Mass-gap theorem
∃ Δ > 0Establishes a positive threshold above the vacuum.
Make the construction useful to physics
From a mass gap to the glueball spectrum.
Existence is mathematically decisive but physically sparse. The glueball project asks the construction for quantitative, falsifiable spectral output.
Glueball spectrum project is in development. It is separate from the Volumes I–III proof claim.
The aim
Produce something a physicist can compare.
Glueballs are colour-neutral bound states made entirely from the gauge field. The project seeks dimensionless masses and mass ratios for the lowest spin, parity, and charge-conjugation channels.
The first lane is four-dimensional pure SU(2). Its initial target is the tensor-to-scalar ground-state ratio, followed by a broader channel roster and additional gauge groups.
Why the theorem is not enough for physics
“There is a gap” gives almost no spectroscopy.
Physics output
M2++ / M0++Resolves states, quantum numbers, orderings, and scale-free ratios.
Pure Yang–Mills generates its scale dynamically. A bare existence statement does not provide the numerical value of the gap, the excited spectrum, quantum numbers, residues, or scattering data. Absolute masses also require one scale convention or calibration. Dimensionless ratios are therefore the cleanest first output.
Initial spectrum
Scientific discipline
Prediction is separated from reproduction.
Fits to known lattice results test the numerical implementation. A result is called a prediction only when its channel roster, scale convention, extraction rule, and scoring method were fixed before comparison.
The glueball calculation is an application and test of the framework. It is not an assumption used to obtain the existence or mass-gap theorem.
A demanding sanity test
Agreement would be evidence—not a proof of the proof.
The spectrum probes the same gauge-invariant excitations that the constructive theory claims to create. If a frozen, proof-derived roster of mass ratios agrees with independent lattice determinations without using those masses as inputs, that is strong evidence that the construction’s objects, normalization, and spectral mechanism are physically sane.
It cannot certify a missing lemma or a bad limit. Conversely, a clear disagreement would expose a serious defect even if the manuscript looked formally persuasive.
Anti-fitting protocol
- 01
Freeze the roster
Fix channels, state assignments, scale convention, errors, and scoring before comparison.
- 02
Separate the data path
The prediction exporter receives proof-derived inputs, never benchmark masses or correlators.
- 03
Score every output
Report failed and missing states; no successful subset may be selected after looking.
- 04
Preserve revisions
Any data-motivated change becomes a new fitted generation; the failed freeze stays in the record.
Existing SU(2) comparison values are already public, so the present lane is correctly described as retrospective and data-path-isolated—not blind. A future precommitted holdout would provide stronger prospective evidence.