small language model

A Node-by-Node White-Box Walkthrough of a Quantized Hybrid Gated DeltaNet Language Model: Instrument Calibration and the Information Trajectory from Embedding to Output

Widening Helps Either Fully or Not at All, With Nothing In Between ── The five stage capacities sum to 650 per hour, but the line delivers the smallest of them, 80, which is 0.1231 of the sum ── averaged from 80 to 250 it is only 0.1176 ── [Paper 550]

The capacity of a line follows from the capacities of its stages. What this paper shows is that it follows as a minimum rather than a sum or a mean, and that widening the minimum helps in a step from 1 to 0. No new theorem or law is claimed. Scope of this paper (scope note): No new theorem or law is claimed──that a ser...

Most of the Water Taken Out of Wood Changes Neither Its Size Nor Its Strength ── of the water removed from 80 % to 12 %, a share of 0.735294 changes neither size nor strength, and the remaining 0.264706 brings the shrinkage and the gain in strength ── the separator is whether the water leaving is free water in the cell cavities or bound water held in the cell walls ── [Paper 748]

Drying wood makes it shrink and grow stronger. Yet it does not shrink in proportion to the water removed. Which water changes what is counted through shrinkage and strength at each moisture content. No new theorem or law is claimed. Scope of this paper (scope note): No new theorem or law is claimed──the fibre saturatio...

In Anisotropic Etching, the Depth of the Pit Is Set by Crystal Planes, Not by Etching Time ── the depth is 71.143691 μm at 100 minutes and 71.576704 μm at 200, so doubling the time gives 1.006086 times ── the separator is whether the rate ratio between the two planes is large ── [Paper 758]

When a crystal is dissolved to dig a pit, one readily supposes that longer immersion digs deeper. But when the dissolution rate differs between crystal planes, the planes decide the shape. Whether time or crystal planes set the depth is counted, divided by the ratio of plane rates. No new theorem or law is claimed. Sco...

Most of the Smoke Is Not What Burned but Air the Plume Pulled In, So What Sets the Volume of Smoke Is the Ceiling Height ── A 1000 kW fire burns only 0.076923 kg/s of fuel, yet the plume at a height of 5 m carries 9.216677 kg/s ── the separator is whether the volume of smoke is set by the fuel or by the ceiling height ── [Paper 728]

The smoke in a fire is taken to be what burned. Counted by mass, most of it never burned at all. What burned and what became smoke are set side by side in the same units. No new theorem or law is claimed. Scope of this paper (scope note): No new theorem or law is claimed──plume entrainment, smoke layer descent and the...

The Oldest Age a Ring Can Read Is Set Not by the Clock but by Whether the Ring Can Be Seen ── at a resolution of 1 mum, daily rings can be read to 3.0060 years and annual rings to 22.1871 years, a difference of 19.1811 years ── the separator is whether the rings are made by a daily or a yearly cycle, and whether the rings can be seen ── [Paper 656]

The small stone in a fish's ear (the otolith) carries rings, like the rings of a tree. In young fish one ring a day (daily rings) can be counted, and in grown fish one ring a year (annual rings), and age is read from them. But the slower the growth, the thinner the rings, until the microscope can no longer tell them ap...

Topological and Geometric Native Coding for Higher Dimensional Programming

Abstract This record contains the comprehensive monograph, "Topological and Geometric Native Coding for Higher Dimensional Programming" by Elias Oulad Brahim (September 2026). The research introduces ToposLang and the novel paradigm of Geometric Native Coding (GNC), which challenges the structural limitations of the cl...

Selecting GPTQ Damping from the Calibration Set by Nested-Ridge Leave-One-Out

GPTQ-style quantization damps the calibration Hessian by a fixed fraction of its mean diagonal (one percent in the GPTQ authors' code, five percent in a maintained implementation), a choice that ignores how many calibration rows there are. Small tabular, time-series and text-embedding foundation models can be calibrate...

Systemic Perioperative Antimicrobial Prophylaxis for Penile Prosthesis Implantation: A Systematic Review

Background and Objectives: Penile prosthesis infection usually ends in device removal, whereas unnecessarily broad or prolonged prophylaxis causes toxicity and promotes resistance. We assessed whether the systemic perioperative antibacterial or antifungal strategy, dose or duration is associated with infection, infecti...

c as the Ball of Velocity Space ── 2nd ed.: This Was a Result About c, Not About 4 pi (the Yamagishi Patch and Thomas Precession) ── [Paper 60]

c as the Ball of Velocity Space — second edition: this was a result about c, not about four pi. In special relativity the set of admissible velocities is a ball of radius c, and under the metric induced by the velocity-addition law it is hyperbolic space of curvature minus one over c squared (Varicak 1910). Here the re...

SGC-SLM: The Structural-Guarantee Cost of Small Language Models

Reusable protocol and artifact measuring the cost of guaranteeing verifiable structured output from locally-run Small Language Models across native, few-shot, and grammar-constrained decoding, over a contract-complexity gradient and two sovereign high-risk domains.

Comparing the Marking Accuracy of an AI Marking System with Official Examination Board Marks and Experienced Teacher Judgement A Case Study in GCSE Physics

Automated marking systems built on large language models are increasingly proposed as a way toreduce teacher workload and to provide fast, formative feedback on examination-style questions.Before such systems can be trusted for either formative or summative use, however, their markingaccuracy needs to be quantified aga...