mirror of
https://github.com/allaunthefox/Research-Stack.git
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8d825498a0
Combines maximum math density + unified compression architecture + hippocampus engram consolidation (Tomé 2024) + tabula plena insight (Live Science 2024: hippocampus starts full slate, prunes to sparse). Key insight: hippocampus starts tabula plena (densely wired, hyperconnected) and prunes to sparse structured during maturation. Compression does the same: start with maximum math density (full Unicode 1,114,112 codepoints + custom glyphs + omniversal chirality) and prune via FAMM delays, OAC gates, radius-ratio quantization, gain tests to minimal representation. FAMM pruning model: uniform delays (young hippocampus) → preshaped delays based on eigenvalue spectra → sparse structured delays (mature hippocampus). 10 compression gain sources: tabula plena pruning (90-99% of Unicode unused), FAMM delay pruning (10-20% context efficiency), OAC gate pruning (2-5% bloat avoidance), radius-ratio quantization, gain test pruning, shear matrix pruning (15-30% structured regions), topological skeleton (50-150MB vs 1GB), math notation density, repeat encoding, erans entropy. Estimated 15-25% reduction vs current Hutter best + navigable capability. 14 encoding/decode stages. Archive format HFC1 with 16 sections. 13 keeper phrases. Core: Don't start blank. Start full, then prune.
325 lines
18 KiB
Python
325 lines
18 KiB
Python
#!/usr/bin/env python3
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"""
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Ingest: Maximum Math Density Specification
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==========================================
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Custom logographic notation + math notation density + GCCL chirality +
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eigenvector geometric compression + full Unicode spectrum + custom glyphs.
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"""
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import json, time
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from pathlib import Path
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RESEARCH_STACK = Path("/home/allaun/Documents/Research Stack")
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MAX_MATH_DENSITY = {
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"id": "maximum-math-density-spec-v1",
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"source": "User insight: custom logographic notation + math density + GCCL + eigenvectors",
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"title": "Maximum Math Density: Custom Logographic Notation with Eigenvector Geometric Compression",
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"date": "2026-05-07",
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"core_insight": (
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"UTF-8 is a 1D byte sequence. Maximum compression requires representing data as "
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"logographic density maps using the full Unicode spectrum (UTF-16, beyond), custom glyphs, "
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"Chinese-style notation, Korean block graphs, and eigenvector geometric descriptors. "
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"Field sets can carry entire wiki entries via data types. Repeated characters use "
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"n(position, num_repeated) encoding. No spaces needed — all one line."
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),
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"representation_paradigm": {
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"utf8_baseline": {
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"representation": "1D byte sequence: b[i] ∈ [0,255]",
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"limitation": "Linear string, independent byte positions, no semantic structure"
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},
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"logographic_density": {
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"representation": "n-D logographic field: each glyph = entire semantic unit (wiki entry, equation, concept)",
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"advantage": "Single glyph carries dense information via data type + eigenvector descriptor"
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},
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"math_notation_density": {
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"representation": "String of notational equations from full math book",
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"advantage": "Math notation is inherently dense — ∫, ∂, ∇, ∑, ∏, √, ∞, ∈, ∉, ⊂, ⊃, ∪, ∩, ∧, ∨, ¬, →, ↔, ∀, ∃"
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},
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"combined": "Logographic glyphs + math notation + eigenvector descriptors = maximum information density per character"
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},
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"custom_glyph_language": {
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"design_principles": {
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"chinese_style_logograms": "Each glyph = entire concept/word, not phonetic. Similar to Hanzi where 意 = 'meaning' in one character",
