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ingest: Hypercube → Hyper-Rhomboid Hutter Prize implications
7 concrete changes to enwik compression: - Shear pre-transform: 15-30% on structured regions (40% of enwik) - S3C shell position encoding: 5-10% positional overhead reduction - OAC speculative motifs: avoids 2-5% bloat, enables aggressive testing - FAMM preshaped context: 10-20% context efficiency gain - PIST n-D token encoding: 5-8% with cross-position probability sharing - Gram matrix dictionary: MB → KB overhead - Metric entropy coding: 10-15% entropy reduction in structured regions The Big Fold: 4 separate Hutter components collapse into 1 shear matrix. Estimated 12-22% overall compressed size reduction.
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Brandon Schneider
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4-Infrastructure/shim/ingest_hutter_rhomboid.py
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4-Infrastructure/shim/ingest_hutter_rhomboid.py
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#!/usr/bin/env python3
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"""
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Hypercube → Hyper-Rhomboid: Hutter Prize Implications
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=======================================================
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What changes for enwik8/enwik9 compression when you shear
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the token space instead of treating positions independently.
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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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HUTTER_RHOMBOID = {
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"id": "hypercube-rhomboid-hutter-prize",
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"source": "User query — what does hypercube → hyper-rhomboid change for Hutter Prize",
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"title": "Sheared Token Manifolds: Hypercube → Hyper-Rhomboid Implications for Hutter Prize Compression",
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"date": "2026-05-07",
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"current_hutter_paradigm": {
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"approach": "1D token sequence → probability distribution per position → entropy code",
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"geometry": "Orthogonal hypercube: each token position is an independent axis. Context window = fixed-size orthogonal slice.",
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"limitation": (
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"Wikipedia text is NOT a sequence of independent positions. "
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"It is a sheared manifold where: infoboxes repeat with minor variations, "
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"citations share author/year/title structure, headings form a hierarchy, "
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"lists are parallel constructions, markup is templated, "
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"and natural language has syntactic correlation at every scale."
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),
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"waste": (
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"An orthogonal model pays separately for every occurrence of '{{cite web|url=' "
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"even though the 5000th citation has the same structure as the 1st. "
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"The axes are at 90° — no sharing of probability mass across correlated positions."
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)
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},
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"rhomboid_paradigm": {
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"approach": "Token space as sheared manifold → correlated positions share axes → entropy code residuals only",
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"geometry": (
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"Hyper-rhomboid: token position axes lean into each other proportional to "
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"mutual information. Repeated structures collapse into shared shells. "
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"The shear matrix A IS the compression model."
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),
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"key_insight": (
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"You don't compress the text. You compress the shear matrix that makes "
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"the text look like noise plus a small residual. The shear matrix is "
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"learned once from the corpus structure; the residual is what you actually "
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"entropy-code."
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)
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},
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"concrete_changes": {
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"pre_transform": {
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"title": "Shear Pre-Transform Before Entropy Coding",
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"current": "Raw bytes → LZ/BWT/PPM/transformer → entropy code",
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"rhomboid": "Raw bytes → S3C shell parse → shear into rhomboid → residual extraction → entropy code",
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"mechanism": (
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"Parse Wikipedia into structural regions (article, infobox, citation, list, heading, template). "
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"Each region type has a canonical shell coordinate. Within each shell, sheared axes encode "
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"the expected structure. Only deviations from the sheared template are entropy-coded."
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),
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"estimated_gain": "15-30% on structured regions (infoboxes, citations, templates — ~40% of enwik)"
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},
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"s3c_shell_batching": {
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"title": "S3C Shell Coordinates for Token Position Encoding",
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"current": "Position encoded as absolute byte offset or transformer positional embedding",
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"rhomboid": "Position encoded as S3C shell (k, a, b⁰, b⁺) — shell = structural context, offset = within-structure position",
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"mechanism": (
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"k = structural depth (0=character, 1=word, 2=phrase, 3=sentence, 4=paragraph, 5=section, 6=article). "
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"a = position within that structure. b⁰ = remaining length. "
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"The throat (a ≈ b⁰) is where compression is maximal — midpoint of a repeated structure "
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"where the model has maximum predictive confidence."
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),
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"estimated_gain": "5-10% on positional encoding overhead"
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},
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"oac_speculative_compression": {
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"title": "OAC Speculative Motif Testing Without Output Pollution",
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"current": "Compressor commits to a transform; if it's bad, output is bloated",
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"rhomboid": "Test compression motifs as Observer-Admissible Cavities — temporary exploration manifolds that don't commit to output unless L(motif) + L(residual) < L(raw)",
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"mechanism": (
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"For each structural region, try multiple shear matrices (citation-shear, list-shear, "
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"template-shear, plaintext-shear). The OAC gate only emits the one that beats raw encoding. "
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"Failed shears become FAMM scars — never tried again for similar regions."
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),
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"estimated_gain": "Avoids 2-5% bloat from bad motif choices; enables aggressive speculation"
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},
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"famm_context_warping": {
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"title": "FAMM Preshaped Context Windows",
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"current": "Fixed context window (e.g., 1024 tokens) for transformer/ppm models",
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"rhomboid": "Preshaped (sheared) context: stretches for high-entropy regions, compresses for low-entropy template regions",
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"mechanism": (
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"Context window is not fixed-length; it's fixed-information. "
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"In a citation template, 50 bytes of context is enough (structure is predictable). "
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"In free text, 500 bytes may be needed. The FAMM delay line preshapes the context "
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"window per shell class — shearing time into the information domain."
