On this page
Open program questions
The source identifies five next questions:
- Characterize diagram-specific finite reconstruction cores.
- Define presentation-invariant reconstruction complexity.
- Construct a genuinely nonabelian relative defect object beyond the filtered tower.
- Relate Ward-descent defects to anomaly transgression.
- Determine when equation descent upgrades to observable descent.
Why the existing results leave these questions
The finite certificates concern declared witness systems and specific reconstruction problems. They do not establish a universal finite core. Raw witness counts are not presentation invariant, and connected filler spaces need not be contractible. The Ward/BV and Yang–Mills interfaces retain their additional hypotheses.
How to approach the questions
Specify the diagram, witness system, allowed presentation changes, and target notion of reconstruction before proposing an invariant or an extension. In the field-theory interfaces, distinguish equation data from represented observables. These are research directions; the source does not supply a single complete resolution criterion covering all five.
Source
Admissible Witness Descent for Higher Gauge Fields, public website edition v1.0, with the companion theorem guide's open-program list. Not peer reviewed.