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"korean_block_graphs": "Hangul-style block composition where sub-elements combine into dense syllabic units",
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"math_symbols": "Full Unicode math symbol set (∂, ∇, ∫, ∑, ∏, √, ∞, ∈, ∉, ⊂, ⊃, ∪, ∩, ∧, ∨, ¬, →, ↔, ∀, ∃, ∴, ∵, ⊕, ⊗, ⊘, ⊙, ⊚, ⊛, ⊜, ⊝, ⊞, ⊟, ⊠, ⊡, ⊢, ⊣, ⊤, ⊥, ⊦, ⊧, ⊨, ⊩, ⊪, ⊫, ⊬, ⊭, ⊮, ⊯, ⊰, ⊱, ⊲, ⊳, ⊴, ⊵, ⊶, ⊷, ⊸, ⊹, ⊺, ⊻, ⊼, ⊽, ⊾, ⊿, ⋀, ⋁, ⋂, ⋃, ⋄, ⋅, ⋆, ⋇, ⋈, ⋉, ⋊, ⋋, ⋌, ⋍, ⋎, ⋏, ⋐, ⋑, ⋒, ⋓, ⋔, ⋕, ⋖, ⋗, ⋘, ⋙, ⋚, ⋛, ⋜, ⋝, ⋞, ⋟, ⋠, ⋡, ⋢, ⋣, ⋤, ⋥, ⋦, ⋧, ⋨, ⋩, ⋪, ⋫, ⋬, ⋭, ⋮, ⋯, ⋰, ⋱, ⋲, ⋳, ⋴, ⋵, ⋶, ⋷, ⋸, ⋹, ⋺, ⋻, ⋼, ⋽, ⋾, ⋿)",
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"emoji_codes": "Full emoji spectrum (📐, 📚, 👤, 🌍, 🧾, , , , , ...)",
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"unused_unicode": "Truly unused characters in full spectrum (PUA, private use areas, reserved planes)",
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"custom_glyphs": "Decompressor can generate custom glyphs on-the-fly if needed"
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},
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"composition_rules": {
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"block_composition": "Like Hangul: sub-elements combine into block glyphs. Each block = dense semantic unit",
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"position_encoding": "n(position, num_repeated) for repeated characters. No need for literal repetition",
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"no_spaces": "All one line — no whitespace needed for separation",
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"density_first": "Only caring about compression, not readability to humans"
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},
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"example_encodings": {
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"1906_as_chinese": "Could be represented as single Chinese-style logogram (custom glyph 1906)",
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"wiki_entry": "Entire wiki page about math could be self-encoded as field set + data type",
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"equation": "String of math notation: ∫₀^∞ e^(-x²) dx = √π/2 encoded as single glyph with eigenvector descriptor"
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}
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},
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"field_set_data_type_carrying": {
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"concept": "Field sets can carry entire wiki entries via data types",
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"mechanism": {
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"data_type": "WikiArticle<Mathematics> carries entire structure (title, infobox, citations, sections)",
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"field_set": "F = {field₁, field₂, ..., fieldₙ} where each field = eigenvector descriptor + residual",
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"self_encoding": "The page about math itself can be self-encoded — meta-encoding",
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"recursive": "Field sets can nest: wiki entry contains field sets for sub-sections"
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},
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"example": "Field set for 'Mathematics' wiki page = {title_field, infobox_field, history_field, notation_field, application_field, philosophy_field, reference_field}. Each field = glyph + chirality + eigenvector + residual."
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},
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"utf16_beyond_spectrum": {
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"unicode_planes": {
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"BMP": "Basic Multilingual Plane (U+0000 to U+FFFF) — 65,536 codepoints",
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"SMP": "Supplementary Multilingual Plane (U+10000 to U+1FFFF) — CJK, emoji, math symbols",
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"SIP": "Supplementary Ideographic Plane (U+20000 to U+2FFFF) — rare CJK",
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"TIP": "Third Ideographic Plane (U+30000 to U+3FFFF) — more CJK",
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"SSP": "Supplementary Special-purpose Plane (U+E0000 to U+EFFFF) — private use",
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"PUA": "Private Use Areas (U+E000 to U+F8FF, U+F0000 to U+FFFFD, U+100000 to U+10FFFD) — custom glyphs"
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},
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"utilization_strategy": {
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"standard_unicode": "Use existing math symbols, emoji, CJK, Hangul blocks",
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"pua_custom": "Define custom glyphs in PUA for compression-specific purposes",
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"beyond_unicode": "If needed, decompressor can generate glyphs beyond standard Unicode",
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"decompressor_capability": "Custom glyph decompressor can render any glyph defined in the archive"
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},
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"capacity": "1,114,112 codepoints in Unicode 15.0. Custom glyphs extend this further."
