small language model

The Energy Fluctuation of Light Is a Particle Term Plus a Wave Term, and the Two Are Equal Exactly When the Occupation Number Is 1 ── in the energy fluctuation of a single mode, the particle term divided by the wave term equals the reciprocal of the occupation number and becomes 1 at hν = kT ln 2; at the Planck peak the particle term is 15.8 times the wave term, and for visible sunlight 91.5 times ── the separator is whether the occupation number is above or below 1 ── [Paper 1022]

In 1909 Einstein showed that the energy fluctuation of a single mode of black-body radiation is the sum of a term like that of light quanta and a term like that of classical waves. This paper checks by three routes, the formula, the distribution of the occupation number and thermodynamics, that the ratio of the two ter...

The Energy Fluctuation of Light Is a Particle Term Plus a Wave Term, and the Two Are Equal Exactly When the Occupation Number Is 1 ── in the energy fluctuation of a single mode, the particle term divided by the wave term equals the reciprocal of the occupation number and becomes 1 at hν = kT ln 2; at the Planck peak the particle term is 15.8 times the wave term, and for visible sunlight 91.5 times ── the separator is whether the occupation number is above or below 1 ── [Paper 1022]

In 1909 Einstein showed that the energy fluctuation of a single mode of black-body radiation is the sum of a term like that of light quanta and a term like that of classical waves. This paper checks by three routes, the formula, the distribution of the occupation number and thermodynamics, that the ratio of the two ter...

The Extrapolation Crosses Zero Because the Heat-Capacity Difference Was Held Constant ── With a melting entropy of 10 and a heat-capacity difference of 30, the extrapolated entropy difference crosses zero at T=214.959393, or 0.716531 of the melting point ── let it vanish as the third law requires and it need not cross at all ── [Paper 503]

The Kauzmann paradox is spoken of as a property of supercooled liquids. This paper shows that crossing zero follows from holding the heat-capacity difference constant──held constant, however small, it always crosses. No new theorem or law is claimed. Scope of this paper (scope note): No new theorem or law is claimed──t...

The Spatial Curvature of a Rotating Disk Is −3Ω²/c², and Its Argument Differs from the −1/c² of Velocity Space ── the Gaussian curvature of the spatial metric of a rotating frame is −3Ω²/c² at the centre and vanishes when Ω is set to 0; for a disk whose rim moves at half the speed of light the circumference over the diameter is πγ = 3.627599 and the area is 1.071797 times the Euclidean one, growing less than the circumference; the curvature −1/c² of velocity space contains no Ω and has different units ── the separator is whether what bends is rotation or the composition of velocities ── [Paper 1027]

The circumference of a rotating disk is longer than π times its diameter (Ehrenfest 1909). Einstein used this disk as a clue that geometry under gravity would not be Euclidean. This paper obtains the Gaussian curvature of the spatial metric of a rotating frame by two routes, symbolic computation and numerical different...

The Extrapolation Crosses Zero Because the Heat-Capacity Difference Was Held Constant ── With a melting entropy of 10 and a heat-capacity difference of 30, the extrapolated entropy difference crosses zero at T=214.959393, or 0.716531 of the melting point ── let it vanish as the third law requires and it need not cross at all ── [Paper 503]

The Kauzmann paradox is spoken of as a property of supercooled liquids. This paper shows that crossing zero follows from holding the heat-capacity difference constant──held constant, however small, it always crosses. No new theorem or law is claimed. Scope of this paper (scope note): No new theorem or law is claimed──t...

Small Models, Big Claims: Choosing and Quantizing Local LLMs on an Integrated GPU

Running large language models locally on integrated graphics is now practical, but the community's model-selection advice is dominated by vibes: "just grab a 2B at Q4." This report presents a controlled, single-machine measurement study of twelve model/quantization configurations across three model families (Qwen2.5-1....

Light-MFND: Efficient Multimodal Fake News Detection via Fine-Tuned Small Vision-Language Model

Representation over Architecture: A Protocol-Controlled Attribution of Frozen ESM-2 Embeddings versus Encoder Design for Secondary Structure Prediction on CB513

Protein secondary structure prediction (PSSP) on the CB513 benchmark [30] has been near a plateau for close to a decade, and many recent models add protein language-model (pLM) representations on top of increasingly elaborate encoders. How much of a reported gain comes from the representation, and how much from the enc...

Window Theory • AI — Paper II: Landing and Verification

Window Theory - AI (wtAI): A Falsifiable Framework for Flexibility-Fragility Coupling in Large Language Models This is a six-part research series examining a structural pattern in decoder-based next-token-prediction systems deployed as dialogue and instruction agents. It is written for readers with a background in mach...

Comprehension as Compliance: How Grounded Content, Not Form, Moves Small Language Models to Act, and Where It Does Not

A small language model, given a task prefixed with a description of a recurring decision, will often recognize the decision and fail to act on it. This paper draws together a program of studies on that effect and states what drives it. The effect is carried by the content of the description, not by its form: a plain im...

The Martian Federalist Series 1: On the Necessity and Principles of Martian Confederation

Abstract The Martian Federalist Series 1 is a twelve-essay series (Numbers 1–12) explaining and defending the proposed Charter for the United Martian States—a voluntary confederation of sovereign city-states designed for the unique realities of early Mars settlement. The series addresses the inhabitants of Martian habi...

The Charter of the United Martian States: A Proposed Constitution for the Future Settlements on Mars

Abstract This document presents a complete constitutional framework for a future human society on Mars. The Charter of the United Martian States is a confederative instrument designed for a small, dispersed, high-risk frontier environment in which sovereign constituent polities voluntarily cooperate under strict limits...