Matthew “Bear” Schulz

I am an independent researcher in Belmont, California, working without an institution. I build coordinate-free instruments: tools that read a whole number, such as how many times a path winds, how two loops link, or what a quantity picks up on the way around a closed loop, instead of measuring a size. I test them on open public data and on simulations: prime numbers, protein and nucleic-acid backbones, stars in the Gaia catalogue, GPS stations along the Cascadia fault, the Sun's magnetic field, and a swimming jellyfish.

The research is part-time volunteer work, done alongside a full-time job. I work with Claude, an AI model made by Anthropic, as a research assistant, and each paper's closing declaration says how.

Every paper here is a preprint. None has been peer reviewed, each has a limited literature search, and each states its failures plainly. Where a later paper found an error in an earlier one, the correction is shown on the earlier paper's page.

Most recent

• The Latch Atlas: Holonomy and Locks That Can't Be Picked30 September 2026
• Dancing on the Sun: A loop count that reads through holonomy, and the current it finds flowing in both polarities30 September 2026
• Linking Is the Latch: reading the integer on a linked filament, and why a bare filament sets no floor22 September 2026
• Instruments for the Magnetic Forest: A tool suite for the integer-forest lattice model, and what it verifies22 September 2026
• Jellyfish: the Holonomist of the Sea - What a bell taught an instrument about memory, hovering, and the loop that encloses nothing22 September 2026