Theodore Magnus Øen

A Fourier–Lévy Normal Form for Localized Weil Positivity: Finite-Rank Boundary Terms, Scalar Resolvents, and a Certified Finite Block and Continuum Fourier Tail

This manuscript develops a Fourier–Lévy operator framework for localized Weil positivity. It derives the normal form A_X = L_X - c_X I + M_X^* J M_X, isolates the finite-rank boundary contribution, and reduces the parity sectors to scalar Herglotz-type resolvents. For the certifi...

Verified Heuristic Memory Management for Long-Context Language Models

This manuscript proposes Verified Heuristic Memory Management (VHM), a theoretical framework for governing memory in long-context language models. Candidate token spans receive dynamic eligibility weights based on salience, recurrence, utility, consistency, freshness, and evidenc...

Transcendental Relationalism: Framework-Indexed Determinacy, Relative Truth, and Invariant Objectivity

Transcendental Relationalism develops a framework-indexed account of determinacy, truth, and objectivity. Its central claim is that an object, identity, property, or truth-value becomes determinate only under conditions specifying a domain, language, criteria of identity, admissi...

The Magnus Matrix Tree IV: Basis-Compressed Kinetic Operators, Projected Rank-Two Transfers, and Online Selector Admission

We develop a basis-compressed operator layer for exact kinetic distance aggregation. Let x1, ..., xn be labelled coordinates in strict current order, let Cij = |xi - xj|, and fix two selector bases P in R^(n×r) and Q in R^(n×s). Rather than maintaining individual contractions, th...

Verified Heuristic Memory Management for Long-Context Language Models

This manuscript proposes Verified Heuristic Memory Management (VHM), a theoretical framework for governing memory in long-context language models. Candidate token spans receive dynamic eligibility weights based on salience, recurrence, utility, consistency, freshness, and evidenc...