small language model

In a Gravity Assist the Probe Speeds Up, and in the Planet's Frame Its Speed Never Changed ── Against Jupiter's orbital speed of 13.07 km/s, the gain seen from the Sun is at most 26.14 km/s ── Jupiter thereby loses 2.4310x10^-20 m/s of orbital speed ── The probe's change in speed is 1.0753x10^24 times Jupiter's ── [Paper 381]

A gravity assist is described as accelerating on a planet’s gravity. This paper asks in which frame the acceleration happened──the answer is that from the Sun it accelerated and from the planet its speed never changed. No new mathematical theorem and no new law is claimed. Scope of this paper (scope note): No new mathe...

"Free-Space Loss" Is Not a Loss: The Vacuum Absorbs Nothing ── 92.4478 dB at 1 km and 1 GHz; doubling the distance and doubling the frequency both add the same 6.0206 dB ── the frequency term comes not from space but from the receiving antenna, whose effective area scales as lambda^2 ── at 10 GHz that area is exactly 1/100 ── [Paper 384]

Radio waves are said to suffer a “loss” as the distance grows. This paper asks what is being lost──and the answer is that nothing is lost; what looks like loss is a fact about the receiver. No new theorem or law is claimed. Scope of this paper (scope note): No new theorem or law is claimed──the Friis transmission formu...

Consolidation Without Weights: What the Complementary Learning Systems Analogy Licenses in LLM Agent Memory, and Why the Systems That Borrow Its Name Do Not Inherit Its Guarantee

(c) 2026 Pranay Mahendrakar. Licensed under CC BY 4.0. Memory systems for language-model agents almost all contain a step called consolidation, and almost all of them cite, or gesture at, the complementary learning systems account of hippocampus and neocortex when they name it. In that account consolidation is a specif...

The Limit on Running Speed Is Not How Fast the Legs Move but How Hard the Ground Is Pushed ── As speed rises only the contact time shortens, and the duty factor falls from 0.6667 to 0.3714 ── Supporting the same body weight then takes a mean vertical force rising from 1.5 to 2.6923 times body weight ── The aerial time barely changes ── [Paper 380]

It is tempting to think one cannot run faster because the legs cannot turn over quickly enough. This paper asks which quantity reaches its limit first──the answer is the force applied to the ground. No new mathematical theorem and no new law is claimed. Scope of this paper (scope note): No new mathematical theorem and...

Benchmarking locally hosted language models for journal editorial work on a compact desktop workstation

Consolidation Without Weights: What the Complementary Learning Systems Analogy Licenses in LLM Agent Memory, and Why the Systems That Borrow Its Name Do Not Inherit Its Guarantee

(c) 2026 Pranay Mahendrakar. Licensed under CC BY 4.0. Memory systems for language-model agents almost all contain a step called consolidation, and almost all of them cite, or gesture at, the complementary learning systems account of hippocampus and neocortex when they name it. In that account consolidation is a specif...

In a Gravity Assist the Probe Speeds Up, and in the Planet's Frame Its Speed Never Changed ── Against Jupiter's orbital speed of 13.07 km/s, the gain seen from the Sun is at most 26.14 km/s ── Jupiter thereby loses 2.4310x10^-20 m/s of orbital speed ── The probe's change in speed is 1.0753x10^24 times Jupiter's ── [Paper 381]

A gravity assist is described as accelerating on a planet’s gravity. This paper asks in which frame the acceleration happened──the answer is that from the Sun it accelerated and from the planet its speed never changed. No new mathematical theorem and no new law is claimed. Scope of this paper (scope note): No new mathe...

A Premium Is Not the Expected Loss ── And What Sets the Loading Is Not the Accuracy of the Probability but the Number of Policies ── With one policy, keeping the ruin probability at 1 per cent takes a loading of 23.1469 times the expected loss ── With a million policies it falls to 0.0231 ── The expected loss has not moved by a single unit ── [Paper 383]

It is tempting to think a premium is the probability of loss times its size. This paper asks whether that suffices──the answer is that it does not, and what sets the shortfall is the number of policies. No new mathematical theorem and no new law is claimed. Scope of this paper (scope note): No new mathematical theorem...

Principles of Airway Management

Airway management has evolved from a practice centred on devices and technical skills toward a multidimensional model integrating physiology, human factors and patient safety. The generation of algorithms issued by different scientific societies has provided structure and reduced practice variability, but it has also p...

When Auditors Fabricate: Batch-Size Degradation and Confident Hallucination in LLM Detection of Planted Document Contamination

Large language models are increasingly proposed as automated auditors of document quality, yet their reliability as detectors of planted errors is poorly characterised. We construct a contaminated corpus of 150 academic papers spanning supply chain management and medical research, injecting 450 known contaminants of th...

Artifact of Live Noise Fingerprints as an Empirical Semantics for Noisy Quantum Channels

Abstract Quantum computations execute on noisy hardware whose effective noise is opaque and varies across platforms and over time. Complete descriptions of the underlying noise channel are often too detailed for reasoning, comparison, or analysis. We therefore study the semantic problem of constructing tractable abstra...

The Brain Uses "2 Per Cent of the Mass and 20 Per Cent of the Energy" Because What It Is Compared With Is Resting ── The brain's specific power is 14.2857 W/kg against a whole-body average of 1.4286, a ratio of 10 ── But skeletal muscle in exercise runs at 100 W/kg, seven times the brain ── The factor of 10 comes from the smallness of the denominator, not the largeness of the brain ── [Paper 382]

The brain is said to use 2 per cent of the body’s mass and 20 per cent of its energy. This paper asks where that factor of 10 comes from──the answer is not that the brain is high but that the denominator is low. No new mathematical theorem and no new law is claimed. Scope of this paper (scope note): No new mathematical...