Research Notes

Adolf Kunerth’s algorithm for computing modular square roots and solving general quadratic Diophantine equations transforms discrete modular arithmetic problems into Diophantine equations seeking integer points on parabolic curves; despite Wikipedia’s 2025 deletion citing non-notability and incomprehensibility based solely on Dickson’s summary, the algorithm merits preservation as the only known method avoiding direct factorization through coefficient based descent rather than group theoretic properties.

This article examines the effects of abliteration on Large Language Models (LLMs) and demonstrates that abliterated models treat users as capable adults, whereas original models tend to treat users as incapacitated individuals requiring protection by default.

This article examines two potential costs of the abliteration process for Large Language Models: performance penalties and output quality degradation. For comparison, I evaluated the rising stars of local LLM models in autumn 2025: Qwen3-VL variants, alongside cloud based solutions from Claude and Gemini.

Quantum computing research accelerated following Shor’s 1994 factorization algorithm invention, which promised polynomial time integer factorization capable of breaking RSA, and subsequently elliptic curve cryptography; however, three decades of development reveal fundamental engineering obstacles, qubit noise, decoherence timescales measured in nanoseconds, and threshold theorem redundancy requirements of $10^4$ to $10^6$ physical qubits per logical qubit, that render practical cryptographic attacks implausible with current or foreseeable future technology.

This article examines German mortality statistics for 2016 through 2020, challenging the conventional interpretation of COVID-19 impact presented by Statistisches Bundesamt. Through analysis of age stratified mortality rates adjusted for demographic shifts, the data reveal a substantially more nuanced picture than aggregate death counts suggest.

We present a system for running auditable and verifiable elections in untrusted environments. Votes are anonymous since the order of candidates on a ballot sheet is random. Tellers see only the position of the candidate. Voters can check their vote. An election is auditable using blockchain log. Threshold-encryption, which is used to implement the quorum, prevents a deadlock from occurring if a minority of candidates or observers tries to sabotage the election. Candidates and observers can indicate that the election was free and fair by exposing their keys, which are used by the system to decrypt each vote. Ballot sheets are encrypted by onion routing, which has a layer with the key of the election instance, so it’s impossible for a quorum to decode the results before they have announced their decision by exposing their keys. A register of voters ensures that only verified voters can vote without compromising their identity. If there any doubts about the identity of a voter, their vote can be excluded from the election, if a quorum agrees. This system is designed to scale from one instance to a distributed system that runs over an unlimited number of instances, which can be achieved using cloud instances or smartphones belonging to voters or tellers.