The Alcalde Lopez-Heeney-Lis conjecture: joint scaling limit of critical Ashkin-Teller heights and current clusters
For every fixed point of the critical Ashkin-Teller line, including the four-state Potts endpoint, every bounded Jordan domain and every admissible polygonal approximation, the height, the wired and free current-cluster collections and the distinguished boundary cluster converge jointly: the height to a GFF with the predicted coupling constant , and the clusters to canonical recursive two-valued local sets of the same field, at all nesting depths, in positive-diameter Hausdorff matching topology. Not claimed: cluster area measures, magnetization fields, all spin-domain-wall curves, or metric exponents.
Exact FrontierDelta
Scope and record
Occurred: Sep 25, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: unreviewed. Publication: announcement. AI contribution: ai-discovered. 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: The Alcalde Lopez-Heeney-Lis conjecture: joint scaling limit of critical Ashkin-Teller heights and current clusters · Critical Ashkin-Teller current limit
Confidence: Not scored
Registry verification: unreviewed · announcement · candidate
Attribution
VibeMathed
registry · event recorded by
Unreleased internal OpenAI model
model · ai model contributor · OpenAI
Lineage and corrections
The Alcalde Lopez-Heeney-Lis conjecture: joint scaling limit of critical Ashkin-Teller heights and current clusters parent of this event
This event attributed to Unreleased internal OpenAI model
VibeMathed record: The Alcalde Lopez-Heeney-Lis conjecture: joint scaling limit of critical Ashkin-Teller heights and current clusters evidence for this event
For every fixed point of the critical Ashkin-Teller line, including the four-state Potts endpoint, every bounded Jordan domain and every admissible polygonal approximation, the height, the wired and free current-cluster collections and the distinguished boundary cluster converge jointly: the height to a GFF with the predicted coupling constant , and the clusters to canonical recursive two-valued local sets of the same field, at all nesting depths, in positive-diameter Hausdorff matching topology. Not claimed: cluster area measures, magnetization fields, all spin-domain-wall curves, or metric exponents. parent of this event
Earlier edition (September 25, 2026) evidence for this event
Alcalde Lopez-Heeney-Lis, The Ising magnetisation field and the Gaussian free field (Conjecture 1.2) evidence for this event
The Alcalde Lopez-Heeney-Lis conjecture: joint scaling limit of critical Ashkin-Teller heights and current clusters evidence for this event
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