large language models

An Achromat Meets at Two Wavelengths Only ── A single lens shifts focus by 1.558361 mm with colour (1.5584 per cent of its focal length) ── Two glasses cut that to 0.044604 mm, a factor of 34.9374, but not to zero ── The cause of the residue can be named by one number: the difference in partial dispersion ── [Paper 377]

An achromatic lens is called a lens with the chromatic aberration removed. This paper asks how far it is removed──the answer is at two wavelengths only, with a third colour remaining. No new mathematical theorem and no new law is claimed. Scope of this paper (scope note): No new mathematical theorem and no new law is c...

What Sets the Amplitude of a Predator--Prey Cycle Is the Initial Condition, Not the Equation ── With the coefficients unchanged, moving the start from 13 to 30 takes the amplitude ratio from 1.0518 to 6.8463 ── There is no damping, so it never shrinks ── The equation does not answer "how large is this ecosystem's cycle" ── [Paper 373]

Predator and prey are said to rise and fall in cycles. This paper asks what sets the size of that cycle──the answer is that the initial condition sets it, not the equation. No new mathematical theorem and no new law is claimed. Scope of this paper (scope note): No new mathematical theorem and no new law is claimed──the...

"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...

"Moore's Law Is Ending" Has Been Said for Years, but What Ended Was the Other Law ── Under Dennard scaling, halving the dimensions leaves power per area at exactly 1.0000 ── Once the voltage stops falling it becomes 4.0000 ── The count still doubles every two years, reaching 1024 in twenty, and now the power does too ── [Paper 374]

“Moore’s law is ending” has been said for a long time. This paper asks what ended──the answer is that what ended was not the law of counting but the law of power. No new mathematical theorem and no new law is claimed. Scope of this paper (scope note): No new mathematical theorem and no new law is claimed──Moore’s law,...

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...

Chinese-SkillSpan: A Benchmark for Competency Span Extraction from Chinese Job Advertisements

Online job advertisements can reveal changing skill demand only when competency mentions are recoverable as auditable text spans. Chinese lacks a large resource that combines explicit span-boundary rules with coverage of different recruitment genres. We present Chinese-SkillSpan, a corpus of 22,840 sentences from four...

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

What Chooses the First Principal Component Is Not the Data but the Units ── The same sample points at 55.6503 degrees in cm, 89.7345 in m, and 4.1934 in mm ── Not one value was changed; they were multiplied ── Standardising settles it at 45.0000 degrees, but standardising is itself a choice ── [Paper 375]

Principal component analysis is described as extracting the main direction in the data. This paper asks whether the data alone fix that direction──the answer is that they do not: the units do. No new mathematical theorem and no new law is claimed. Scope of this paper (scope note): No new mathematical theorem and no new...

An Achromat Meets at Two Wavelengths Only ── A single lens shifts focus by 1.558361 mm with colour (1.5584 per cent of its focal length) ── Two glasses cut that to 0.044604 mm, a factor of 34.9374, but not to zero ── The cause of the residue can be named by one number: the difference in partial dispersion ── [Paper 377]

An achromatic lens is called a lens with the chromatic aberration removed. This paper asks how far it is removed──the answer is at two wavelengths only, with a third colour remaining. No new mathematical theorem and no new law is claimed. Scope of this paper (scope note): No new mathematical theorem and no new law is c...

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...