Abstract
We study a class of mean–interaction collapse architectures organized by the exterior circulation exponent α. Under an explicitly source-free leading-core premise, a strained-core width law, saturated self-similar supply and axial balance, circulation growth and vanishing core energy reduce to the structural window 0 < α < 1/3. The cut-dependent collapse Reynolds number cancels from this criterion. For the specified interaction-wave family, covariance realizability is governed by a circular cone aligned with the radial shear. Its exterior parameter satisfies vs − 2 = α, connecting the kinematic and realizability descriptions.
We express the demanded stress through radial primitives and height-dependent moment identities, retain the full profile state, and state the moment-repair interface with its transcription and uniformity hypotheses. An exact finite perturbation constructs an active midplane layer; a separate linear lift gives a stress-free global midplane preparation under a quantified non-resonance condition. Height continuation is a coupled boundary-value problem. We identify its scalar fold, quasi-elliptic (2,6) axis core and common modal structure, then prove that the full frozen-window resolvent on its original domain is bounded below by a quantity tending to infinity at large real height frequency. This excludes normalized high-frequency quasimodes without asserting a power-law rate.
OpenAI's external construction maps to α = 2h < 1/50 and supplies a realization only conditional on its correctness. Finite-frequency non-resonance, range closure, variable profiles, height continuation and complete Navier–Stokes verification are beyond the results proved here.
Submission package
The main manuscript is accompanied by its claim ledger and five technical attachments. The PDF files below are the supplied submission editions.
- Main paper — Structural Classification of the Exterior-Exponent Collapse Mechanism Open main paper
- Claim Ledger for Paper I Open claim ledger
- Attachment A — Exterior Exponent of a Collapsing Vortex Open Attachment A
- Attachment B — Cone Realizability and Midplane Open Attachment B
- Attachment C — Global Quasimodes Open Attachment C
- Attachment D — Compactness Closure Open Attachment D
- Attachment E — Lean Formalization Correspondence Open Attachment E