orthographic mass
blaize rouyea · corey bourgeois
we define the orthographic mass of a written word as the magnitude of the first circular moment of the angular distribution of its utf-8 nibbles. the construction is parameter-free and corpus-free: it reads only the bytes of a single written form. computed over 833,116 lemmas across fourteen languages and five writing systems, orthographic mass separates alphabetic scripts (high concentration) from logographic and abugida scripts (low concentration).
circular statisticsdirectional statisticsorthographywriting systemsUTF-8linguisticstypology
graph signature arithmetic
blaize rouyea · corey bourgeois
graph signature arithmetic is an arithmetic on finite simple graphs built from two counts: vertices and edges. a graph g has signature σ(g) = (v(g),e(g)) and score s(g) = v(g) + e(g). two operations make this arithmetic nontrivial: fusion of isolated numerals (turning m and n into the complete bipartite graph k_m,n) and the lexicographic product o[r]. product scores fall into arithmetic lanes, and dirichlet's theorem gives infinitely many prime scores in live lanes. the score layer is deliberately blind to topology — nonisomorphic payloads with the same signature cast the same arithmetic shadow.
graph theoryarithmeticprime numberscombinatoricsdirichlet theoremcrossing number
the bourgeois triangle
blaize rouyea · corey bourgeois
the bourgeois triangle is a pascal-type array with a unit left border, a signed right border, and ordinary addition in the interior. four mechanisms are exact: row polynomials obey a one-line recursion and a green-cone formula, the alternating row value is a perfect selector, the von mangoldt doorway places psi(n) on the diagonal with near-edge difference exactly lambda(n), and the survivor border is a ramanujan-fourier wheel signal with lane amplitudes equal to ramanujan sums.
number theoryprime distributionramanujan sumsanalytic number theoryzeta functionli coefficients
lane-partitioned tensor storage
blaize rouyea · corey bourgeois
we present iota, a lane-partitioned tensor format that splits bf16 weights into significance-ordered lanes. this separation enables o(1) precision surgery, zero-cost entropy sensing, and budgeted lane-aware loading — streaming a 29.5gb model at 78mb rss on raspberry pi 5.
neural inferencecompressionmemory optimization
entropy-guided adaptive precision
corey bourgeois · blaize rouyea
entropy density transitions from metric to control signal. the same signal guides decode cost, keep level, sleeping, promotion, and demotion — at both training and inference time. training with entropy-budgeted precision recovered 92% of the gap between full precision and naive quantization.
precision controlentropytraining optimization
rouyea shave
blaize rouyea · corey bourgeois
shave removes significance waste by projecting weights onto their natural significance manifold. combined with cast (orientation waste) and drift (relational waste), these three projections expose the real structure hiding in trained neural network weights.
weight normalizationmodel compressionlocal-law
bourgeois orbience
corey bourgeois · blaize rouyea
lattice moves iota toward shared structural prototypes. store blocks as anchor + prototype + orbit + optional residual. compute directly from compact structure instead of reconstructing every weight — the goal shifted from rebuild-then-compute to compute-from-structure.
structural inferencelattice executioncompute optimization
