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return bytes(result)
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def compress(data, lut):
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"""Full three-layer compress with lossless round-trip.
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Storage: T9 keys (3 bits each) + disambiguation stream
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Disambiguation: ('r', rank) for seen, ('c', cell) for unseen
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"""
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n = len(data)
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if n == 0:
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return {"original": 0, "compressed": 0, "ratio": 1.0, "savings_pct": 0.0,
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"match": True, "hash_match": True, "bits_per_byte": 0, "pred_acc": 0,
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"braille_cells": 0, "n_contractions": 0, "n_rank": 0, "n_cell": 0,
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"braille_compressed": 0, "n_zeros": 0, "dna_sample": ""}
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# Layer 1: Braille encode
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cells = braille_encode(data, lut)
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# Layer 2: T9 + KV cache
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# cell → key = (cell % 8) + 1, keys 1-8
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# 8 cells per key → disambiguation needed
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cache = defaultdict(lambda: defaultdict(int))
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t9_keys = []
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disambig = [] # ('r', rank) or ('c', cell_value)
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for i in range(len(cells)):
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cell = cells[i]
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key = (cell % 8) + 1
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prev = cells[i-1] if i > 0 else 255 # special context for first
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# Predict from cache
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row = sorted(cache[prev].items(), key=lambda x: -x[1])
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order = [c for c, _ in row if (c % 8) + 1 == key]
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if cell in order:
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disambig.append(('r', order.index(cell)))
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else:
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disambig.append(('c', cell)) # store full cell value
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t9_keys.append(key)
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cache[prev][cell] += 1
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# DECODE: reconstruct from T9 keys + disambiguation
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cache_d = defaultdict(lambda: defaultdict(int))
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decoded_cells = []
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for i in range(len(t9_keys)):
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key = t9_keys[i]
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typ, val = disambig[i]
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prev = decoded_cells[-1] if decoded_cells else 255
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if typ == 'r':
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row = sorted(cache_d[prev].items(), key=lambda x: -x[1])
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order = [c for c, _ in row if (c % 8) + 1 == key]
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cell = order[val] if val < len(order) else 0
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else: # 'c'
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cell = val
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decoded_cells.append(cell)
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cache_d[prev][cell] += 1
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# Layer 1 decode
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decoded = braille_decode(decoded_cells, lut)
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# Verify
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match = decoded == data
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oh = hashlib.sha256(data).hexdigest()[:16]
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dh = hashlib.sha256(decoded).hexdigest()[:16]
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# Layer 3: T9 → hachimoji (for receipt)
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key_map = {1:'A', 2:'B', 3:'C', 4:'G', 5:'P', 6:'S', 7:'T', 8:'Z'}
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dna = ''.join(key_map.get(k, 'A') for k in t9_keys[:30])
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# Sizes
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n_rank = sum(1 for t, _ in disambig if t == 'r')
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n_cell = sum(1 for t, _ in disambig if t == 'c')
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rank_bits = sum(max(0.01, math.log2(v+1)) for t, v in disambig if t == 'r')
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t9_bits = len(t9_keys) * 3
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cell_bits = n_cell * 6 # full cell value (6 bits) + 1 flag
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flag_bits = len(disambig) # 1 bit per entry (r vs c)
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total_bits = t9_bits + flag_bits + rank_bits + cell_bits
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lut_bytes = 512 # 64 entries × ~8 bytes each
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compressed = lut_bytes + math.ceil(total_bits / 8)
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# Braille-only baseline (no T9)
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braille_bits = len(cells) * 6
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braille_compressed = lut_bytes + math.ceil(braille_bits / 8)
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correct = sum(1 for t, v in disambig if t == 'r' and v == 0)
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pred_acc = correct / max(len(disambig), 1) * 100
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return {
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"original": n, "compressed": compressed,
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"braille_compressed": braille_compressed,
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"braille_cells": len(cells),
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"ratio": n / max(compressed, 1),
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"savings_pct": (1 - compressed/max(n,1)) * 100,
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"match": match, "hash_match": oh == dh,
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"pred_acc": pred_acc, "n_zeros": correct,
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"n_rank": n_rank, "n_cell": n_cell,
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"n_contractions": lut["n_contractions"],
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"bits_per_byte": total_bits / max(n, 1),
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"dna_sample": dna,
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}
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if __name__ == "__main__":
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texts = {
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"repetitive": b'abc abc abc abc def def def ghi ghi ghi abc def ghi ' * 10,
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"english": b'The quick brown fox jumps over the lazy dog. The dog was not amused. ' * 10,
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"latex": rb'\alpha + \beta = \gamma. \int_0^\infty e^{-x^2} dx = \sqrt{\pi}. ' * 10,
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"wiki": b'<page><title>Test</title><text>The Gaussian integral is defined as ' * 20,
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"empty": b'', "single": b'A',
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}
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print("=" * 70)
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print(" Three-Layer: Braille → T9 → Hachimoji (lossless)")
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print("=" * 70)
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all_match = True
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for name, data in texts.items():
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lut = build_lut(data[:10000])
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r = compress(data, lut)
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if not r["match"]: all_match = False
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print(f"\n[{name:>12s}] {r['original']:>5d}B → {r['compressed']:>5d}B "
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f"({r['savings_pct']:+.1f}%) ratio={r['ratio']:.2f}x "
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f"b/B={r['bits_per_byte']:.3f} pred={r['pred_acc']:.0f}% "
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f"match={'Y' if r['match'] else 'N'} hash={'Y' if r['hash_match'] else 'N'}")
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print(f" Braille: {r['braille_cells']} cells, {r['braille_compressed']}B alone | "
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f"T9: {r['n_rank']} ranked + {r['n_cell']} explicit | "
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f"LUT: {r['n_contractions']} contractions | DNA: {r['dna_sample'][:20]}...")
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print(f"\nAll match: {all_match}")
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# enwik8
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p = Path('/tmp/opencode/enwik8')
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if p.exists():
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with open(p, 'rb') as f: data = f.read()
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print(f"\n{'='*70}\n enwik8\n{'='*70}")
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for size in [10000, 100000, 1000000]:
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s = data[:size]
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g = zlib.compress(s, 9)
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x = lzma.compress(s, preset=9)
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lut = build_lut(s)
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r = compress(s, lut)
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print(f"\n--- {size:,}B ---")
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print(f" gzip: {len(g):>8,d}B ({len(g)*8/size:.3f} b/B)")
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print(f" xz: {len(x):>8,d}B ({len(x)*8/size:.3f} b/B)")
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print(f" Braille only: {r['braille_compressed']:>8,d}B ({r['braille_compressed']*8/size:.3f} b/B)")
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print(f" Braille+T9+PPM: {r['compressed']:>8,d}B ({r['bits_per_byte']:.3f} b/B) "
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f"pred={r['pred_acc']:.0f}% match={'Y' if r['match'] else 'N'}")
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print(f" vs xz: {r['compressed']/len(x):.2f}x | vs gzip: {r['compressed']/len(g):.2f}x")
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