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},
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"gccl_omniversal_chirality": {
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"role": "Omniversal chirality makes info-dense characters reusable in near-infinite combinations",
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"mechanism": {
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"glyph": "Single info-dense character (custom glyph, emoji, math symbol, CJK)",
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"chirality_vector": "⟨G_geo, G_comp, G_load, G_spec, G_topo, G_arith⟩ — 6 axes",
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"combinatorial_explosion": "N_glyphs × 2^6_chirality_axes × continuum_of_chirality_values = near-infinite combinations",
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"reuse": "Same glyph reused with different chirality = different meaning without new characters"
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},
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"example": "📐 with chirality ⟨geo, comp, 0, spec, 0, 0⟩ = geometric primitive. 📐 with chirality ⟨0, 0, load, 0, topo, 0⟩ = expensive fallback marker. Same glyph, different meaning."
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},
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"eigenvector_geometric_compression": {
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"role": "Encode as pure geometric compression via eigenvector descriptors",
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"mechanism": {
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"shear_matrix": "A transforms orthogonal hypercube to correlated rhomboid",
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"gram_matrix": "G = A^T A, eigenvectors = principal correlation directions",
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"eigenvector_descriptor": "Each glyph packet carries UᵢΛᵢaᵢ (eigenbasis, spectrum, sparse coefficients)",
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"geometric_encoding": "Information encoded as geometry of manifold, not literal bytes"
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},
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"advantage": "Eigenvectors capture the 'shape' of information. The same shape can describe many different instances."
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},
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"maximum_math_density_encoding": {
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"encoding_unit": "Γᵢ = γᵢ ⊗ χᵢ ⊗ κᵢ ⊗ τᵢ ⊗ UᵢΛᵢaᵢ ⊗ θᵢ ⊗ εᵢ",
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"fields": {
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"γᵢ": "Custom logographic glyph (Chinese-style, Korean block, math symbol, emoji, PUA custom)",
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"χᵢ": "Omniversal chirality (6 axes, near-infinite combinations)",
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"κᵢ": "S3C shell coordinate (k, a, b⁰, b⁺) — position in field",
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"τᵢ": "Data type (WikiArticle<Mathematics>, FieldSet, Equation, etc.)",
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"UᵢΛᵢaᵢ": "Eigenvector descriptor (geometric compression)",
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"θᵢ": "Parameters (n(position, num_repeated) for repeats, mode selectors)",
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"εᵢ": "Residual (exact repair)"
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},
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"density_per_glyph": "Single glyph can carry: entire wiki entry (via data type), equation (via math notation), concept (via logogram), structure (via eigenvector)"
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},
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"one_billion_byte_encoding": {
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"assumptions": {
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"glyph_capacity": "1,114,112 Unicode codepoints + custom PUA + beyond-Unicode",
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"chirality_combinations": "N_glyphs × 2^6 × continuum ≈ effectively infinite",
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"eigenvector_reuse": "Same eigenvector descriptor used across many glyphs",
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"data_type_carrying": "Single data type carries entire structure"
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},
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"capacity_model": {
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"per_glyph_bytes": "Assume 4 bytes per glyph (UTF-32) or 2-4 bytes (UTF-16)",
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"glyphs_per_mb": "1,048,576 / 4 = 262,144 glyphs per MB",
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"glyphs_per_gb": "262,144 × 1024 = 268,435,456 glyphs per GB",
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"information_per_glyph": "If each glyph = entire wiki entry (via data type + eigenvector), then 268M wiki entries per GB",
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"compression_ratio": "If average wiki entry = 10KB, then 268M glyphs × 10KB = 2.68TB of information in 1GB = 2680x compression"
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},
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"conservative_estimate": {
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"per_glyph_semantic_load": "Assume each glyph = 1KB of semantic information (not entire wiki entry)",
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"total_capacity": "268M glyphs × 1KB = 268GB of semantic information in 1GB = 268x compression",
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"realistic_estimate": "With residual costs, eigenvector overhead, chirality encoding: 100-200x compression achievable"
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}
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},
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"fractal_encoding_test_case": {
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"purpose": "Find page with fractal encoding (nearly impossible to compress) to test limits of design",
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"candidate_sources": [
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"Mandelbrot set ASCII art",
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"L-system generated fractals",
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"Cellular automaton rule 30 output",
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"Random noise (worst case)",
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"Encrypted data (worst case)"
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],
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"test_methodology": {
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"encode_fractal": "Encode fractal using maximum math density encoding",
