Matthew Hall

Lean-Verified Chronos Navier-Stokes Certificates: Unified Clock System for OpenAI's Periodic Candidate - Formal Validation Milestone 2

This record contains the publication-facing verification report and the complete reproducible Lean 4 certificate package for Formal Validation Milestone 2 of the Chronos Navier-Stokes program. The formal adapter was compiled against OpenAI's public NavierStokesAndEuler repository...

Temporal Structure in Multivariate Forecasting: A Mathematical Bridge from Causal Sequence Models to Time-Field-Informed Prediction

This working paper develops an open mathematical bridge between modern multivariate forecasting systems and explicit temporal structure, using Google Research’s TimesFM-3 architecture as a current engineering case study. The paper proves, within clearly stated operational definit...

Temporal Mirror Bench Execution Kit: Frozen Randomization, Tamper-Evident Logging, and Fault-Recovery Dry Runs

This paper presents Version 0.6 of the Temporal Mirror bench-validation program, an ongoing research branch within the broader Chronos working framework. The work converts the earlier instrument-only protocol into an executable testing system. It includes balanced hidden randomiz...

Temporal Mirror Bench Execution Kit: Frozen Randomization, Tamper-Evident Logging, and Fault-Recovery Dry Runs

This paper presents Version 0.6 of the Temporal Mirror bench-validation program, an ongoing research branch within the broader Chronos working framework. The work converts the earlier instrument-only protocol into an executable testing system. It includes balanced hidden randomiz...

Temporal Structure in Multivariate Forecasting: A Mathematical Bridge from Causal Sequence Models to Time-Field-Informed Prediction

This working paper develops an open mathematical bridge between modern multivariate forecasting systems and explicit temporal structure, using Google Research’s TimesFM-3 architecture as a current engineering case study. The paper proves, within clearly stated operational definit...

The Preconditions of Zero: Structured Absence, Temporal Certification, and the Mathematics Hidden Behind Nothing

This paper investigates what must already be structurally available before zero can become mathematically or operationally meaningful. Building from the temporal reconstruction developed in The Temporal Origin of Number, it distinguishes absolute nothing from structured absence a...

Twisted Shell Topology and Spectral Closure: An Eight-State Phase-Return Construction

This preprint develops a reduced geometric model in which a four-phase compact progression undergoes an orientation reversal after one complete traversal and returns to its full original state after a second traversal. The construction produces an eight-state phase-return orbit f...

What Is Chronos Theory? A Plain-Language Guide to Time, the Temporal Field, and the Chronos Research Program

What Is Chronos Theory? is a plain-language introduction and research guide to the Chronos Theory program developed by Matthew J. Hall. Chronos begins from the proposition that time is physically meaningful and fundamental rather than something produced by motion, entropy, observ...

Canonical Spectral Response from Twisted Shell Geometry: Projective Reduction, Common-Support Invariance, and Modulus Closure

This working preprint develops a canonical continuum bridge between the finite twisted-shell construction introduced in Twisted Shell Topology and Spectral Closure and the primitive stability response derived in The Chronos Stability Coordinate x. The construction begins with fou...