Harmonic norms on quiver representations without spherical completeness (Haiden-Katzarkov-Kontsevich-Pandit Question 6.24)
Yes, for finite quivers: over any complete non-archimedean field, every polystable finite-dimensional representation admits a split harmonic norm, and a representation admitting a harmonic norm is semistable, so both implications of Theorem 6.23 hold without spherical completeness. The norm produced is split (diagonalisable), which is the natural form here, since without spherical completeness norms need not diagonalise.
Exact FrontierDelta
Scope and record
Occurred: Oct 1, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: unreviewed. Publication: preprint. AI contribution: ai-assisted. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.
Canonical aliases: Harmonic norms on quiver representations without spherical completeness (Haiden-Katzarkov-Kontsevich-Pandit Question 6.24) · HKKP Question 6.24
Confidence: Not scored
Registry verification: unreviewed · preprint · candidate
Attribution
VibeMathed
registry · event recorded by
ChatGPT-6.0 Sol
model · ai model contributor · OpenAI
Oren Ben-Bassat
human · human collaborator
Lineage and corrections
VibeMathed record: Harmonic norms on quiver representations without spherical completeness (Haiden-Katzarkov-Kontsevich-Pandit Question 6.24) evidence for this event
This event attributed to Oren Ben-Bassat
Harmonic norms on quiver representations without spherical completeness (Haiden-Katzarkov-Kontsevich-Pandit Question 6.24) parent of this event
Harmonic norms on quiver representations without spherical completeness (Haiden-Katzarkov-Kontsevich-Pandit Question 6.24) evidence for this event
Yes, for finite quivers: over any complete non-archimedean field, every polystable finite-dimensional representation admits a split harmonic norm, and a representation admitting a harmonic norm is semistable, so both implications of Theorem 6.23 hold without spherical completeness. The norm produced is split (diagonalisable), which is the natural form here, since without spherical completeness norms need not diagonalise. parent of this event
This event attributed to ChatGPT-6.0 Sol
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