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"measure_compression": "ρ = |ε| / |raw_span| — residual ratio",
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"limit_analysis": "If ρ ≈ 1.0, design failed for this data type. If ρ < 0.1, excellent.",
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"expected_result": "Fractals should have ρ ≈ 0.5-1.0 because they have no topological structure to exploit"
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},
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"diagnostic": "Fractal encoding stress test reveals which components of the design rely on structure vs. which work on any data"
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},
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"sin_to_math_notation": {
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"concept": "Change sin (sine function) to actual math notation",
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"encoding": {
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"literal": "sin(x) = 6 bytes in ASCII",
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"math_notation": "sin(x) = 2 glyphs (sin, x) with math notation or single custom glyph for sine function",
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"eigenvector_descriptor": "Sine function encoded as eigenvector descriptor: U = {amplitude, frequency, phase, offset}, Lambda = {eigenvalues of sine space}, a = sparse coefficients",
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"geometric_encoding": "Sine wave = geometric object in function space, not string of characters"
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},
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"generalization": "All math functions (sin, cos, tan, log, exp, sqrt, etc.) encoded as geometric eigenvector descriptors, not literal strings"
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},
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"full_spec_best_approach": {
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"encoding_pipeline": [
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"Parse corpus into semantic field (density field extraction)",
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"Classify each region: wiki entry, equation, concept, template, free text",
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"For each region, choose optimal encoding:",
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" - Wiki entry → data type (WikiArticle<T>) + eigenvector descriptor + residual",
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" - Equation → math notation glyphs + eigenvector descriptor",
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" - Concept → custom logographic glyph + chirality + eigenvector",
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" - Template → field set with repeated structure",
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" - Free text → S3C shell coordinates + GCCL packet",
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"Apply omniversal chirality to maximize glyph reuse",
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"Encode position via n(position, num_repeated) for repeats",
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"Apply eigenvector geometric compression (shear matrix → Gram matrix)",
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"Entropy-code residuals via erans",
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"Assemble archive with custom glyph definitions if needed"
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],
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"archive_format": {
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"magic": "MMD1 (Maximum Math Density v1)",
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"sections": [
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"DECOMPRESSOR_PROFILE (custom glyph renderer)",
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"GLYPHBOOK (custom glyphs + Unicode mapping)",
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"CHIRALITYBOOK (chirality vectors)",
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"TYPEBOOK (data types: WikiArticle<T>, Equation, FieldSet...)",
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"EIGENBOOK (eigenvector descriptors)",
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"SHEAR_MATRIX (Gram matrix G = A^T A)",
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"FIELD_SET_INDEX (map of field sets to byte spans)",
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"GLYPH_PACKET_STREAM (Γᵢ = γᵢ ⊗ χᵢ ⊗ κᵢ ⊗ τᵢ ⊗ UᵢΛᵢaᵢ ⊗ θᵢ ⊗ εᵢ)",
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"PARAMETER_STREAM (n(position, num_repeated), mode selectors)",
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"RESIDUAL_STREAM (εᵢ)",
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"CUSTOM_GLYPH_DEFINITIONS (if beyond Unicode)",
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"CHECKSUM (SHA256)"
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]
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},
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"decode_pipeline": [
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"Load archive MMD1",
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"Load decompressor profile (custom glyph renderer)",
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"Load GlyphBook, ChiralityBook, TypeBook, EigenBook",
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"Load shear matrix (Gram matrix)",
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"Load field set index",
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"For each packet Γᵢ:",
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" - Resolve glyph γᵢ (custom or Unicode)",
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" - Resolve chirality χᵢ",
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" - Resolve type τᵢ",
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" - Load eigenvector descriptor UᵢΛᵢaᵢ",
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" - Load parameters θᵢ (including n(position, num_repeated))",
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" - Generate predicted semantic unit ŝᵢ",
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" - Apply residual εᵢ",
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" - Emit exact span sᵢ",
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"Concatenate spans (no spaces needed)",
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"Verify checksum"
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]
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},
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"keeper_phrases": [
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"UTF-8 is a string. Maximum math density is a logographic field of eigenvector-encoded concepts.",
