navstokgap

An open research project in mathematical physics

What survives
when we look closer?

Draw a motion with shorter and shorter steps. Describe a field with smaller and smaller cells. Can a physical scale survive when those divisions disappear?

Explore the two questions Read the illustrated introduction
01Newton De MotuMOTION
A curved path and its straight-step approximation Orange line segments join points on a curved path. Refining adds more points and shorter segments. This illustrates a geometric limit, not a minimum physical action. starttime → shorter steps, same interval

straight steps smooth path

02Yang Mills LQFTFIELD THEORY
A lattice covering a fixed region of space A square grid covers the same region as its cells become smaller. One cell is highlighted. This two-dimensional sketch illustrates refinement; the research target is a four-dimensional theory. smaller cells, same region

one cell lattice quantum field theory

Illustrations of refinement, not simulations or proofs. Drawing finer divisions is the beginning; controlling the physical limit is the research problem.

Two questions, still open

Where could a positive scale come from?

01 / NEWTON & QUANTUM ACTIONOpen goal

Must recording motion carry a minimum action cost?

An action scale has units of energy × time. We ask which physical assumptions could make a positive quantum action scale unavoidable.

energytimeaction
In hand
Recording and disturbance bounds within quantum mechanics, with a positive action scale supplied.
Still needed
An independent physical reason that forces that scale to be positive.
Follow the Newton question

02 / YANG–MILLS & THE MASS GAPOpen goal

Can a field have a smallest excitation energy?

Pure SU(3) Yang–Mills describes interacting gauge fields. The target is a rigorous four-dimensional theory with a positive energy gap above its vacuum.

The target energy spectrum, shown schematicallyThe vacuum is at zero energy. A positive gap separates it from a continuous band of excitations. This is the research goal, not a result established here. gapexcitationsvacuum · zero energy
In hand
Exact refinement identities and controlled lattice results in stated regimes.
Still needed
The continuum construction and a physical gap that survives the required limits.
Follow the mass-gap question

The common method

Add detail. Compare. Control the limit.

  1. Insert a new piece

    Add an intermediate time to a motion, or an edge to a lattice.

  2. Compare descriptions

    Find which observations and interactions survive removing the added variable.

  3. Prove what survives

    Control the errors through unlimited refinement and test whether a physical scale remains.

Read the mathematical comparison

Choose a way in

Pictures first, proofs when you’re ready.

Each working note names its assumptions and what remains open. The detailed map connects the results, corrections and next steps.

START HEREThe illustrated introductionGO DEEPERResults and open questionsREAD THE ARGUMENTPaper drafts and PDFs