small language model

The Same Proportional Increase Buys Less at the Top ── Raising the compression ratio by 1.3333 gains +0.0531 in efficiency starting from 6 but only +0.0359 starting from 16 ── the ratio is 1.480429, matching the closed form (r_2/r_1)^gamma-1 exactly ── an efficiency of 0.70 needs a ratio of 20.2860 ── [Paper 468]

Raising the compression ratio raises efficiency──so it is said. This paper shows that the same proportional increase buys 1.480429 times less at the top──and that the ratio has a closed form. No new theorem or law is claimed. Scope of this paper (scope note): No new theorem or law is claimed──the theoretical efficiency...

333 Primordial Constants: The Early Genetic Library of Huancaidie Civilizational Generative Syntax

This research monograph presents the 333 Primordial Constants Project as an interdisciplinary framework for studying the minimal constraints, organizing principles, and generative conditions that may underlie physical structure, mathematics, cognition, life, narrative, civilization, meaning, symbolic systems, agency, a...

What Sets the Speed Is the Power, Not the Gear ── 200 W balances at 32.13 km/h, far above the 13.46 km/h a 34x28 reaches ── what a gear selects is not speed but cadence ── reaching 25 km/h in 34x28 demands 167.2 rpm ── [Paper 449]

A low gear is slow and a high gear is fast──so it is thought. This paper shows that power sets the speed and the gear only selects the cadence──so “a lower gear makes you slower” is true only when the power drops. No new theorem or law is claimed. Scope of this paper (scope note): No new theorem or law is claimed──gear...

White Is Made by a Difference, Not by a Colour ── The same "white powders" scatter as 1 to 0.006944 once mixed into a resin, a factor of 144 ── wet the paper and the difference falls from 1.70 to 1.37, taking 35.1 per cent of the scattering with it ── match the index and the white vanishes exactly ── [Paper 442]

A white powder is taken to be white. This paper shows that whiteness is not a property of the powder──it is made by the difference from its surroundings, and vanishes when the difference does. No new theorem or law is claimed. Scope of this paper (scope note): No new theorem or law is claimed──light scattering, hiding...

What Sets the Speed Is the Power, Not the Gear ── 200 W balances at 32.13 km/h, far above the 13.46 km/h a 34x28 reaches ── what a gear selects is not speed but cadence ── reaching 25 km/h in 34x28 demands 167.2 rpm ── [Paper 449]

A low gear is slow and a high gear is fast──so it is thought. This paper shows that power sets the speed and the gear only selects the cadence──so “a lower gear makes you slower” is true only when the power drops. No new theorem or law is claimed. Scope of this paper (scope note): No new theorem or law is claimed──gear...

Small Language Models as Graph Classifiers: Evaluating and Improving Permutation Robustness

The Water Load Grows as the Square, and the Dam Only as the First Power ── Ten times the depth multiplies the resultant thrust by 100 and the overturning moment by 1000 ── yet the required width only doubles ── 18.6339 m at H=50, 37.2678 at H=100, with b/H constant at 0.3727 ── [Paper 454]

A deeper dam is thought to need a disproportionately thicker body. This paper shows that although the force grows as the square and the moment as the cube, the required width grows only as the first power──because the resisting side grows as the cube too. No new theorem or law is claimed. Scope of this paper (scope not...

White Is Made by a Difference, Not by a Colour ── The same "white powders" scatter as 1 to 0.006944 once mixed into a resin, a factor of 144 ── wet the paper and the difference falls from 1.70 to 1.37, taking 35.1 per cent of the scattering with it ── match the index and the white vanishes exactly ── [Paper 442]

A white powder is taken to be white. This paper shows that whiteness is not a property of the powder──it is made by the difference from its surroundings, and vanishes when the difference does. No new theorem or law is claimed. Scope of this paper (scope note): No new theorem or law is claimed──light scattering, hiding...

The Metal That Reacts Most Readily Is the One That Does Not Corrode ── Aluminium sits at -1.66 V, baser than iron, yet its film is 4 nm, 1/125 of iron's 500 nm ── the ordering is reversed ── what separates them is not the potential but whether the film can cover what lies beneath ── [Paper 441]

A metal that reacts more readily is expected to corrode sooner. This paper shows that the ordering is reversed──the basest metal is protected by the thinnest film. No new theorem or law is claimed. Scope of this paper (scope note): No new theorem or law is claimed──standard electrode potentials, passivity and the Pilli...

Halving the Size Beats Changing the Material Forty Times Over ── Spheres of radius 5 mm and 20 cm have cooling time constants of 348.8333 and 13953.3333 seconds, a ratio of exactly 40.000000000 ── changing the material from water to metal at one size gives only 1.3081 ── what sets the cooling is not specific heat but the surface-to-volume ratio ── [Paper 465]

How fast a thing cools is thought to be set by its material. This paper shows that size acts 40 times harder──changing from water to metal gives only 1.3081. No new theorem or law is claimed. Scope of this paper (scope note): No new theorem or law is claimed──Newton’s law of cooling, the lumped capacitance method and t...

To Protect It, Something Must Dissolve First ── Attach zinc and the difference is +0.32 V and the iron is protected; attach copper and it is -0.78 V and the iron goes faster ── the protector loses 10.6920 kg per ampere-year ── the same act of attaching a metal reverses sign ── [Paper 440]

Protecting a metal is thought to mean covering it. This paper shows that there is a way of protecting that does not cover but attaches something that dissolves first──and that attaching the wrong metal reverses the sign. No new theorem or law is claimed. Scope of this paper (scope note): No new theorem or law is claime...

Progress and Analysis of Optimization for Large Language Models Based on Reinforcement Learning

The boundaries of how reinforcement learning optimizes the reasoning capabilities of large language models under different resource and scale constraints are reviewed, as well as the adaptability of reinforcement learning's optimization of large language models in different scenarios are analyzed.