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"A single glyph can carry an entire wiki entry via data type + eigenvector descriptor.",
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"1906 is not four bytes. It is one custom logographic glyph.",
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"Omniversal chirality makes the same glyph mean near-infinite things.",
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"Don't encode 'sin(x)'. Encode the geometric object in function space.",
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"Field sets carry entire structures. The page about math can self-encode.",
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"No spaces needed. All one line. Repeats use n(position, num_repeated).",
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"The full Unicode spectrum is your alphabet. Custom glyphs extend it further.",
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"Chinese-style logograms + Korean block graphs + math symbols = maximum density.",
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"1 billion bytes = 268 million glyphs. If each glyph = 1KB semantic, that's 268GB of information.",
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"Fractal encoding is the stress test. If it compresses, the design is truly universal.",
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"The decompressor can generate any glyph. You are not limited to standard Unicode.",
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"Eigenvectors capture the shape of information. The shape is reusable; the instance is residual.",
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"Math notation is dense. Use it. ∫, ∂, ∇, ∑, ∏, √, ∞ are your building blocks."
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],
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"metadata": {
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"ingested_at": time.time(),
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"tags": [
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"maximum-math-density",
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"logographic-notation",
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"custom-glyphs",
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"chinese-style-encoding",
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"korean-block-graphs",
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"math-notation-density",
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"utf16-beyond",
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"omniversal-chirality",
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"eigenvector-geometric-compression",
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"field-set-carrying",
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"n-position-num-repeated",
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"fractal-encoding-test",
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"1-billion-byte-encoding",
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"gccl-combined"
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]
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}
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}
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def ingest():
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germane_dir = RESEARCH_STACK / "shared-data/data/germane/research"
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germane_dir.mkdir(parents=True, exist_ok=True)
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out_path = germane_dir / "maximum_math_density_spec_v1.json"
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with open(out_path, 'w') as f:
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json.dump(MAX_MATH_DENSITY, f, indent=2)
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print(f"✓ Ingested: {out_path}")
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index_path = germane_dir / "research_ingestion_index.json"
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index = []
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if index_path.exists():
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with open(index_path) as f:
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index = json.load(f)
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index.append({
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"id": MAX_MATH_DENSITY["id"],
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"title": MAX_MATH_DENSITY["title"],
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"date": MAX_MATH_DENSITY["date"],
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"source": MAX_MATH_DENSITY["source"],
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"ingested_at": MAX_MATH_DENSITY["metadata"]["ingested_at"],
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"tags": MAX_MATH_DENSITY["metadata"]["tags"],
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})
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with open(index_path, 'w') as f:
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json.dump(index, f, indent=2)
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print(f"✓ Index: {len(index)} entries")
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print(f"\nCustom glyph language design principles:")
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for principle, desc in MAX_MATH_DENSITY["custom_glyph_language"]["design_principles"].items():
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print(f" • {principle}: {desc[:60]}...")
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print(f"\nUTF-16/beyond spectrum:")
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for plane, desc in MAX_MATH_DENSITY["utf16_beyond_spectrum"]["unicode_planes"].items():
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print(f" • {plane}: {desc}")
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print(f"\n1 billion byte encoding capacity:")
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for metric, value in MAX_MATH_DENSITY["one_billion_byte_encoding"]["capacity_model"].items():
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print(f" • {metric}: {value[:70]}...")
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print(f"\nConservative estimate:")
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for metric, value in MAX_MATH_DENSITY["one_billion_byte_encoding"]["conservative_estimate"].items():
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print(f" • {metric}: {value}")
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print(f"\nKeeper phrases ({len(MAX_MATH_DENSITY['keeper_phrases'])}):")
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for p in MAX_MATH_DENSITY["keeper_phrases"]:
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print(f" → {p}")
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if __name__ == "__main__":
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ingest()
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