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Experiments disagree on whether this shape rule works in real tissues.","posed_since":"2015","precise":"The 2D vertex model with energy $E = \\sum_i [K_A (A_i - A_0)^2 + K_P (P_i - P_0)^2]$ ($A_i, P_i$ = cell area and perimeter) has a rigidity transition at target shape index $p_0 = P_0/\\sqrt{A_0} \\sim 3.81$. Determine whether the observed shape index $q = \\langle P/\\sqrt{A}\\rangle$ classifies fluid versus solid epithelia in vivo across tissues and species, or whether fluctuations, division and active tension remodeling set fluidity independently of q.","problem_ref":"8222004f4c0a29681ed24fe0acbc623c1b047355a40aca3bfc33dfe3281d7de5","references":"","settled_by":"Simultaneous in vivo measurement of q and of tissue rheology (cell rearrangement rate, stress relaxation) across several tissues and perturbations.","status_note":"Support from airway epithelia (2015) contrasts with 2026 reports of shape-independent fluidity in epithelial monolayers (arXiv 2603.05548).","title":"Does cell shape predict whether a tissue flows or 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