Conjecture and Gaps
An incomplete research proposal with invalid deductions corrected. No conditional regularity theorem is established here.
Claim auditStandard identities, refuted deductions and open gaps. The proposed regularity theorem is unproved. Counterexamples refute specific earlier deductions; these are not merely open claims. The step labels below say what kind of statement each step is: three elementary identities, three missing steps, one refuted deduction. Status labels used in this repository →
identity — An elementary analytical identity under stated assumptions. Repository label: standard.
gap — A step the earlier outline needed and never supplied. Repository label: open.
refuted — A deduction of the earlier outline shown to be false.
Not part of the mathematics
Clinical Motivation
These model motivations are clinical analogies, not clinical evidence or a demonstrated identification of collapse with a PDE singularity. The closed-sphere construction was refuted under its assumptions; changing the model requires new analysis.
- Surface tension, geometry and distributed resistance/compliance motivate simplified respiratory models. Their assumptions must be stated separately from the PDE.
- The demo prescribes compliance and recovery; it does not infer a treatment effect or represent surfactant pharmacology.
- A low-Reynolds-number Stokes approximation requires negligible inertia at the specified scales. It is not an exact description of every alveolar dynamic, moving interface or open airway.
- Air can leave through an airway, so a closed incompressible material sphere does not model alveolar emptying.
The analytical identities above have explicit assumptions. Numerical samples check their implementation only. This page does not assess the current status of a general Navier–Stokes problem. Synthetic teaching use only; not validated for patient care.