large language models

The Same 19.471221 Degrees Arises from Two Distinct Roots ── the half-angle of a ship's wake, arcsin(1/3)=19.471221 degrees, is a constant containing no speed, while the Mach angle arcsin(1/M) reaches the same value at the single point M=3 ── [Paper 515]

When two angles agree, one mechanism is readily assumed to be at work. This paper shows that 19.471221 degrees arises for two separate reasons──one independent of speed, the other taking that value only at M=3. No new theorem or law is claimed. Scope of this paper (scope note): No new theorem or law is claimed──the Kel...

Longitudinal and Transverse Belong to the Field; x and y Belong to the Coordinates ── rotating the coordinates leaves the longitudinal share at 0.647222222222 without moving a digit, while the x share moves with every rotation ── both are called "splitting the field in two", and only one of them belongs to the field ── [Paper 517]

There are many ways to split a vector field in two. What this paper shows is that which of them belongs to the field and which to the coordinates can be measured by rotating the coordinates. No new theorem or law is claimed. Scope of this paper (scope note): No new theorem or law is claimed──the Helmholtz decomposition...

Evaluating Mathematical Reasoning in Large Language Models: A Comprehensive Analysis of Prompting Strategies on the Google DeepMind Mathematics Dataset

Photon Condensation Beyond Spacetime: A Higher-Dimensional Geometric Model for Dark Matter, Dark Energy, and Early Universe Anomalies via Van Hove Saddles

TITLE: Photon Condensation Beyond Spacetime: A Higher-Dimensional Geometric Metric Framework via M4 and M5 Morse Saddles DESCRIPTION: This work presents an independent geometric framework and formal cosmological supplement that addresses contemporary astrophysical anomalies without postulating hypothetical dark sector...

The Size of the Falling Box in Which Gravity Cannot Be Told Is Set Not by Physics but by the Precision of the Instrument ── the difference in gravity between the top and bottom of the box is the tidal gradient 2GM/r³ times the height, and the height at which the box gives gravity away is precision divided by gradient: at the Earth's surface 3.243790 mm for a precision of 10⁻⁸ m/s² and 3.243790 μm for 10⁻¹¹, at the horizon of a solar-mass black hole 9.709164×10⁻¹⁹ m, and at the horizon of a billion solar masses 0.9709164 m ── the separator is whether what shrinks the box is precision or gradient ── [Paper 1029]

Einstein called the idea that gravity vanishes inside a falling box the happiest thought of his life. But gravity differs between the top and bottom of the box, by the tidal gradient times the height, and with a fine enough instrument gravity can be told in any box. This paper counts that difference and the box height...

Three Separate Answers Are All Decided Where Something Is Tangent ── The Legendre transform's contact point solves f'(x)=p, giving x=2.500000 and a conjugate of 6.250000 at p=5 ── the common tangent touches at v=+/-1 with slope 0.300000000, and between them the curve falls below it at 0 points ── [Paper 507]

A transform, a bound and a phase coexistence are taken to be separate tools. This paper shows that all three have their answers decided where something is tangent──the location of the contact point is the answer. No new theorem or law is claimed. Scope of this paper (scope note): No new theorem or law is claimed──the L...

Semantically-Guided LLM Pipeline for Business Architecture Modelling with Incremental Knowledge Acquisition

Memory Structure Web: A Structured Memory Architecture for Confusion in Long-Context Memory

Starting from the phenomenon of "remembering, but not matching up" in long-context memory, this paper proposes a possibility: the problem of large language models' long-term memory may not necessarily be information forgetting, but may instead occur in the processes of information compression, retrieval, and recombinat...

Tristack Maglev Elevator Bridge Deck: Dynamic Multi-Tier Kinetic Infrastructure and Lateral Docking Primaries [GenSI-Ref: GA-AL-FL-2026-0920]

ABSTRACT, GLOBAL PRIOR-ART AXIS, & SOVEREIGN COMMERCIAL RESERVATION Principal Innovator: Stephan Richard Lee (ORCID: 0009-0008-1177-3857) Corporate Assignee: GenSi Holdings LLC // GenSI Technology and Infrastructure Services Official Operations Matrix: gensi.25.1@protonmail.com Timeline Horizon Priority: June 2026 Base...

Scaling Interactive Learning Resources for LLM Agents: A Survey of Environment and Task Synthesis

Large language model (LLM) agents can learn through interaction with external environments, obtain training signals and reusable experience from task execution. Scaling this form of learning requires a sufficient supply of interactive environments and tasks grounded in those environments, with explicit objectives and c...

Data, code and model outputs for: Benchmarking large language model elicitation formats against expert analytic hierarchy process weights for soil quality mapping in the Tigris River Basin

Version 2.0.0. This version archives the elicitation experiment repeated on 20 September 2026 with exactly the 11 indicators, 55 pairwise comparisons and English prompts described in the manuscript, and every analysis recomputed from it. It supersedes version 1.0.0, whose archived run had presented 13 parameters and 78...

Overview of HIPE-2026: Person–Place Relation Extraction from Multilingual Historical Texts