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),
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"estimated_gain": "10-20% context efficiency — more predictive power per context byte"
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},
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"pist_token_manifold": {
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"title": "PIST n-Dimensional Token Encoding",
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"current": "Tokens encoded as 1D integer IDs",
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"rhomboid": "Tokens encoded as n-dimensional PIST coordinates (k, t, fiber₀, ..., fiber_{n-2}) where n = number of correlated features",
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"mechanism": (
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"Each token gets: k = frequency/shell class, t = local offset, "
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"fiber₀ = part-of-speech class, fiber₁ = dependency depth, "
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"fiber₂ = template membership, fiber₃ = capitalization pattern. "
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"The fiber dimensions are the sheared axes — they encode correlation structure "
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"that a 1D token ID loses."
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),
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"estimated_gain": "5-8% on token encoding; enables cross-position probability sharing"
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},
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"gram_dictionary": {
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"title": "Gram Matrix as Learned Compression Dictionary",
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"current": "Static dictionary (LZ) or learned embeddings (transformer)",
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"rhomboid": "Gram matrix G = A^T A of the shear transform IS the dictionary — eigenvectors are principal correlation directions, eigenvalues are compression gains",
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"mechanism": (
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"The shear matrix A is learned by minimizing: L(A) + L(residual | A). "
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"A is stored once in the compressed header. The decoder applies A^{-1} "
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"to reconstruct expected structure, then replays residuals. "
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"A is tiny compared to the text — a few KB for the entire corpus."
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),
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"estimated_gain": "Dictionary overhead reduced from MB to KB"
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},
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"metric_entropy_code": {
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"title": "Information-Geometric Entropy Coding",
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"current": "Entropy coding assumes independent symbols (product distribution)",
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"rhomboid": "Entropy coding uses the sheared metric g_{μν} — symbols are coded relative to their position in the sheared manifold, not independently",
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"mechanism": (
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"The coding probability for token x_i is conditioned on its sheared context: "
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"P(x_i | context) = P(x_i | g_{μν}(context)). "
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"In a heavily sheared region (template), P is sharply peaked — near 1.0 for expected token. "
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"In a flat region (free text), P is broad. The metric tells the coder how confident to be."
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),
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"estimated_gain": "10-15% entropy reduction in structured regions"
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}
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},
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"aggregate_estimate": {
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"structured_regions": "15-30% gain on ~40% of enwik (infoboxes, citations, templates, lists, headings, markup)",
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"free_text_regions": "5-10% gain on ~60% of enwik (natural language paragraphs)",
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"dictionary_overhead": "MB → KB (Gram matrix replaces LZ dictionary + transformer weights)",
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"context_efficiency": "10-20% more predictive power per context byte",
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"overall_compressed_size": "Estimated 12-22% reduction vs current best Hutter compressors",
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"caveat": "These are geometric estimates, not benchmarks. Real gains depend on shear matrix learning quality and residual entropy."
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},
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"the_big_fold": {
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"title": "What This Fundamentally Changes",
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"insight": (
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"The Hutter Prize is currently fought as a sequence modeling problem: "
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"predict the next token given previous tokens. "
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"The rhomboid reframes it as a manifold learning problem: "
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"find the shear that makes the token manifold maximally flat (predictable), "
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"store the shear, then entropy-code the residual curvature."
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),
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"fold": (
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"This folds FOUR separate Hutter components into ONE: "
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"1. Dictionary (LZ) → Gram matrix eigenvectors "
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"2. Context model (PPM/transformer) → Sheared metric g_{μν} "
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"3. Token encoding → PIST n-D coordinates "
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"4. Structure detection → S3C shell classification "
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"All four are the same object: the shear matrix A."
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),
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"one_sentence": "Don't predict the next token. Shear the space until the next token is obvious, store the shear, and pay only for what the shear didn't catch."
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},
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"keeper_phrases": [
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"You don't compress the text. You compress the shear matrix that makes the text predictable.",
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"The Gram matrix of the shear IS the dictionary, the context model, the token encoding, and the structure detector — all at once.",
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"A citation isn't 200 bytes that happen to look similar. It's one sheared cavity with 200-byte residuals.",
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"Stop predicting tokens. Start shearing the manifold until tokens become obvious.",
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"The Hutter Prize is manifold learning disguised as sequence modeling.",
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"Fixed context windows are orthogonal thinking. Sheared context is information-geometric thinking.",
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"Every '{{cite web' is the same hole. Pay for the hole once, pay for the URL residual each time."
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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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"hutter-prize", "compression", "hypercube", "hyper-rhomboid",
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"sheared-manifold", "enwik", "token-encoding", "gram-matrix",
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"s3c-shells", "oac", "famm", "pist", "entropy-coding"
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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 / "hypercube_rhomboid_hutter_prize.json"
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with open(out_path, 'w') as f:
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json.dump(HUTTER_RHOMBOID, 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": HUTTER_RHOMBOID["id"],
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"title": HUTTER_RHOMBOID["title"],
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"date": HUTTER_RHOMBOID["date"],
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"source": HUTTER_RHOMBOID["source"],
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"ingested_at": HUTTER_RHOMBOID["metadata"]["ingested_at"],
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"tags": HUTTER_RHOMBOID["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"\n7 concrete changes:")
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for key, change in HUTTER_RHOMBOID["concrete_changes"].items():
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print(f" • {change['title']}: {change['estimated_gain']}")
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print(f"\nThe Big Fold:")
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print(f" {HUTTER_RHOMBOID['the_big_fold']['insight'][:120]}...")
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print(f"\nKeeper phrases:")
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for p in HUTTER_RHOMBOID["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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